Patent Publication Number: US-11643974-B2

Title: Reliable gearbox for gas turbine engine

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a continuation of U.S. application Ser. No. 16/820,963 filed Mar. 17, 2020, which is based on and claims priority under 35 U.S.C. 119 from British Patent Application No. 1917762.5 filed on Dec. 5, 2019. The contents of the above applications are incorporated herein by reference. 
    
    
     The present disclosure relates to gearboxes for use in aircraft engines, to geared gas turbine engines for use in aircraft, and to methods of operating such an aircraft. Aspects of the disclosure relate to epicyclic gearboxes having gear mesh stiffnesses meeting specified criteria, and to propulsors for aircraft, such as gas turbine engines, including such a gearbox. 
     As used herein, a range “from value X to value Y” or “between value X and value Y”, or the likes, denotes an inclusive range; including the bounding values of X and Y. As used herein, the term “axial plane” denotes a plane extending along the length of an engine, parallel to and containing an axial centreline of the engine, and the term “radial plane” denotes a plane extending perpendicular to the axial centreline of the engine, so including all radial lines at the axial position of the radial plane. Axial planes may also be referred to as longitudinal planes, as they extend along the length of the engine. A radial distance or an axial distance is therefore a distance extending in a radial direction in a radial plane, or extending in an axial direction in an axial plane, respectively. 
     According to a first aspect there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted, the gearbox having an overall gear mesh stiffness. The overall gear mesh stiffness of the gearbox is greater than or equal to 1.05×10 9  N/m, and optionally may be less than or equal to 8.0×10 9  N/m. 
     The inventor appreciated that, even with high-precision manufacturing, small errors in alignment of gears (e.g. on the order of 100 μm) and/or in gear tooth shape (e.g. on the order of 10 μm) may be present. The inventor discovered that providing some flexibility in the overall gearbox gear mesh, and in particular a gearbox mesh stiffness within the defined range, allows for adjustment for these misalignments or shape errors, so improving load share and evenness of wear of gears. At the same time, too much flexibility in the gear mesh could lead to a less reliable and/or less efficient gearbox, for example with excessive gear tooth deformation and/or excessive torsional vibrations. The inventor discovered that maintaining overall gearbox mesh stiffness within the specified range provides optimum gearbox performance. 
     The gearbox may be defined as having a gearbox diameter defined as the pitch circle diameter (PCD) of the ring gear. The gearbox diameter may be in the range from 0.55 m to 1.2 m, and optionally from 0.57 to 1.0 m 
     Turning to gearbox size, and in particular to ring gear pitch circle diameter (PCD) as a measure of gearbox size, the inventor appreciated that, in various embodiments, an optimal PCD may also be selected by considering the relationship between improved performance due to improved use of the lever effect for larger gearbox sizes, and the effect of increased drag for larger gearbox sizes (diminishing returns on the improved lever effect from the larger size above a certain PCD, and increased size and weight of the larger size). Ring gear materials may be selected to ensure that a maximum expected torque density for the PCD size would be well within tolerance limits. 
     Gearbox mesh stiffness may be proportional to the cube of the gear tooth size (also referred to as gear module). The inventor appreciated that gear tooth size may be invariant with PCD in some arrangements, or proportional to PCD in different embodiments (e.g. maintaining a constant number of teeth as PCD increases). The gear tooth size may scale by the square root of the PCD in still other arrangements. Gearbox mesh stiffness may therefore be independent of PCD, or may vary proportionally to PCD to the power of X, where X may optionally be in the range from 1 to 4 and optionally from 1.5 to 3. 
     The overall gear mesh stiffness of the gearbox may be in the range from 1.08×10 9  to 4.9×10 9  N/m. 
     A gear mesh stiffness between the planet gears and the ring gear may be in the range from 1.4×10 9  to 2.0×10 10  N/m. 
     A gear mesh stiffness between the planet gears and the sun gear may be in the range from 1.20×10 9  to 1.60×10 10  N/m. 
     The fan may have a fan diameter in the range from 240 to 280 cm. In such embodiments, the overall gear mesh stiffness of the gearbox may be in the range from 1.05×10 9  to 3.6×10 9  N/m. 
     The fan may have a fan diameter in the range from 330 to 380 cm. In such embodiments, the overall gear mesh stiffness of the gearbox may be in the range from 1.2×10 9  to 4.9×10 9  N/m. 
     A torsional stiffness of the planet carrier may be greater than or equal to 1.60×10 8  Nm/rad. 
     A ring to sun mesh ratio of: 
     
       
         
           
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               ring 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               sun 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
           
         
       
     
     may be in the range from 0.90 to 1.28, and optionally less than or equal to 1.23. 
     A carrier sun mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               sun 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
           
         
       
     
     may be greater than or equal to 0.26, and optionally may be greater than or equal to 4.5. 
     A carrier to of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               ring 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
           
         
       
     
     may be greater than or equal to 0.2, and optionally greater than or equal to 3.8. 
     The engine may comprise a fan shaft extending between the gearbox and the fan, and a gearbox support arranged to mount the gearbox within the engine, the fan shaft, core shaft, the gearbox and the gearbox support together forming a transmission. 
     The effective linear torsional stiffness of the transmission may be greater than or equal to 1.60×10 8  N/m. 
     A gear mesh to transmission stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               transmission 
             
           
         
       
     
     may be greater than or equal to 0.34, and optionally may be in the range from 0.34 to 11. 
     According to a second aspect, there is provided a method of operation of a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted, the gearbox having an overall gear mesh stiffness. The overall gear mesh stiffness of the gearbox is greater than or equal to 1.05×10 9  N/m, and optionally may be less than or equal to 8.0×10 9  N/m. The method comprises operating the gas turbine engine to provide propulsion under cruise conditions. 
     The gas turbine engine may have any of the features as described with respect to the first aspect, for example, the PCD of the gearbox may be in the range from 0.55 m to 1.2 m, and optionally from 0.57 to 1.0 m. 
     The method may comprise driving the gearbox with an input torque of greater than or equal to 10,000 Nm at cruise. The method may comprise driving the gearbox with an input torque of greater than or equal to 28,000 Nm at Maximum Take-Off (MTO). 
     According to a third aspect, there is provided a propulsor for an aircraft, the propulsor comprising a fan comprising a plurality of fan blades; a gearbox; and a power unit for driving the fan via the gearbox. The gearbox is an epicyclic gearbox arranged to receive an input from a core shaft driven by the power unit and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft, and comprises a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. The overall gear mesh stiffness of the gearbox is greater than or equal to 1.05×10 9  N/m, and optionally may be less than or equal to 8.0×10 9  N/m. 
     The propulsor may have some or all of the features as described for the gas turbine engine of the first aspect, for example, the PCD of the gearbox may be in the range from 0.55 m to 1.2 m, and optionally from 0.57 to 1.0 m. 
     According to a fourth aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted, the gearbox having a gear mesh stiffness between the planet gears and the ring gear and a gear mesh stiffness between the planet gears and the sun gear. A ring to sun mesh ratio of: 
     
       
         
           
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     between 
                   
                 
               
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     planet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gears 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ring 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     between 
                   
                 
               
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     planet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gears 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sun 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
           
         
       
     
     is in the range from 0.90 to 1.28. 
     The inventor appreciated that, even with high-precision manufacturing, small errors in alignment of gears (e.g. on the order of 100 μm) and/or in gear tooth shape (e.g. on the order of 10 μm) may be present. The inventor discovered that providing some flexibility in the gear meshes between the planet gears and the sun and ring gears may allow for adjustment for these misalignments or shape errors, so improving load share and evenness of wear of gears. At the same time, too much flexibility in the gear meshes could lead to a less reliable and/or less efficient gearbox, for example with excessive gear tooth deformation. The inventor discovered that maintaining the claimed ratio within the specified range provides optimum gearbox performance. 
     In particular, the inventor discovered that having more flexibility in the ring gear as compared to the sun gear (and therefore generally a lower value of the ring to sun mesh ratio than in known engines) may be beneficial in some embodiments, as the ring gear is an internal gear and may deform further than the sun gear whilst maintain stresses and gearbox functioning within acceptable bounds. 
     The ring to sun mesh ratio may be in the range from 0.95 to 1.23. 
     An overall gear mesh stiffness of the gearbox may be greater than or equal to 1.05×10 9  N/m. The overall gear mesh stiffness of the gearbox may be in the range from 1.05×10 9  to 8.00×10 9  N/m, and optionally from 1.08×10 9  to 4.9×10 9  N/m. 
     The gearbox may be defined as having a gearbox diameter defined as the pitch circle diameter of the ring gear. The gearbox diameter may be in the range from 0.55 to 1.2 m, and optionally from 0.57 to 1.0 m. 
     The gear mesh stiffness between the planet gears and the ring gear may be greater than or equal to 1.4×10 9  N/m, and optionally in the range from 2.45×10 9  to 1.05×10 10  N/m. 
     The gear mesh stiffness between the planet gears and the sun gear may be greater than or equal to 1.20×10 9  N/m, and optionally in the range from 2.0×10 9  to 9.5×10 9  N/m. 
     The fan may have a fan diameter in the range from 240 to 280 cm. In such embodiments, the ring to sun mesh ratio may be in the range from 0.95 to 1.28. 
     The fan may have a fan diameter in the range from 330 to 380 cm. In such embodiments, the ring to sun mesh ratio may be in the range from 0.90 to 1.23. 
     The gear mesh stiffness between the planet gears and the ring gear multiplied by the gear mesh stiffness between the planet gears and the sun gear may be greater than or equal to 4.7×10 18  N 2 m −2 , and optionally less than 1.5×10 19  N 2 m −2 . 
     A torsional stiffness of the planet carrier may be greater than or equal to 1.60×10 8  Nm/rad. 
     A carrier to sun mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               sun 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
           
         
       
     
     may be greater than or equal to 0.26, and optionally greater than or equal to 4.5. 
     A carrier to ring mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               ring 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
           
         
       
     
     may be greater than or equal to 0.2, and optionally greater than or equal to 3.8. 
     The engine may comprise a fan shaft extending between the gearbox and the fan, and a gearbox support arranged to mount the gearbox within the engine, the fan shaft, core shaft, the gearbox, and the gearbox support together forming a transmission. 
     A gear mesh to transmission stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               transmission 
             
           
         
       
     
     may be in the range from 0.34 to 11. 
     The effective linear torsional stiffness of the transmission may be greater than or equal to 1.60×10 8  N/m or 3.8×10 8  N/m. 
     According to a fifth aspect, there is provided a method of operation of a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor, a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has a gear mesh stiffness between the planet gears and the ring gear and a gear mesh stiffness between the planet gears and the sun ear. A ring to sun mesh ratio of: 
     
       
         
           
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     between 
                   
                 
               
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     planet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gears 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ring 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     between 
                   
                 
               
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     planet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gears 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sun 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
           
         
       
     
     is in the range from 0.90 to 1.28. The method comprises operating the gas turbine engine to provide propulsion under cruise conditions. 
     The gas turbine engine may have any or all of the features as described with respect to the fourth aspect. 
     The method may comprise driving the gearbox with an input torque of greater than or equal to 10,000 Nm at cruise. The method may comprise driving the gearbox with an input torque of greater than or equal to 28,000 Nm at Maximum Take-Off (MTO). 
     According to a sixth aspect, there is provided a propulsor for an aircraft, the propulsor comprising a fan comprising a plurality of fan blades; a gearbox; and a power unit for driving the fan via the gearbox. The gearbox is an epicyclic gearbox arranged to receive an input from a core shaft and to output drive to a fan so as to drive the fan at a lower rotational speed than the core shaft, the gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has a gear mesh stiffness between the planet gears and the ring gear and a gear mesh stiffness between the planet gears and the sun gear. A ring to sun mesh ratio of: 
     
       
         
           
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     between 
                   
                 
               
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     planet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gears 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ring 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     between 
                   
                 
               
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     planet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gears 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sun 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
           
         
       
     
     is in the range from 0.90 to 1.28. 
     The propulsor may have any or all of the features as described for the gas turbine engine of the fourth aspect. 
     In other aspects, value ranges for product of the components of the ring to sun mesh ratio may be specified instead of, or as well as, value ranges for the ratios. 
     In particular, ring and sun mesh product defined as the gear mesh stiffness between the planet gears and the ring gear multiplied by the gear mesh stiffness between the planet gears and the sun gear may have a value greater than or equal to 4.7×10 18 N 2 m −2 , and optionally less than 1.5×10 19  N 2 m −2 , and optionally may be greater than or equal to 5.1×10 18  N 2 m −2 , and optionally less than 1.3×10 19  N 2 m −2 . 
     According to one such aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor, a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted, the gearbox having a gear mesh stiffness between the planet gears and the ring gear and a gear mesh stiffness between the planet gears and the sun gear. A ring and sun mesh product defined as the gear mesh stiffness between the planet gears and the ring gear multiplied by the gear mesh stiffness between the planet gears and the sun gear is greater than or equal to 4.7×10 18  N 2 m −2 . 
     The skilled person would appreciate that method and propulsor aspects may be formulated accordingly. 
     According to a seventh aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The planet carrier has an effective linear torsional stiffness and the gearbox has a gear mesh stiffness between the planet gears and the sun gear. A carrier to sun mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               sun 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
           
         
       
     
     is greater than or equal to 0.26, and optionally may be less than or equal to 1.1×10 3 . 
     The inventor discovered that the torsional stiffness of the carrier may beneficially be arranged to be relatively high compared to the gear mesh stiffness between the planet gears and the sun gear (as compared to known engines) so as to reduce or avoid wind-up of the gearbox, so reducing or eliminating bending of teeth, whilst still allowing some flexibility within the gear mesh between the planet gears and the sun gear to accommodate differences between teeth and/or gears. The inventor discovered that maintaining the specified ratio within the claimed range provides optimum gearbox performance. An effective linear torsional stiffness of the carrier is used for ease of comparison with the (linear) gear mesh stiffness. 
     The carrier to sun mesh ratio may be greater than or equal to 4.5. 
     An overall gear mesh stiffness of the gearbox may be greater than or equal to 1.05×10 9  N/m. 
     The gearbox may be defined as having a gearbox diameter defined as the pitch circle diameter (PCD) of the ring gear. The gearbox diameter may be in the range from 0.55 m to 1.2 m, and optionally from 0.57 to 1.0 m. 
     A gear mesh stiffness between the planet gears and the ring gear may be greater than or equal to 1.4×10 9  N/m, and optionally in the range from 2.45×10 9  to 1.05×10 10  N/m. 
     The gear mesh stiffness between the planet gears and the sun gear may be greater than or equal to 1.20×10 9  N/m, and optionally in the range from 2.0×10 9  to 9.5×10 9  N/m. 
     The fan may have a fan diameter in the range from 240 to 280 cm. In such embodiments, the carrier to sun mesh ratio may be in the range from 0.6 to 58. 
     The fan may have a fan diameter in the range from 330 to 380 cm. In such embodiments, the carrier to sun mesh ratio may be in the range from 0.94 to 95. 
     The effective linear torsional stiffness of the planet carrier may be greater than or equal to 7.00×10 9  N/m. 
     The product of the effective linear torsional stiffness of the planet carrier and the gear mesh stiffness between the planet gears and the sun gear may be greater than or equal to 5.0×10 18  N 2 m −2 . 
     A ring to sun mesh ratio of: 
     
       
         
           
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     between 
                   
                 
               
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     planet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gears 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ring 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     between 
                   
                 
               
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     planet 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gears 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sun 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
           
         
       
     
     may be in the range from 0.90 to 1.28. 
     A carrier to ring mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               
                 
                   
                     
                       
                         gear 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         mesh 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         stiffness 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         between 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         the 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         planet 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         gears 
                       
                       ⁢ 
                       
                           
                       
                     
                   
                 
                 
                   
                     
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ring 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gear 
                     
                   
                 
               
               ⁢ 
               
                   
               
             
           
         
       
     
     may be greater than or equal to 0.2, and optionally greater than or equal to 3.8. 
     The gas turbine engine may comprise a fan shaft extending between the gearbox and the fan, and a gearbox support arranged to mount the gearbox within the engine, the fan shaft, core shaft, gearbox, and gearbox support together forming a transmission. 
     A gear mesh to transmission stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               transmission 
             
           
         
       
     
     may be in the range from 0.34 to 11. 
     The effective linear torsional stiffness of the transmission may be greater than or equal to 1.60×10 8  N/m. 
     According to an eighth aspect, there is provided a method of operation of a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor, a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The planet carrier has an effective linear torsional stiffness and the gearbox has a gear mesh stiffness between the planet gears and the sun gear. A carrier to sun mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               
                 
                   
                     
                       
                         gear 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         mesh 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         stiffness 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         between 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         the 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         planet 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         gears 
                       
                       ⁢ 
                       
                           
                       
                     
                   
                 
                 
                   
                     
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       sun 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gear 
                     
                   
                 
               
               ⁢ 
               
                   
               
             
           
         
       
     
     is greater than or equal to 0.26, and optionally may be less than or equal to 1.1×10 3 . The method comprises operating the gas turbine engine to provide propulsion under cruise conditions. 
     The gas turbine engine may have any or all of the features as described with respect to the seventh aspect. 
     The method may comprise driving the gearbox with an input torque of greater than or equal to 10,000 Nm at cruise. The method may comprise driving the gearbox with an input torque of greater than or equal to 28,000 Nm at Maximum Take-Off (MTO). 
     According to a ninth aspect, there is provided a propulsor for an aircraft, the propulsor comprising a fan comprising a plurality of fan blades; a gearbox; and a power unit for driving the fan via the gearbox. The gearbox is an epicyclic gearbox arranged to receive an input from a core shaft driven by the power unit and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft, and comprises a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The planet carrier has an effective linear torsional stiffness and the gearbox has a gear mesh stiffness between the planet gears and the sun gear. A carrier to sun mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               
                 
                   
                     
                       
                         gear 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         mesh 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         stiffness 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         between 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         the 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         planet 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         gears 
                       
                       ⁢ 
                       
                           
                       
                     
                   
                 
                 
                   
                     
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       sun 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gear 
                     
                   
                 
               
               ⁢ 
               
                   
               
             
           
         
       
     
     is greater than or equal to 0.26, and optionally may be less than or equal to 1.1×10 3 . 
     The propulsor may have any or all of the features as described for the gas turbine engine of the seventh aspect. 
     In other aspects, value ranges for a product of the components of the carrier to sun mesh ratio may be specified instead of, or as well as, a value range for the ratio. 
     In particular, a carrier and sun mesh product defined as the effective linear torsional stiffness of the planet carrier multiplied by the gear mesh stiffness between the planet gears and the sun gear may have a value greater than or equal to 5.0×10 18  N 2 m −2 , and optionally less than 2.0×10 22  N 2 m −2 , and optionally may be greater than or equal to 1.8×10 19  N 2 m −2 , and optionally less than 1.0×10 21  N 2 m −2 . 
     According to one such aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The planet carrier has an effective linear torsional stiffness and the gearbox has a gear mesh stiffness between the planet gears and the sun gear. A carrier and sun mesh product defined as the effective linear torsional stiffness of the planet carrier multiplied by the gear mesh stiffness between the planet gears and the sun gear is value greater than or equal to 5.0×10 18  N 2 m −2 . 
     The skilled person would appreciate that method and propulsor aspects may be formulated accordingly. 
     According to a tenth aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The planet carrier has an effective linear torsional stiffness and the gearbox has a gear mesh stiffness between the planet gears and the ring gear. A carrier to ring mesh ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               
                 
                   
                     
                       
                         gear 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         mesh 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         stiffness 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         between 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         the 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         planet 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         gears 
                       
                       ⁢ 
                       
                           
                       
                     
                   
                 
                 
                   
                     
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ring 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gear 
                     
                   
                 
               
               ⁢ 
               
                   
               
             
           
         
       
     
     is greater than or equal to 0.2, and optionally may be less than or equal to 900. 
     The inventor discovered that the torsional stiffness of the carrier may beneficially be arranged to be relatively high compared to the gear mesh stiffness between the planet gears and the sun gear so as to reduce or avoid wind-up of the gearbox, so reducing or eliminating bending of teeth, whilst still allowing some flexibility within the gear mesh between the planet gears and the ring gear to accommodate differences between teeth and/or gears. The inventor discovered that maintaining the specified ratio within the claimed range can provide optimum gearbox performance. An effective linear torsional stiffness of the carrier is used for ease of comparison with the (linear) gear mesh stiffness. 
     The carrier to ring mesh ratio may be greater than or equal to 3.8. 
     An overall gear mesh stiffness of the gearbox may be in the range from 1.05×10 9  to 8.00×10 9  N/m, and optionally in the range from 1.08×10 9  to 4.9×10 9  N/m. 
     The gearbox may be defined as having a gearbox diameter defined as the pitch circle diameter (PCD) of the ring gear. The gearbox diameter may be in the range from 0.55 m to 1.2 m, and optionally from 0.57 to 1.0 m. 
     The gear mesh stiffness between the planet gears and the ring gear may be greater than or equal to 1.4×10 9  N/m, and optionally in the range from 2.45×10 9  to 1.05×10 10  N/m. 
     A gear mesh stiffness between the planet gears and the sun gear may be greater than or equal to 1.20×10 9  N/m, and optionally in the range from 2.0×10 9  to 9.5×10 9  N/m. 
     The fan may have a fan diameter in the range from 240 to 280 cm. In such embodiments, the carrier to ring mesh ratio may be greater than or equal to 3.8, and optionally in the range from 3.8 to 90. 
     The fan may have a fan diameter in the range from 330 to 380 cm. In such embodiments, the carrier to ring mesh ratio may be greater than or equal to 4.0, and optionally in the range from 4.0 to 500. 
     The effective linear torsional stiffness of the planet carrier may be greater than or equal to 7.00×10 9  N/m. 
     The product of the effective linear torsional stiffness of the planet carrier and the gear mesh stiffness between the planet gears and the ring gear may be greater than or equal to 5.0×10 18  N 2 m −2 . 
     A ring to sun mesh ratio of: 
     
       
         
           
             
               
                 
                   
                     
                       
                         the 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         gear 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         mesh 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         stiffness 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         between 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         the 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         planet 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         gears 
                       
                       ⁢ 
                       
                           
                       
                     
                   
                 
                 
                   
                     
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ring 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gear 
                     
                   
                 
               
               ⁢ 
               
                   
               
             
             
               
                 
                   
                     
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gear 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       mesh 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       stiffness 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       between 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       planet 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gears 
                     
                     ⁢ 
                     
                         
                     
                   
                 
               
               
                 
                   
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sun 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
           
         
       
     
     may be in the range from 0.90 to 1.28. 
     A carrier to sun mesh ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               
                 
                   
                     
                       
                         gear 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         mesh 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         stiffness 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         between 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         the 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         planet 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         gears 
                       
                       ⁢ 
                       
                           
                       
                     
                   
                 
                 
                   
                     
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       sun 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gear 
                     
                   
                 
               
               ⁢ 
               
                   
               
             
           
         
       
     
     may be greater than or equal to 0.26, and optionally greater than or equal to 4.5. 
     The gas turbine engine may comprise a fan shaft extending between the gearbox and the fan, and a gearbox support arranged to mount the gearbox within the engine, the fan shaft, core shaft, gearbox and gearbox support together forming transmission. A gear mesh to transmission stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               transmission 
             
           
         
       
     
     may be in the range from 0.34 to 11. 
     The effective linear torsional stiffness of the transmission may be greater than or equal to 1.60×10 8  N/m. 
     According to an eleventh aspect, there is provided a method of operation of a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor, a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The planet carrier has an effective linear torsional stiffness and the gearbox has a gear mesh stiffness between the planet gears and the ring gear. A carrier to ring mesh ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               
                 
                   
                     
                       
                         gear 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         mesh 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         stiffness 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         between 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         the 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         planet 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         gears 
                       
                       ⁢ 
                       
                           
                       
                     
                   
                 
                 
                   
                     
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ring 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gear 
                     
                   
                 
               
               ⁢ 
               
                   
               
             
           
         
       
     
     is greater than or equal to 0.2, and optionally may be less than or equal to 900. The method comprises operating the gas turbine engine to provide propulsion under cruise conditions. 
     The gas turbine engine may be as described with respect to the tenth aspect. 
     The method may comprise driving the gearbox with an input torque of greater than or equal to 10,000 Nm at cruise. The method may comprise driving the gearbox with an input torque of greater than or equal to 28,000 Nm at Maximum Take-Off (MTO). 
     According to a twelfth aspect, there is provided a propulsor for an aircraft, the propulsor comprising a fan comprising a plurality of fan blades; a gearbox; and a power unit for driving the fan via the gearbox. The gearbox is an epicyclic gearbox arranged to receive an input from a core shaft driven by the power unit and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft, and comprises a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The planet carrier has an effective linear torsional stiffness and the gearbox has a gear mesh stiffness between the planet gears and the ring gear. A carrier to ring mesh ratio of: 
     
       
         
           
             
               the 
               ⁢ 
                   
               effective 
               ⁢ 
                   
               linear 
               ⁢ 
                   
               torsional 
               ⁢ 
                   
               stiffness 
               ⁢ 
                   
               of 
               ⁢ 
                   
               the 
               ⁢ 
                   
               planet 
               ⁢ 
                   
               carrier 
             
             
               gear 
               ⁢ 
                   
               mesh 
               ⁢ 
                   
               stiffness 
               ⁢ 
                   
               between 
               ⁢ 
                   
               the 
               ⁢ 
                   
               planet 
               ⁢ 
                   
               gears 
               ⁢ 
                   
               and 
               ⁢ 
                   
               the 
               ⁢ 
                   
               ring 
               ⁢ 
                   
               gear 
             
           
         
       
     
     is greater than or equal to 0.2, and optionally may be less than or equal to 900. 
     The propulsor may have any or all of the features as described for the gas turbine engine of the tenth aspect. 
     In other aspects, value ranges for the product of the components of the carrier to ring mesh ratio may be specified instead of, or as well as, a value range for the ratio. 
     In particular, a carrier and ring mesh product defined as the effective linear torsional stiffness of the planet carrier multiplied by the gear mesh stiffness between the planet gears and the ring gear may be greater than or equal to 5.0×10 18  N 2 m −2 , and optionally less than 2.6×10 22  N 2 m −2 , and optionally may be greater than or equal to 2.2×10 19  N 2 m −2 , and optionally less than 2.6×10 21  N 2 m −2 . 
     According to one such aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The planet carrier has an effective linear torsional stiffness and the gearbox has a gear mesh stiffness between the planet gears and the ring gear. A carrier and ring mesh product defined as the effective linear torsional stiffness of the planet carrier multiplied by the gear mesh stiffness between the planet gears and the ring gear is greater than or equal to 5.0×10 18  N 2 m −2 . 
     The skilled person would appreciate that method and propulsor aspects may be formulated accordingly. 
     According to a thirteenth aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, a gearbox, a gearbox support arranged to mount the gearbox within the engine, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a fan shaft. The gearbox is arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. The fan shaft, the core shaft, the gearbox, and the gearbox support together form a transmission having an effective linear torsional stiffness. A gear mesh to transmission stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               transmission 
             
           
         
       
     
     is greater than or equal to 0.34. 
     The gear mesh to transmission stiffness ratio may be in the range from 0.34 to 11, or from 0.90 to 4.6. 
     The fan may have a fan diameter in the range from 240 to 280 cm. In such embodiments, the gear mesh to transmission stiffness ratio may be in the range from 1.4 to 2.7. 
     The fan may have a fan diameter in the range from 330 to 380 cm. In such embodiments, the gear mesh to transmission stiffness ratio may be in the range from 0.5 to 4.6. 
     According to a fourteenth aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, a gearbox, a gearbox support arranged to mount the gearbox within the engine, the gearbox support having an effective linear torsional stiffness, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a fan shaft. The gearbox is arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A gear mesh to gearbox support stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
               ⁢ 
               
                   
               
               ⁢ 
               support 
             
           
         
       
     
     is greater than or equal to 6.5×10 −2 , and optionally less than or equal to 2.6×10 1 . 
     The gear mesh to gearbox support stiffness ratio may be greater than or equal to 2.6×10 −1 , and optionally in the range from 0.26 to 8.0. 
     According to a fifteenth aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, a gearbox, a gearbox support arranged to mount the gearbox within the engine, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a fan shaft, the fan shaft having an effective linear torsional stiffness. The gearbox is arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A gear mesh to fan shaft stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               fan 
               ⁢ 
               
                   
               
               ⁢ 
               shaft 
             
           
         
       
     
     is in the range from 0.3 to 1.6. 
     According to a sixteenth aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, a gearbox, a gearbox support arranged to mount the gearbox within the engine, and a core shaft connecting the turbine to the compressor, the core shaft having an effective linear torsional stiffness; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a fan shaft. The gearbox is arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A gear mesh to core shaft stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               core 
               ⁢ 
               
                   
               
               ⁢ 
               shaft 
             
           
         
       
     
     is greater than or equal to 0.20. The gear mesh to core shaft stiffness ratio may be in the range from 0.20 to 90, and optionally from 0.20 to 29. 
     The inventor has discovered that the stiffness of a transmission—including in particular the overall gear mesh stiffness of the gearbox and the torsional stiffness of the transmission—should be distributed in one or more of the claimed proportions to allow some flexibility within the gear mesh between the gears to accommodate differences between teeth and/or gears whilst reducing or avoiding excessive deflections due to torsional vibrations. The transmission includes the fan shaft, gearbox input shaft, and gearbox support. The inventor appreciated that the torsional stiffnesses of each component may therefore be considered in the same way, as compared to the overall gear mesh stiffness, and discovered that maintaining the corresponding ratios within one or more of the described ranges may provide optimum gearbox performance. An effective linear torsional stiffness of the transmission is used for ease of comparison with the (linear) gear mesh stiffness. 
     The inventor has realised that decreasing the torsional stiffnesses of the transmission below the ranges defined herein may result in deleterious torsion vibrations at low modal frequencies (the skilled person would appreciate that the lower modal frequency whirl modes have larger amplitudes/deflections than the higher modes, and so are more important to avoid), whilst increasing the torsional stiffness above the ranges defined herein may result in excessive size and/or weight of the shaft without a corresponding improvement in performance. 
     Turning to the core shaft/the gearbox input shaft, the inventor has discovered that the torsional stiffness of the gearbox input shaft has an effect on the torsional stiffness of the whole transmission, but a relatively minimal effect on gearbox operation as torsional deflection results in wind up only, and no misalignment of gears. The gearbox input shaft may therefore have a lower torsional stiffness than the carrier without deleterious effects. Similar considerations may apply to the fan shaft (the gearbox output shaft). 
     The inventor has realised that decreasing the torsional stiffnesses of the shafts below the ranges defined herein may result in deleterious torsion vibrations at low modal frequencies (the skilled person would appreciate that the lower modal frequency whirl modes have larger amplitudes/deflections than the higher modes, and so are more important to avoid), whilst increasing the torsional stiffness above the ranges defined herein may result in excessive size and/or weight of the shaft without a corresponding improvement in performance. 
     In any of the thirteenth to sixteenth aspects, one or more of the following may apply: 
     The overall gear mesh stiffness of the gearbox may be greater than or equal to 1.05×10 9  N/m. 
     The gearbox may be defined as having a gearbox diameter defined as the pitch circle diameter (PCD) of the ring gear. The gearbox diameter may be in the range from 0.55 m to 1.2 m, and optionally from 0.57 to 1.0 m. 
     A gear mesh stiffness between the planet gears and the ring gear may be greater than or equal to 1.40×10 9  N/m, and optionally in the range from 2.45×10 9  to 1.05×10 10  N/m. 
     A gear mesh stiffness between the planet gears and the sun gear may be greater than or equal to 1.20×10 9  N/m, and optionally in the range from 2.0×10 9  to 9.5×10 9  N/m. 
     A ring to run mesh ration of: 
     
       
         
           
             
               
                 
                   
                     
                       gear 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       mesh 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       stiffness 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       between 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       planet 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gears 
                     
                     ⁢ 
                     
                         
                     
                   
                 
               
               
                 
                   
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ring 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
             
               
                 
                   
                     
                       gear 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       mesh 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       stiffness 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       between 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       the 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       planet 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       gears 
                     
                     ⁢ 
                     
                         
                     
                   
                 
               
               
                 
                   
                     and 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sun 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                   
                 
               
             
           
         
       
     
     may be in the range from 0.90 to 1.28. 
     A carrier to sun mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               sun 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
           
         
       
     
     may be greater than or equal to 0.26, and optionally greater than or equal to 4.5. 
     A carrier to ring mesh ratio of: 
     
       
         
           
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               carrier 
             
             
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               between 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               planet 
               ⁢ 
               
                   
               
               ⁢ 
               gears 
               ⁢ 
               
                   
               
               ⁢ 
               and 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               ring 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
             
           
         
       
     
     may be greater than or equal to 0.2, and optionally greater than or equal to 3.8. 
     The effective linear torsional stiffness of the core shaft may be greater than or equal to 4.0×10 8  N/m. 
     The effective linear torsional stiffness of the fan shaft may be greater than or equal to 1.2×10 9  N/m. 
     The effective linear torsional stiffness of the gearbox support may be greater than or equal to 7.1×10 8  N/m. 
     The effective linear torsional stiffness of the planet carrier may be greater than or equal to 7.0×10 9  N/m. 
     According to a seventeenth aspect, there is provided a method of operation of a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft, the gearbox being an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted, and the gearbox having an overall gear mesh stiffness; and a gearbox support arranged to mount the gearbox within the engine. The fan shaft, core shaft, gearbox, and gearbox support together form a transmission having an effective linear torsional stiffness. A gear mesh to transmission stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               transmission 
             
           
         
       
     
     is greater than or equal to 0.34, and optionally may be less than or equal to 11. The method comprises operating the gas turbine engine to provide propulsion under cruise conditions. 
     According to an eighteenth aspect, there is provided a method of operation of a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; a gearbox arranged to receive an input from the core shaft and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft, and a gearbox support arranged to mount the gearbox within the engine, the gearbox support having an effective linear torsional stiffness. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A gear mesh to gearbox support stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
               ⁢ 
               
                   
               
               ⁢ 
               support 
             
           
         
       
     
     is greater than or equal to 6.5×10 −2 , and optionally may be less than or equal to 2.6×10 1 . The method comprises operating the gas turbine engine to provide propulsion under cruise conditions. 
     According to a nineteenth aspect, there is provided a method of operation of a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; a fan shaft, the fan shaft having an effective linear torsional stiffness; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A gear mesh to fan shaft stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               fan 
               ⁢ 
               
                   
               
               ⁢ 
               shaft 
             
           
         
       
     
     is in the range from 0.3 to 1.6. The method comprises operating the gas turbine engine to provide propulsion under cruise conditions. 
     According to a twentieth aspect, there is provided a method of operation of a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor, the core shaft having an effective linear torsional stiffness; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; a fan shaft; and a gearbox arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A gear mesh to core shaft stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               core 
               ⁢ 
               
                   
               
               ⁢ 
               shaft 
             
           
         
       
     
     is greater than or equal to 0.2, and optionally in the range from 0.2 to 90 or from 0.2 to 29. The method comprises operating the gas turbine engine to provide propulsion under cruise conditions. 
     The method of any of the seventeenth to twentieth aspects may further comprise driving the gearbox with an input torque of:
         (i) greater than or equal to 10,000 Nm at cruise; and/or   (ii) greater than or equal to 28,000 Nm at Maximum Take-Off.       

     The engine used in the method of any of the seventeenth to twentieth aspects may be the gas turbine engine as described for any of the thirteenth to sixteenth aspects. 
     According to a twenty-first aspect, there is provided a propulsor for an aircraft, the propulsor comprising a fan comprising a plurality of fan blades; a gearbox; a gearbox support arranged to mount the gearbox within the engine; and a power unit for driving the fan via the gearbox. The gearbox is an epicyclic gearbox arranged to receive an input from a core shaft driven by the power unit and to output drive to the fan via a fan shaft so as to drive the fan at a lower rotational speed than the core shaft, and comprises a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. The fan shaft, core shaft, gearbox, and gearbox support together form a transmission having an effective linear torsional stiffness. A ear mesh to transmission stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               transmission 
             
           
         
       
         
         
           
             is in the range from 0.34 to 11. 
           
         
       
    
     According to a twenty-second aspect, there is provided a propulsor for an aircraft, the propulsor comprising a fan comprising a plurality of fan blades; a gearbox; a gearbox support arranged to mount the gearbox within the engine; and a power unit for driving the fan via the gearbox. The gearbox is an epicyclic gearbox arranged to receive an input from a core shaft driven by the power unit and to output drive to the fan so as to drive the fan at a lower rotational speed than the core shaft, and comprises a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A gear mesh to gearbox support stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 effective 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 linear 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 torsional 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 stiffness 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 gear 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 box 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 support 
               
               ⁢ 
               
                   
               
             
           
         
       
     
     is greater than or equal to 6.5×10 −2 , and optionally less than or equal to 2.6×10 1 . 
     According to a twenty-third aspect, there is provided a propulsor for an aircraft, the propulsor comprising a fan comprising a plurality of fan blades; a gearbox; a power unit for driving the fan via the gearbox; a fan shaft; and a core shaft driven by the power unit. The fan shaft has an effective linear torsional stiffness. The gearbox is an epicyclic gearbox arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft, the gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A gear mesh to fan shaft stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               fan 
               ⁢ 
               
                   
               
               ⁢ 
               shaft 
             
           
         
       
     
     is in the range from 0.3 to 1.6. 
     According to a twenty-fourth aspect, there is provided a propulsor for an aircraft, the propulsor comprising a fan comprising a plurality of fan blades; a gearbox; a power unit for driving the fan via the gearbox; a fan shaft; and a core shaft driven by the power unit. The core shaft has an effective linear torsional stiffness. The gearbox is an epicyclic gearbox arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft, the gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. A ear mesh to core shaft stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               core 
               ⁢ 
               
                   
               
               ⁢ 
               shaft 
             
           
         
       
     
     is greater than or equal to 0.2, and optionally in the range from 0.2 to 29 or from 0.2 to 90. 
     The propulsor of any of the twenty-first to twenty-fourth aspects may be, or have any applicable features of, the gas turbine engine as described for any of the thirteenth to sixteenth aspects. 
     In other aspects, value ranges for products of the components of the various ratios may be specified instead of, or as well as, value ranges for the ratios. For example: 
     A gear mesh and transmission stiffness product defined as the overall gear mesh stiffness of the gearbox multiplied by the effective linear torsional stiffness of the transmission may have a value greater than or equal to 1.6×10 17  N 2 m −2 , and optionally greater than or equal to 3.2×10 17  N 2 m −2 . In various embodiments, the value may be in the range from 1.6×10 17  to 2.9×10 19  N 2 m −2 , and optionally in the range from 3.2×10 17  to 1.5×10 19  N 2 m −2 . 
     A gear mesh and gearbox support stiffness product defined as the overall gear mesh stiffness of the gearbox multiplied by the effective linear torsional stiffness of the gearbox support may have a value greater than or equal to 2.0×10 17  N 2 m −2 , and optionally greater than or equal to 9.0×10 17  N 2 m −2 . In various embodiments, the gear mesh and gearbox support stiffness product may be in the range from 2.0×10 17  to 4.1×10 19  N 2 m −2 , and optionally in the range from 9.0×10 17  to 2.1×10 19  N 2 m −2 . 
     A gear mesh to fan shaft stiffness product defined as the overall gear mesh stiffness of the gearbox multiplied by the effective linear torsional stiffness of the fan shaft may have a value greater than or equal to 1.3×10 18  N 2 m −2 , and optionally less than 5.0×10 19  N 2 m −2 . Optionally the value may be greater than or equal to 1.4×10 18  N 2 m −2 , and further optionally less than 3.0×10 19  N 2 m −2 . 
     A gear mesh and core shaft stiffness product defined as the overall gear mesh stiffness of the gearbox multiplied by the effective linear torsional stiffness of the core shaft may have a value in the range from 1.0×10 17  to 3.0×10 19  N 2 m −2 , and optionally in the range from 4.5×10 17  to 9.0×10 18  N 2 m −2 . 
     According to one such aspect, there is provided a gas turbine engine for an aircraft, the engine comprising an engine core comprising a turbine, a compressor, a gearbox, a gearbox support arranged to mount the gearbox within the engine, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a fan shaft. The gearbox is arranged to receive an input from the core shaft and to output drive to the fan via the fan shaft so as to drive the fan at a lower rotational speed than the core shaft. The gearbox is an epicyclic gearbox comprising a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted. The gearbox has an overall gear mesh stiffness. The fan shaft, the core shaft, the gearbox, and the gearbox support together form a transmission having an effective linear torsional stiffness. A gear mesh and transmission stiffness product defined as the overall gear mesh stiffness of the gearbox multiplied by the effective linear torsional stiffness of the transmission is greater than or equal to 1.6×10 17  N 2 m −2 . 
     The skilled person would appreciate that method and propulsor aspects may be formulated accordingly, and that gas turbine engine, method and propulsor aspects for the other products listed above may be formulated accordingly 
     In any of the preceding aspects, any one or more of the following may apply as applicable: 
     The turbine may be a first turbine, the compressor a first compressor, and the core shaft a first core shaft. The engine core may further comprise a second turbine, a second compressor, and a second core shaft connecting the second turbine to the second compressor. The second turbine, second compressor, and second core shaft may be arranged to rotate at a higher rotational speed than the first core shaft. 
     The planet carrier may comprise a forward plate and a rearward plate and pins extending therebetween. Each pin may be arranged to have a planet gear mounted thereon. The planet carrier may further comprise lugs extending between the forward and rearward plates, the lugs being arranged to pass between adjacent planet gears. 
     The gearbox may comprise an odd number of planet gears, and optionally may comprise 3, 5 or 7 planet gears. 
     The fan may have a fan diameter greater than 240 cm and less than or equal to 380 cm, and optionally greater than 300 cm and less than or equal to 380 cm. 
     The gearbox input shaft may provide a soft mounting for the sun gear such that some movement of the sun gear is facilitated. The core shaft may comprise a more stiff section and a less stiff section, the less stiff section providing the gearbox input shaft and being arranged to lie between the more stiff section and the sun gear and being arranged to provide, or to contribute to, the soft mounting of the sun gear. 
     The rotational speed of the fan at cruise conditions may be less than 2500 rpm, and optionally less than 2300 rpm. 
     The fan may have a fan diameter in the range from 240 cm to 280 cm. In such embodiments, the rotational speed of the fan at cruise conditions may be in the range of from 1700 rpm to 2500 rpm, and optionally in the range of from 1800 rpm to 2300 rpm, 
     The fan may have a fan diameter in the range from 330 cm to 380 cm. In such embodiments, the rotational speed of the fan at cruise conditions may be in the range of from 1200 rpm to 2000 rpm, and optionally in the range of from 1300 rpm to 1800 rpm. 
     A gear ratio of the gearbox may be in any range defined herein, for example in the range from 3.2 to 4.5, and optionally from 3.3 to 4.0. 
     A specific thrust of the engine at cruise may be in the range from 70 to 90 NKg −1 s. 
     A bypass ratio at cruise may be in the range from 12.5 to 18; and optionally from 13 to 16. 
     For any parameter or ratio of parameters X claimed or disclosed herein, a limit on the values that X can take that is expressed as “X is greater than or equal to Y” can alternatively be expressed as “1/X is less than or equal to 1/Y”. Any of the ratios or parameters defined in the aspects and statements above may therefore be expressed as “1/X is less than or equal to 1/Y” rather than “X is greater than or equal to Y”. Zero may be taken as the lower bound on the value of 1/X. 
     Various parameters of the gearbox, and/or of the engine more generally, may be adjusted to allow the engine to meet the specifications of the various aspects summarised above. Comments on various such parameters are provided below, with examples of ways in which these may be adjusted provided later in the description of the components. 
     With respect to gearbox size, and in particular to ring gear pitch circle diameter (PCD) as a measure of gearbox size, the inventor appreciated that an optimal PCD may be selected by considering the relationship between improved performance due to improved use of the lever effect for larger gearbox sizes, and the effect of increased drag for larger gearbox sizes (diminishing returns on the improved lever effect from the larger size above a certain PCD, and increased size and weight of the larger size). Ring gear materials may be selected to ensure that a maximum expected torque density for the PCD size would be well within tolerance limits. 
     The skilled person would appreciate that gear mesh stiffness may be controlled by selecting one or more of tooth material and/or tooth size; in particular, there may be a trade-off between bending strength of teeth and contact strength of teeth. A larger tooth length may allow for more sliding and hence more risk of damage, whilst providing a larger contact area for distribution of load. Fewer teeth, each tooth being wider and stronger than for a gear of the same size with more teeth, may generally be preferred, with an upper limit on tooth size set by considerations of sliding and misalignment. The inventor appreciated that too low a gear mesh stiffness may allow excessively large torsion vibrations, resulting in deleterious misalignments and potential tooth damage. 
     The inventor appreciated that, whilst a lower gear mesh stiffness may offer benefits for correction of misalignment, reducing the stiffness below the levels described herein may result in deleterious torsion vibrations—in particular, the skilled person would appreciate that torsional vibrations with low modal frequency have relatively high amplitudes (as the product of amplitude and frequency may be at least substantially constant/they may be at least substantially inversely proportional) and should be avoided or reduced to avoid excessive deflections. 
     One or more of gearbox size, gearbox geometry (including presence or absence of lugs in the carrier, and the number, size, and/or shape of any lugs present), and material choice, amongst other factors, may be selected or adjusted to achieve a desired carrier stiffness. The materials of which the carrier is made (often steels) may, for example, have a Young&#39;s modulus in the range from 100 to 250 GPa, or 105 to 215 GPa, and optionally around 210 GPa—different grades of steel may be selected to achieve different stiffnesses for the same size and geometry. For example, steels with a Young&#39;s modulus in the range 190 to 215 GPa, titanium alloys with a Young&#39;s modulus in the range 105 to 120 GPa, or a metal such as titanium with a Young&#39;s modulus of around 110 GPa may be used in various embodiments. 
     Flexibility of the carrier (effectively the inverse of stiffness) allows changes in alignment of the gears and bearings—the inventor appreciated that a certain amount of flexibility in some places may advantageously allow manufacturing misalignments to be corrected in use, that a certain misalignment may be tolerated, and that a larger misalignment could deleteriously affect running of the engine, and discovered various stiffness relationships to capture the advantages of appropriate stiffness ranges. 
     One or more of shaft diameter, material(s), and wall thickness may be adjusted so as to obtain shaft stiffnesses in the desired ranges. 
     As noted elsewhere herein, the present disclosure may relate to a gas turbine engine. Such a gas turbine engine may comprise an engine core comprising a turbine, a combustor, a compressor, and a core shaft connecting the turbine to the compressor. Such a gas turbine engine may comprise a fan (having fan blades) located upstream of the engine core. 
     The gas turbine engine may comprise a gearbox that receives an input from the core shaft and outputs drive to the fan so as to drive the fan at a lower rotational speed than the core shaft. The input to the gearbox may be directly from the core shaft, or indirectly from the core shaft, for example via a spur shaft and/or gear. The core shaft may rigidly connect the turbine and the compressor, such that the turbine and compressor rotate at the same speed (with the fan rotating at a lower speed). 
     The gas turbine engine as described and/or claimed herein may have any suitable general architecture. For example, the gas turbine engine may have any desired number of shafts that connect turbines and compressors, for example one, two or three shafts. Purely by way of example, the turbine connected to the core shaft may be a first turbine, the compressor connected to the core shaft may be a first compressor, and the core shaft may be a first core shaft. The engine core may further comprise a second turbine, a second compressor, and a second core shaft connecting the second turbine to the second compressor. The second turbine, second compressor, and second core shaft may be arranged to rotate at a higher rotational speed than the first core shaft. 
     In such an arrangement, the second compressor may be positioned axially downstream of the first compressor. The second compressor may be arranged to receive (for example directly receive, for example via a generally annular duct) flow from the first compressor. 
     The gearbox may be arranged to be driven by the core shaft that is configured to rotate (for example in use) at the lowest rotational speed (for example the first core shaft in the example above). For example, the gearbox may be arranged to be driven only by the core shaft that is configured to rotate (for example in use) at the lowest rotational speed (for example only be the first core shaft, and not the second core shaft, in the example above). Alternatively, the gearbox may be arranged to be driven by any one or more shafts, for example the first and/or second shafts in the example above. 
     The gearbox may be a reduction gearbox (in that the output to the fan is a lower rotational rate than the input from the core shaft). Any type of gearbox may be used. For example, the gearbox may be a “planetary” or “star” gearbox, as described in more detail elsewhere herein. The gearbox may have any desired reduction ratio (defined as the rotational speed of the input shaft divided by the rotational speed of the output shaft), for example greater than 2.5, for example in the range of from 3 to 4.2, or 3.2 to 3.8, for example on the order of or at least 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4, 4.1 or 4.2. The gear ratio may be, for example, between any two of the values in the previous sentence. Purely by way of example, the gearbox may be a “star” gearbox having a ratio in the range of from 3.1 or 3.2 to 3.8. In some arrangements, the gear ratio may be outside these ranges. 
     In any gas turbine engine as described and/or claimed herein, a combustor may be provided axially downstream of the fan and compressor(s). For example, the combustor may be directly downstream of (for example at the exit of) the second compressor, where a second compressor is provided. By way of further example, the flow at the exit to the combustor may be provided to the inlet of the second turbine, where a second turbine is provided. The combustor may be provided upstream of the turbine(s). 
     The or each compressor (for example the first compressor and second compressor as described above) may comprise any number of stages, for example multiple stages. Each stage may comprise a row of rotor blades and a row of stator vanes, which may be variable stator vanes (in that their angle of incidence may be variable). The row of rotor blades and the row of stator vanes may be axially offset from each other. 
     The or each turbine (for example the first turbine and second turbine as described above) may comprise any number of stages, for example multiple stages. Each stage may comprise a row of rotor blades and a row of stator vanes. The row of rotor blades and the row of stator vanes may be axially offset from each other. 
     Each fan blade may be defined as having a radial span extending from a root (or hub) at a radially inner gas-washed location, or 0% span position, to a tip at a 100% span position. The ratio of the radius of the fan blade at the hub to the radius of the fan blade at the tip may be less than (or on the order of) any of: 0.4, 0.39, 0.38, 0.37, 0.36, 0.35, 0.34, 0.33, 0.32, 0.31, 0.3, 0.29, 0.28, 0.27, 0.26, or 0.25. The ratio of the radius of the fan blade at the hub to the radius of the fan blade at the tip may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds), for example in the range of from 0.28 to 0.32. These ratios may commonly be referred to as the hub-to-tip ratio. The radius at the hub and the radius at the tip may both be measured at the leading edge (or axially forwardmost) part of the blade. The hub-to-tip ratio refers, of course, to the gas-washed portion of the fan blade, i.e. the portion radially outside any platform. 
     The radius of the fan may be measured between the engine centreline and the tip of a fan blade at its leading edge. The fan diameter (which may simply be twice the radius of the fan) may be greater than (or on the order of) any of: 220 cm, 230 cm, 240 cm, 250 cm (around 100 inches), 260 cm, 270 cm (around 105 inches), 280 cm (around 110 inches), 290 cm (around 115 inches), 300 cm (around 120 inches), 310 cm, 320 cm (around 125 inches), 330 cm (around 130 inches), 340 cm (around 135 inches), 350 cm, 360 cm (around 140 inches), 370 cm (around 145 inches), 380 (around 150 inches) cm, 390 cm (around 155 inches), 400 cm, 410 cm (around 160 inches) or 420 cm (around 165 inches). The fan diameter may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds), for example in the range of from 240 cm to 280 cm or 330 cm to 380 cm. 
     The rotational speed of the fan may vary in use. Generally, the rotational speed is lower for fans with a higher diameter. Purely by way of non-limitative example, the rotational speed of the fan at cruise conditions may be less than 2500 rpm, for example less than 2300 rpm. Purely by way of further non-limitative example, the rotational speed of the fan at cruise conditions for an engine having a fan diameter in the range of from 220 cm to 300 cm (for example 240 cm to 280 cm or 250 cm to 270 cm) may be in the range of from 1700 rpm to 2500 rpm, for example in the range of from 1800 rpm to 2300 rpm, for example in the range of from 1900 rpm to 2100 rpm. Purely by way of further non-limitative example, the rotational speed of the fan at cruise conditions for an engine having a fan diameter in the range of from 330 cm to 380 cm may be in the range of from 1200 rpm to 2000 rpm, for example in the range of from 1300 rpm to 1800 rpm, for example in the range of from 1400 rpm to 1800 rpm. 
     In use of the gas turbine engine, the fan (with associated fan blades) rotates about a rotational axis. This rotation results in the tip of the fan blade moving with a velocity U tip . The work done by the fan blades 13 on the flow results in an enthalpy rise dH of the flow. A fan tip loading may be defined as dH/U tip   2 , where dH is the enthalpy rise (for example the 1-D average enthalpy rise) across the fan and U tip  is the (translational) velocity of the fan tip, for example at the leading edge of the tip (which may be defined as fan tip radius at leading edge multiplied by angular speed). The fan tip loading at cruise conditions may be greater than (or on the order of) any of: 0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39 or 0.4. The fan tip loading may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds), for example in the range of from 0.28 to 0.31, or 0.29 to 0.3. 
     Gas turbine engines in accordance with the present disclosure may have any desired bypass ratio, where the bypass ratio is defined as the ratio of the mass flow rate of the flow through the bypass duct to the mass flow rate of the flow through the core at cruise conditions. In some arrangements the bypass ratio may be greater than (or on the order of) any of the following: 10, 10.5, 11, 11.5, 12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5, 16, 16.5, 17, 17.5, 18, 18.5, 19, 19.5 or 20. The bypass ratio may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds), for example in the range of form 12 to 16, 13 to 15, or 13 to 14. The bypass duct may be substantially annular. The bypass duct may be radially outside the core engine. The radially outer surface of the bypass duct may be defined by a nacelle and/or a fan case. 
     The overall pressure ratio of a gas turbine engine as described and/or claimed herein may be defined as the ratio of the stagnation pressure upstream of the fan to the stagnation pressure at the exit of the highest pressure compressor (before entry into the combustor). By way of non-limitative example, the overall pressure ratio of a gas turbine engine as described and/or claimed herein at cruise may be greater than (or on the order of) any of the following: 35, 40, 45, 50, 55, 60, 65, 70, 75. The overall pressure ratio may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds), for example in the range of from 50 to 70. 
     Specific thrust of an engine may be defined as the net thrust of the engine divided by the total mass flow through the engine. At cruise conditions, the specific thrust of an engine described and/or claimed herein may be less than (or on the order of) any of the following: 110 Nkg −1 s, 105 Nkg −1 s, 100 Nkg −1 s, 95 Nkg −1 s, 90 Nkg −1 s, 85 Nkg −1 s or 80 Nkg −1 s. The specific thrust may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds), for example in the range of from 80 Nkg −1 s to 100 Nkg −1 s, or 85 Nkg −1 s to 95 Nkg −1 s. Such engines may be particularly efficient in comparison with conventional gas turbine engines. 
     A gas turbine engine as described and/or claimed herein may have any desired maximum thrust. Purely by way of non-limitative example, a gas turbine as described and/or claimed herein may be capable of producing a maximum thrust of at least (or on the order of) any of the following: 160 kN, 170 kN, 180 kN, 190 kN, 200 kN, 250 kN, 300 kN, 350 kN, 400 kN, 450 kN, 500 kN, or 550 kN. The maximum thrust may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds). Purely by way of example, a gas turbine as described and/or claimed herein may be capable of producing a maximum thrust in the range of from 330 kN to 420 kN, for example 350 kN to 400 kN. The thrust referred to above may be the maximum net thrust at standard atmospheric conditions at sea level plus 15 degrees C. (ambient pressure 101.3 kPa, temperature 30 degrees C.), with the engine static. 
     In use, the temperature of the flow at the entry to the high pressure turbine may be particularly high. This temperature, which may be referred to as TET, may be measured at the exit to the combustor, for example immediately upstream of the first turbine vane, which itself may be referred to as a nozzle guide vane. At cruise, the TET may be at least (or on the order of) any of the following: 1400K, 1450K, 1500K, 1550K, 1600K or 1650K. The TET at cruise may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds). The maximum TET in use of the engine may be, for example, at least (or on the order of) any of the following: 1700K, 1750K, 1800K, 1850K, 1900K, 1950K or 2000K. The maximum TET may be in an inclusive range bounded by any two of the values in the previous sentence (i.e. the values may form upper or lower bounds), for example in the range of from 1800K to 1950K. The maximum TET may occur, for example, at a high thrust condition, for example at a maximum take-off (MTO) condition. 
     As used herein, a maximum take-off (MTO) condition has the conventional meaning. Maximum take-off conditions may be defined as operating the engine at International Standard Atmosphere (ISA) sea level pressure and temperature conditions +15° C. at maximum take-off thrust at end of runway, which is typically defined at an aircraft speed of around 0.25 Mn, or between around 0.24 and 0.27 Mn. Maximum take-off conditions for the engine may therefore be defined as operating the engine at a maximum take-off thrust (for example maximum throttle) for the engine at International Standard Atmosphere (ISA) sea level pressure and temperature +15° C. with a fan inlet velocity of 0.25 Mn. 
     A fan blade and/or aerofoil portion of a fan blade described and/or claimed herein may be manufactured from any suitable material or combination of materials. For example at least a part of the fan blade and/or aerofoil may be manufactured at least in part from a composite, for example a metal matrix composite and/or an organic matrix composite, such as carbon fibre. By way of further example at least a part of the fan blade and/or aerofoil may be manufactured at least in part from a metal, such as a titanium based metal or an aluminium based material (such as an aluminium-lithium alloy) or a steel based material. The fan blade may comprise at least two regions manufactured using different materials. For example, the fan blade may have a protective leading edge, which may be manufactured using a material that is better able to resist impact (for example from birds, ice or other material) than the rest of the blade. Such a leading edge may, for example, be manufactured using titanium or a titanium-based alloy. Thus, purely by way of example, the fan blade may have a carbon-fibre or aluminium based body (such as an aluminium lithium alloy) with a titanium leading edge. 
     A fan as described and/or claimed herein may comprise a central portion, from which the fan blades may extend, for example in a radial direction. The fan blades may be attached to the central portion in any desired manner. For example, each fan blade may comprise a fixture which may engage a corresponding slot in the hub (or disc). Purely by way of example, such a fixture may be in the form of a dovetail that may slot into and/or engage a corresponding slot in the hub/disc in order to fix the fan blade to the hub/disc. By way of further example, the fan blades maybe formed integrally with a central portion. Such an arrangement may be referred to as a bladed disc or a bladed ring. Any suitable method may be used to manufacture such a bladed disc or bladed ring. For example, at least a part of the fan blades may be machined from a block and/or at least part of the fan blades may be attached to the hub/disc by welding, such as linear friction welding. 
     The gas turbine engines described and/or claimed herein may or may not be provided with a variable area nozzle (VAN). Such a variable area nozzle may allow the exit area of the bypass duct to be varied in use. The general principles of the present disclosure may apply to engines with or without a VAN. 
     The fan of a gas turbine as described and/or claimed herein may have any desired number of fan blades, for example 14, 16, 18, 20, 22, 24 or 26 fan blades. 
     As used herein, cruise conditions have the conventional meaning and would be readily understood by the skilled person. Thus, for a given gas turbine engine for an aircraft, the skilled person would immediately recognise cruise conditions to mean the operating point of the engine at mid-cruise of a given mission (which may be referred to in the industry as the “economic mission”) of an aircraft to which the gas turbine engine is designed to be attached. In this regard, mid-cruise is the point in an aircraft flight cycle at which 50% of the total fuel that is burned between top of climb and start of descent has been burned (which may be approximated by the midpoint—in terms of time and/or distance—between top of climb and start of descent. Cruise conditions thus define an operating point of the gas turbine engine that provides a thrust that would ensure steady state operation (i.e. maintaining a constant altitude and constant Mach Number) at mid-cruise of an aircraft to which it is designed to be attached, taking into account the number of engines provided to that aircraft. For example where an engine is designed to be attached to an aircraft that has two engines of the same type, at cruise conditions the engine provides half of the total thrust that would be required for steady state operation of that aircraft at mid-cruise. 
     In other words, for a given gas turbine engine for an aircraft, cruise conditions are defined as the operating point of the engine that provides a specified thrust (required to provide—in combination with any other engines on the aircraft—steady state operation of the aircraft to which it is designed to be attached at a given mid-cruise Mach Number) at the mid-cruise atmospheric conditions (defined by the International Standard Atmosphere according to ISO 2533 at the mid-cruise altitude). For any given gas turbine engine for an aircraft, the mid-cruise thrust, atmospheric conditions and Mach Number are known, and thus the operating point of the engine at cruise conditions is clearly defined. 
     Purely by way of example, the forward speed at the cruise condition may be any point in the range of from Mach 0.7 to 0.9, for example 0.75 to 0.85, for example 0.76 to 0.84, for example 0.77 to 0.83, for example 0.78 to 0.82, for example 0.79 to 0.81, for example on the order of Mach 0.8, on the order of Mach 0.85 or in the range of from 0.8 to 0.85. Any single speed within these ranges may be part of the cruise condition. For some aircraft, the cruise conditions may be outside these ranges, for example below Mach 0.7 or above Mach 0.9. 
     Purely by way of example, the cruise conditions may correspond to standard atmospheric conditions (according to the International Standard Atmosphere, ISA) at an altitude that is in the range of from 10000 m to 15000 m, for example in the range of from 10000 m to 12000 m, for example in the range of from 10400 m to 11600 m (around 38000 ft), for example in the range of from 10500 m to 11500 m, for example in the range of from 10600 m to 11400 m, for example in the range of from 10700 m (around 35000 ft) to 11300 m, for example in the range of from 10800 m to 11200 m, for example in the range of from 10900 m to 11100 m, for example on the order of 11000 m. The cruise conditions may correspond to standard atmospheric conditions at any given altitude in these ranges. 
     Purely by way of example, the cruise conditions may correspond to an operating point of the engine that provides a known required thrust level (for example a value in the range of from 30 kN to 35 kN) at a forward Mach number of 0.8 and standard atmospheric conditions (according to the International Standard Atmosphere) at an altitude of 38000 ft (11582 m). Purely by way of further example, the cruise conditions may correspond to an operating point of the engine that provides a known required thrust level (for example a value in the range of from 50 kN to 65 kN) at a forward Mach number of 0.85 and standard atmospheric conditions (according to the International Standard Atmosphere) at an altitude of 35000 ft (10668 m). 
     In use, a gas turbine engine described and/or claimed herein may operate at the cruise conditions defined elsewhere herein. Such cruise conditions may be determined by the cruise conditions (for example the mid-cruise conditions) of an aircraft to which at least one (for example 2 or 4) gas turbine engine may be mounted in order to provide propulsive thrust. 
     According to an aspect, there is provided an aircraft comprising a gas turbine engine as described and/or claimed herein. The aircraft according to this aspect is the aircraft for which the gas turbine engine has been designed to be attached. Accordingly, the cruise conditions according to this aspect correspond to the mid-cruise of the aircraft, as defined elsewhere herein. 
     According to an aspect, there is provided a method of operating a gas turbine engine as described and/or claimed herein. The operation may be at the cruise conditions as defined elsewhere herein (for example in terms of the thrust, atmospheric conditions and Mach Number). 
     According to an aspect, there is provided a method of operating an aircraft comprising a gas turbine engine as described and/or claimed herein. The operation according to this aspect may include (or may be) operation at the mid-cruise of the aircraft, as defined elsewhere herein. 
     Whilst in the arrangements described herein the source of drive for the propulsive fan is provided by a gas turbine engine, the skilled person will appreciate the applicability of the gearbox configurations disclosed herein to other forms of aircraft propulsor comprising alternative drive types. For example, the above-mentioned gearbox arrangements may be utilised in aircraft propulsors comprising a propulsive fan driven by an electric motor. In such circumstances, the electric motor may be configured to operate at higher rotational speeds and thus may have a lower rotor diameter and may be more power-dense. The gearbox configurations of the aforesaid aspects may be employed to reduce the rotational input speed for the fan or propeller to allow it to operate in a more favourable efficiency regime. Thus, according to an aspect, there is provided an electric propulsion unit for an aircraft, comprising an electric machine configured to drive a propulsive fan via a gearbox, the gearbox and/or its inputs/outputs/supports being as described and/or claimed herein. 
     The skilled person will appreciate that except where mutually exclusive, a feature or parameter described in relation to any one of the above aspects may be applied to any other aspect. Furthermore, except where mutually exclusive, any feature or parameter described herein may be applied to any aspect and/or combined with any other feature or parameter described herein. 
    
    
     
       Embodiments will now be described by way of example only, with reference to the Figures, in which: 
         FIG.  1    is a sectional side view of a gas turbine engine; 
         FIG.  2    is a close up sectional side view of an upstream portion of a gas turbine engine; 
         FIG.  3    is a partially cut-away view of a gearbox for a gas turbine engine; 
         FIG.  4    is a schematic diagram illustrating automatic load-share adjustments; 
         FIG.  5    is a schematic diagram illustrating torsional stiffness of a cantilevered beam; 
         FIG.  6    is a schematic diagram illustrating gear mesh stiffness; 
         FIG.  7    is a side view of a carrier illustrating torsional stiffness; 
         FIG.  8    is a front view of a different carrier from that shown in  FIG.  7   , illustrating torsional stiffness of the carrier; 
         FIG.  9    is a front view of the carrier of  FIG.  8   , illustrating torsional stiffness; 
         FIG.  10    is a front/sectional view of a carrier comprising lugs; 
         FIG.  11    is a schematic diagram illustrating overall gearbox mesh stiffness; 
         FIG.  12    is a sectional side view of an engine, illustrating the transmission; 
         FIG.  13    is a sectional side view of an engine, illustrating the core shaft, and more particularly the gearbox input shaft; 
         FIG.  14    is a schematic diagram illustrating the torsional stiffness of the gearbox input shaft 
         FIG.  15    is a schematic diagram illustrating connection of the fan shaft to a star gearbox; 
         FIG.  16    is a schematic diagram illustrating connection of the fan shaft to a planetary gearbox; 
         FIG.  17    is a schematic diagram illustrating fan shaft torsional stiffness in an engine with a star gearbox; 
         FIG.  18    is a schematic diagram illustrating a portion of an engine with a star gearbox; 
         FIG.  19    is a graph of displacement against load, illustrating an elastic region within which stiffnesses of components may be determined; 
         FIG.  20    includes a side view and a front/radial view of the gearbox support illustrating torsional stiffness of the gearbox support; and 
         FIG.  21    illustrates a method. 
     
    
    
       FIG.  1    illustrates a gas turbine engine  10  having a principal rotational axis  9 . The engine  10  comprises an air intake  12  and a propulsive fan  23  that generates two airflows: a core airflow A and a bypass airflow B. The gas turbine engine  10  comprises a core  11  that receives the core airflow A. The engine core  11  comprises, in axial flow series, a low pressure compressor  14 , a high-pressure compressor  15 , combustion equipment  16 , a high-pressure turbine  17 , a low pressure turbine  19  and a core exhaust nozzle  20 . A nacelle  21  surrounds the gas turbine engine  10  and defines a bypass duct  22  and a bypass exhaust nozzle  18 . The bypass airflow B flows through the bypass duct  22 . The fan  23  is attached to and driven by the low pressure turbine  19  via a shaft  26  and an epicyclic gearbox  30 . 
     In use, the core airflow A is accelerated and compressed by the low pressure compressor  14  and directed into the high pressure compressor  15  where further compression takes place. The compressed air exhausted from the high pressure compressor  15  is directed into the combustion equipment  16  where it is mixed with fuel and the mixture is combusted. The resultant hot combustion products then expand through, and thereby drive, the high pressure and low pressure turbines  17 ,  19  before being exhausted through the nozzle  20  to provide some propulsive thrust. The high pressure turbine  17  drives the high pressure compressor  15  by a suitable interconnecting shaft  27 . The fan  23  generally provides the majority of the propulsive thrust. The epicyclic gearbox  30  is a reduction gearbox. 
     An exemplary arrangement for a geared fan gas turbine engine  10  is shown in  FIG.  2   . The low pressure turbine  19  (see  FIG.  1   ) drives the shaft  26 , which is coupled to a sun wheel, or sun gear,  28  of the epicyclic gear arrangement  30 . Radially outwardly of the sun gear  28  and intermeshing therewith is a plurality of planet gears  32  that are coupled together by a planet carrier  34 . The planet carrier  34  constrains the planet gears  32  to precess around the sun gear  28  in synchronicity whilst enabling each planet gear  32  to rotate about its own axis. The planet carrier  34  is coupled via linkages  36  to the fan  23  in order to drive its rotation about the engine axis  9 . Radially outwardly of the planet gears  32  and intermeshing therewith is an annulus or ring gear  38  that is coupled, via linkages  40 , to a stationary supporting structure  24 . 
     The linkages  36  may be referred to as a fan shaft  36 , the fan shaft  36  optionally comprising two or more shaft portions  36   a ,  36   b  coupled together. For example, the fan shaft  36  may comprise a gearbox output shaft portion  36   a  extending from the gearbox  30  and a fan portion  36   b  extending between the gearbox output shaft portion and the fan  23 . In the embodiment shown in  FIGS.  1  and  2   , the gearbox  30  is a planetary gearbox and the gearbox output shaft portion  36   a  is connected to the planet carrier  34 —it may therefore be referred to as a carrier output shaft  36   a . In star gearboxes  30 , the gearbox output shaft portion  36   a  may be connected to the ring gear  38 —it may therefore be referred to as a ring output shaft  36   a . In the embodiment shown in  FIGS.  1  and  2   , the fan portion  36   b  of the fan shaft  36  connects the gearbox output shaft portion  36   a  to the fan  23 . The output of the gearbox  30  is therefore transferred to the fan  23 , to rotate the fan, via the fan shaft  36 . In alternative embodiments, the fan shaft  36  may comprise a single component, or more than two components. Unless otherwise indicated or apparent to the skilled person, anything described with respect to an engine  10  with a star gearbox  30  may equally be applied to an engine with a planetary gearbox  30 , and vice versa. 
     Note that the terms “low pressure turbine” and “low pressure compressor” as used herein may be taken to mean the lowest pressure turbine stages and lowest pressure compressor stages (i.e. not including the fan  23 ) respectively and/or the turbine and compressor stages that are connected together by the interconnecting shaft  26  with the lowest rotational speed in the engine (i.e. not including the gearbox output shaft that drives the fan  23 ). In some literature, the “low pressure turbine” and “low pressure compressor” referred to herein may alternatively be known as the “intermediate pressure turbine” and “intermediate pressure compressor”. Where such alternative nomenclature is used, the fan  23  may be referred to as a first, or lowest pressure, compression stage. 
     The epicyclic gearbox  30  is shown by way of example in greater detail in  FIG.  3   . Each of the sun gear  28 , planet gears  32  and ring gear  38  comprise teeth about their periphery to intermesh with the other gears. However, for clarity only exemplary portions of the teeth are illustrated in  FIG.  3   . There are four planet gears  32  illustrated, although it will be apparent to the skilled reader that more or fewer planet gears  32  may be provided within the scope of the claimed invention. Practical applications of a planetary epicyclic gearbox  30  generally comprise at least three planet gears  32 . 
     The epicyclic gearbox  30  illustrated by way of example in  FIGS.  2  and  3    is of the planetary type, in that the planet carrier  34  is coupled to an output shaft via linkages  36 , with the ring gear  38  fixed. However, any other suitable type of epicyclic gearbox  30  may be used. By way of further example, the epicyclic gearbox  30  may be a star arrangement, in which the planet carrier  34  is held fixed, with the ring (or annulus) gear  38  allowed to rotate. In such an arrangement the fan  23  is driven by the ring gear  38 . By way of further alternative example, the gearbox  30  may be a differential gearbox in which the ring gear  38  and the planet carrier  34  are both allowed to rotate. 
     It will be appreciated that the arrangement shown in  FIGS.  2  and  3    is by way of example only, and various alternatives are within the scope of the present disclosure. Purely by way of example, any suitable arrangement may be used for locating the gearbox  30  in the engine  10  and/or for connecting the gearbox  30  to the engine  10 . By way of further example, the connections (such as the linkages  36 ,  40  in the  FIG.  2    example) between the gearbox  30  and other parts of the engine  10  (such as the input shaft  26 , the output shaft and the fixed structure  24 ) may have any desired degree of stiffness or flexibility. By way of further example, any suitable arrangement of the bearings between rotating and stationary parts of the engine (for example between the input and output shafts from the gearbox and the fixed structures, such as the gearbox casing) may be used, and the disclosure is not limited to the exemplary arrangement of  FIG.  2   . For example, where the gearbox  30  has a star arrangement (described above), the skilled person would readily understand that the arrangement of output and support linkages and bearing locations would typically be different to that shown by way of example in  FIG.  2   . 
     Accordingly, the present disclosure extends to a gas turbine engine having any arrangement of gearbox styles (for example star or planetary), support structures, input and output shaft arrangement, and bearing locations. 
     Optionally, the gearbox may drive additional and/or alternative components (e.g. the intermediate pressure compressor and/or a booster compressor). 
     Other gas turbine engines to which the present disclosure may be applied may have alternative configurations. For example, such engines may have an alternative number of compressors and/or turbines and/or an alternative number of interconnecting shafts. By way of further example, the gas turbine engine shown in  FIG.  1    has a split flow nozzle  18 ,  20  meaning that the flow through the bypass duct  22  has its own nozzle  18  that is separate to and radially outside the core engine nozzle  20 . However, this is not limiting, and any aspect of the present disclosure may also apply to engines in which the flow through the bypass duct  22  and the flow through the core  11  are mixed, or combined, before (or upstream of) a single nozzle, which may be referred to as a mixed flow nozzle. One or both nozzles (whether mixed or split flow) may have a fixed or variable area. Whilst the described example relates to a turbofan engine, the disclosure may apply, for example, to any type of gas turbine engine, such as an open rotor (in which the fan stage is not surrounded by a nacelle) or turboprop engine, for example. 
     The geometry of the gas turbine engine  10 , and components thereof, is defined by a conventional axis system, comprising an axial direction (which is aligned with the rotational axis  9 ), a radial direction (in the bottom-to-top direction in  FIG.  1   ), and a circumferential direction (perpendicular to the page in the  FIG.  1    view). The axial, radial and circumferential directions are mutually perpendicular. 
     In the described arrangement, the carrier  34  comprises two plates  34   a ,  34   b ; in particular a forward plate  34   a  and a rearward plate  34   b . Each plate  34   a ,  34   b  extends in a radial plane, with the forward plate  34   a  lying further forward in the engine  10 /closer to the fan  23  than the rearward plate  34   b.    
     The carrier  34  may take any suitable form. For example, the carrier may or may not be symmetric about its axial mid-point. Purely by way of example, in the described arrangement, the carrier  34  is not symmetric about its axial mid-point, but rather the rearward plate  34   b  is stiffer than the forward plate  34   a  (for example by 50 to 300%) to compensate for an asymmetric torque variation across the gearbox  30 . In some embodiments, no forward plate  34   a  may be provided, or only a smaller forward plate  34   a . In some embodiments, the plates  34   a ,  34   b  of the carrier  34  may have equal stiffnesses (for example, in various planetary gearbox arrangements; stiffer rearward plates  34   b  may be preferred in some star gearbox arrangements). 
     A plurality of pins  33  extend across the carrier  34  (between the forward and rearward plates  34   a,b  in the arrangement being described), as shown, for example, in  FIGS.  7  to  10   . The pins  33  form a part of the carrier  34 . Each pin  33  has a planet gear  34  mounted thereon. 
     The carrier stiffness in a region at each of the front and rear ends of each pin  33  is arranged to be relatively low in the embodiments being described, to facilitate a more even load distribution; i.e. to improve load-share factor. This may be described as soft mountings for each pin  33 . The soft mountings  33   a ,  33   b  may allow some movement of the pins  33  relative to each other, and relative to the carrier plates  34   a ,  34   b , so allowing differences between planet gears  34 , or other manufacturing defects, to be accommodated without a significant difference in load between different planet gears  34 . In various embodiments, the soft mountings  34   a ,  34   b  may be provided by a portion of the pin  33 , by a separate component, and/or by a portion of the respective carrier plate  34   a ,  34   b.    
     The soft mountings  34   a ,  34   b  may be designed to accommodate movements to address one or more of carrier bearing location accuracy and clearance, planet pin runout of bearing surface to mounting feature(s), planet gear teeth to bearing runout, planet gear teeth spacing and thickness variation/manufacturing tolerances, sun gear teeth spacing and thickness variation/manufacturing tolerances, and/or gearbox input shaft mainline bearing location accuracy and clearance, or the likes. For example, in various embodiments the soft mountings  34   a ,  34   b  may be arranged to allow around 500 μm of pin movement. 
     Pin size, design and/or material may be adjusted to provide appropriate stiffnesses to the carrier  34 . In some arrangements, such as that shown in  FIG.  10   , lugs  34   c  are provided, extending between the carrier plates  34   a ,  34   b  and past the planet gears  32 . The presence/absence of lugs  34   c , and the number, shape, and/or material(s) of the lug(s) may vary in various embodiments, and may be adjusted to provide appropriate stiffnesses to the carrier  34 . 
     Use of flexibility within the gearbox  30  to improve load-share is illustrated schematically in  FIG.  4   , which shows a planetary gearbox  30  with three planet gears  32   a ,  32   b ,  32   c . In this example, the sun gear  28  is slightly off-centre with respect to the ring gear  38 , and in particular is closer to two planet gears  32   a  and  32   b  than it is to the third planet gear  32   c . In the schematic example shown, there is no contact between the third planet gear  32   c , leaving the other two planet gears  32   a ,  32   b  to take 50% of the load each, rather than around 33%. This relatively extreme example is provided for ease of reference only—in reality, situations in which contact with one planet gear  32   c  is reduced, but not completely eliminated, would be more likely, for example leading to a percentage load-share of 20:40:40 or 26:37:37 or 31:34:34 or the likes rather than the ideal even load share of ⅓:⅓:⅓ (i.e. 33:33:33 as a percentage load share, rounded to the nearest integer). 
     In the example shown in  FIG.  4   , each of the two planet gears  32   a ,  32   b  in contact with the sun gear  28  exerts a force F a , F b  on the sun gear  28 . The resultant force, F R , on the sun gear  28  pushes the sun gear  28  towards the third planet gear  32   c , so re-establishing contact and making the load-share between planets  32  more even. A soft mounting of the sun gear  28 /flexibility in the core input shaft  26  facilitates this re-balancing. Such soft mountings of the sun gear  28  may be designed to accommodate movements to address one or more of carrier bearing location accuracy and clearance, planet and/or sun gear teeth spacing and thickness variation/manufacturing tolerances, and/or gearbox input shaft mainline bearing location accuracy and clearance, or the likes. For example, in various embodiments such a soft mounting may be arranged to allow around 1000 μm of sun gear movement. 
     The skilled person would appreciate that a similar effect would apply if one of the planet gears  32  were closer to the sun gear  28  than the others; pushing the relevant planet gear  32  back towards the ring gear  38 , or if one of the planet gears  32  were larger or smaller than the others. Soft mounting of the pins  33 /flexibility in the carrier  34  facilitates this re-balancing. Having an odd number of planet gears  32  (e.g. 3, 5 or 7 planet gears) may facilitate this automatic re-distribution of load-share. 
     Small variations between planet gears  32  and/or misalignments of pins  33  or shafts  26  may therefore be accommodated by flexibility within the gearbox  30 . 
     The following general definitions of stiffnesses and other parameters may be used herein: 
     Torsional Stiffness 
       FIG.  5    illustrates the definition of the torsional stiffness of a shaft  401  or other body. A torque, τ, applied to the free end of the beam causes a rotational deformation, θ (e.g. twist) along the length of the beam. The torsional stiffness is the torque applied for a given angle of twist i.e. τ/θ. The torsional stiffness has SI units of Nm/rad. 
     An effective linear torsional stiffness may be determined for a component having a given radius. The effective linear torsional stiffness is defined in terms of an equivalent tangential force applied at a point on that radius (with magnitude of torque divided by the radius) and the distance δ (with magnitude of the radius multiplied by θ) moved by a point corresponding to the rotational deformation θ of the component. 
     Gearbox Diameter 
     As used herein, gearbox diameter is the diameter of the ring gear  38 , and more specifically the pitch circle diameter (PCD) of the ring gear  38 . The skilled person would appreciate that the ring gear diameter limits a minimum diameter of the gearbox  30 , and is representative of the gearbox size. The size and shape of a gearbox casing outside of the ring gear diameter may vary depending on materials, required strengths, available space, auxiliary system locations and the likes. The PCD of the ring gear  38  is therefore taken as a more meaningful and transferable measure of the size of the gearbox  30  than an extent of a casing. 
     The pitch circle of a gear is an imaginary circle that rolls without slipping with the pitch circle of any other gear with which the first gear is meshed. The pitch circle passes through the points where the teeth of two gears meet as the meshed gears rotate—the pitch circle of a gear generally passes through a mid-point of the length of the teeth of the gear. The PCD can be roughly estimated by taking the average of the diameter between tips of the gear teeth and the diameter between bases of the gear teeth. In various embodiments the PCD of the ring gear  38 , which may also be thought of as a diameter of the gearbox  30 , may be around 0.55 to 1.2 m, and optionally in the range from 0.57 to 1.0 m. 
     Gear Mesh Stiffness 
     A gear mesh stiffness is defined as the resistance to deformation caused by the contact force acting on the teeth of the gears along the line of action of the contact force. The concept of the gear mesh stiffness is illustrated in  FIG.  6   , which shows two gears  402 ,  403  which mesh together so that rotation of the first gear  402  drives rotation of the second  403 . The contact force between them acts along a line of action  404 . The line of action  404  is a common tangent to the base circle  405 ,  406  of both of the gears  402 ,  403 . The base circles  405 ,  406  are defined as the circles from which the involute shape of the teeth is defined as would be understood by the skilled person. The gear mesh stiffness is expressed as a linear stiffness along the line of action of the contact force, and is taken as an averaged value over the revolution of at least one of the respective gears  402 ,  403  (optionally a full revolution of the gear with most teeth in embodiments in which numbers of teeth are not equal), and optionally over a full cycle of the gearbox back to its initial position. 
     Gear mesh stiffness is a standard parameter widely used in the field of gearboxes, and would be understood by the skilled person. 
     Gear mesh stiffness is assessed in isolation from the carrier  34 —the carrier  34  is treated as being rigid (infinitely stiff)/the stiffness of the carrier  34  is ignored, so as to assess the contribution to stiffness from the gear meshes only. Gear mesh stiffness of a pair of gears, or the overall gear mesh stiffness of a gearbox  30 , can be thought of as resistance to movement when the output shaft  36  is held stationary whilst the input shaft  26  is rotated. 
     More specific definitions of stiffnesses relating to embodiments described herein are provided below for ease of understanding. 
     Carrier Torsional Stiffness 
     The planet carrier  34  holds the planet gears  32  in place. In various arrangements including the embodiment being described, the planet carrier  34  comprises a forward plate  34   a  and a rearward plate  34   b , and pins  33  extending between the plates, as illustrated in  FIGS.  7  to  10   . The pins  33  are arranged to be parallel to the engine axis  9 . In alternative embodiments, a plate  34   b  may be provided on only one side—no plate or only a partial plate may be provided on the other side of the carrier  34 . In the embodiment shown in  FIG.  10   , the carrier  34  additionally comprises lugs  34   c , which may also be referred to as wedges or a web, between the forward and rearward plates  34   a ,  34   b . The lugs  34   c  may increase the overall stiffness of the carrier  34 . 
     The stiffness of the carrier  34  is selected to be relatively high to react centrifugal forces and/or to maintain gear alignment. The skilled person would appreciate that stiffness is a measure of the displacement that results from any applied forces or moments, and may not relate to strength of the component. Hence to react a high load, any stiffness is acceptable so long as the resulting displacement is tolerable. How high a stiffness is desired to keep a displacement within acceptable limits therefore depends on position and orientation of the gears, which is generally referred to as gear alignment (or mis-alignment). 
     Carrier torsional stiffness is a measure of the resistance of the carrier  34  to an applied torque, τ, as illustrated in  FIG.  7    (axial cross-section) and  FIGS.  8  to  10    (radial cross-section). The axis of the torque is parallel to the engine axis  9 . The diagonal lining of the plate  34   b  at the rearward end of the carrier  30  in  FIG.  7    indicates that plate  34   b  being treated as rigid and non-rotating (as for a cantilever beam mounting). In embodiments with only one plate  34   a , the ends of the pins  33  (and of the lugs  34   c  if present) further from the single plate  34   a  are held in place instead. 
     The torque, τ, is applied to the carrier  34  (at the position of the axial mid-point of the forward plate  34   a ) and causes a rotational deformation, θ (e.g. twist) along the length of the carrier  34 . The twist causes the carrier  34  to “wind up” as the ends of the pins  33  (and of the lugs  34   c  if present) are held at a fixed radius on the carrier plates  34   a ,  34   b . The angle through which a point on an imaginary circle  902  on the forward plate  34   a  passing through the longitudinal axis of each pin  33  moves is θ, where θ is the angle measured in radians. The imaginary circle  902  may be referred to as the pin pitch circle diameter (pin PCD). In various embodiments, the pin PCD may be in the range from 0.38 to 0.65 m, for example being equal to 0.4 m or 0.55 m. An effective linear torsional stiffness can therefore be defined for the carrier  34  as described above, using the radius r of the imaginary circle  902  (e.g. as illustrated in  FIG.  8   ). 
     In various embodiments, the torsional stiffness of the carrier  34  is greater than or equal to 1.60×10 8  Nm/rad, and optionally greater than or equal to 2.7×10 8  Nm/rad. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torsional stiffness of the carrier  34  may be greater than or equal to 1.8×10 8  Nm/rad, and optionally may be greater than or equal to 2.5×10 8  Nm/rad (and optionally may be equal to 4.83×10 8  Nm/rad). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the carrier  34  may greater than or equal to 6.0×10 8  Nm/rad and optionally may be greater than or equal to 1.1×10 9  Nm/rad (and optionally may be equal to 2.17×10 9  Nm/rad). 
     In various embodiments, the torsional stiffness of the carrier  34  is in the range from 1.60×10 8  to 1.00×10 11  Nm/rad, and optionally in the range from 2.7×10 8  to 1×10 10  Nm/rad. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torsional stiffness of the carrier  34  may be in the range from 1.8×10 8  to 4.8×10 9  Nm/rad, and optionally may be in the range from 2.5×10 8  to 6.5×10 8  Nm/rad (and optionally may be equal to 4.83×10 8  Nm/rad). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the carrier  34  may be in the range from 6.0×10 8  to 2.2×10 10  Nm/rad and optionally may be in the range from 1.1×10 9  to 3.0×10 9  Nm/rad (and optionally may be equal to 2.17×10 9  Nm/rad). 
     In various embodiments, the effective linear torsional stiffness of the carrier  34  may be greater than or equal to 7.00×10 9  N/m, and optionally greater than or equal to 9.1×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the carrier  34  may be greater than or equal to 7.70×10 9  N/m. In other such embodiments, the effective linear torsional stiffness of the carrier  34  may be greater than or equal to 9.1×10 9  N/m, optionally greater than or equal to 1.1×10 10  N/m (and optionally may be equal to 1.26×10 10  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the carrier  34  may be greater than or equal to 1.2×10 10  N/m and optionally may be greater than or equal to 2.1×10 10  N/m (and optionally may be equal to 2.88×10 10  N/m). 
     In various embodiments, the effective linear torsional stiffness of the carrier  34  may be in the range from 7.00×10 9  to 1.20×10 11  N/m, and optionally in the range from 9.1×10 9  to 8.0×10 10  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the carrier  34  may be in the range from 9.1×10 9  to 6.0×10 10  N/m, and optionally may be in the range from 7×10 9  to 2×10 10  N/m, or from 8.5×10 9  to 2.0×10 10  N/m (and optionally may be equal to 1.26×10 10  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the carrier  34  may be in the range from 1.2×10 10  to 1.2×10 11  N/m and optionally may be in the range from 1.0×10 10  to 5.0×10 10  N/m (and optionally may be equal to 2.88×10 10  N/m). 
     The torsional stiffness of the carrier  34  may be controlled so as to be within a desired range by adjusting one or more parameters, including carrier material(s), carrier geometry, and the presence or absence of lugs. 
     Gear Mesh Stiffnesses 
     As shown in  FIG.  3   , the planet gears  32  engage with both the sun gear  28  and the ring gear  38 . The epicyclic gearbox  30  therefore has a gear mesh stiffness between the planet gears  32  and the ring gear  38  and a gear mesh stiffness between the planet gears  32  and the sun gear  28 , with each gear mesh stiffness being defined in the standard way described above. Each planet gear  32  has fewer teeth than the ring gear  38 . In the embodiment being described, the gear mesh stiffness between the planet gears  32  and the ring gear  38  is taken as an averaged value over one full revolution of:
         (i) for a star gearbox  30 : the ring gear  38 , the planet carrier  34  being stationary; or   (ii) for a planetary gearbox  30 : the planet carrier  34 , the ring gear  38  being stationary.       

     Averaging over a full rotation may allow any asymmetries in the gears (e.g. due to manufacturing tolerance) to be accounted for. In alternative embodiments, the averaged value over a full cycle of the gearbox back to its initial position, over a single rotation of a planet gear  32 , or just over a single tooth interaction (i.e. over the roll angle change from a selected tooth making contact with the opposing gear and then losing contact with the opposing gear), may be used instead. Further, in the arrangement being described, an average of the values obtained for each planet gear  32  is used. The skilled person would appreciate that the values for each planet  32  should be the same within tolerances, with any significant deviations suggesting a manufacturing error or damaged gear. 
     In various embodiments, the gear mesh stiffness between the planet gears  32  and the ring gear  38  is greater than or equal to 1.40×10 9  N/m, and optionally greater than or equal to 2.45×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh stiffness between the planet gears  32  and the ring gear  38  may be greater than or equal to 2.4×10 9  N/m, and optionally greater than or equal to 2.5×10 9 , and optionally may be equal to 2.62×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, gear mesh stiffness between the planet gears  32  and the ring gear  38  may be greater than or equal to 2.8×10 9  N/m, and optionally greater than or equal to 3.2×10 9  (and optionally may be equal to 3.50×10 9  N/m). 
     In various embodiments, the gear mesh stiffness between the planet gears  32  and the ring gear  38  is in the range from 1.40×10 9  to 2.00×10 10  N/m, and optionally in the range from 2.45×10 9  to 1.05×10 10  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh stiffness between the planet gears  32  and the ring gear  38  may be in the range from 2.4×10 9  to 7.5×10 9  N/m, and optionally in the range from 2.5×10 9  to 5.5×10 9  N/m, and optionally may be equal to 2.62×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, gear mesh stiffness between the planet gears  32  and the ring gear  38  may be in the range from 2.8×10 9  to 1.05×10 10  N/m, and optionally in the range from 3.2×10 9  to 6.5×10 9  N/m (and optionally may be equal to 3.50×10 9  N/m). 
     The planet to ring gear mesh stiffness may be controlled to be within the desired range by adjusting parameters such as tooth size and materials, as for other gear mesh stiffnesses. 
     In the embodiment being described, the gear mesh stiffness between the planet gears  32  and the sun gear  28  is taken as an averaged value over one full revolution of:
         (i) if the sun gear  28  has more teeth than each planet gear  32 , the sun gear  28 ; or   (ii) if each planet gear  32  has more teeth than the sun gear  28 , the planet gear  32 .       

     The skilled person would appreciate that gear mesh stiffness may vary depending on how many teeth on each gear are in contact at the time, and also on which portion(s) of a given tooth are in contact with a given tooth on a meshed gear at a time (e.g. tip to root, middle to middle, or root to tip)—these generally vary with roll angle, and a step change in gear mesh stiffness may be observed as contact with one tooth is lost and/or contact with another tooth gained. Using helical gear teeth may help to smooth any such step change due to different parts of the helical tooth loosing/gaining contact with the opposing tooth as roll angle changes, but variation, and often discontinuities, over the tooth interaction process are generally expected. At a minimum, the gear mesh stiffnesses used are therefore averaged over at least one full tooth interaction process (i.e. over the roll angle change from a selected tooth making contact with the opposing gear and then losing contact with the opposing gear). Averaging over a full rotation of a gear, or optionally of the entire gearbox  30 , may allow any asymmetries in the gears/variations between teeth on the same gear (e.g. due to manufacturing tolerance) to be accounted for. In some embodiments, the averaged value over a full cycle of the gearbox back to its initial position may be used instead. 
     In various embodiments, the gear mesh stiffness between the planet gears  32  and the sun gear  28  is greater than or equal to 1.20×10 9  N/m, and optionally greater than or equal to 2.0×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh stiffness between the planet gears  32  and the sun gear  28  may be greater than or equal to 1.9×10 9  N/m, and optionally greater than or equal to 2.0×10 9  N/m, and optionally may be equal to 2.16×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, gear mesh stiffness between the planet gears  32  and the sun gear  28  may be greater than or equal to 2.3×10 9  N/m, and optionally greater than or equal to 2.8×10 9  N/m, and optionally may be equal to 3.04×10 9  N/m. 
     In various embodiments, the gear mesh stiffness between the planet gears  32  and the sun gear  28  is in the range from 1.20×10 9  to 1.60×10 10  N/m, and optionally in the range from 2.0×10 9  to 9.5×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh stiffness between the planet gears  32  and the sun gear  28  may be in the range from 1.9×10 9  to 6.5×10 9  N/m, and optionally in the range from 2.0×10 9  to 3.0×10 9  N/m, and optionally may be equal to 2.16×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, gear mesh stiffness between the planet gears  32  and the sun gear  28  may be in the range from 2.3×10 9  to 9.5×10 9  N/m, and optionally in the range from 2.8×10 9  to 4.0×10 9  N/m (and optionally may be equal to 3.04×10 9  N/m). 
     The planet to sun gear mesh stiffness may be controlled to be within the desired range by adjusting parameters such as tooth size and materials, as for other gear mesh stiffnesses. 
     An overall gear mesh stiffness for the gearbox  30  is also defined. The overall gear mesh stiffness, T, of the gearbox  30  for a gearbox  30  having N planet gears, where N is an integer greater than or equal to two, may be defined as: 
     
       
         
           
             
               1 
               T 
             
             = 
             
               
                 1 
                 
                   
                     ∑ 
                     
                       n 
                       = 
                       1 
                     
                     N 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     P 
                     n 
                     S 
                   
                 
               
               + 
               
                 1 
                 
                   
                     ∑ 
                     
                       n 
                       = 
                       1 
                     
                     N 
                   
                   ⁢ 
                   
                     P 
                     n 
                     R 
                   
                 
               
             
           
         
       
     
     where: 
     P n   S  is the gear mesh stiffness between the planet gear  32  and the sun gear  28  for the nth planet gear  32 ; and 
     P n   R  is the gear mesh stiffness between the planet gear  32  and the ring gear  38  for the nth planet gear  32 . 
     The sum over the planets (Σ n=1   N P n ) may be replaced with N times the appropriate (average) gear mesh stiffness as defined above, for both the sun gear mesh (Σ n=1   N P n   S ) and the ring gear mesh (Σ n=1   N P n   R ). 
     In the embodiment being described, the averaged value over a full cycle of the gearbox  30  back to its initial position is used. 
     The overall gear mesh stiffness of the gearbox  30  is illustrated in  FIG.  11   , which schematically shows the connections between the sun gear  28  and the planet carrier  34  (via the planet gears  32 , with gear mesh stiffnesses P n   S ) and the connections between the planet carrier  34  and the ring gear  38  (via the planet gears  32 , with gear mesh stiffnesses P n   R ). 
     In various embodiments, the overall gear mesh stiffness of the gearbox  30  is greater than or equal to 1.05×10 9  N/m, optionally in the range from 1.05×10 9  to 8.00×10 9  N/m, and further optionally in the range from 1.08×10 9  to 4.9×10 9  N/m, or to 3.4×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the overall gear mesh stiffness of the gearbox  30  may be in the range from 1.05×10 9  to 3.6×10 9  N/m, and optionally in the range from 1.08×10 9  to 1.28×10 9  N/m, and optionally may be equal to 1.18×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, overall gear mesh stiffness of the gearbox  30  may be in the range from 1.2×10 9  to 4.9×10 9  N/m, and optionally in the range from 1.4×10 9  to 2.2×10 9  N/m (and optionally may be equal to 1.63×10 9  N/m). 
     The skilled person would appreciate that tooth and gearbox dimensions, and gear materials, may be selected as appropriate to obtain a desired gear mesh stiffness. For example, tooth size may be selected considering two competing factors—a minimum required bending strength of the tooth may set a minimum size for a tooth of a given material, and a maximum allowed amount of slide between teeth may set an upper size limit for a tooth. The skilled person would appreciate that larger teeth can result in more heat generation at the gear mesh, and/or excessive contact between meshed gears, which may waste energy and/or increase wear on gears. Having a larger number of smaller teeth (for a given gear diameter), e.g. 80 or more teeth, is therefore generally preferable, with a lower limit being set by a minimum acceptable tooth bending strength. 
     Transmission Torsional Stiffness 
     Transmission torsional stiffness is a measure of the resistance of the whole transmission—from the gearbox input shaft  26  to the interface with the fan  23 —to an applied torque, τ, as illustrated in  FIG.  12   . It may be described as resistance to twisting, or winding, of the shaft transmission. The axis of the moment is parallel to the engine axis  9 . 
     In particular, the transmission may be defined between the bearing  26   c  of the core shaft  26  (at or near the rearward end of the gearbox input shaft  26   a , as described below) and the fan input position, Y, as defined below. The bearing  26   c  (connecting the shaft  26  to the stationary supporting structure  24 ) and the connection of the gearbox support  40  to the stationary supporting structure  24  are held rigidly (non-rotating) as indicated by the diagonally-lined boxes in  FIG.  12   . A torque is then applied to the fan shaft  36  at the axial position of the fan input position. For the purpose of measuring the transmission torsional stiffness, the gearbox input shaft  26  is held not to rotate at the location of the bearing  26   c . A rotation angle θ is measured at the fan input position. 
     The gear mesh stiffnesses are included in the transmission stiffness—the black shading in  FIG.  12    indicates components which contribute to transmission stiffness (namely the gearbox input shaft  26 , output/fan shaft  36 , gearbox  30  and gearbox support  40 ). 
     The torque, τ, is applied to the fan shaft  36  (at the fan input position, Y) and causes a rotational deformation along the length of the transmission. The angle through which a point on the fan shaft circumference at the fan input position moves is θ, where θ is the angle measured in radians. An effective linear torsional stiffness can therefore be defined for the transmission as described above, using the radius, r, of the fan shaft  36 . In embodiments in which the radius of the fan shaft varies, the radius at the fan input position, Y, may be used. 
     In various embodiments, the effective linear torsional stiffness of the transmission is greater than or equal to 1.60×10 8  N/m, and optionally greater than or equal to 3.8×10 8  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the transmission may be greater than or equal to 3.8×10 8  N/m, and optionally may greater than or equal to 4.2×10 8  N/m (and optionally may be equal to 4.8×10 8  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the transmission may be greater than or equal to 3.8×10 8  N/m and optionally may be greater than or equal to 7.7×10 8  N/m (and optionally may be equal to 8.2×10 8  N/m). 
     In various embodiments, the effective linear torsional stiffness of the transmission is in the range from 1.60×10 8  to 3.20×10 9  N/m, and optionally in the range from 3.8×10 8  to 1.9×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the transmission may be in the range from 3.8×10 8  to 8.6×10 8  N/m, and optionally may be in the range from 4.2×10 8  to 5.4×10 8  N/m (and optionally may be equal to 4.8×10 8  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the transmission may be in the range from 3.8×10 8  to 3.2×10 9  N/m and optionally may be in the range from 7.7×10 8  to 9.3×10 8  N/m (and optionally may be equal to 8.2×10 8  N/m). 
     The torsional stiffness of the transmission may therefore be thought of as a combined torsional stiffness of the fan shaft  36 , the gearbox  30  (the overall gearbox mesh stiffness), the core shaft  26  (sun input shaft  26 ), and the gearbox support  40 . To adjust the torsional stiffness of the transmission to a desired value, the skilled person would appreciate that any one or more of the parameters discussed for the components of the transmission, as described elsewhere herein, may be adjusted as appropriate. 
     The overall gearbox mesh stiffness is as defined above. The torsional stiffnesses of the other transmission components may be as defined below: 
     Gearbox Input Shaft Torsional Stiffness 
     In the arrangement being described, the gearbox input shaft  26   a  drives the sun gear  28 . The gearbox input shaft  26   a  may therefore be referred to as a sun input shaft  26   a . The gearbox input shaft  26   a  may be a sun input shaft  26   a  in star arrangements (as well as planetary). The gearbox input shaft  26   a  may also be referred to as a part of the core shaft  26 —a forward portion  26   a  of the core shaft  26  provides the input to the gearbox  30 . 
     The core shaft  26  therefore comprises a gearbox input shaft  26   a , which rotates with the rest of the core shaft  26  but may have a different stiffness from the rest of the core shaft. In the arrangement being described with respect to  FIGS.  1  and  2   , the core shaft extends between the turbine  19  and the gearbox  30 , connecting the turbine  19  to the compressor  14 , and the turbine and compressor to the gearbox  30 . A rearward portion  26   b  of the core shaft  26  extends between the turbine  19  and the compressor  14 , connecting the turbine to the compressor. A forward portion  26   a  extends between the compressor  14  and the gearbox, connecting the turbine and compressor to the gearbox  30 . As this forward portion provides the torque to the gearbox  30 , it is referred to as the gearbox input shaft. In the arrangement shown, a bearing  26   c  is present on the core shaft  26  at or near the axial position at which the rearward portion  26   b  meets the gearbox input shaft  26   a.    
     In some gearboxes  30 , the planet carrier  34  may be driven by the core shaft  26 , and more specifically by the gearbox input shaft  26   a , for example—in such embodiments, the gearbox input shaft  26   a  may not be a sun input shaft  26   a . However, this may make mounting of the sun gear  28  more difficult. 
     In the described arrangement, the core shaft  26  is divided into two sections as shown in  FIG.  13   ; a first section  26   a  (the gearbox input shaft) extending from the gearbox  30  and connected to the sun gear  28 , and a second section  26   b  (which may be referred to as a turbine shaft) extending rearwardly from the first section and connected to the turbine  19 . In the described arrangement, the first section  26   a  is designed to have a lower stiffness than the second section  26   b —the gearbox input shaft  26   a  may therefore provide a soft mounting for the sun gear  28  whilst maintaining rigidity elsewhere in the engine  10 . In the described arrangement, the second section  26   b  is designed to be effectively rigid (as compared to the stiffness of the first section  26   a ). The second section  26   b  connecting the turbine  19  and the compressor  14  and the gearbox  30  may be referred to as the turbine shaft  26   b . The turbine shaft  26   b  is arranged to transmit the torsional loads to drive the compressor and the gearbox  30 , as well as to handle the compressor and turbine axial loads. 
     In alternative embodiments, the core shaft  26  may not be divided into sections of different stiffness, and may instead have a constant stiffness. In alternative or additional embodiments, the core  26  may be divided into a larger number of sections. 
     The core shaft  26  is mounted using a bearing  26   c —the bearing  26   c  is the first bearing on the core shaft  26  axially downstream of the gearbox  30 . In the described arrangement, the bearing  26   c  is on the second section  26   b  of the shaft  26 —in other embodiments, it may be on a different, or on the only, shaft section. The stiffnesses of the gearbox input shaft  26   a  are measured holding the bearing  26   c  rigid, and taking the connection of the bearing  26   c  to the rest  26   b  of the core shaft  26  as rigid, such that only the stiffnesses of the first portion  26   a  are considered (the remainder being treated as effectively rigid). For the purpose of determining torsional stiffness, the gearbox input shaft  26   a  is considered to be free at the end to which the applied torque τ is applied. 
     Gearbox input shaft torsional stiffness is a measure of the resistance of the shaft  26   a  to an applied torque, τ, as illustrated in  FIG.  14   . It may be described as resistance to twisting, or winding, of the shaft  26   a . The axis of the moment is parallel to the engine axis  9 . The diagonally lined box  402  at the location of the bearing  26   c  of the shaft  26   a  is shown to indicate the connection to the bearing  26   c /the shaft  26  at the position of the bearing being treated as rigid and non-rotating (as for a cantilever beam mounting). The shaft  26   a  is otherwise treated as a free body (the sun gear-planet gear mesh stiffness is not included). A torque, τ, is applied to the shaft  26   a  (at the forward position—the position of the axial mid-point of the sun gear  28 ) and causes a rotational deformation, θ (e.g. twist) along the length of the shaft  26   a . θ is measured at the position of application of the torque. As described above, the core shaft  26  is held to be non-rotating at the location of the bearing  26   c , such that the value of the twist increases from zero to θ along the length of the first shaft portion  26   a.    
     In the embodiment shown, the position of the axial mid-point of the sun gear  28  is also at or near the forward end of the shaft  26 . In alternative embodiments, the shaft  26  may extend further forward of the sun gear  28 ; the forward position used for the application of the torque, force or moment is still taken to be the position of the axial mid-point of the sun gear  28  in such embodiments. 
     The angle through which a point on the shaft circumference at the forward position moves is θ, where θ is the angle measured in radians. An effective linear torsional stiffness can therefore be defined for the gearbox input shaft  26   a  as described above, using the radius, r, of the gearbox input shaft  26   a . In embodiments in which the gearbox input shaft  26   a  varies in radius, the radius of the shaft  26   a  at the interface to the sun gear  28  may be used as the radius r (i.e. the radius at the forward end of the shaft for the embodiment shown). 
     In various embodiments, the torsional stiffness of the gearbox input shaft  26   a  is greater than or equal to 1.4×10 6  Nm/radian, and optionally greater than or equal to 1.6×10 6  Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torsional stiffness of the gearbox input shaft may be greater than or equal to 1.4×10 6  Nm/radian or 2×10 6  Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the gearbox input shaft may be greater than or equal to 3×10 6  Nm/radian or 5×10 6  Nm/radian. 
     In various embodiments, the torsional stiffness of the gearbox input shaft  26   a  is in the range from 1.4×10 6  to 2.5×10 8  Nm/radian, and optionally in the range from 1.6×10 6  to 2.5×10 7  Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torsional stiffness of the gearbox input shaft may be in the range from 1.4×10 6  to 2.0×10 7  Nm/radian, and optionally may be in the range from 1.8×10 6  to 3.0×10 6  Nm/radian (and optionally may be equal to 2.0×10 6  Nm/radian). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the gearbox input shaft may be in the range from 3×10 6  to 1×10 8  Nm/radian and optionally may be in the range from 5×10 6  to 6×10 6  Nm/radian (and optionally may be equal to 5.7×10 6  Nm/radian). 
     In various embodiments, the effective linear torsional stiffness of the gearbox input shaft  26   a  is greater than or equal to 4.0×10 8  N/m, and optionally greater than or equal to 4.3×10 8  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the gearbox input shaft may be greater than or equal to 4.0×10 8  N/m or 4.4×10 8  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, effective linear torsional stiffness of the gearbox input shaft may be greater than or equal to 4.3×10 8  N/m or 6.0×10 8  N/m. 
     In various embodiments, effective linear torsional stiffness of the gearbox input shaft is in the range 4.0×10 8  to 3.0×10 10  N/m, and optionally in the range from 4.3×10 8  to 9.0×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the gearbox input shaft may be in the range from 4.0×10 8  to 1.5×10 10  N/m, and optionally may be in the range from 4.4×10 8  to 5.4×10 8  N/m (and optionally may be equal to 4.9×10 8  N/m, and optionally 4.92×10 8  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the gearbox input shaft may be in the range from 4.3×10 8  to 3.0×10 10  N/m and optionally may be in the range from 5.0×10 8  or 6.0×10 8  to 8.0×10 8  N/m (and optionally may be equal to 6.8×10 8  N/m, and optionally 6.84×10 8  N/m). 
     One or more of gearbox input shaft  26   a  material(s), diameter and structure (e.g. hollow or solid, wall thickness) may be adjusted to achieve a stiffness within the desired range. 
     Fan Shaft Torsional Stiffness 
     The fan shaft  36  is defined as the torque transfer component that extends from the output of the gearbox  30  to the fan input. It therefore includes part or all of any gearbox output shaft and fan input shaft that may be provided between those points. For the purposes of defining the stiffness of the fan shaft  36  it is considered to extend between a fan input position, Y, and a gearbox output position, X, and to include all of the torque transfer components between those points. It does not therefore include any components of the gearbox (e.g. the planet carrier or connecting plate coupled to it) which transmit discrete forces, rather than the fan shaft torque. The gearbox output position (X) therefore may be defined as the point of connection between the fan shaft  36  and the gearbox  30 . The fan input position (Y) may be defined as the point of connection between the fan shaft  36  and the fan. 
     The torsional stiffness of the fan shaft  36  is measured between the forward and rearward ends of the fan shaft; the forward end being the interface with the fan  23  and the rearward end being the interface with the gearbox  30 . 
     Fan shaft torsional stiffness is a measure of the resistance of the shaft  36  to an applied torque, τ, as illustrated in  FIG.  17   . It may be described as resistance to twisting, or winding, of the shaft  36 . The axis of the moment is parallel to the engine axis  9 . Referring to  FIGS.  15  and  17   , where the gearbox  30  is a star gearbox, the gearbox output position is defined as the point of connection  702  between the ring gear  38  and the fan shaft  36 . More specifically, it is the point of connection to the annulus of the ring gear  38  (with any connection component extending from the outer surface of the annulus being considered to be part of the ring gear). Where the point of connection is formed by an interface extending in a direction having an axial component, the point of connection, X, is considered to be the axial centreline of that interface as illustrated in  FIG.  17   . The fan shaft  36  includes all torque transmitting components up to the point of connection  702  with the ring gear  38 . It therefore includes any flexible portions or linkages  704  of the fan shaft  36  that may be provided, and any connection(s)  706  (e.g. spline connections) between them. 
     Where the gearbox  30  has a planetary configuration, the gearbox output position is again defined as the point of connection between the fan shaft  36  and the gearbox  30 . An example of this is illustrated in  FIG.  16   , which shows a carrier comprising a forward plate  34   a  and rearward plate  34   b , with a plurality of pins  33  extending between them and on which the planet gears are mounted. The fan shaft  36  is connected to the forward plate  34   a  via a spline connection  708 . In arrangements such as this, the gearbox output position is taken as any point on the interface between the fan shaft  36  and the forward plate  34   a . The forward plate  34   a  is considered to transmit discrete forces, rather than a single torque, and so is taken to be part of the gearbox  30  rather than the fan shaft.  FIG.  16    shows only one example of a type of connection between the fan shaft and planet carrier  34 . In embodiments having different connection arrangements, the gearbox output position is still taken to be at the interface between components transmitting a torque (i.e. that are part of the fan shaft) and those transmitting discrete forces (e.g. that are part of the gearbox). The spline connection  708  is only one example of a connection that may be formed between the fan shaft  36  and gearbox  30  (i.e. between the fan shaft and the forward plate  34   b  in the presently described embodiment). In other embodiments, the interface which forms the gearbox output position may be formed by, for example, a curvic connection, a bolted joint or other toothed or mechanically dogged arrangement. 
     The fan input position, Y, is defined as a point on the fan shaft  36  at the axial midpoint of the interface between the fan  23  and the fan shaft  36 . In the presently described embodiment, the fan  23  comprises a support arm  23   a  arranged to connect the fan  23  to the fan shaft  36 . The support arm  23   a  is connected to the fan shaft by a spline coupling  36   a  that extends along the length of a portion of the fan shaft  36 . The fan input position is defined as the axial midpoint of the spline coupling as indicated by axis Y in  FIG.  17   . The spline coupling shown in  FIG.  17    is only one example of a coupling that may form the interface between the fan and fan shaft. In other embodiments, for example, a curvic connection, a bolted joint or other toothed or mechanically dogged arrangement may be used. The fan input position, Y, may be unaffected by gearbox type. 
     The fan shaft  36  has a degree of flexibility characterised in part by its torsional stiffness. 
     The diagonally-lined ring gear  38  in  FIG.  17    indicates the ring gear  38  being treated as rigid and non-rotating for the purpose of assessing torsional stiffness. A torque, τ, is applied to the shaft  36  at the fan input position, Y, and causes a rotational deformation, θ (e.g. twist) along the length of the shaft  36 . The angle through which a point on the shaft circumference at the fan input position moves is θ, when θ is the angle measured in radians. An effective linear torsional stiffness can therefore be defined for the fan shaft  36  as described above using the radius, r, of the fan shaft  36 . In embodiments in which the fan shaft  36  varies in radius, such as the embodiment being described, the radius of the shaft  36  at the fan input position may be used as the radius r (i.e. the radius at the forward end of the shaft for the embodiment shown). For the purpose of determining torsional stiffness, the fan shaft  36  is considered to be free at the end to which the applied torque τ is applied. 
     In various embodiments, the torsional stiffness of the fan shaft  36  is equal to or greater than 1.3×10 7  Nm/rad, and optionally equal to or greater than 1.4×10 7  Nm/rad. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the torsional stiffness of the fan shaft  36  may equal to or greater than 1.3×10 7  Nm/radian, and optionally may be equal to or greater than 1.4×10 7  Nm/radian (and optionally may be equal to 1.8×10 7  Nm/radian). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the fan shaft  36  may be equal to or greater than 2.5×10 7  Nm/radian and optionally may be equal to or greater than 3.5×10 7  Nm/radian (and optionally may be equal to 5.2×10 7  Nm/radian). 
     In various embodiments, the torsional stiffness of the fan shaft  36  is in the range from 1.3×10 7  to 2.5×10 9  Nm/rad, and optionally in the range from 1.4×10 7  to 3.0×10 8  Nm/rad. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the torsional stiffness of the fan shaft  36  may be in the range from 1.3×10 7  to 2.0×10 8  Nm/radian, and optionally may be in the range from 1.3×10 7  to 2.3×10 7  Nm/radian (and optionally may be equal to 1.8×10 7  Nm/radian). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the fan shaft  36  may be in the range from 2.5×10 7  to 2.5×10 9  Nm/radian and optionally may be in the range from 3.5×10 7  to 7.5×10 7  Nm/radian (and optionally may be equal to 5.2×10 7  Nm/radian). 
     In various embodiments, the effective linear torsional stiffness of the fan shaft  36  may be greater than or equal to 1.2×10 9  N/m, and optionally greater than or equal to 1.35×10 9  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the fan shaft  36  may be greater than or equal to 1.2×10 9  N/m, and optionally may be greater than 1.3×10 9  Nm/radian (and optionally may be equal to 1.5×10 9  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the fan shaft  36  may be greater than or equal to 1.5×10 9  N/m and optionally may be greater than or equal to 1.8×10 9  Nm/radian (and optionally may be equal to 2.1×10 9  N/m). 
     In various embodiments, the effective linear torsional stiffness of the fan shaft  36  is in the range from 1.2×10 9  to 2.0×10 10  N/m, and optionally in the range from 1.35×10 9  to 1.0×10 10  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the fan shaft  36  may be in the range from 1.2×10 9  to 1.5×10 10  N/m, and optionally may be in the range from 1.3×10 9  to 2.3×10 9  Nm/radian (and optionally may be equal to 1.5×10 9  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the fan shaft  36  may be in the range from 1.5×10 9  to 2.0×10 10  N/m and optionally may be in the range from 1.8×10 9  to 3.5×10 9  Nm/radian (and optionally may be equal to 2.1×10 9  N/m). 
     One or more of fan shaft  36  material(s), diameter and structure (e.g. hollow or solid, wall thickness) may be adjusted to achieve a stiffness within the desired range. 
     Gearbox Support Torsional Stiffness 
     An exemplary embodiment of the gas turbine engine is shown in  FIG.  18   , which shows a region of the engine core  11  around the gearbox  30  in close up. The same reference numbers have been used for components corresponding to those shown in  FIGS.  1  to  3   . In the arrangement shown in  FIG.  18    the gearbox  30  has a star arrangement, in which the ring gear  38  is coupled to the fan shaft  36  and the carrier  34  is held in a fixed position relative to the static structure  502 ,  24  of the engine core  11 . As noted elsewhere herein, all features and characteristics described herein may apply to a star gearbox and a planetary gearbox, unless explicitly stated otherwise. 
     The engine core  11  comprises a gearbox support  40  (corresponding to the linkage described with reference to  FIG.  2   ) arranged to at least partially support the gearbox  30  in a fixed position within the engine. The gearbox support is coupled at a first end to the stationary supporting structure  24  which extends across the core duct carrying the core airflow A as illustrated in  FIG.  18   . In the presently described arrangement, the stationary support structure  24  is or comprises an engine section stator (ESS) that acts as both a structural component to provide a stationary mounting for core components such as the gearbox support  40 , and as a guide vane provided to direct airflow from the fan  23 . In other embodiments, the stationary supporting structure  24  may comprise a strut extending across the core gas flow path and a separate stator vane provided to direct airflow. In the present embodiment, the gearbox support  40  is coupled at a second end to the planet carrier  34 . The gearbox support  40  therefore acts against rotation of the planet carrier  34  relative to the static structure of the engine core  11 . In embodiments where the gearbox  30  is in a planetary arrangement, the gearbox support  40  is coupled to the ring gear  38  so as to resist its rotation relative to the static structure of the engine core  11 . 
     The gearbox support  40  is defined between the point at which it connects to the gearbox (e.g. to the planet carrier  34  in the present embodiment with a star gearbox  30 , or to the ring gear  38  in planetary embodiments) and a point at which it connects to the stationary supporting structure  24 . The gearbox support  40  may be formed by any number of separate components providing a coupling between those two points. The gearbox support  40  connects to the gearbox  30  to the static gear or gear set—i.e. to the ring gear  38  of a planetary gearbox or the planet carrier/planet gear set  34  of a star gearbox. 
     The gearbox support  40  has a degree of flexibility. Gearbox support torsional stiffness is a measure of the resistance of the support  40  to an applied torque, τ, as illustrated in  FIG.  20   . It may be described as resistance to twisting, or winding, of the support  40 . The axis of the moment is parallel to the engine axis  9 . 
     For a star gearbox  30 , the torsional stiffness of the gearbox support  40  is defined between a circle  902  passing through the centre of each planet gear  32  of the planetary gear set (i.e. through the longitudinal axis of each pin  33 ) and the interface to the stationary support structure  24 , which is treated as fixed. The torsional load is applied at the planet carrier  34 , and reacted at the stationary support structure  24 . 
     For a planetary gearbox  30 , the torsional stiffness of the gearbox support  40  is defined between the pitch circle diameter (PCD) of the ring gear  38 , and the interface to the stationary support structure  24 , which is treated as fixed. The torsional load is applied at the ring gear  38 , and reacted at the stationary support structure  24 . 
     The diagonal lines on the stationary support structure  24  are provided to indicate the connection to the support  40  being treated as rigid and non-rotating. 
     For the example of a planetary gearbox  30 , a torque, τ, is applied to the teeth of the ring gear  38  and causes a rotational deformation, θ (e.g. twist) of the support  40 . The angle through which a point on the PCD moves is θ, where θ is the angle measured in radians. An effective linear torsional stiffness can therefore be defined for the gearbox support  40  for a planetary gearbox  30  as described above using the radius r=PCD/2. Here, r is the radius of the ring gear  38  (i.e. half of the PCD of the ring gear). 
     In various embodiments the PCD of the ring gear  38 , which may also be thought of as a diameter of the gearbox  30 , may be greater than or equal to 0.55 m, and optionally greater than or equal to 0.57 m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gearbox diameter may be greater than or equal to 0.55 m, and may be equal to 0.61 m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gearbox diameter may be greater than or equal to 0.75 m, and may be equal to 0.87 m. 
     In various embodiments the diameter of the gearbox  30  may be in the range from 0.55 m to 1.2 m, and optionally in the range from 0.57 to 1.0 m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the gearbox diameter may be in the range from 0.55 to 0.70 m, and optionally may be in the range from 0.58 to 0.65 m (and optionally may be equal to 0.61 m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gearbox diameter may be in the range from 0.75 to 1.0 m, and optionally may be in the range from 0.8 to 0.9 m (and optionally may be equal to 0.87 m). 
     Correspondingly, an effective linear torsional stiffness can therefore be defined for the gearbox support  40  for a star gearbox  30  as described above using the radius r of the circle  902  passing through the longitudinal axis of each pin  33  on the carrier  34 . The diameter of this circle  902  may be described as a PCD of the planetary gear set, or a pin PCD, so providing r=PCD/2 as for the planetary gearbox example. In various embodiments the PCD of the planetary gear set (the pin PCD) may be in the range from 0.38 to 0.65 m, for example being equal to 0.4 m or 0.55 m. 
     In various embodiments, the torsional stiffness of the gearbox support  40  is greater than or equal to 4.2×10 7  Nm/rad, and optionally greater than or equal to 4.8×10 7  Nm/rad. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the torsional stiffness of the gearbox support  40  may be greater than or equal to 4.2×10 7  Nm/rad, and optionally may be greater than or equal to 5×10 7  Nm/rad (and optionally may be equal to 6.1×10 7  Nm/rad). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the gearbox support  40  may be greater than or equal to 7.0×10 7  Nm/rad, and optionally may be greater than or equal to 9×10 7  Nm/rad (and optionally may be equal to 1.8×10 8  Nm/rad). 
     In various embodiments, the torsional stiffness of the gearbox support  40  is in the range from 4.2×10 7  to 1.0×10 10  Nm/rad, and optionally in the range from 4.8×10 7  to 1.0×10 9  Nm/rad. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the torsional stiffness of the gearbox support  40  may be in the range from 4.2×10 7  to 6.0×10 10  Nm/rad, and optionally may be in the range from 5×10 7  to 7×10 7  Nm/rad (and optionally may be equal to 6.1×10 7  Nm/rad). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the gearbox support  40  may be in the range from 7.0×10 7  to 1.0×10 10  Nm/ad, and optionally may be in the range from 9×10 7  to 4×10 8  Nm/rad (and optionally may be equal to 1.8×10 8  Nm/rad). 
     In various embodiments, the effective linear torsional stiffness of the gearbox support  40  is greater than or equal to 7.1×10 8  N/m, and optionally greater than or equal to 8.4×10 8  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the effective linear torsional stiffness of the gearbox support  40  may be greater than or equal to 7.1×10 8  N/m, and optionally may be greater than or equal to 8×10 8  N/m (and optionally may be equal to 9.2×10 8  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the gearbox support  40  may be greater than or equal to 9.0×10 8  N/m, and optionally may be greater than or equal to 1.0×10 9  N/m (and optionally may be equal to 1.2×10 9  N/min). 
     In various embodiments, the effective linear torsional stiffness of the gearbox support  40  is in the range from 7.1×10 8  to 6.0×10 10  N/m, and optionally in the range from 8.4×10 8  to 3.0×10 10  N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the effective linear torsional stiffness of the gearbox support  40  may be in the range from 7.1×10 8  to 5.0×10 10  N/m, and optionally may be in the range from 8×10 8  to 1×10 9  N/m (and optionally may be equal to 9.2×10 8  N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the gearbox support  40  may be in the range from 9.0×10 8  to 6.0×10 10  N/m, and optionally may be in the range from 9.0×10 8  or 1.0×10 9  N/m to 2.0×10 9  N/m (and optionally may be equal to 1.2×10 9  N/m). 
     One or more of gearbox support  40  geometry, materials, and connection type for the connection to the stationary support structure  24  may be selected or adjusted as appropriate to obtain the desired stiffness. The skilled person would appreciate that the stiffness of the gearbox support  40  may be defined in a corresponding way for embodiments with different epicyclic gearboxes. 
     The inventor has discovered that particular ratios of the parameters defined above have significant impact on gearbox performance. In particular, one, some or all of the below conditions may apply to any embodiment: 
     In various embodiments, the overall gear mesh stiffness of the gearbox  30  is greater than or equal to 1.05×10 9  N/m, and optionally in the range from 1.05×10 9  to 8.00×10 9  N/m. The gearbox diameter and/or the overall gear mesh stiffness of the gearbox  30  in such embodiments may fit within any of the ranges specified above. 
     In various embodiments, a ring to sun mesh ratio of: 
     
       
         
           
             
               
                   
               
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                       gear 
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                       mesh 
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                       stiffness 
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                       between 
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                       the 
                     
                   
                 
                 
                   
                     
                       planet 
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                       gears 
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                       32 
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                       and 
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                       the 
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                       ring 
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                       gear 
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                       38 
                     
                   
                 
               
             
             
               
                 
                   
                     
                       gear 
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                       mesh 
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                       stiffness 
                       ⁢ 
                       
                           
                       
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                       between 
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                       the 
                     
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                     planet 
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                     gears 
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                     32 
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                     and 
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                     the 
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                     sun 
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                     gear 
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                     28 
                   
                 
               
             
           
         
       
     
     is less than or equal to 1.28, and optionally less than or equal to 1.235 or less than or equal to 1.23. In alternative or additional embodiments, the ring to sun mesh ratio may be greater than or equal to 0.9, and optionally in the range from 0.9 to 1.3. or from 0.90 to 1.28. 
     In various embodiments, the ring to sun mesh ratio is in the range from 9.00×10 −1  to 1.28×10 0  (i.e. 0.900 to 1.28), and optionally from 0.95 to 1.23. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the ring to sun mesh ratio may be in the range from 0.95 to 1.28, and optionally may be in the range from 0.95 to 1.23 (and optionally may be equal to 1.21). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the ring to sun mesh ratio may be in the range from 0.9 to 1.23 (and optionally may be equal to 1.15). 
     In various embodiments, a product of the components of the ring to sun mesh ratio, i.e. the gear mesh stiffness between the planet gears  32  and the ring gear  38  multiplied by the gear mesh stiffness between the planet gears  32  and the sun gear  28 , may be calculated. The value of this product, in various embodiments, may be greater than or equal to 4.7×10 18  N 2 m −2 , and optionally less than 1.5×10 19  N 2 m −2 , and optionally may be greater than or equal to 5.1×10 18  N 2 m −2 , and optionally less than 1.3×10 19  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the product value may be greater than or equal to 4.7×10 18  N 2 m −2 , and optionally less than 8.0×10 18  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the product value may be greater than or equal to 6.0×10 18  N 2 m −2 , and optionally less than 1.5×10 19  N 2 m −2 . 
     In various embodiments, a carrier to sun mesh ratio of: 
     
       
         
           
             
               effective 
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               linear 
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               torsional 
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               stiffness 
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               of 
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               the 
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               planet 
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               carrier 
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               34 
             
             
               
                 
                   
                     
                       gear 
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                       stiffness 
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                       between 
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                       the 
                     
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                     planet 
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                     32 
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                     and 
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                     the 
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                     28 
                   
                 
               
             
           
         
       
     
     is greater than or equal to 2.60×10 −1 . 
     In various embodiments, the carrier to sun mesh ratio may be greater than or equal to 2.60×10 −1 , and optionally greater than or equal to 4.5×10 0 , and further optionally greater than or equal to 5.1. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the carrier to sun mesh ratio may be greater than or equal to 0.6, and optionally may be greater than or equal to 2 or 5 (and optionally may be equal to 5.82). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the carrier to sun mesh ratio may be greater than or equal to 0.94, and optionally greater than or equal to 5 (and optionally may be equal to 9.47). 
     In various embodiments, the carrier to sun mesh ratio is in the range from 2.60×10 −1  to 1.10×10 3 , and optionally from 4.5×10 0  or 5.1×10 0  to 9.5×10 1  (i.e. from 4.5 or 5.1 to 95). In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the carrier to sun mesh ratio may be in the range from 0.6 to 58, and optionally may be in the range from 2 or 5 to 10 (and optionally may be equal to 5.82). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the carrier to sun mesh ratio may be in the range from 0.94 to 95, and optionally in the range from 5 to 16 (and optionally may be equal to 9.47). 
     In various embodiments, a product of the components of the carrier to sun mesh ratio, i.e. the effective linear torsional stiffness of the planet carrier  34  multiplied by the gear mesh stiffness between the planet gears  32  and the sun gear  28 , may be calculated. The value of this product, in various embodiments, may be greater than or equal to 5.0×10 18  N 2 m −2 , and optionally less than 2.0×10 22  N 2 m −2 , and optionally may be greater than or equal to 1.8×10 19  N 2 m −2 , and optionally less than 1.0×10 21  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the product value may be greater than or equal to 1.8×10 19  N 2 m −2 , and optionally less than 8.0×10 20  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the product value may be greater than or equal to 5.0×10 9  N 2 m −2 , and optionally less than 8.0×10 21  N 2 m −2 . 
     In various embodiments, a carrier to ring mesh ratio of: 
     
       
         
           
             
               effective 
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               linear 
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               torsional 
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               stiffness 
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               of 
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               the 
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               planet 
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               34 
             
             
               
                 
                   
                     
                       gear 
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                       mesh 
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                       stiffness 
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                       between 
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                       the 
                     
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                     planet 
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                     gears 
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                     32 
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                     and 
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                     the 
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                     ring 
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                     38 
                   
                 
               
             
           
         
       
     
     is greater than or equal to 0.2. 
     In various embodiments, the carrier to ring mesh ratio may be greater than or equal to 2.00×10 −1  (i.e. 0.200), and optionally may be greater than or equal to 3.8×10 0  (i.e. 3.8). In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the carrier to ring mesh ratio may be greater than or equal to 3.8, and optionally greater than or equal to 3.9 (and optionally may be equal to 4.79). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the carrier to ring mesh ratio may be greater than or equal to 4.0, and optionally may be greater than or equal to 5 (and optionally may be equal to 8.24). 
     In various embodiments, the carrier to ring mesh ratio is in the range from 2.00×10 −1  to 9.00×10 2 , and optionally from 3.8×10 0  to 9.0×10 1  (i.e. from 3.8 to 90). In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the carrier to ring mesh ratio may be in the range from 3.8 to 90, and optionally may be in the range from 3.9 to 7.0 (and optionally may be equal to 4.79). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the carrier to ring mesh ratio may be in the range from 4.0 to 5.0×10 2 , and optionally in the range from 5 to 20 (and optionally may be equal to 8.24). 
     In various embodiments, a product of the components of the carrier to ring mesh ratio, i.e. the effective linear torsional stiffness of the planet carrier  34  multiplied by the gear mesh stiffness between the planet gears  32  and the ring gear  38 , may be calculated. The value of this product, in various embodiments, may be greater than or equal to 5.0×10 18  N 2 m −2 , and optionally less than 2.6×10 22  N 2 m −2 , and optionally may be greater than or equal to 2.2×10 19  N 2 m −2 , and optionally less than 2.6×10 21  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the product value may be greater than or equal to 2.2×10 19  N 2 m −2 , and optionally less than 2.6×10 21  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the product value may be greater than or equal to 2.5×10 19  N 2 m −2 , and optionally less than 6.0×10 21  N 2 m −2 . 
     In various embodiments, a gear mesh to transmission stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
               ⁢ 
               
                   
               
               ⁢ 
               30 
             
             
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               transmission 
             
           
         
       
     
     is less than or equal to 11, and optionally less than or equal to 4.6. 
     In various embodiments, the gear mesh to transmission stiffness ratio is less than or equal to 2.7, and optionally less than or equal to 2.70. 
     In various embodiments, the gear mesh to transmission stiffness ratio is in the range from 3.4×10 −1  to 1.1×10 1  (i.e. from 0.34 to 11), and optionally in the range from 0.90 to 4.6. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm the gear mesh to transmission stiffness ratio may be in the range from 1.4 to 2.7, and optionally may be in the range from 2.0 to 2.6 (and optionally may be equal to 2.45). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gear mesh to transmission stiffness ratio may be in the range from 0.50 to 4.6, and optionally in the range from 1.2 to 2.3 (and optionally may be equal to 1.99). 
     In various embodiments, a gear mesh and transmission stiffness product of: 
     
       
         
           
             overall 
             ⁢ 
             
                 
             
             ⁢ 
             gear 
             ⁢ 
             
                 
             
             ⁢ 
             mesh 
             ⁢ 
             
                 
             
             ⁢ 
             stiffness 
             ⁢ 
             
                 
             
             ⁢ 
             of 
             ⁢ 
             
                 
             
             ⁢ 
             the 
             ⁢ 
             
                 
             
             ⁢ 
             gearbox 
             ⁢ 
             
                 
             
             ⁢ 
             30 
             × 
             effective 
             ⁢ 
             
                 
             
             ⁢ 
             linear 
             ⁢ 
             
                 
             
             ⁢ 
             torsional 
             ⁢ 
             
                 
             
             ⁢ 
             stiffness 
             ⁢ 
             
                 
             
             ⁢ 
             of 
             ⁢ 
             
                 
             
             ⁢ 
             the 
             ⁢ 
             
                 
             
             ⁢ 
             transmission 
           
         
       
     
     is greater than or equal to 1.6×10 17  N 2 m −2 , and optionally greater than or equal to 3.2×10 17  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh and transmission stiffness product may be greater than or equal to 4.2×10 17  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gear mesh and transmission stiffness product may be greater than or equal to 5.8×10 17  N 2 m −2 . 
     In various embodiments, the gear mesh and transmission stiffness product is in the range from 1.6×10 17  to 2.9×10 19  N 2 m −2 , and optionally in the range from 3.2×10 17  to 1.5×10 19  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh and transmission stiffness product may be in the range from 4.2×10 17  to 1.5×10 19  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gear mesh and transmission stiffness product may be in the range from 5.8×10 17  to 2.9×10 19  N 2 m −2 . 
     In various embodiments, a gear mesh to fan shaft stiffness ratio of: 
     
       
         
           
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     overall 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gearbox 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     30 
                   
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     effective 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     linear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     torsional 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     fan 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     shaft 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     36 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     is less than or equal to 1.6, and optionally greater than 0.3. 
     In various embodiments, the gear mesh to fan shaft stiffness ratio may be less than or equal to 1.6×10 0  (i.e. 1.6), and optionally may be less than or equal to 0.85. In some embodiments, the gear mesh to fan shaft stiffness ratio may be less than or equal to 0.80, and optionally may be less than or equal to 0.79 or 0.75. 
     In various embodiments, the gear mesh to fan shaft stiffness ratio may be in the range from 3.0×10 −1  (i.e. 0.30) to 1.6×10 0  (i.e. 1.6), and optionally may be in the range from 0.4 to 0.85. In some embodiments, the gear mesh to fan shaft stiffness ratio may be in the range from 0.45 to 0.80, and optionally may be in the range from 0.50 to 0.75. For example, the gear mesh to fan shaft stiffness ratio may be at least substantially equal to 0.78, for example being 0.782 or 0.778. 
     In various embodiments, a product of the components of the gear mesh to fan shaft stiffness ratio, i.e. the overall gear mesh stiffness of the gearbox  30  multiplied by the effective linear torsional stiffness of the fan shaft  36 , may be calculated. The value of this product, in various embodiments, may be greater than or equal to 1.3×10 18  N 2 m −2 , and optionally less than 5.0×10 19  N 2 m −2 , and optionally may be greater than or equal to 1.4×10 18  N 2 m −2 , and optionally less than 3.0×10 19  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the product value may be greater than or equal to 1.5×10 18  N 2 m −2 , and optionally less than 8.5×10 18  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the product value may be greater than or equal to 1.7×10 18  N 2 m −2 , and optionally less than 5.0×10 19  N 2 m −2 . 
     In various embodiments, a gear mesh to core shaft stiffness ratio of: 
     
       
         
           
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               overall 
               ⁢ 
               
                   
               
               ⁢ 
               gear 
               ⁢ 
               
                   
               
               ⁢ 
               mesh 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               gearbox 
               ⁢ 
               
                   
               
               ⁢ 
               30 
             
             
               the 
               ⁢ 
               
                   
               
               ⁢ 
               effective 
               ⁢ 
               
                   
               
               ⁢ 
               linear 
               ⁢ 
               
                   
               
               ⁢ 
               torsional 
               ⁢ 
               
                   
               
               ⁢ 
               stiffness 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               core 
               ⁢ 
               
                   
               
               ⁢ 
               shaft 
               ⁢ 
               
                   
               
               ⁢ 
               26 
             
           
         
       
     
     is greater than or equal to 0.2, and optionally smaller than or equal to 90 or smaller than or equal to 29, and further optionally smaller than or equal to 2.9. 
     In various embodiments, the gear mesh to core shaft stiffness ratio is less than or equal to 2.9×10 1 , and optionally less than or equal to 9.0×10 1 . In some embodiments, the gear mesh to core shaft stiffness ratio may be less than or equal to 2.4, and optionally may be less than or equal to 2.40. In some embodiments the gear mesh to core shaft stiffness ratio may be less than or equal to 2.9×10 1 , and optionally may be less than or equal to 2.50, or to 2.38. 
     In various embodiments, the gear mesh to core shaft stiffness ratio is in the range from 2.0×10 −1  to 2.9×10 1 , and optionally in the range from 9.0×10 −1  to 9.0×10 1 . In some embodiments, the gear mesh to core shaft stiffness ratio may be in the range from 2.0×10 −1  to 2.4, and optionally may be in the range from 2.25 to 2.4 (and optionally may be equal to 2.40). In some embodiments, the gear mesh to core shaft stiffness ratio may be in the range from 2.4 to 2.9×10 1 , and optionally may be in the range from 2.10 to 2.50 (and optionally may be equal to 2.38). 
     In various embodiments, a gear mesh and core shaft stiffness product of: 
     
       
         
           
             overall 
             ⁢ 
             
                 
             
             ⁢ 
             gear 
             ⁢ 
             
                 
             
             ⁢ 
             mesh 
             ⁢ 
             
                 
             
             ⁢ 
             stiffness 
             ⁢ 
             
                 
             
             ⁢ 
             of 
             ⁢ 
             
                 
             
             ⁢ 
             the 
             ⁢ 
             
                 
             
             ⁢ 
             gearbox 
             ⁢ 
             
                 
             
             ⁢ 
             30 
             × 
             effective 
             ⁢ 
             
                 
             
             ⁢ 
             linear 
             ⁢ 
             
                 
             
             ⁢ 
             torsional 
             ⁢ 
             
                 
             
             ⁢ 
             stiffness 
             ⁢ 
             
                 
             
             ⁢ 
             of 
             ⁢ 
             
                 
             
             ⁢ 
             the 
             ⁢ 
             
                 
             
             ⁢ 
             core 
             ⁢ 
             
                 
             
             ⁢ 
             shaft 
             ⁢ 
             
                 
             
             ⁢ 
             26 
           
         
       
     
     is in the range from 1.0×10 17  to 3.0×10 19  N 2 m −2 , and optionally in the range from 4.5×10 17  to 9.0×10 18  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh and core shaft stiffness product may be in the range from 4.5×10 17  to 8.0×10 18  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gear mesh and core shaft stiffness product may be in the range from 8.0×10 17  to 3.0×10 19  N 2 m −2 . 
     In various embodiments, a gear mesh to gearbox support stiffness ratio of: 
     
       
         
           
             
               
                 
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     overall 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     mesh 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gearbox 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     30 
                   
                   
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     effective 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     linear 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     torsional 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     stiffness 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     the 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     gearbox 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     support 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     40 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     is in the range from 6.5×10 −2  to 2.6×10 1 , and optionally in the range from 1.0 to 1.6. 
     In various embodiments, the gear mesh to gearbox support stiffness ratio is in the range from 6.5×10 −2  to 2.6×10 1 , and optionally in the range from 2.6×10 −1  to 8.0. In some embodiments, the gear mesh to gearbox support stiffness ratio may be in the range from 6.5×10 −2  to 1.1, or from 6.5×10 −2  to 1.4, and optionally may be in the range from 1.20 to 1.32 (and optionally may be equal to 1.29). In some embodiments, the gear mesh to gearbox support stiffness ratio may be in the range from 1.1 to 2.6×10 1 , and optionally may be in the range from 1.34 to 1.60 (and optionally may be equal to 1.37). 
     In various embodiments, a gear mesh and gearbox support stiffness product of: 
     
       
         
           
             overall 
             ⁢ 
             
                 
             
             ⁢ 
             gear 
             ⁢ 
             
                 
             
             ⁢ 
             mesh 
             ⁢ 
             
                 
             
             ⁢ 
             stiffness 
             ⁢ 
             
                 
             
             ⁢ 
             of 
             ⁢ 
             
                 
             
             ⁢ 
             the 
             ⁢ 
             
                 
             
             ⁢ 
             gearbox 
             ⁢ 
             
                 
             
             ⁢ 
             30 
             × 
             
                 
               
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 effective 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 linear 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 torsional 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 stiffness 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 gearbox 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 support 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 40 
               
             
           
         
       
     
     is greater than or equal to 2.0×10 17  N 2 m −2 , and optionally greater than or equal to 9.0×10 17  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh and core shaft stiffness product may be greater than or equal to 5.0×10 17  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gear mesh and core shaft stiffness product may be greater than or equal to 1.0×10 18  N 2 m −2 . 
     In various embodiments, the gear mesh and gearbox support stiffness product is in the range from 2.0×10 17  to 4.1×10 19  N 2 m −2 , and optionally in the range from 9.0×10 17  to 2.1×10 19  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gear mesh and core shaft stiffness product may be in the range from 5.0×10 7  to 1.0×10 19  N 2 m −2 . In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gear mesh and core shaft stiffness product may be in the range from 1.0×10 18  to 4.1×10 19  N 2 m −2 . 
       FIG.  19    illustrates how the stiffnesses defined herein may be measured.  FIG.  19    shows a plot of the displacement δ resulting from the application of a load L (e.g. a force, moment or torque) applied to a component for which the stiffness is being measured. At levels of load from zero to L P  there is a non-linear region in which displacement is caused by motion of the component (or relative motion of separate parts of the component) as it is loaded, rather than deformation of the component; for example moving within clearance between parts. At levels of load above L Q  the elastic limit of the component has been exceeded and the applied load no longer causes elastic deformation—plastic deformation or failure of the component may occur instead. Between points P and Q the applied load and resulting displacement have a linear relationship. The stiffnesses defined herein may be determined by measuring the gradient of the linear region between points P and Q (with the stiffness being the inverse of that gradient). The gradient may be found for as large a region of the linear region as possible to increase the accuracy of the measurement by providing a larger displacement to measure. For example, the gradient may be found by applying a load equal to or just greater than L P  and equal to or just less than L Q . Values for L P  and L Q  may be estimated prior to testing based on materials characteristics so as to apply suitable loads. Although the displacement is referred to as δ in this description, the skilled person would appreciate that equivalent principles would apply to a linear or angular displacement. 
     The stiffnesses defined herein, unless otherwise stated, are for the corresponding component(s) when the engine is off (i.e. at zero speed/on the bench). The stiffnesses generally do not vary significantly over the operating range of the engine; the stiffness at cruise conditions of the aircraft to which the engine is used (those cruise conditions being as defined elsewhere herein) may therefore be the same as for when the engine is not in use. However, where the stiffness varies over the operating range of the engine, the stiffnesses defined herein are to be understood as being values for when the engine is at room temperature and unmoving. 
     The present disclosure also relates to methods  1300  of operating a gas turbine engine  10  on an aircraft. The methods  1300  are illustrated in  FIG.  21   . 
     The method  1300  comprises starting up and operating  1302  the engine  10  (e.g. taxiing on a runway, take-off, and climb of the aircraft, as suitable) to reach cruise conditions. Once cruise conditions have been reached, the method  1300  then comprises operating  1304  the gas turbine engine  10 , which may be as described in one or more embodiments elsewhere herein, to provide propulsion under cruise conditions. 
     The gas turbine engine  10  is such that, and/or is operated such that, any or all of the parameters or ratios defined herein are within the specified ranges. 
     The torque on the core shaft  26  may be referred to as the input torque, as this is the torque which is input to the gearbox  30 . The torque supplied by the turbine  19  to the core shaft (i.e. the torque on the core shaft) at cruise conditions may be greater than or equal to 10,000 Nm, and optionally greater than or equal to 11,000 Nm. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torque on the core shaft  26  at cruise conditions may be greater than or equal to 10,000 or 11,000 Nm (and optionally may be equal to 12,760 Nm). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torque on the core shaft  26  at cruise conditions may be greater than or equal to 25,000 Nm, and optionally greater than or equal to 30,000 Nm (and optionally may be equal to 34,000 Nm). 
     The torque on the core shaft at cruise conditions may be in the range from 10,000 to 50,000 Nm, and optionally from 11,000 to 45,000 Nm. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torque on the core shaft  26  at cruise conditions may be in the range from 10,000 to 15,000 Nm, and optionally from 11,000 to 14,000 Nm (and optionally may be equal to 12,760 Nm). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torque on the core shaft  26  at cruise conditions may be in the range from 25,000 Nm to 50,000 Nm, and optionally from 30,000 to 40,000 Nm (and optionally may be equal to 34,000 Nm). 
     Under maximum take-off (MTO) conditions, the torque on the core shaft  26  may be greater than or equal to 28,000 Nm, and optionally greater than or equal to 30,000 Nm. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torque on the core shaft  26  under MTO conditions may be greater than or equal to 28,000, and optionally greater than or equal to 35,000 Nm (and optionally may be equal to 36,300 Nm). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torque on the core shaft  26  under MTO conditions may greater than or equal to 70,000 Nm, and optionally greater than or equal to 80,000 or 82,000 Nm (and optionally may be equal to 87,000 Nm). 
     Under maximum take-off (MTO) conditions, the torque on the core shaft  26  may be in the range from 28,000 Nm to 135,000 Nm, and optionally in the range from 30,000 to 110,000 Nm. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torque on the core shaft  26  under MTO conditions may be in the range from 28,000 to 50,000 Nm, and optionally from 35,000 to 38,000 Nm (and optionally may be equal to 36,300 Nm). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torque on the core shaft  26  under MTO conditions may be in the range from 70,000 Nm to 135,000 Nm, and optionally from 80,000 to 90,000 Nm or 82,000 to 92,000 Nm (and optionally may be equal to 87,000 Nm). 
     Torque has units of [force]×[distance] and may be expressed in units of Newton metres (N·m), and is defined in the usual way as would be understood by the skilled person. 
     It will be understood that the invention is not limited to the embodiments above-described and various modifications and improvements can be made without departing from the concepts described herein. Except where mutually exclusive, any of the features may be employed separately or in combination with any other features and the disclosure extends to and includes all combinations and sub-combinations of one or more features described herein.