Abstract:
A system for sensing a force applied to an aircraft includes a first sensor, a second sensor, and a processor operative to define a first velocity vector as a function of a first velocity due to a rotation motion of the aircraft, define a second velocity vector as a function of a second velocity due to the rotation motion of the aircraft, define an instant axis of rotation of the aircraft as a function of the first velocity vector and the second velocity vector, determine whether a force has been exerted on a first portion of the aircraft, and output an indication that a force has been exerted on the first portion of the aircraft responsive to determining that the force has been exerted on the first portion of the aircraft.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The subject matter disclosed herein relates to detecting impact forces on aircraft, and in particular to detecting landing gear impact on aircraft. 
         [0002]    Aircraft such as, for example, rotary wing aircraft and fixed wing aircraft use a variety of sensors to provide feedback to aircraft control systems. Detecting when a force, such as weight, is applied to the landing assemblies or other portions of an aircraft provides useful feedback to aircraft systems. Previous systems used sensors located on each landing assembly to determine whether weight was applied to a landing assembly. The use of these sensors increased the weight and complexity of the aircraft, and had limited fidelity in sensing actual weight applied to a landing assembly. 
       BRIEF DESCRIPTION OF THE INVENTION 
       [0003]    According to one aspect of the invention, a method for sensing a force applied to an aircraft includes defining a first velocity vector as a function of a first velocity due to a rotation motion of the aircraft, defining a second velocity vector as a function of a second velocity due to the rotation motion of the aircraft, defining an instant axis of rotation of the aircraft as a function of the first velocity vector and the second velocity vector, determining whether a force has been exerted on a first portion of the aircraft, and outputting an indication that a force has been exerted on the first portion of the aircraft responsive to determining that the force has been exerted on the first portion of the aircraft. 
         [0004]    According to another aspect of the invention, a system for sensing a force applied to an aircraft includes a first sensor, a second sensor, and a processor operative to define a first velocity vector as a function of a first velocity due to a rotation motion of the aircraft, define a second velocity vector as a function of a second velocity due to the rotation motion of the aircraft, define an instant axis of rotation of the aircraft as a function of the first velocity vector and the second velocity vector, determine whether a force has been exerted on a first portion of the aircraft, and output an indication that a force has been exerted on the first portion of the aircraft responsive to determining that the force has been exerted on the first portion of the aircraft. 
         [0005]    These and other advantages and features will become more apparent from the following description taken in conjunction with the drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         [0006]    The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The foregoing and other features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which: 
           [0007]      FIG. 1  illustrates a block diagram of an exemplary embodiment of an aircraft  100 . 
           [0008]      FIG. 2  illustrates an example of the geometric relationship between sensors and a nose landing assembly of  FIG. 1 . 
           [0009]      FIG. 3  illustrates a block diagram of an exemplary embodiment of logic performed by the processor of  FIG. 1 . 
           [0010]      FIG. 4  illustrates an exemplary diagram of a Euler Axis estimation. 
           [0011]      FIG. 5  illustrates an exemplary diagram of a Euler Axis and a landing assembly. 
       
    
    
       [0012]    The detailed description explains embodiments of the invention, together with advantages and features, by way of example with reference to the drawings. 
       DETAILED DESCRIPTION OF THE INVENTION 
       [0013]      FIG. 1  illustrates a block diagram of an exemplary embodiment of an aircraft  100 . The aircraft  100  includes a nose landing assembly  101 , a left landing assembly  103 , and a right landing assembly  105 . The landing assemblies may include, for example, a landing gear assembly that includes an inflatable wheel, or any other device that is operative to contact a landing surface. For example a skid assembly may be used, and portions of the skid assembly may be designated as contact points similar to the gear described above. The aircraft  100  includes a processor  102  that is communicatively connected to flight controls  104  and sensors  106  that may include, for example, a gyro sensor, one or more accelerometers, two or more velocity sensors from, for example, a global positioning system (GPS), or any other inertial sensors. The processor  102  may also be communicatively connected to a memory  110  and a display  108 . 
         [0014]      FIG. 2  illustrates an example of the geometric relationship between a sensor  106 , sensor  107  and the nose landing assembly  101  including an example of coordinate systems that are associated with the sensor  106 , the sensor  107  and the nose landing assembly  101 . 
         [0015]      FIG. 3  illustrates a block diagram of an exemplary embodiment of logic performed by the processor  102  (of  FIG. 1 ). In this regard, the processor  102  receives input data from the sensors (sensors_i; where i=1, 2, 3, . . . )  106 . The input includes acceleration (a i   x , a i   y , and a i   z ) from, for example, an accelerometer, velocity (v i   x , v i   y , v i   z ) from, for example, a GPS or derived from an accelerometer, and a rate of change in orientation (P, Q, R) from, for example, a gyro. In block  302 , the processor  102  performs an initialization routine that receives minimum rotation parameters (α, β, γ)  301  where α is the minimum angular velocity norm threshold value, β is the minimum angular velocity derivative norm threshold value and γ is the minimum acceleration norm threshold value, and determines whether a minimum rotation norm (MRN) condition has been satisfied as follows: 
         [0000]      MRN:={(|{right arrow over (ω)}|&gt;α)&amp;({dot over ({right arrow over (ω)}|&gt;β}  (1)
 
         [0016]    The processor  102  resets the aircraft velocities and accelerations values as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       At 
                        
                       
                         : 
                       
                        
                       
                           
                       
                        
                       t 
                     
                     = 
                     
                       
                         t 
                         1 
                       
                        
                       
                           
                       
                        
                       where 
                        
                       
                           
                       
                        
                       
                         { 
                         
                           MRN 
                            
                           
                               
                           
                            
                           is 
                            
                           
                               
                           
                            
                           true 
                         
                         } 
                       
                     
                   
                   , 
                   
                     then 
                      
                     
                       : 
                     
                      
                     
                         
                     
                      
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   v 
                                   → 
                                 
                                 trans 
                                 i 
                               
                               = 
                               
                                 
                                   
                                     v 
                                     → 
                                   
                                   i 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             &amp; 
                           
                         
                         
                           
                             
                               
                                 
                                   a 
                                   → 
                                 
                                 trans 
                                 i 
                               
                               = 
                               
                                 
                                   
                                     a 
                                     → 
                                   
                                   i 
                                 
                                  
                                 
                                   ( 
                                   
                                     t 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0017]    Thereafter the initialization routine outputs velocities and accelerations due to the rotation motion of the aircraft only ({right arrow over (v)} rot   i  and {right arrow over (v)} rot   i ) where: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       For 
                        
                       
                         : 
                       
                        
                       
                           
                       
                        
                       t 
                     
                     &gt; 
                     
                       
                         t 
                         1 
                       
                        
                       
                           
                       
                        
                       where 
                        
                       
                           
                       
                        
                       
                         { 
                         
                           MRN 
                            
                           
                               
                           
                            
                           is 
                            
                           
                               
                           
                            
                           true 
                         
                         } 
                       
                     
                   
                   , 
                   
                     then 
                      
                     
                       : 
                     
                      
                     
                         
                     
                      
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   v 
                                   → 
                                 
                                 rot 
                                 i 
                               
                               = 
                               
                                 
                                   
                                     v 
                                     → 
                                   
                                   i 
                                 
                                 - 
                                 
                                   
                                     v 
                                     → 
                                   
                                   trans 
                                   i 
                                 
                               
                             
                           
                         
                         
                           
                             &amp; 
                           
                         
                         
                           
                             
                               
                                 
                                   a 
                                   → 
                                 
                                 rot 
                                 i 
                               
                               = 
                               
                                 
                                   
                                     a 
                                     → 
                                   
                                   i 
                                 
                                 - 
                                 
                                   
                                     a 
                                     → 
                                   
                                   trans 
                                   i 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0018]    The initialization routine determines whether the acceleration norm due to the rotation motion of the aircraft exceed the acceleration norm threshold value (γ) to output an enabling signal (Enable) to enable the landing detection process, as follows: 
         [0000]      if {(MRN is true) &amp; ({right arrow over (α)} rot   i |&gt;γ)}, then: Enable=1  (4)
 
         [0019]    In block  304  the processor  102  receives sensor coordinates (P i   sensor )  303 , which includes locations of the sensors, and performs Euler-Axis routine that determines an instant axis of rotation of the aircraft defined as the intersection line of two non-parallel planes as illustrated in  FIG. 4 . Geometrically, the intersection line, axis of rotation, is defined by a unit directional vector {right arrow over (u)} axis  and a specific point defined P axts  on the axis. The parametric equation of the axis of rotation is given by: 
         [0000]        P   axis ( s )= P   axis   +{right arrow over (u)}   axis   ·s   (5)
 
         [0020]    In a three dimensional space, plane A is defined by a point P and a normal vector {right arrow over (n)}. Two planes Δ 1  and Δ 2  are not parallel if their normal vectors {right arrow over (n)} 1  and {right arrow over (n)} 2  are not parallel; this is equivalent to the cross product norm condition (CPN), where CPN=|{right arrow over (n)} 1 ×{right arrow over (n)} 2 |≧μ&gt;&gt;0. To determine the axis of rotation directional unit vector {right arrow over (u)} axis ; the best two non parallel velocity vectors are selected by maximizing CPN, where: 
         [0000]      CPN=max{| {right arrow over (v)}   rot   1   ×{right arrow over (v)}   rot   2   |,{right arrow over (v)}   rot   1   ×{right arrow over (v)}   rot   3   |,|{right arrow over (v)}   rot   2   ×{right arrow over (v)}   rot   3 |}  (6)
 
         [0021]    In vector space, the axis of rotation directional unit vector is given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       u 
                       → 
                     
                     axis 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       v 
                                        
                                       
                                           
                                       
                                     
                                     → 
                                   
                                   rot 
                                   1 
                                 
                                 × 
                                 
                                   
                                     v 
                                     → 
                                   
                                   rot 
                                   2 
                                 
                               
                               
                                  
                                 
                                   
                                     
                                       
                                         v 
                                          
                                         
                                             
                                         
                                       
                                       → 
                                     
                                     rot 
                                     1 
                                   
                                   × 
                                   
                                     
                                       v 
                                       → 
                                     
                                     rot 
                                     2 
                                   
                                 
                                  
                               
                             
                             , 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               CPN 
                             
                             = 
                             
                                
                               
                                 
                                   
                                     
                                       v 
                                        
                                       
                                           
                                       
                                     
                                     → 
                                   
                                   rot 
                                   1 
                                 
                                 × 
                                 
                                   
                                     v 
                                     → 
                                   
                                   rot 
                                   2 
                                 
                               
                                
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       v 
                                        
                                       
                                           
                                       
                                     
                                     → 
                                   
                                   rot 
                                   1 
                                 
                                 × 
                                 
                                   
                                     v 
                                     → 
                                   
                                   rot 
                                   3 
                                 
                               
                               
                                  
                                 
                                   
                                     
                                       
                                         v 
                                          
                                         
                                             
                                         
                                       
                                       → 
                                     
                                     rot 
                                     1 
                                   
                                   × 
                                   
                                     
                                       v 
                                       → 
                                     
                                     rot 
                                     2 
                                   
                                 
                                  
                               
                             
                             , 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               CPN 
                             
                             = 
                             
                                
                               
                                 
                                   
                                     
                                       v 
                                        
                                       
                                           
                                       
                                     
                                     → 
                                   
                                   rot 
                                   1 
                                 
                                 × 
                                 
                                   
                                     v 
                                     → 
                                   
                                   rot 
                                   3 
                                 
                               
                                
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       v 
                                        
                                       
                                           
                                       
                                     
                                     → 
                                   
                                   rot 
                                   2 
                                 
                                 × 
                                 
                                   
                                     v 
                                     → 
                                   
                                   rot 
                                   3 
                                 
                               
                               
                                  
                                 
                                   
                                     
                                       
                                         v 
                                          
                                         
                                             
                                         
                                       
                                       → 
                                     
                                     rot 
                                     2 
                                   
                                   × 
                                   
                                     
                                       v 
                                       → 
                                     
                                     rot 
                                     3 
                                   
                                 
                                  
                               
                             
                             , 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               CPN 
                             
                             = 
                             
                                
                               
                                 
                                   
                                     
                                       v 
                                        
                                       
                                           
                                       
                                     
                                     → 
                                   
                                   rot 
                                   2 
                                 
                                 × 
                                 
                                   
                                     v 
                                     → 
                                   
                                   rot 
                                   3 
                                 
                               
                                
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0022]    To simplify the example, CPN==|{right arrow over (v)} rot   1 ×{right arrow over (v)} rot   2 |, thus selecting sensor_ 1  and sensor_ 2  for the detection process. 
         [0023]    To determine the intersection line, axis of rotation, a specific point is found on the line, that is, to find a point P axis  that lies in both planes Δ 1  and Δ 2 , thereby solving implicit equations of Δ 1  and Δ 2  for P axis : 
         [0000]      Δ 1   :{right arrow over (v)}   rot   1 ·( P   axis   −P   sensor   1 )=0
 
         [0000]      Δ 2   :{right arrow over (v)}   rot   2 ·( P   axis   −P   sensor   2 )=0  (8)
 
         [0024]    Equivalently solving for three coordinates P axis     —     x , P axis     —     y , and P axis     —     z : 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   x 
                                 
                                 1 
                               
                                
                               
                                 P 
                                 
                                   axis 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   x 
                                 
                                 1 
                               
                             
                             + 
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   y 
                                 
                                 1 
                               
                                
                               
                                 P 
                                 
                                   axis 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   y 
                                 
                                 1 
                               
                             
                             + 
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   z 
                                 
                                 1 
                               
                                
                               
                                 P 
                                 
                                   axis 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   z 
                                 
                                 1 
                               
                             
                           
                           = 
                           
                             d 
                             1 
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   x 
                                 
                                 2 
                               
                                
                               
                                 P 
                                 
                                   axis 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   x 
                                 
                                 2 
                               
                             
                             + 
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   y 
                                 
                                 2 
                               
                                
                               
                                 P 
                                 
                                   axis 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   y 
                                 
                                 2 
                               
                             
                             + 
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   z 
                                 
                                 2 
                               
                                
                               
                                 P 
                                 
                                   axis 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   z 
                                 
                                 2 
                               
                             
                           
                           = 
                           
                             d 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0025]    Where d 1  and d 2  are known constants given by: 
         [0000]    
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             d 
                             1 
                           
                           = 
                           
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   x 
                                 
                                 1 
                               
                                
                               
                                 P 
                                 
                                   sensor 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   x 
                                 
                                 1 
                               
                             
                             + 
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   y 
                                 
                                 1 
                               
                                
                               
                                 P 
                                 
                                   sensor 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   y 
                                 
                                 1 
                               
                             
                             + 
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   z 
                                 
                                 1 
                               
                                
                               
                                 P 
                                 
                                   sensor 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   z 
                                 
                                 1 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             d 
                             2 
                           
                           = 
                           
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   x 
                                 
                                 2 
                               
                                
                               
                                 P 
                                 
                                   sensor 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   x 
                                 
                                 2 
                               
                             
                             + 
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   y 
                                 
                                 2 
                               
                                
                               
                                 P 
                                 
                                   sensor 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   y 
                                 
                                 2 
                               
                             
                             + 
                             
                               
                                 v 
                                 
                                   rot 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   z 
                                 
                                 2 
                               
                                
                               
                                 P 
                                 
                                   sensor 
                                    
                                   
                                       
                                   
                                    
                                   _ 
                                    
                                   
                                       
                                   
                                    
                                   z 
                                 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0026]    For a robust solution of Equation 9, a direct linear equation algorithm is used. First a largest absolute coordinate value, noted δ, of {right arrow over (u)} axis  given by equation 7, is selected by: 
         [0000]      δ=max{absolute( u   axis     —     x   ,u   axis     —     y   ,u   axis     —     z )}  (11)
 
         [0027]    Depending of the value of 6 from equation 11, the corresponding coordinate of P axis  is set to zero. Solving for the two other coordinates, the equation 9 gives the general solution for P axis  expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     P 
                     axis 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   0 
                                   , 
                                   
                                     
                                       
                                         d 
                                         2 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           z 
                                         
                                         1 
                                       
                                     
                                     - 
                                     
                                       
                                         d 
                                         1 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           z 
                                         
                                         2 
                                       
                                     
                                   
                                   , 
                                   
                                     
                                       
                                         d 
                                         1 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           y 
                                         
                                         2 
                                       
                                     
                                     - 
                                     
                                       
                                         d 
                                         2 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           y 
                                         
                                         1 
                                       
                                     
                                   
                                 
                                 ) 
                               
                               
                                 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       y 
                                     
                                     1 
                                   
                                   · 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       z 
                                     
                                     2 
                                   
                                 
                                 - 
                                 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       z 
                                     
                                     1 
                                   
                                   · 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       y 
                                     
                                     2 
                                   
                                 
                               
                             
                             ; 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               δ 
                             
                             = 
                             
                               abs 
                                
                               
                                 ( 
                                 
                                   u 
                                   
                                     axis 
                                      
                                     
                                         
                                     
                                      
                                     _ 
                                      
                                     
                                         
                                     
                                      
                                     x 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         d 
                                         2 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           z 
                                         
                                         1 
                                       
                                     
                                     - 
                                     
                                       
                                         d 
                                         1 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           z 
                                         
                                         2 
                                       
                                     
                                   
                                   , 
                                   0 
                                   , 
                                   
                                     
                                       
                                         d 
                                         1 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           x 
                                         
                                         2 
                                       
                                     
                                     - 
                                     
                                       
                                         d 
                                         2 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           x 
                                         
                                         1 
                                       
                                     
                                   
                                 
                                 ) 
                               
                               
                                 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       x 
                                     
                                     1 
                                   
                                   · 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       z 
                                     
                                     2 
                                   
                                 
                                 - 
                                 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       z 
                                     
                                     1 
                                   
                                   · 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       x 
                                     
                                     2 
                                   
                                 
                               
                             
                             ; 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               δ 
                             
                             = 
                             
                               abs 
                                
                               
                                 ( 
                                 
                                   u 
                                   
                                     axis 
                                      
                                     
                                         
                                     
                                      
                                     _ 
                                      
                                     
                                         
                                     
                                      
                                     y 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         d 
                                         2 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           y 
                                         
                                         1 
                                       
                                     
                                     - 
                                     
                                       
                                         d 
                                         2 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           y 
                                         
                                         2 
                                       
                                     
                                   
                                   , 
                                   
                                     
                                       
                                         d 
                                         1 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           x 
                                         
                                         2 
                                       
                                     
                                     - 
                                     
                                       
                                         d 
                                         2 
                                       
                                       · 
                                       
                                         v 
                                         
                                           rot 
                                            
                                           
                                               
                                           
                                            
                                           _ 
                                            
                                           
                                               
                                           
                                            
                                           x 
                                         
                                         1 
                                       
                                     
                                   
                                   , 
                                   0 
                                 
                                 ) 
                               
                               
                                 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       x 
                                     
                                     1 
                                   
                                   · 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       y 
                                     
                                     2 
                                   
                                 
                                 - 
                                 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       y 
                                     
                                     1 
                                   
                                   · 
                                   
                                     v 
                                     
                                       rot 
                                        
                                       
                                           
                                       
                                        
                                       _ 
                                        
                                       
                                           
                                       
                                        
                                       x 
                                     
                                     2 
                                   
                                 
                               
                             
                             ; 
                           
                         
                         
                           
                             
                               if 
                                
                               
                                   
                               
                                
                               δ 
                             
                             = 
                             
                               abs 
                                
                               
                                 ( 
                                 
                                   u 
                                   
                                     axis 
                                      
                                     
                                         
                                     
                                      
                                     _ 
                                      
                                     
                                         
                                     
                                      
                                     z 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0028]    In block  306 , the axis-distances routine receives gear coordinates 305 that include locations of the gears P k   gear    101 ,  103 ,  105  (of  FIG. 1 ), and using equations 13 and 14, computes and outputs λ k   axis-gear  and λ cg  parameters defined as the distances from the estimated instant axis of rotation to the extended landing gears end points and the aircraft center of gravity as illustrated in  FIG. 5 . 
         [0000]      λ axis-gear   k =|( P   gear   k   −P   axis )× {right arrow over (u)}   axis   |; K= 1, 2, 3  (13)
 
         [0000]      λ cg   =|P   axis   ×{right arrow over (u)}   axis |  (14)
 
         [0029]    In block  308 , the detection logic determines if the distance from the axis of rotation to a given gear is the minimum of the axis-distances values and is less than a gear-axis-distance threshold value defined as a gear-cylinder-diameter λ cylinder    307  and the distance from the axis of rotation to center of gravity of the aircraft exceeds the gear-axis-distance threshold value then the detection logic identifies the landing gear as center-of-rotation. The detection logic outputs a weight on wheel (force on wheel) signal  310  indicating contact: 
         [0000]    
       
         
           
             
               
                 
                   WoW 
                   = 
                   
                     K 
                      
                     
                         
                     
                      
                     if 
                      
                     
                         
                     
                      
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   min 
                                   k 
                                 
                                  
                                 
                                   ( 
                                   
                                     λ 
                                     
                                       axis 
                                       - 
                                       gear 
                                     
                                     k 
                                   
                                   ) 
                                 
                               
                               &lt; 
                               
                                 λ 
                                 cylinder 
                               
                             
                           
                         
                         
                           
                             &amp; 
                           
                         
                         
                           
                             
                               
                                 λ 
                                 cg 
                               
                               &gt; 
                               
                                 λ 
                                 cylinder 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0000]    With: WOW=1→left gear; WOW=2→right gear; WOW=3→foward gear. 
         [0030]    The gear WoW signal  310  in  FIG. 3  indicates that a weight on wheel has occurred on the gear. The indication provides information to the aircraft  100  operator and/or automatic control systems of the aircraft  100  that assists in operating the aircraft. Particularly, the weight on wheel signal may indicate that the aircraft has landed or has taken off from a landing area. 
         [0031]    While the invention has been described in detail in connection with only a limited number of embodiments, it should be readily understood that the invention is not limited to such disclosed embodiments. Rather, the invention can be modified to incorporate any number of variations, alterations, substitutions or equivalent arrangements not heretofore described, but which are commensurate with the spirit and scope of the invention. Additionally, while various embodiments of the invention have been described, it is to be understood that aspects of the invention may include only some of the described embodiments. Accordingly, the invention is not to be seen as limited by the foregoing description, but is only limited by the scope of the appended claims.