Abstract:
A trajectory analysis device automatically determines an auxiliary takeoff trajectory including a curvilinear lateral profile, which allows to maximize the takeoff weight of the aircraft. To this end, the device includes an initial data generation device, an auxiliary takeoff trajectory determination device, and a display device. The crew of the aircraft may then review the optimized auxiliary takeoff trajectory.

Description:
TECHNICAL FIELD 
     The present invention relates to a method and a device for determining a takeoff trajectory of an aircraft for maximizing the takeoff weight of the aircraft, in particular of a transport airplane. 
     BACKGROUND 
     It is known that the takeoff of aircrafts should meet safety requirements being defined by the air regulation. In particular, when an engine breakdown occurs upon the takeoff of an aircraft, it is necessary to make sure that flying over obstacles such as mountains, antennas, trees or buildings, being located in the vicinity of the takeoff runway along the trajectory followed by the aircraft, remains possible, and this, with a sufficient safety margin. 
     Such a constraint could require the crew to limit the maximum takeoff weight of the aircraft, so as to allow the latter to generate a climbing slope sufficient for avoiding the obstacles. 
     In order to reduce the extent of such a constraint on the value of the maximum weight, an auxiliary takeoff trajectory (commonly referred to using the English acronym EOSID, for &lt;&lt;Engine Out Standard Instrument Departure&gt;&gt;) enabling a takeoff with a defective engine is determined in addition to a rectilinear standard takeoff trajectory (commonly referred to using the English acronym SID, for &lt;&lt;Standard Instrument Departure&gt;&gt;) being contemplated for a takeoff of the aircraft without any engine breakdown. Such an auxiliary takeoff trajectory diverges, at a divergence point, from the standard takeoff trajectory (being thus defined for an aircraft having all the engines thereof operating normally). Said takeoff (standard and auxiliary) trajectories allow to fly over obstacles located along their respective lateral profiles. The auxiliary takeoff trajectory that enables to by-pass high obstacles thus allows for a higher maximum takeoff weight than the standard takeoff trajectory. 
     Said divergence point is defined so that, if an engine breakdown occurs upstream (or at the level) of such a divergence point, the pilot turns off the aircraft to the auxiliary takeoff trajectory when the aircraft reaches said divergence point. On the other hand, if the engine breakdown occurs when the aircraft has exceeded the divergence point, the pilot continues the takeoff of the aircraft on the standard takeoff trajectory. 
     Furthermore, a decision speed is known, being defined so that, if an engine breakdown occurs while running on the runway for taking off while the aircraft has not reached such a decision speed yet, the remaining runway length is sufficient for allowing the aircraft to slow down and to stop within the boundaries of the runway. On the other hand, when an engine breakdown occurs while the speed of the aircraft is equal to or higher than such a decision speed, the aircraft is no longer able to stop on the remaining runway length and should therefore continue the takeoff. 
     A method for determining an EOSID auxiliary takeoff trajectory is known. Such a method is implemented either directly by airline companies when they have available a department able to perform such a task successfully, or by the aircraft manufacturer. This is a laborious task requiring the interactive use of several specific softwares and could take up to one week of work for a specialized team. Despite the use of softwares, such a usual method thus supposes a significant and expensive human involvement. 
     In addition, such a known method does not take into consideration, for determining the auxiliary takeoff trajectory, a possible engine breakdown occurring at a speed of the aircraft higher than the decision speed. Now, in such a situation, the effective speed of the aircraft on the auxiliary takeoff trajectory from the divergence point is higher than the speed of the aircraft contemplated for an engine breakdown occurring at the decision speed. 
     Since the turn radius is an increasing function of the aircraft speed and a decreasing function of the rolling angle of the aircraft, the follow-up of the piloting instructions for the nominal auxiliary takeoff (that is, established for an engine breakdown occurring at the decision speed), for which turns are taken at constant rolling, for example at 15 degrees, results in more significant turn radii than for a breakdown at the decision speed. Too late an engine breakdown could therefore result in an effective auxiliary takeoff trajectory, the ground track of which substantially differs from that of the nominal auxiliary takeoff trajectory, that could create collision risks with obstacles, more particular in a mountain area. 
     Furthermore, if an auxiliary takeoff trajectory has been found allowing for the takeoff of the aircraft at a high maximum weight, it is not ensured that the aircraft will be able to fly over, with such a high maximum weight, obstacles on the standard takeoff trajectory with all its engines in operation, and all the more with an engine breakdown occurring after the divergence point. 
     The present invention aims at remedying such drawbacks and determining an optimum auxiliary takeoff trajectory regarding the maximum takeoff weight, while meeting the regulation constraints (calculated for breakdown occurring at the decision speed) and ensuring flying over obstacles for an engine breakdown occurring at any subsequent time. 
     SUMMARY OF INVENTION 
     More precisely, the present invention relates to a method for determining at least one auxiliary takeoff trajectory of an aircraft for maximizing the takeoff weight of the aircraft, said auxiliary takeoff trajectory comprising a curvilinear lateral profile and diverging at a divergence point from a standard takeoff trajectory comprising a lateral (generally rectilinear) profile and being defined for an aircraft having all its engines operating normally, said auxiliary takeoff trajectory being defined in turn for an aircraft having at least one engine being defective, said takeoff trajectories allowing to fly over obstacles located along their respective lateral profiles. 
     To this end, according to this invention, said method wherein: 
     a) initial data comprising the lateral profile of the standard takeoff trajectory, data relating to the environment of the takeoff airport, and nominal takeoff conditions are generated; 
     b) based on said initial data, an auxiliary takeoff trajectory is determined, as well as obstacles likely to be flown over for the nominal takeoff conditions; and 
     c) the results of the processings carried out at step b) are presented to an operator, 
     is remarkable in that step b) is carried out completely automatically, and in that at step b), an optimization is carried out so as to obtain an optimum auxiliary takeoff trajectory taking into consideration various takeoff conditions (not being restricted only to the nominal conditions), as well as additional obstacles likely to be flown over for non nominal takeoff conditions. 
     Within the scope of this invention, the nominal takeoff conditions include particular, so-called nominal, weather conditions (wind, temperature) and aerodynamic configuration, representing the preliminarily contemplated situation, and they take into consideration a breakdown occurring at the decision speed. 
     Thus, by this invention, the trajectory (auxiliary takeoff trajectory) is automatically determined for maximizing the takeoff weight of the aircraft, allowing to remedy the problem of a very significant work load resulting from the usual determination of such a trajectory. 
     In addition, according to the invention, said method is optimized so as to obtain an optimum auxiliary takeoff trajectory taking into consideration various takeoff conditions (non being restricted only to the nominal conditions). It also allows to obtain additional obstacles likely to be flown over for non nominal takeoff conditions (weather conditions different from nominal weather conditions, aerodynamic configuration different from the nominal configuration, an engine breakdown occurring at a speed different from the decision speed). 
     In a preferred embodiment, at step b), the following steps are automatically implemented:
         b1) from the lateral profile of the standard takeoff trajectory, an initial maximum weight and initial characteristic speeds are determined allowing to carry out a takeoff on said standard takeoff trajectory;   b2) by a first evaluator (carrying out iterative processing), a maximum takeoff weight and associated characteristic speeds are determined, relating to a given auxiliary trajectory and to nominal conditions, as well as dimensioning obstacles for such nominal conditions, said first evaluator using, to this end, said initial maximum weight and said initial characteristic speeds, as well as an additional set of obstacles and piloting instructions describing an auxiliary takeoff trajectory;   b3) said first evaluator is integrated into a second evaluator (also carrying out iterative processing) allowing to identify the set of dimensioning obstacles for breakdowns occurring between a decision speed and the speed at said divergence point for the auxiliary takeoff trajectory and at the divergence speed for the standard takeoff trajectory; and   b4) an optimization is carried out modifying the auxiliary takeoff trajectory used at step b2), and this, until an optimum auxiliary takeoff trajectory is obtained.       

     Moreover, advantageously, for implementing step b), processing means of the genetic type are used. 
     The method according to this invention thus allows to determine an optimum auxiliary takeoff trajectory regarding the maximum takeoff weight, while meeting the regulation constraints (calculated for breakdown occurring at the decision speed) and ensuring flying over obstacles for an engine breakdown occurring at any subsequent time. 
     Furthermore, advantageously, by said optimum auxiliary takeoff trajectory and said obstacles likely to be flown over, the maximum takeoff weight is calculated, corresponding to a takeoff along said optimum auxiliary takeoff trajectory obtained as set forth herein above. 
     The present invention further relates to a device for determining at least one auxiliary takeoff trajectory of an aircraft for maximizing the takeoff weight of the aircraft. 
     According to the invention, the device is of the type comprising:
         an initial data generation device for generating initial data comprising the lateral profile of the standard takeoff trajectory, data relating to the environment of the takeoff airport, and nominal takeoff conditions;   an auxiliary trajectory determination device for determining, based on said initial data, an auxiliary takeoff trajectory, as well as obstacles likely to be flown over for the nominal takeoff conditions; and   a display device for presenting the results of the processing carried out by the an auxiliary trajectory determination device to an operator,       

     and is remarkable in that the auxiliary trajectory determination device is completely automatic, and in that the auxiliary trajectory determination device comprises elements for carrying out an optimization so as to obtain an auxiliary takeoff trajectory taking into consideration various takeoff conditions, as well as additional obstacles likely to be flown over for non nominal takeoff conditions. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The FIGS. of the appended drawing will better explain how this invention can be implemented. In such FIGS., identical reference numerals relate to similar components. 
         FIG. 1  is a diagram emphasizing different takeoff trajectories likely to be followed by an aircraft. 
         FIG. 2  is a block diagram of a device according to this invention. 
         FIGS. 3 and 4  schematically show different devices and components being part of a device according to this invention. 
     
    
    
     DETAILED DESCRIPTION 
     The trajectory analysis device  1  according to this invention and schematically shown in  FIG. 2  is provided for determining at least one takeoff trajectory of an aircraft, in particular of a transport aircraft AC.  FIG. 1  schematically illustrates the takeoff of an aircraft AC being carried out from a takeoff runway  2 , in the vicinity of which obstacles OB are present, in the present case, a mountain or a high hill. Generally, the takeoff of the aircraft AC is carried out following a standard takeoff trajectory T 1 , the lateral profile TL 1  of which (representing the vertical projection of the trajectory T 1  on the ground comprising a horizontal plane HO) is rectilinear and extends according to the axis  2 A of the runway  2  to be used for the takeoff. Such a standard takeoff trajectory T 1  is commonly referred to using the English acronym SID, for &lt;&lt;Standard Instrument Departure&gt;&gt;. In order to save the aircraft AC from having to fly over obstacles OB, an auxiliary takeoff trajectory T 2  is also determined (commonly referred to using the English acronym EOSID, for &lt;&lt;Engine Out Standard Instrument Departure&gt;&gt;) allowing to meet the regulation constraints in case an engine breakdown occurs upon the takeoff. Such an auxiliary takeoff trajectory T 2  of the EOSID type diverges, at a divergence point PV, from the standard takeoff trajectory T 1  of the SID type (being defined for an aircraft having all its engines operating normally) and comprises an optimized lateral profile TL 2  enabling to by-pass high obstacles. The takeoff (standard and auxiliary) trajectories T 1  and T 2  allow to fly over obstacles located along their respective lateral profiles TL 1  and TL 2 . It is to be noticed that the auxiliary takeoff trajectory T 2  enabling to by-pass high obstacles OB allows for a higher maximum takeoff weight than the standard takeoff trajectory T 1 . 
       FIG. 1  also shows a takeoff trajectory T 3  of the SID type, being defined on the axis  2 A of the runway  2  and being followed by the aircraft AC when a breakdown occurs at a point P 1  where the aircraft AC is running on the runway  2  at a decision speed V 1  as set forth herein below. In such a case, the aircraft AC is not able to fly over the obstacles OB. 
     The divergence point PV is defined so that, if a breakdown of an engine occurs upstream (or at the level) of such a divergence point PV, the pilot turns off the aircraft AC to the auxiliary takeoff trajectory T 2  when the aircraft AC reaches such a divergence point PV. On the other hand, if the engine breakdown occurs when the aircraft AC has exceeded the divergence point PV, the pilot follows the takeoff of the aircraft AC on the standard takeoff trajectory of the SID type. 
     Furthermore, the decision speed V 1  is defined so that, if an engine breakdown occurs upon running on the runway  2  for taking off while the aircraft AC has not reached such a decision speed V 1  yet, that is upstream the point P 1 , the remaining runway length is sufficient for allowing the aircraft AC to slow down and to stop within the boundaries of the runway  2 . On the other hand, when an engine breakdown occurs while the speed of the aircraft AC is equal to or higher than such a decision speed V 1 , the aircraft is no longer able to stop on the remaining runway length and should therefore continue the takeoff. 
     Consequently, three cases (being respectively illustrated by phases PH 1 , PH 2  and PH 3  in  FIG. 1 ) are to be taken into consideration depending on the time when the engine breakdown occurs, that is:
         if the engine breakdown occurs before the aircraft AC reaches the decision speed V 1  (phase PH 1 ), the pilot performs a braking and the aircraft AC stops within the boundaries of the runway  2 ;   if the engine breakdown occurs between the decision speed V 1  and the divergence point PV (phase PH 2 ), or otherwise stated, when the aircraft AC is located between the point P 1  and the divergence point PV, the pilot continues the takeoff and turns off to the auxiliary takeoff trajectory T 2  of the EOSID type, when it reaches the divergence point PV; and   if the engine breakdown occurs after the divergence point PV (phase PH 3 ), the pilot continues his takeoff on the standard takeoff trajectory of the SID type.       

     Naturally, in the absence of an engine breakdown, the pilot carries out a standard takeoff along the standard takeoff trajectory T 1  (of the SID type) that has been defined for a takeoff with no engine breakdown, following a lateral, preferably rectilinear, trajectory TL 1  (but non exclusively). 
     The aim of the trajectory analysis device  1  according to this invention is to determine an optimum auxiliary takeoff trajectory T 2  concerning the maximum takeoff weight, while meeting the regulation constraints (calculated for a breakdown occurring at the decision speed V 1 ) and ensuring flying over the obstacles OB for an engine breakdown occurring at any subsequent time. 
     To this end, the trajectory analysis device  1  comprises, as shown in  FIG. 2 :
         an initial data generation device  3  for generating initial data comprising the lateral profile of the standard takeoff trajectory, data relating to the environment of the takeoff airport, and nominal takeoff conditions. Such initial data generation device  3  are, preferably, interface devices allowing an operator to enter in the trajectory analysis device  1  the above-mentioned information, in particular a computer keyboard and/or a mouse associated with a screen;   an auxiliary trajectory determination device  4  being connected via links  5  and  6  to the initial data generation device  3  and being formed so as to automatically determine by the initial data, an auxiliary takeoff EOSID trajectory, as well as obstacles OB likely to be flown over for nominal takeoff conditions; and   a display device  7  being connected via links  8  and  9  to the auxiliary trajectory determination device  4  and being formed so as to automatically present the results of the processing carried out by the auxiliary trajectory determination device  4  to an operator of the aircraft AC, in particular to the pilot of the aircraft AC.       

     According to the invention, the auxiliary trajectory determination devices  4  are completely automatic and they more specifically comprise a automatic trajectory optimizer device  12  for carrying out an optimization so as to obtain an auxiliary takeoff trajectory T 2  taking into consideration various takeoff conditions, as well as additional obstacles OB likely to be flown over for non nominal takeoff conditions. 
     So, the trajectory analysis device  1  according to this invention automatically determines the trajectory (auxiliary takeoff trajectory T 2 ) for maximizing the takeoff weight of the aircraft AC, allowing the work load of an operator to be reduced when using the trajectory analysis device  1  to simply entering data using the initial data generation device  3 . 
     The initial data generation device  3  allows to enter the following data:
         data relative to ground and the neighborhoods thereof presenting the relief and obstacles OB (level curves, that is, the altitude or the height with respect to the runway  2 );   characteristics of the takeoff runway  2 , such as the length thereof, supplied, for example, by usual maps of the Jeppessen type;   the lateral profile of the SID trajectory, supplied, for example, by usual maps of the Jeppessen type; and   nominal takeoff conditions (weather conditions, aerodynamic configuration of the aircraft AC).       

     The auxiliary trajectory determination device  4  comprises a characteristics calculation device  10  for automatically calculating the characteristics of the takeoff according to the lateral profile of the SID trajectory, supplied by the initial data generation device  3 . The characteristics calculation device  10  allows to determine the highest weight allowing to meet all the regulation constraints of the flight manual upon a takeoff following the SID trajectory. More precisely, the characteristics calculation device  10  determines, usually, by a known software, for the entered data relating to the SID trajectory:
         the maximum takeoff weight; and   characteristic speeds of the takeoff, namely:   the decision speed V 1 ;   a rotation speed VR upon takeoff; and   a speed V 2  representing the speed of the aircraft AC at a height of 35 feet above the ground with one defective engine.       

     Such data calculated by the characteristics calculation device  10  is, respectively, referred to as the initial weight and the initial characteristic speeds. 
     The auxiliary trajectory determination device  4  further comprises an automatic trajectory optimizer device  12  comprising a maximum weight evaluator  13  being shown in  FIG. 3 . Such a maximum weight evaluator  13  is in turn provided with a nominal obstacle evaluator  14  being shown in  FIG. 4 . 
     The nominal obstacle evaluator  14  comprises a nominal lateral profile calculation device  16  receiving:
         via the link  5 , nominal takeoff conditions being entered by the operator;   via a link  17 , an EOSID trajectory to be described herein below (being defined, usually, as a sequence of piloting instructions); and   via a link  19  being connected to the characteristics calculation device  10 , the initial weight and the initial characteristic speeds determined by the characteristics calculation device  10 .       

     Such nominal lateral profile calculation device  16  calculates, from the maximum weight and the speed V 2  of the aircraft AC at the takeoff end, the nominal lateral profile of the EOSID trajectory resulting therefrom, as well as a nominal set of obstacles (that is, a set of obstacles likely to be flown over). Such information is transmitted via a link  20  to the weight/speed calculation device  21 . Furthermore, the nominal set of obstacles is transmitted via a link  8 A to the outlet of the maximum weight evaluator  13 . 
     The weight/speed calculation device  21  calculates, from information received from the nominal lateral profile calculation device  16  and additional obstacles (to be described herein below) received via a link  23 , the maximum weight, as well as the associated characteristic speeds V 1 , VR and V 2  ensuring that regulation constraints are respected. Such information are transmitted via a link  24  to the convergence detection device  25  checking whether there is some convergence regarding the weight and the speeds. Should the response be positive, the convergence detection device  25  transmits the maximum weight and the characteristic speeds received from the weight/speed calculation device  21 , via links  22 A and  22 B. On the other hand, should the response be negative, the convergence detection device  25  retransmits such information via a link  26  to the nominal lateral profile calculation device  16  that reinitiates the above mentioned processing. Such processing is thus carried out in an iterative way until a convergence is achieved about the weight and the characteristic speeds. 
     Within the scope of this invention, it is considered that there is a convergence on a parameter when the value of such a parameter, coming out of a calculation loop, converges to the value previously entered into this loop, that is when the difference between those (entering and outgoing) values is lower than a predetermined threshold. 
     The nominal obstacle evaluator  14  thus provides, from a set of piloting instructions, describing an EOSID trajectory, and an additional set of obstacles being received via the link  23 , the maximum takeoff weight and the associated characteristic speeds V 1 , VR and V 2  for checking the set of regulation constraints (for a breakdown at the decision speed V 1 ), as well as the set of dimensioning obstacles on the nominal trajectory. 
     Such a nominal obstacle evaluator  14  is integrated within a loop for identifying the set of dimensioning obstacles for engine breakdowns occurring after the decision speed V 1 . The thus formed set makes up the evaluator  13  of  FIG. 3 . 
     Such a maximum weight evaluator  13  comprises, in addition to the nominal obstacle evaluator  14 , a set of current calculation devices M 1 , M 2 , . . . , Mn−1, Mn providing at the outlet thereof to additional obstacle set collection device  32 , via respectively links L 1 , L 2 , Ln−1, Ln, an additional set of obstacles defined for non nominal conditions. 
     The devices M 1  to Mn−1 each calculate calculates currently an EOSID trajectory respectively for one of a plurality of breakdown instants, for example for ten breakdown instants, located between points P 1  and PV and provide to the outlets thereof the corresponding obstacles. Such n−1 different breakdown instants (respectively used by devices M 1  to Mn−1) may be:
         predetermined instants; or   randomly selected instants; or   instants corresponding to points being distributed, for example uniformly, between points P 1  and PV.       

     Moreover, the device Mn usually calculates the SID trajectory for an engine breakdown occurring at the divergence point PV, and supply the corresponding obstacles likely to be flown over in such conditions. 
     The additional obstacle set collection device  32  transmits such an additional set of obstacles, via a link  33 , to the conveyance checking device  34  checking the convergence of the set of obstacles. Should the response be positive, such obstacles are transmitted via a link  8 B together to the nominal set of obstacles received from the nominal obstacle evaluator  14  via the link  8 A, the links  8 A and  8 B making up the link  8 . On the other hand, should the response be negative, such an additional set of obstacles is re-injected into the nominal obstacle evaluator  14  via the link  23 . And the above mentioned processing is reinitiated until a convergence is obtained on the set of obstacles. 
     Furthermore, as illustrated in  FIG. 2 , the automatic trajectory optimizer device  12  comprises, in addition to the maximum weight evaluator  13 , current EOSID trajectory population determining device  27  for randomly determining an initial population of EOSID trajectories. 
     The maximum weight evaluator  13  enables to associate with an EOSID candidate a maximum weight corresponding to the nominal takeoff and taking into consideration additional obstacles, should a breakdown occur after the decision speed V 1 . Such a maximum weight evaluator  13  comprises the evaluation function being used in the optimization loop implemented in the automatic trajectory optimizer device  12 , via, more specifically, the trajectory optimization algorithm  28  comprising an overall optimization algorithm and modifying the EOSID population transmitted to the maximum weight evaluator  13  via a link  29 . The maximum weight being determined by the maximum weight evaluator  13  is provided via the link  22 B to the convergence checking device  30  checking the convergence on the weight. Should the response be positive, they transmit the optimum EOSID trajectory, via the link  9 , to the display device  7 . On the other hand, should the response be negative, they inform the trajectory optimization algorithm device  28  via a link  31  so that the latter modify the EOSID population used by the maximum weight evaluator  13 . The latter processing is carried out in an iterative way until a convergence is reached on the weight. 
     The optimization implemented by auxiliary trajectory determination device  4 , preferably, uses a genetic algorithm having the double particularity of supplying an optimum solution being really independent from the initial solution being transmitted to it, and of generating, not a single solution, but a family of different good quality solutions. 
     The trajectory analysis device  1  according to this invention therefore allows to find auxiliary takeoff trajectories of better qualities, both from the stand point of the maximum weight, as from the standpoint of safety, in so far as it allows to contemplate numerous different takeoff conditions, in particular relating to the breakdown instants. 
     It should further be noticed that the present invention:
         introduces within the EOSID optimization loop itself, checking the possibility of flying over obstacles on the EOSID trajectory for an engine breakdown occurring between the decision speed V 1  and the divergence point PV, and on the SID standard takeoff trajectory for a breakdown occurring after the divergence point PV. Thus, not only other cases than breakdowns at the decision speed V 1  and the convergence point PV are taken into consideration for calculating the optimized criterion, but, in addition, the drawbacks that those other cases induce in terms of takeoff weight are minimized; and   implements an overall optimization algorithm allowing:   to lead to a better solution without requiring to foresee, at first sight, the behaviour of the trajectory; and   to supply several alternative solutions, close to the optimum solution from the standpoint of the maximum weight, but not necessarily from the standpoint of the lateral profile thereof.       

     Thus, a robustness analysis could be implemented on the most relevant trajectories, so as to select the one that leads to the largest mean takeoff weight for the set of possible takeoff conditions (weather conditions, aerodynamic configuration). 
     The trajectory analysis device  1  also comprises devices (not shown and being part, for example, of display device  7 ) for calculating the maximum takeoff weight, via the optimum auxiliary takeoff trajectory and obstacles likely to be flown over, determined by the auxiliary trajectory determination device  4 .