CN115062497B - Estimation Method of Aircraft Braking Energy - Google Patents

Estimation Method of Aircraft Braking Energy Download PDF

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CN115062497B
CN115062497B CN202210996410.0A CN202210996410A CN115062497B CN 115062497 B CN115062497 B CN 115062497B CN 202210996410 A CN202210996410 A CN 202210996410A CN 115062497 B CN115062497 B CN 115062497B
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商立英
徐声明
张超
任江涛
张泰安
明亚丽
潘世轩
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AVIC First Aircraft Institute
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Abstract

The invention discloses an aircraft brake energy estimation method, and relates to the technical field of aviation aircraft flight calculation. The method comprises the following steps: obtaining a total kinetic energy model of the airplane from landing to stopping; obtaining an engine slow-vehicle thrust work doing model of the airplane in the process from landing to stopping; obtaining a total energy model which needs to be overcome in the process from landing to stopping of the airplane according to the total kinetic energy model and the engine slow-vehicle thrust work-doing model; acquiring an aerodynamic work model of the airplane in the process from landing to stopping, and then acquiring a contribution rate model of aerodynamic work to total energy; and obtaining a braking energy model according to the total energy model and the contribution rate model. According to the invention, a new evaluation means is provided for the capacity design of the brake system and the capacity design of the pneumatic speed reducer through the brake energy model, so that the more accurate evaluation of the design requirement is realized and the design scheme can be iterated efficiently; and obtaining the brake speed limiting data when the airplane lands according to the data such as the brake energy, the friction coefficient and the like determined by the test flight.

Description

飞机刹车能量估算方法Estimation Method of Aircraft Braking Energy

技术领域technical field

本发明涉及航空飞行器飞行计算技术领域，尤其是涉及一种飞机刹车能量估算方法。The invention relates to the technical field of aviation aircraft flight calculations, in particular to an aircraft braking energy estimation method.

背景技术Background technique

飞机着陆滑跑距离是飞机重要的飞行性能设计指标。着陆滑跑距离越短，飞机对机场适应性越高。因此尽量缩短着陆滑跑距离是飞机着陆性能设计的重要目标。影响飞机着陆滑跑距离的主要因素有：着陆重量、着陆构型的气动特性、着陆滑跑阶段的发动机慢车推力、刹车摩擦力系数以及可用于减速的刹车系统的最大刹车能量值，简称刹车能量。Aircraft landing run distance is an important flight performance design index of aircraft. The shorter the landing roll distance, the higher the adaptability of the aircraft to the airport. Therefore, shortening the landing run distance as much as possible is an important goal in the design of aircraft landing performance. The main factors affecting the landing roll distance of the aircraft are: landing weight, aerodynamic characteristics of the landing configuration, engine idle thrust during the landing roll phase, brake friction coefficient, and the maximum braking energy value of the braking system that can be used for deceleration, referred to as braking energy .

飞机刹车能量设计对于缩短着陆距离具有重要意义。如果最大刹车能量设计值太低，那么在滑跑速度较大的情况下就无法使用刹车，飞机的着陆滑跑距离太长；如果刹车热熔值太大，那么刹车系统的自重太大，飞机的任务性能减弱。The design of aircraft braking energy is of great significance for shortening the landing distance. If the design value of the maximum braking energy is too low, the brakes cannot be used when the taxiing speed is high, and the landing distance of the aircraft is too long; task performance is reduced.

相关技术中，一种是采用粗略估算法，将飞机减速停止的总动能确定为刹车系统最大刹车能量需求值，该方法由于未考虑着陆滑跑过程中发动机慢车做功和气动力减速作用，结果与实际需求差异大，不够精确。另一种是根据动力学和空气动力学的原理，通过数学和图形分析的方法进行计算，但该方法计算过程复杂，难以实现快速的计算分析和设计方案迭代。In related technologies, one is to use a rough estimation method to determine the total kinetic energy of the aircraft to decelerate and stop as the maximum braking energy demand value of the braking system. Since this method does not take into account the slowing work of the engine and the aerodynamic deceleration during the landing roll, the result is not consistent with the actual Requirements vary greatly and are not precise enough. The other is to calculate through mathematical and graphic analysis methods based on the principles of dynamics and aerodynamics, but the calculation process of this method is complicated, and it is difficult to achieve rapid calculation analysis and design iteration.

因此，有必要改善上述相关技术方案中存在的一个或者多个问题。Therefore, it is necessary to improve one or more problems existing in the above related technical solutions.

需要说明的是，在上述背景技术部分公开的信息仅用于加强对本公开的背景的理解，因此可以包括不构成对本领域普通技术人员已知的现有技术的信息。It should be noted that the information disclosed in the above background section is only for enhancing the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to those of ordinary skill in the art.

发明内容Contents of the invention

本发明的目的在于提供一种飞机刹车能量估算方法，进而至少在一定程度上克服由于相关技术的限制和缺陷而导致的一个或者多个问题。The purpose of the present invention is to provide a method for estimating the braking energy of an aircraft, thereby overcoming one or more problems caused by limitations and defects of related technologies at least to a certain extent.

本发明提供一种飞机刹车能量估算方法，包括：The invention provides a method for estimating the braking energy of an aircraft, comprising:

获得飞机从着陆接地到停止过程的总动能模型；Obtain the total kinetic energy model of the aircraft from landing to stop;

获得所述飞机从着陆接地到停止过程的发动机慢车推力做功模型，并将该模型折算为相对重量做功的模型；Obtain the engine idle thrust work model of the aircraft from landing to stop, and convert the model into a model of relative weight work;

根据总动能模型和发动机慢车推力做功模型得到所述飞机从着陆接地到停止过程需要克服的总能量模型；According to the total kinetic energy model and the engine idle thrust work model, obtain the total energy model that the aircraft needs to overcome from the landing process to the stop process;

获得所述飞机从着陆接地到停止过程中气动力做功模型；Obtain the aerodynamic work model of the aircraft from landing to stop;

根据所述气动力做功模型和所述总能量模型获取气动力做功对所述总能量的贡献率模型；Obtaining a contribution rate model of aerodynamic work to the total energy according to the aerodynamic work model and the total energy model;

根据所述总能量模型和所述贡献率模型获得刹车能量模型。A braking energy model is obtained according to the total energy model and the contribution rate model.

优选的，所述总动能模型为

Figure 217648DEST_PATH_IMAGE001
，其中，E 动能为飞机从着陆接地到停止 过程需要克服的总能量，m为所述飞机着陆质量，b表示飞机处于刹车状态，V b 为所述飞机着 陆时的速度。 Preferably, the total kinetic energy model is
Figure 217648DEST_PATH_IMAGE001
, wherein, Ekinetic energy is the total energy that the aircraft needs to overcome from the landing process to the stop process, m is the landing mass of the aircraft, b indicates that the aircraft is in a braking state, and V b is the speed of the aircraft when it lands.

优选的，将慢车推力做功模型折算为相对重量做功得到折算后所述发动机慢车推力做功模型的方法，包括：Preferably, the method of converting the idle thrust work model into the relative weight work model and obtaining the converted engine idle thrust work model includes:

建立第一发动机慢车推力做功模型，

Figure 100002_DEST_PATH_IMAGE002
其中，i 表示飞机的发动机处于慢车工作状态，E i 为发动机慢车推力做功，F i 为飞机慢车推力，a为飞 机加速度，t b 为飞机着陆接地到停止所需时间； Establish the idle thrust work model of the first engine,
Figure 100002_DEST_PATH_IMAGE002
Among them, i represents that the engine of the aircraft is in the idle working state, E i is the work done by the engine idle thrust, F i is the idle thrust of the aircraft, a is the acceleration of the aircraft, and t b is the time required for the aircraft to land and stop;

将所述飞机着陆接地到停止过程的慢车推力取平均值

Figure 72471DEST_PATH_IMAGE003
，加速度a取平均加速度
Figure 100002_DEST_PATH_IMAGE004
，代入所述第一发动机慢车推力做功模型得到第二发动机慢车推力做功模 型
Figure 524312DEST_PATH_IMAGE005
，其中，L为飞机 着陆接地到停止过程的滑跑距离； Taking the average of the idle thrust of the aircraft landing touchdown to stop process
Figure 72471DEST_PATH_IMAGE003
, the acceleration a takes the average acceleration
Figure 100002_DEST_PATH_IMAGE004
, into the first engine idle thrust work model to obtain the second engine idle thrust work model
Figure 524312DEST_PATH_IMAGE005
, where, L is the running distance from the landing to the stop of the aircraft;

令m i 为飞机发动机慢车推力做功的折算重量，从而获得所述飞机从着陆接地到停 止过程的发动机慢车推力做功模型

Figure 100002_DEST_PATH_IMAGE006
。 Let mi be the converted weight of the aircraft engine idle thrust work, so as to obtain the engine idle thrust work model of the aircraft from landing to stop
Figure 100002_DEST_PATH_IMAGE006
.

优选的，根据总动能模型和发动机慢车推力做功模型得到的所述飞机从着陆接地到停止过程需要克服的总能量模型为：Preferably, according to the total kinetic energy model and the engine idle thrust work model, the total energy model that needs to be overcome by the aircraft from landing touchdown to stop process is:

Figure 653942DEST_PATH_IMAGE007
，其中，
Figure 100002_DEST_PATH_IMAGE008
，E 克服为飞机从 着陆接地到停止过程需要克服的总能量。
Figure 653942DEST_PATH_IMAGE007
,in,
Figure 100002_DEST_PATH_IMAGE008
, E overcomes the total energy that needs to be overcome for the aircraft from landing to stop.

优选的，所述气动力做功包括阻力做功和升力做功。Preferably, the aerodynamic work includes resistance work and lift work.

优选的，获得所述飞机从着陆接地到停止过程中气动力做功模型的步骤，包括：Preferably, the step of obtaining the aerodynamic work model of the aircraft from landing to stop includes:

获得所述飞机从着陆接地到停止过程中阻力做功模型；Obtaining the resistance work model of the aircraft from landing touchdown to stopping;

获得所述飞机从着陆接地到停止过程中升力做功模型；Obtain the lift work model of the aircraft from landing to stop;

将所述阻力做功模型和所述升力做功模型相加获得所述气动力做功模型。Adding the resistance work model and the lift work model to obtain the aerodynamic work model.

优选的，获得所述飞机从着陆接地到停止过程中阻力做功模型的步骤，包括：Preferably, the step of obtaining the resistance work model of the aircraft from landing to stop includes:

建立所述飞机从着陆接地到停止过程中第一气动阻力做功模型

Figure 137489DEST_PATH_IMAGE009
，其中，W D 为气动阻 力做功，S为所述飞机机翼面积，ρ为空气密度，F D 为气动阻力，C D 为阻力系数，加速度a取平均 加速度
Figure 100002_DEST_PATH_IMAGE010
； Establish the first aerodynamic drag work model of the aircraft from landing to stop
Figure 137489DEST_PATH_IMAGE009
, where W D is the work done by aerodynamic drag, S is the wing area of the aircraft, ρ is the air density, F D is the aerodynamic drag, CD is the drag coefficient, and the acceleration a is the average acceleration
Figure 100002_DEST_PATH_IMAGE010
;

将

Figure 694372DEST_PATH_IMAGE011
，
Figure 100002_DEST_PATH_IMAGE012
代入所述第一气动阻力做功模型，得 到所述阻力做功模型
Figure 633509DEST_PATH_IMAGE013
。 Will
Figure 694372DEST_PATH_IMAGE011
,
Figure 100002_DEST_PATH_IMAGE012
Substitute into the first aerodynamic resistance work model to obtain the resistance work model
Figure 633509DEST_PATH_IMAGE013
.

优选的，获得所述飞机从着陆接地到停止过程中升力做功模型的步骤，包括：Preferably, the step of obtaining the lift work model during landing and stopping of the aircraft includes:

建立所述飞机从着陆接地到停止过程中第一摩擦力做功模型

Figure 100002_DEST_PATH_IMAGE014
，其中，W F 为摩擦力 做功，F L 为升力阻力，C L 为升力系数，g为重力加速度，
Figure 566830DEST_PATH_IMAGE015
，
Figure DEST_PATH_IMAGE016
为减速过程中的平均摩擦 系数，加速度a取平均加速度
Figure 173392DEST_PATH_IMAGE017
； Establish the first friction work model of the aircraft from landing to stop
Figure 100002_DEST_PATH_IMAGE014
, where, W F is the friction work, F L is the lift resistance, C L is the lift coefficient, g is the gravitational acceleration,
Figure 566830DEST_PATH_IMAGE015
,
Figure DEST_PATH_IMAGE016
is the average friction coefficient during the deceleration process, and the acceleration a takes the average acceleration
Figure 173392DEST_PATH_IMAGE017
;

将

Figure 100002_DEST_PATH_IMAGE018
代入所述第一摩擦力做功模型，得到第二摩擦力做功模型
Figure 838860DEST_PATH_IMAGE019
； Will
Figure 100002_DEST_PATH_IMAGE018
Substituting the first friction work model into the second friction work model
Figure 838860DEST_PATH_IMAGE019
;

根据所述第二摩擦力做功模型

Figure 100002_DEST_PATH_IMAGE020
，得到升力做功模型
Figure 327610DEST_PATH_IMAGE021
，W S 为升力做功。 According to the second friction work model
Figure 100002_DEST_PATH_IMAGE020
, get the lift work model
Figure 327610DEST_PATH_IMAGE021
, W S does work for the lift force.

优选的，所述气动力做功模型为

Figure 100002_DEST_PATH_IMAGE022
，其 中，W A 为气动力做功，所述气动力做功对所述总能量的贡献率模型为： Preferably, the aerodynamic work model is
Figure 100002_DEST_PATH_IMAGE022
, where W A is the aerodynamic work, and the contribution rate model of the aerodynamic work to the total energy is:

Figure 736726DEST_PATH_IMAGE023
，其中，
Figure 100002_DEST_PATH_IMAGE024
为气动力做功对总能量的贡献率。
Figure 736726DEST_PATH_IMAGE023
,in,
Figure 100002_DEST_PATH_IMAGE024
The contribution rate of work done for aerodynamic forces to the total energy.

优选的，所述刹车能量模型为：Preferably, the braking energy model is:

Figure 994532DEST_PATH_IMAGE025
，其中，E b 为刹车能量；将上式进一步简化为：
Figure DEST_PATH_IMAGE026
。
Figure 994532DEST_PATH_IMAGE025
, where E b is the braking energy; the above formula can be further simplified as:
Figure DEST_PATH_IMAGE026
.

本发明提供的技术方案包括以下有益效果：The technical scheme provided by the invention includes the following beneficial effects:

本发明中，上述飞机刹车能量估算方法，一方面主要以着陆速度和着陆滑跑距离为自变量，通过刹车能量模型为刹车系统能力设计、气动减速装置能力设计提供一种新的评估手段，能够实现设计需求的较准确评估，且设计方案可以高效迭代；另一方面可以根据试飞确定的刹车能量、摩擦系数等数据获知飞机着陆时的刹车限制速度数据。In the present invention, the above-mentioned method for estimating the braking energy of the aircraft, on the one hand, mainly takes the landing speed and the landing run distance as independent variables, and provides a new evaluation means for the braking system capability design and the aerodynamic deceleration device capability design through the braking energy model, which can Accurate evaluation of design requirements can be achieved, and the design scheme can be iterated efficiently; on the other hand, the braking limit speed data when the aircraft lands can be obtained according to the braking energy, friction coefficient and other data determined by the flight test.

应当理解的是，以上的一般描述和后文的细节描述仅是示例性和解释性的，并不能限制本公开。It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure.

附图说明Description of drawings

此处的附图被并入说明书中并构成本说明书的一部分，示出了符合本公开的实施例，并与说明书一起用于解释本公开的原理。显而易见地，下面描述中的附图仅仅是本公开的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the disclosure and together with the description serve to explain the principles of the disclosure. Apparently, the drawings in the following description are only some embodiments of the present disclosure, and those skilled in the art can obtain other drawings according to these drawings without creative efforts.

图1示出本公开示例性实施例中飞机刹车能量估算方法流程图。Fig. 1 shows a flowchart of a method for estimating braking energy of an aircraft in an exemplary embodiment of the present disclosure.

具体实施方式detailed description

现在将参考附图更全面地描述示例实施方式。然而，示例实施方式能够以多种形式实施，且不应被理解为限于在此阐述的范例；相反，提供这些实施方式使得本公开将更加全面和完整，并将示例实施方式的构思全面地传达给本领域的技术人员。所描述的特征、结构或特性可以以任何合适的方式结合在一个或更多实施方式中。Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete and will fully convey the concept of example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

本示例实施方式中首先提供了一种飞机刹车能量估算方法，参考图1中所示，该方法可以包括下述步骤：In this exemplary embodiment, a method for estimating the braking energy of an aircraft is firstly provided, as shown in FIG. 1 , the method may include the following steps:

步骤S101：获得飞机从着陆接地到停止过程的总动能模型；Step S101: Obtain the total kinetic energy model of the aircraft from landing to stop;

步骤S102：获得所述飞机从着陆接地到停止过程的发动机慢车推力做功模型，并将该模型折算为相对重量做功的模型；Step S102: Obtain the engine idle thrust work model of the aircraft from landing to stop, and convert the model into a relative weight work model;

步骤S103：根据总动能模型和发动机慢车推力做功模型得到所述飞机从着陆接地到停止过程需要克服的总能量模型；Step S103: According to the total kinetic energy model and the engine idle thrust work model, the total energy model to be overcome by the aircraft from landing to stop is obtained;

步骤S104：获得所述飞机从着陆接地到停止过程中气动力做功模型；Step S104: Obtain the aerodynamic work model of the aircraft from landing to stop;

步骤S105：根据所述气动力做功模型和所述总能量模型获取气动力做功对所述总能量的贡献率模型；Step S105: Obtain a contribution rate model of aerodynamic work to the total energy according to the aerodynamic work model and the total energy model;

步骤S106：根据所述总能量模型和所述贡献率模型获得刹车能量模型。Step S106: Obtain a braking energy model according to the total energy model and the contribution rate model.

具体的，通过将飞机慢车推力做功折算为重量做功，从而得到飞机的发动机慢车推力做功模型。并且通过气动力做功对所述总能量的贡献率模型和总能量模型来构建刹车能量模型，使得构建的刹车能量模型主要以着陆速度或着陆滑跑距离为自变量，从而使得该模型能够较快速的计算，且针对不同的飞机能够快速迭代，使用效率高。Specifically, the engine idle thrust work model of the aircraft is obtained by converting the aircraft idle thrust work into weight work. And the braking energy model is constructed through the contribution rate model and the total energy model of the aerodynamic work to the total energy, so that the braking energy model constructed mainly takes the landing speed or the landing roll distance as independent variables, so that the model can be faster The calculation can be quickly iterated for different aircraft, and the use efficiency is high.

上述飞机刹车能量估算方法，一方面，主要以着陆速度和着陆滑跑距离为自变量，通过刹车能量模型为刹车系统能力设计、气动减速装置能力设计提供一种新的评估手段，能够实现设计需求的较准确评估且设计方案可以高效迭代；另一方面，可以根据试飞确定的刹车能量、摩擦系数等数据获知飞机着陆时的刹车限制速度数据。The above-mentioned aircraft braking energy estimation method, on the one hand, mainly uses the landing speed and landing roll distance as independent variables, and provides a new evaluation method for the design of the braking system capacity and the design of the aerodynamic deceleration device through the braking energy model, which can meet the design requirements The more accurate evaluation and the design scheme can be iterated efficiently; on the other hand, the braking limit speed data when the aircraft lands can be obtained according to the braking energy, friction coefficient and other data determined by the test flight.

下面，将参考图1对本示例实施方式中的上述方法的各个步骤进行更详细的说明。Next, each step of the above-mentioned method in this exemplary embodiment will be described in more detail with reference to FIG. 1 .

在一个实施例中，所述总动能模型为

Figure 96480DEST_PATH_IMAGE001
，其中，E 动能为飞机从着陆接 地到停止过程需要克服的总能量，m为所述飞机着陆质量，b表示飞机处于刹车状态，V b 为所 述飞机着陆时的速度。具体的，飞机的总动能模型为飞机着陆到停止的动能。 In one embodiment, the total kinetic energy model is
Figure 96480DEST_PATH_IMAGE001
, wherein, Ekinetic energy is the total energy that the aircraft needs to overcome from the landing process to the stop process, m is the landing mass of the aircraft, b indicates that the aircraft is in a braking state, and V b is the speed of the aircraft when it lands. Specifically, the total kinetic energy model of the aircraft is the kinetic energy of the aircraft from landing to stopping.

在一个实施例中，将慢车推力做功模型折算为相对重量做功得到折算后所述发动机慢车推力做功模型的方法，包括：In one embodiment, the method of converting the idle thrust work model into the relative weight work model and obtaining the converted engine idle thrust work model includes:

建立第一发动机慢车推力做功模型，

Figure 806947DEST_PATH_IMAGE027
其中，i 表示飞机的发动机处于慢车工作状态，E i 为发动机慢车推力做功，F i 为飞机慢车推力，a为飞 机加速度，t b 为飞机着陆接地到停止所需时间； Establish the idle thrust work model of the first engine,
Figure 806947DEST_PATH_IMAGE027
Among them, i represents that the engine of the aircraft is in the idle working state, E i is the work done by the engine idle thrust, F i is the idle thrust of the aircraft, a is the acceleration of the aircraft, and t b is the time required for the aircraft to land and stop;

将所述飞机着陆接地到停止过程的慢车推力取平均值

Figure 100002_DEST_PATH_IMAGE028
，加速度a取平均加速度
Figure 813561DEST_PATH_IMAGE029
，代入所述第一发动机慢车推力做功模型得到第二发动机慢车推力做功模 型
Figure 100002_DEST_PATH_IMAGE030
，其中，L为飞机 着陆接地到停止过程的滑跑距离； Taking the average of the idle thrust of the aircraft landing touchdown to stop process
Figure 100002_DEST_PATH_IMAGE028
, the acceleration a takes the average acceleration
Figure 813561DEST_PATH_IMAGE029
, into the first engine idle thrust work model to obtain the second engine idle thrust work model
Figure 100002_DEST_PATH_IMAGE030
, where, L is the running distance from the landing to the stop of the aircraft;

令m i 为飞机发动机慢车推力做功的折算重量，从而获得所述飞机从着陆接地到停 止过程的发动机慢车推力做功模型

Figure 129136DEST_PATH_IMAGE031
。 Let mi be the converted weight of the aircraft engine idle thrust work, so as to obtain the engine idle thrust work model of the aircraft from landing to stop
Figure 129136DEST_PATH_IMAGE031
.

具体的，将慢车推力做功折算为重量做功得到所述发动机慢车推力做功模型，可以使最终获得的刹车能量模型主要以着陆速度和着陆滑跑距离为自变量，便于进行计算。Specifically, the engine idle thrust work model is obtained by converting the idle thrust work into the weight work, so that the finally obtained braking energy model mainly takes landing speed and landing roll distance as independent variables, which is convenient for calculation.

在一个实施例中，根据总动能模型和发动机慢车推力做功模型得到的所述飞机从着陆接地到停止过程需要克服的总能量模型为：In one embodiment, the total energy model that the aircraft needs to overcome from landing and grounding to stop process obtained according to the total kinetic energy model and the engine idle thrust work model is:

Figure DEST_PATH_IMAGE032
，其中，
Figure 198723DEST_PATH_IMAGE033
，E 克服为飞机从 着陆接地到停止过程需要克服的总能量。
Figure DEST_PATH_IMAGE032
,in,
Figure 198723DEST_PATH_IMAGE033
, E overcomes the total energy that needs to be overcome for the aircraft from landing to stop.

在一个实施例中，所述气动力做功包括阻力做功和升力做功。In one embodiment, the aerodynamic work includes resistance work and lift work.

在一个实施例中，获得所述飞机从着陆接地到停止过程中气动力做功模型的步骤，包括：In one embodiment, the step of obtaining the aerodynamic work model of the aircraft from landing to stopping includes:

获得所述飞机从着陆接地到停止过程中阻力做功模型；Obtaining the resistance work model of the aircraft from landing touchdown to stopping;

获得所述飞机从着陆接地到停止过程中升力做功模型；Obtain the lift work model of the aircraft from landing to stop;

将所述阻力做功模型和所述升力做功模型相加获得所述气动力做功模型。Adding the resistance work model and the lift work model to obtain the aerodynamic work model.

在一个实施例中，获得所述飞机从着陆接地到停止过程中阻力做功模型的步骤，包括：In one embodiment, the step of obtaining the resistance work model of the aircraft from landing on touchdown to stopping includes:

建立所述飞机从着陆接地到停止过程中第一气动阻力做功模型

Figure DEST_PATH_IMAGE034
，其中，W D 为气动阻 力做功，S为所述飞机机翼面积，ρ为空气密度，F D 为气动阻力，C D 为阻力系数，加速度a取平均 加速度
Figure 599749DEST_PATH_IMAGE035
； Establish the first aerodynamic drag work model of the aircraft from landing to stop
Figure DEST_PATH_IMAGE034
, where W D is the work done by aerodynamic drag, S is the wing area of the aircraft, ρ is the air density, F D is the aerodynamic drag, CD is the drag coefficient, and the acceleration a is the average acceleration
Figure 599749DEST_PATH_IMAGE035
;

将

Figure DEST_PATH_IMAGE036
，
Figure 616246DEST_PATH_IMAGE012
代入所述第一气动阻力做功模型，得 到所述阻力做功模型
Figure 379803DEST_PATH_IMAGE037
。 Will
Figure DEST_PATH_IMAGE036
,
Figure 616246DEST_PATH_IMAGE012
Substitute into the first aerodynamic resistance work model to obtain the resistance work model
Figure 379803DEST_PATH_IMAGE037
.

在一个实施例中，获得所述飞机从着陆接地到停止过程中升力做功模型的步骤，包括：In one embodiment, the step of obtaining the lift work model of the aircraft from landing to stop includes:

建立所述飞机从着陆接地到停止过程中第一摩擦力做功模型

Figure 620292DEST_PATH_IMAGE014
，其中，W F 为摩擦力 做功，F L 为升力阻力，C L 为升力系数，g为重力加速度，
Figure 774192DEST_PATH_IMAGE015
，
Figure 125539DEST_PATH_IMAGE016
为减速过程中的平均摩擦 系数，加速度a取平均加速度
Figure 946865DEST_PATH_IMAGE017
； Establish the first friction work model of the aircraft from landing to stop
Figure 620292DEST_PATH_IMAGE014
, where, W F is the friction work, F L is the lift resistance, C L is the lift coefficient, g is the gravitational acceleration,
Figure 774192DEST_PATH_IMAGE015
,
Figure 125539DEST_PATH_IMAGE016
is the average friction coefficient during the deceleration process, and the acceleration a takes the average acceleration
Figure 946865DEST_PATH_IMAGE017
;

将

Figure DEST_PATH_IMAGE038
代入所述第一摩擦力做功模型，得到第二摩擦力做功模型
Figure 623834DEST_PATH_IMAGE039
； Will
Figure DEST_PATH_IMAGE038
Substituting the first friction work model into the second friction work model
Figure 623834DEST_PATH_IMAGE039
;

根据所述第二摩擦力做功模型

Figure DEST_PATH_IMAGE040
，得到升力做功模型
Figure 733872DEST_PATH_IMAGE041
，W S 为升力做功。 According to the second friction work model
Figure DEST_PATH_IMAGE040
, get the lift work model
Figure 733872DEST_PATH_IMAGE041
, W S does work for the lift force.

在一个实施例中，所述气动力做功模型为

Figure DEST_PATH_IMAGE042
，其中，W A 为气动力做功，所述气动力做功对所 述总能量的贡献率模型为： In one embodiment, the aerodynamic work model is
Figure DEST_PATH_IMAGE042
, where W A is the aerodynamic work, and the contribution rate model of the aerodynamic work to the total energy is:

Figure 888910DEST_PATH_IMAGE043
，其中，
Figure DEST_PATH_IMAGE044
为气动力做功对总能量的贡献率。
Figure 888910DEST_PATH_IMAGE043
,in,
Figure DEST_PATH_IMAGE044
The contribution rate of work done for aerodynamic forces to the total energy.

在一个实施例中，所述刹车能量模型为：In one embodiment, the braking energy model is:

Figure 30654DEST_PATH_IMAGE045
，其中，E b 为刹车能量；将上式进一步简化为：
Figure DEST_PATH_IMAGE046
。
Figure 30654DEST_PATH_IMAGE045
, where E b is the braking energy; the above formula can be further simplified as:
Figure DEST_PATH_IMAGE046
.

具体实施例一：Specific embodiment one:

某双发动机飞机刹车系统设计中，摩擦系数设计值为µ=0.25，最大着陆重量为70t，机翼面积为144m2，滑跑距离指标要求为：海平面标准大气条件下（密度ρ=1.225kg/m3）不超过600m，飞机接地时的接地速度按200km/h，着陆构型滑跑时对应的阻力系数为0.3，升力系数为0.1，计算飞机刹车系统需提供的刹车能量需求。In the design of the braking system of a twin-engine aircraft, the design value of the friction coefficient is µ=0.25, the maximum landing weight is 70t, the wing area is 144m 2 , and the requirements for the sliding distance index are: under standard atmospheric conditions at sea level (density ρ=1.225kg /m 3 ) does not exceed 600m, the ground speed when the aircraft touches down is 200km/h, the corresponding drag coefficient is 0.3, and the lift coefficient is 0.1 when the landing configuration rolls, calculate the braking energy demand to be provided by the aircraft braking system.

计算过程如下：The calculation process is as follows:

（1）根据该型飞机的发动机在海平面标准大气条件下，慢车状态单台发动机推力 平均值

Figure 81787DEST_PATH_IMAGE047
=500kgf，则两台发动机的慢车推力做功折算重量为： (1) According to the engine of this type of aircraft under sea level standard atmospheric conditions, the average thrust of a single engine in the idle state
Figure 81787DEST_PATH_IMAGE047
=500kgf, then the converted weight of the idle thrust of the two engines is:

Figure DEST_PATH_IMAGE048
=2×500×2×9.8×600/（200/3.6）2=3810kg
Figure DEST_PATH_IMAGE048
=2×500×2×9.8×600/(200/3.6) 2 =3810kg

（2）该飞机从着陆接地到停止过程的总动能为：(2) The total kinetic energy of the aircraft from touchdown to stop is:

Figure 475859DEST_PATH_IMAGE049
=1/2×（70000+3810）×（200/3.6）2=113.9MJ
Figure 475859DEST_PATH_IMAGE049
=1/2×(70000+3810)×(200/3.6) 2 =113.9MJ

（3）气动阻力做功对所述总能量的贡献率为：(3) The contribution rate of aerodynamic drag work to the total energy is:

Figure DEST_PATH_IMAGE050
=1.225×144×（0.3-0.25×0.1）×600/ [2×（70000+3810）]=19.7%
Figure DEST_PATH_IMAGE050
=1.225×144×(0.3-0.25×0.1)×600/ [2×(70000+3810)]=19.7%

（4）对该飞机刹车系统的刹车能量的设计需求量为：(4) The design demand for braking energy of the aircraft braking system is:

Figure 637850DEST_PATH_IMAGE051
=113.9-113.9×19.7%=91.46MJ
Figure 637850DEST_PATH_IMAGE051
=113.9-113.9×19.7%=91.46MJ

具体实施例二：Specific embodiment two:

根据某双发动机飞机方案刹车系统的设计能力，摩擦系数预计为µ=0.25，刹车系统提供的最大刹车能量设计能力预计为75MJ，最大着陆重量为70t，机翼面积为144m2，海平面标准大气（密度ρ=1.225kg/m3）条件下的着陆滑跑距离指标要求为600m，飞机接地时的接地速度为200km/h，着陆构型滑跑迎角对应的升力系数为0.1，欲为该飞机设计减速装置以满足滑跑距离指标要求，则减速装置总的阻力系数设计值需不低于多少。According to the design capability of the braking system of a dual-engine aircraft scheme, the friction coefficient is estimated to be µ=0.25, the maximum braking energy design capability provided by the braking system is estimated to be 75MJ, the maximum landing weight is 70t, the wing area is 144m 2 , and the sea level standard atmosphere (density ρ=1.225kg/m 3 ), the landing run distance index requirement is 600m, the touchdown speed of the aircraft is 200km/h, and the lift coefficient corresponding to the roll angle of attack of the landing configuration is 0.1. If the reduction device is designed to meet the requirements of the roll distance index, the design value of the total drag coefficient of the reduction device must not be lower than this value.

计算过程如下：The calculation process is as follows:

（1）根据该型飞机的发动机在海平面标准大气条件下，慢车状态单台发动机推力 平均值

Figure DEST_PATH_IMAGE052
=500kgf，则两台发动机的慢车推力做功折算重量为： (1) According to the engine of this type of aircraft under sea level standard atmospheric conditions, the average thrust of a single engine in the idle state
Figure DEST_PATH_IMAGE052
=500kgf, then the converted weight of the idle thrust of the two engines is:

Figure DEST_PATH_IMAGE053
=2×600×2×9.8×500/（200/3.6）2=3810kg
Figure DEST_PATH_IMAGE053
=2×600×2×9.8×500/(200/3.6) 2 =3810kg

（2）该飞机从着陆接地到停止过程的总能量为：(2) The total energy of the aircraft from landing to stop is:

Figure 637030DEST_PATH_IMAGE049
=1/2×（70000+3810）×（200/3.6）2=113.9MJ
Figure 637030DEST_PATH_IMAGE049
=1/2×(70000+3810)×(200/3.6) 2 =113.9MJ

（3）根据已知条件中刹车系统的刹车能量为75MJ，则该刹车能量占总能量比值为75/113.9=65.8%，由此可知气动力做功对总能量的贡献率需要达到：1-65.8%=34.2%；(3) According to the known conditions, the braking energy of the braking system is 75MJ, and the ratio of the braking energy to the total energy is 75/113.9=65.8%. It can be seen that the contribution rate of the aerodynamic work to the total energy needs to reach: 1-65.8 %=34.2%;

（4）通过气动力做功对所述总能量的贡献率模型

Figure 390222DEST_PATH_IMAGE050
，可以得到：(4) Contribution rate model of aerodynamic work to the total energy
Figure 390222DEST_PATH_IMAGE050
, you can get:

34.2%=1.225×144×（C D -0.25×0.1）×600/[2×（70000+3810）]34.2%=1.225×144×( C D -0.25×0.1)×600/[2×(70000+3810)]

得到飞机减速装置的阻力系数设计值需达到C D ≥0.502。To obtain the design value of the drag coefficient of the aircraft deceleration device, C D ≥ 0.502 must be achieved.

具体实施例三：Specific embodiment three:

某双发动机飞机根据试飞结果刹车摩擦系数为µ=0.25，最大着陆重量为70t，机翼面积为144m2，刹车系统提供的最大刹车能量为80MJ，海平面标准的大气条件下最大着陆重量的着陆滑跑距离为700m，着陆构型滑跑迎角应对的阻力系数为0.3，升力系数为0.1，着陆滑跑中的慢车推力近似为0，需根据最大刹车能量确定该飞机着陆重量50t～70t的刹车限制速度。According to the flight test results of a twin-engine aircraft, the braking friction coefficient is µ=0.25, the maximum landing weight is 70t, the wing area is 144m 2 , the maximum braking energy provided by the braking system is 80MJ, and the landing weight of the maximum landing weight is The rolling distance is 700m, the landing configuration rolling angle of attack should have a drag coefficient of 0.3, a lift coefficient of 0.1, and the idle thrust during the landing roll is approximately 0. The maximum braking energy of the aircraft should be determined according to the maximum braking energy. Brakes limit speed.

计算过程如下：The calculation process is as follows:

（1）慢车推力近似为0，则慢车推力折算重量为0；(1) The idle thrust is approximately 0, so the converted weight of the idle thrust is 0;

（2）根据已知条件通过计算可以得到气动阻力做功对所述总能量的贡献率为：(2) According to known conditions, the contribution rate of aerodynamic drag work to the total energy can be obtained by calculation:

Figure 68328DEST_PATH_IMAGE050
=1.225×144×（0.3-0.25×0.1）×700/ （2×70000）=24.26%
Figure 68328DEST_PATH_IMAGE050
=1.225×144×(0.3-0.25×0.1)×700/ (2×70000)=24.26%

（3）由上述可知刹车系统提供的刹车能量对所述总能量的贡献率为：1-24.26%=75.74%(3) The contribution rate of the braking energy provided by the braking system to the total energy is: 1-24.26%=75.74%

（4）由上述可知，刹车过程中克服的总能量为80/75.74%=106MJ(4) From the above, it can be seen that the total energy overcome during the braking process is 80/75.74%=106MJ

（5）根据刹车过程中克服的总能量得到飞机着陆重量和飞机着陆时刹车限制速度的关系，请见表1：(5) According to the total energy overcome in the braking process, the relationship between the landing weight of the aircraft and the braking speed limit when the aircraft lands is obtained, see Table 1:

表1 飞机着陆重量和飞机着陆时刹车限制速度的关系Table 1 The relationship between the landing weight of the aircraft and the braking limit speed of the aircraft when landing

Figure DEST_PATH_IMAGE054
Figure DEST_PATH_IMAGE054

需要说明的是，尽管在附图中以特定顺序描述了本公开中方法的各个步骤，但是，这并非要求或者暗示必须按照该特定顺序来执行这些步骤，或是必须执行全部所示的步骤才能实现期望的结果。附加的或备选的，可以省略某些步骤，将多个步骤合并为一个步骤执行，以及/或者将一个步骤分解为多个步骤执行等。另外，也易于理解的是，这些步骤可以是例如在多个模块/进程/线程中同步或异步执行。It should be noted that although the steps of the method in the present disclosure are described in a specific order in the drawings, this does not require or imply that these steps must be performed in this specific order, or that all shown steps must be performed to achieve achieve the desired result. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step for execution, and/or one step may be decomposed into multiple steps for execution, etc. In addition, it is easy to understand that these steps may be executed synchronously or asynchronously in multiple modules/processes/threads, for example.

通过以上的实施方式的描述，本领域的技术人员易于理解，这里描述的示例实施方式可以通过软件实现，也可以通过软件结合必要的硬件的方式来实现。因此，根据本公开实施方式的技术方案可以以软件产品的形式体现出来，该软件产品可以存储在一个非易失性存储介质（可以是CD-ROM，U盘，移动硬盘等）中或网络上，包括若干指令以使得一台计算设备（可以是个人计算机、服务器、或者网络设备等）执行根据本公开实施方式的上述云手机应用管理方法。Through the description of the above implementations, those skilled in the art can easily understand that the example implementations described here can be implemented by software, or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of software products, and the software products can be stored in a non-volatile storage medium (which can be CD-ROM, U disk, mobile hard disk, etc.) or on the network , including several instructions to enable a computing device (which may be a personal computer, a server, or a network device, etc.) to execute the above cloud mobile phone application management method according to an embodiment of the present disclosure.

本领域技术人员在考虑说明书及实践这里公开的发明后，将容易想到本公开的其它实施方案。本申请旨在涵盖本公开的任何变型、用途或者适应性变化，这些变型、用途或者适应性变化遵循本公开的一般性原理并包括本公开未公开的本技术领域中的公知常识或惯用技术手段。说明书和实施例仅被视为示例性的，本公开的真正范围和精神由所附的权利要求指出。Other embodiments of the present disclosure will be readily apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, and these modifications, uses or adaptations follow the general principles of the present disclosure and include common knowledge or conventional technical means in the technical field not disclosed in the present disclosure . The specification and examples are to be considered exemplary only, with the true scope and spirit of the disclosure indicated by the appended claims.

Claims (8)

1.一种飞机刹车能量估算方法，其特征在于，包括：1. A method for estimating braking energy of an aircraft is characterized in that, comprising: 获得飞机从着陆接地到停止过程的总动能模型；Obtain the total kinetic energy model of the aircraft from landing to stop; 获得所述飞机从着陆接地到停止过程的发动机慢车推力做功模型，并将该模型折算为相对重量做功的模型；Obtain the engine idle thrust work model of the aircraft from landing to stop, and convert the model into a model of relative weight work; 根据总动能模型和发动机慢车推力做功模型得到所述飞机从着陆接地到停止过程需要克服的总能量模型；According to the total kinetic energy model and the engine idle thrust work model, obtain the total energy model that the aircraft needs to overcome from the landing process to the stop process; 获得所述飞机从着陆接地到停止过程中气动力做功模型；Obtain the aerodynamic work model of the aircraft from landing to stop; 根据所述气动力做功模型和所述需要克服的总能量模型获取气动力做功对需要克服的总能量的贡献率模型；Acquiring a contribution rate model of aerodynamic work to the total energy to be overcome according to the aerodynamic work model and the total energy to be overcome model; 根据所述需要克服的总能量模型和所述贡献率模型获得刹车能量模型；obtaining a braking energy model according to the total energy model to be overcome and the contribution rate model; 其中，所述气动力做功模型为
Figure DEST_PATH_IMAGE001
，其中，W A 为气动力做功，W D 为气动阻力做功，W S 为升力做功，
Figure DEST_PATH_IMAGE002
，ρ为空气密度，S为所述飞机机翼面积，C D 为阻力系数，
Figure DEST_PATH_IMAGE003
为减速过程中的平均摩擦系数，
Figure DEST_PATH_IMAGE004
，C L 为升力系数，所述气动力做功对所述总能量的贡献率模型为：Wherein, the aerodynamic work model is
Figure DEST_PATH_IMAGE001
, where W A is the work done by aerodynamic force, W D is the work done by aerodynamic drag, WS is the work done by lift force,
Figure DEST_PATH_IMAGE002
, ρ is the air density, S is the wing area of the aircraft, C D is the drag coefficient,
Figure DEST_PATH_IMAGE003
is the average friction coefficient during deceleration,
Figure DEST_PATH_IMAGE004
, C L is the lift coefficient, and the contribution rate model of the aerodynamic work to the total energy is:
Figure DEST_PATH_IMAGE006
，其中，
Figure DEST_PATH_IMAGE007
为气动力做功对总能量的贡献率，E 克服为飞机从着陆接地到停止过程需要克服的总能量，m为所述飞机着陆质量，m i 为飞机发动机慢车推力做功的折算重量，b表示飞机处于刹车状态，V b 为所述飞机着陆时的速度，
Figure DEST_PATH_IMAGE008
，t b 为飞机着陆接地到停止所需时间，L为飞机着陆接地到停止过程的滑跑距离；
Figure DEST_PATH_IMAGE006
,in,
Figure DEST_PATH_IMAGE007
is the contribution rate of aerodynamic work to the total energy, E is the total energy that needs to be overcome by the aircraft from landing to stop, m is the landing mass of the aircraft, m i is the converted weight of the idle thrust of the aircraft engine, and b is the aircraft is in the braking state, V b is the speed of the aircraft when it lands,
Figure DEST_PATH_IMAGE008
, t b is the time required for the aircraft to touch down from landing to stop, and L is the running distance from landing to stop of the aircraft; 所述刹车能量模型为：The braking energy model is:
Figure DEST_PATH_IMAGE010
，其中，E b 为刹车能量；将上式进一步简化为：
Figure DEST_PATH_IMAGE011
。
Figure DEST_PATH_IMAGE010
, where E b is the braking energy; the above formula can be further simplified as:
Figure DEST_PATH_IMAGE011
. 2.根据权利要求1所述飞机刹车能量估算方法，其特征在于，所述总动能模型为
Figure DEST_PATH_IMAGE012
，其中，E 动能为飞机从着陆接地到停止过程的总能量，m为所述飞机着陆质量，b表示飞机处于刹车状态，V b 为所述飞机着陆时的速度。2. according to the described aircraft braking energy estimation method of claim 1, it is characterized in that, described total kinetic energy model is
Figure DEST_PATH_IMAGE012
, wherein, Ekinetic energy is the total energy of the aircraft from landing to stop, m is the landing mass of the aircraft, b indicates that the aircraft is in a braking state, and V b is the speed of the aircraft when it lands. 3.根据权利要求2所述飞机刹车能量估算方法，其特征在于，将慢车推力做功模型折算为相对重量做功得到折算后所述发动机慢车推力做功模型的方法，包括：3. according to the described aircraft braking energy estimation method of claim 2, it is characterized in that, the method of said engine idle thrust work model after converting the idle thrust work model into relative weight work obtained after converting, comprises: 建立第一发动机慢车推力做功模型，
Figure DEST_PATH_IMAGE013
其中，i表示飞机的发动机处于慢车工作状态，E i 为发动机慢车推力做功，F i 为飞机慢车推力，a为飞机加速度，t b 为飞机着陆接地到停止所需时间；Establish the idle thrust work model of the first engine,
Figure DEST_PATH_IMAGE013
Among them, i represents that the engine of the aircraft is in the idle working state, E i is the work done by the engine idle thrust, F i is the idle thrust of the aircraft, a is the acceleration of the aircraft, and t b is the time required for the aircraft to land and stop; 将所述飞机着陆接地到停止过程的慢车推力取平均值
Figure DEST_PATH_IMAGE014
，加速度a取平均加速度
Figure DEST_PATH_IMAGE015
，代入所述第一发动机慢车推力做功模型得到第二发动机慢车推力做功模型
Figure DEST_PATH_IMAGE017
，其中，L为飞机着陆接地到停止过程的滑跑距离；Taking the average of the idle thrust of the aircraft landing touchdown to stop process
Figure DEST_PATH_IMAGE014
, the acceleration a takes the average acceleration
Figure DEST_PATH_IMAGE015
, into the first engine idle thrust work model to obtain the second engine idle thrust work model
Figure DEST_PATH_IMAGE017
, where, L is the running distance from the landing to the stop of the aircraft; 令m i 为飞机发动机慢车推力做功的折算重量，从而获得所述飞机从着陆接地到停止过程的发动机慢车推力做功模型
Figure DEST_PATH_IMAGE018
。Let mi be the converted weight of the aircraft engine idle thrust work, so as to obtain the engine idle thrust work model of the aircraft from landing touchdown to stop process
Figure DEST_PATH_IMAGE018
. 4.根据权利要求3所述飞机刹车能量估算方法，其特征在于，根据总动能模型和发动机慢车推力做功模型得到的所述飞机从着陆接地到停止过程需要克服的总能量模型为：4. according to the described aircraft braking energy estimation method of claim 3, it is characterized in that, the total energy model that the described aircraft that obtains according to total kinetic energy model and engine idle thrust work model is from landing grounding to stop process needs to overcome is:
Figure DEST_PATH_IMAGE019
，其中，
Figure DEST_PATH_IMAGE020
，E 克服为飞机从着陆接地到停止过程需要克服的总能量。
Figure DEST_PATH_IMAGE019
,in,
Figure DEST_PATH_IMAGE020
, E overcomes the total energy that needs to be overcome for the aircraft from landing to stop. 5.根据权利要求4所述飞机刹车能量估算方法，其特征在于，气动力做功包括阻力做功和升力做功。5. The aircraft braking energy estimation method according to claim 4, wherein the aerodynamic work includes resistance work and lift work. 6.根据权利要求5所述飞机刹车能量估算方法，其特征在于，获得所述飞机从着陆接地到停止过程中气动力做功模型的步骤，包括：6. The method for estimating the braking energy of an aircraft according to claim 5, wherein the step of obtaining the aerodynamic work model of the aircraft from landing on touchdown to stopping includes: 获得所述飞机从着陆接地到停止过程中阻力做功模型；Obtaining the resistance work model of the aircraft from landing touchdown to stopping; 获得所述飞机从着陆接地到停止过程中升力做功模型；Obtain the lift work model of the aircraft from landing to stop; 将所述阻力做功模型和所述升力做功模型相加获得所述气动力做功模型。Adding the resistance work model and the lift work model to obtain the aerodynamic work model. 7.根据权利要求6所述飞机刹车能量估算方法，其特征在于，获得所述飞机从着陆接地到停止过程中阻力做功模型的步骤，包括：7. The method for estimating the braking energy of an aircraft according to claim 6, wherein the step of obtaining the resistance work model of the aircraft from landing on touchdown to stopping includes: 建立所述飞机从着陆接地到停止过程中第一气动阻力做功模型
Figure DEST_PATH_IMAGE022
，其中，W D 为气动阻力做功，S为所述飞机机翼面积，ρ为空气密度，F D 为气动阻力，C D 为阻力系数，加速度a取平均加速度
Figure DEST_PATH_IMAGE023
；Establish the first aerodynamic drag work model of the aircraft from landing to stop
Figure DEST_PATH_IMAGE022
, where W D is the work done by aerodynamic drag, S is the wing area of the aircraft, ρ is the air density, F D is the aerodynamic drag, CD is the drag coefficient, and the acceleration a is the average acceleration
Figure DEST_PATH_IMAGE023
; 将
Figure 722378DEST_PATH_IMAGE002
，
Figure DEST_PATH_IMAGE024
代入所述第一气动阻力做功模型，得到所述阻力做功模型
Figure DEST_PATH_IMAGE025
。Will
Figure 722378DEST_PATH_IMAGE002
,
Figure DEST_PATH_IMAGE024
Substitute into the first aerodynamic resistance work model to obtain the resistance work model
Figure DEST_PATH_IMAGE025
. 8.根据权利要求6所述飞机刹车能量估算方法，其特征在于，获得所述飞机从着陆接地到停止过程中升力做功模型的步骤，包括：8. The method for estimating the braking energy of an aircraft according to claim 6, wherein the step of obtaining the lift work model of the aircraft from landing on touchdown to stopping includes: 建立所述飞机从着陆接地到停止过程中第一摩擦力做功模型
Figure DEST_PATH_IMAGE027
，其中，W F 为摩擦力做功，F L 为升力阻力，C L 为升力系数，g为重力加速度，
Figure DEST_PATH_IMAGE028
，
Figure 514885DEST_PATH_IMAGE003
为减速过程中的平均摩擦系数，加速度a取平均加速度
Figure 763463DEST_PATH_IMAGE008
；Establish the first friction work model of the aircraft from landing to stop
Figure DEST_PATH_IMAGE027
, where, W F is the friction work, F L is the lift resistance, C L is the lift coefficient, g is the gravitational acceleration,
Figure DEST_PATH_IMAGE028
,
Figure 514885DEST_PATH_IMAGE003
is the average friction coefficient during the deceleration process, and the acceleration a takes the average acceleration
Figure 763463DEST_PATH_IMAGE008
; 将
Figure 893093DEST_PATH_IMAGE004
代入所述第一摩擦力做功模型，得到第二摩擦力做功模型
Figure DEST_PATH_IMAGE029
；Will
Figure 893093DEST_PATH_IMAGE004
Substituting the first friction work model into the second friction work model
Figure DEST_PATH_IMAGE029
; 根据所述第二摩擦力做功模型
Figure DEST_PATH_IMAGE030
，得到升力做功模型
Figure DEST_PATH_IMAGE031
，W S 为升力做功。According to the second friction work model
Figure DEST_PATH_IMAGE030
, get the lift work model
Figure DEST_PATH_IMAGE031
, W S does work for the lift force.
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