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1. 北京航空航天大学 大型飞机高级人才培训班, 北京 100083;
2. 北京航空航天大学 航空科学与工程学院, 北京 100083

Mathematical simulation and assessment of airworthiness compliance of climb gradient during takeoff of civil aircraft
MENG Xiangguang1 , WANG Lixin2 , LIU Hailiang2
1. Large Aircraft Advanced Training Center, Beijing University of Aeronautics and Astronautics, Beijing 100083, China ;
2. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-09-22; Accepted: 2015-10-18; Published online: 2016-01-21 08:44
Foundation item: National High-tech Research and Development Program of China (2014AA110501)
Corresponding author. WANG Lixin, Tel.:010-82338821, E-mail:wlx_c818@163.com
Abstract: The climb gradient along the takeoff path reflects the civil aircraft's ability of flying over the ground obstacles to reach the safe height. According to the requirements of airworthiness regulations for takeoff procedure and climb performance, an airworthiness compliance assessment method of climb gradient with one engine inoperative was proposed based on the pilot-in-loop flight simulation and calculation. A nonlinear aircraft model, a landing gear model and pilot control models were established and assessment criteria were set up. A simulation task of takeoff with one engine inoperative as well as the control procedure of the pilot was designed. The climb gradient of various states was assessed based on the closed-loop digital flight simulation. This method can be applied to the preliminary design phase of civil aircrafts to provide support for the configuration design and the determination of takeoff weight limit, and offer theoretical references for flight tests of climb performance with one engine inoperative.
Key words: climb gradient     airworthiness     one engine inoperative     digital flight simulation     pilot control model

1 适航条款的要求与理解

CCAR-25R4第25.121条(a)～(c)款对民机在单发停车情况下起飞飞行航迹不同阶段的最小爬升梯度做出了规定[6]。单发停车爬升梯度的适航符合性验证需要考虑起落架位置、起飞重量以及结冰条件等因素。其中，起落架的位置应按照CCAR-25R4第25.111条的规定形态进行设置，起飞重量应选为最大起飞重量，在民机的方案设计阶段可主要针对非结冰条件进行适航符合性验证。CCAR-25R4第25.121(a)条规定的验证状态为：飞机在离地速度VLOF时，起落架在放下位置，关键发动机停车且其余发动机处于开始收起落架时的可用功率状态；第25.121(b)条规定的验证状态为：飞机在起飞安全速度V2时，起落架在收起位置，关键发动机停车且其余发动机处于开始收起落架时的可用功率状态；第25.121(c)条规定的验证状态为：飞机在起飞航迹末端的航路形态，关键发动机停车且其余发动机处于可用的最大连续功率状态。

 发动机数 最小爬升梯度/% 离地速度VLOF 起飞安全速度V2 起飞航迹末端 双发 > 0 2.4 1.2 三发 0.3 2.7 1.5 四发 0.5 3.0 1.7

 图 1 起飞参考速度关系 Fig. 1 Relationship of reference speeds during takeoff

2 飞机数学仿真计算模型 2.1 飞机本体动力学模型

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2.2 起落架运动模型

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2.3 发动机模型

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2.4 驾驶员操纵模型

 图 2 起飞任务仿真控制结构框图[14] Fig. 2 Structure block diagram of model for pilot-in-loop takeoff control simulation[14]

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 图 3 驾驶员操纵模型结构图 Fig. 3 Structure chart of pilot control model

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Heq为视觉补偿项，其数学描述为[16-17]

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Km为运动补偿增益，取值范围为1～100。

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3 数学仿真计算与评估方法 3.1 适航符合性评估流程

 图 4 单发停车起飞爬升性能评估流程 Fig. 4 Assessment process of climb performance during takeoff with one engine inoperative
3.2 飞行仿真任务设计

1) 飞机采用起飞构型，起飞前飞机静止停在跑道上，机体纵轴线与跑道中心线对齐。将油门杆推至起飞功率位置，前轮对准跑道中心线。

2) 飞机从起始点加速至VEF，此时关键发动机停车，1 s后飞机加速至V1，并且飞行员意识到关键发动机停车，操纵方向舵平衡偏航力矩并维持飞机起飞姿态继续加速至抬前轮速度VR

3) 速度达到VR后，飞行员拉杆抬前轮，在速度达到离地速度VLOF时飞机离地，开始爬升，并同时开始收起起落架。

4) 飞机离地后继续起飞，直至飞行速度达到V2，起落架完全收上。

5) 飞机以预定的姿态继续爬升，距离地面高度达到120 m之前，襟翼位置不变，速度保持表速不变；高度达到120 m以后，襟翼收上，等表速爬升至高450 m。

3.3 关键速度计算

 速度 数值条件 VEF VEF≥VMCG V1 V1≥1.05VMCG，V1≤VR VR VR≥1.05VMCA

 图 5 VEF限制值的确定流程 Fig. 5 Determination process of maximum value of VEF

VR的取值将影响飞机离地前的地面滑跑距离[19]。较小的VR会导致离地起飞所需的升力不足，飞机继续两轮滑跑加速的过程中会产生更大的阻力，延长了离地的时间，同时增加了滑跑距离。较大的VR则意味飞机抬前轮时间较晚，也会增大滑跑距离。因此，在满足表 2要求的前提下，应综合多次数字飞行仿真计算的结果确定VR的取值以尽量缩短起飞距离。

3.4 爬升梯度计算

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4 算例及结果分析

 图 6 飞行状态参数及舵面偏转时间历程曲线 Fig. 6 Time histories of airframe state parameters and deflections of control surfaces

 图 7 起落架参数时间历程曲线 Fig. 7 Time histories of landing gear state parameters

5 结论

1) 针对适航条款对于民机单发停车起飞爬升梯度的要求和起飞程序的规定，建立了包含飞机本体动力学模型、起落架运动模型和驾驶员操纵模型的人机闭环数学仿真模型；设计了飞行仿真任务和驾驶员操纵程序，并最终建立了基于人机闭环数学仿真计算的单发停车起飞爬升梯度适航符合性评估方法。

2) 基于人机闭环数学仿真的起飞爬升梯度计算方法考虑了关键发动机停车后非对称推力对飞机起飞姿态和航迹的影响，以及飞机离地前起落架对于驾驶员纠偏操纵的影响。该方法可以反映飞行过程中飞机的动态响应特性，能够更精确地对各验证状态下的爬升梯度进行适航符合性评估。

3) 在单发停车起飞的过程中，飞机离地前主要依靠起落架轮胎与地面之间的摩擦力平衡侧力并控制侧向偏离，副翼偏度较小以保持机翼水平。飞机离地后，驾驶员操纵副翼和方向舵使飞机恢复预定爬升姿态。

4) 在民机的方案设计阶段可采用本文方法对其单发失效的起飞爬升性能进行适航符合性评估，为飞机的设计和起飞重量的确定等提供依据，并为其适航符合性试飞验证提供理论参考。

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#### 文章信息

MENG Xiangguang, WANG Lixin, LIU Hailiang

Mathematical simulation and assessment of airworthiness compliance of climb gradient during takeoff of civil aircraft

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(10): 2222-2230
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0617