Numerical value integral improvement algorithm of aircraft take-off running distance
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摘要: 应用数值计算理论对飞机起飞滑跑距离数值积分算法进行了研究, 用插值法对发动机瞬时推力和起飞气动数据的确定方法进行了改进, 用迭代法确定了离地速度, 基于改进算法编制了起飞滑跑距离计算程序。在发动机推力曲线已知时, 对5种飞机的起飞滑跑距离进行计算, 原算法的平均误差为55.6 m, 改进算法的平均误差为23.4 m; 在发动机推力曲线未知时, 用程序计算某型飞机在12种条件下的起飞滑跑距离与实际滑跑距离对比的平均相对误差为2.9%。计算结果表明改进算法计算精度优于原算法。Abstract: The numerical value integral algorithm of aircraft take-off running distance was studied by numerical value calculation theory, and an improvement algorithm was put up.The calculation method of engine instantaneous thrust and take-off aerodynamics data was improved by interpolation method.The liftoff speed was calculated by iteration method.Aircraft take-off running distance calculation was programmed based on the improved algorithm.In order to test the improved algorithm, the take-off running distances of 5 aircrafts were computed when their engine thrust curves were offered.The average error of the former algorithm is 55.6 m, while the one of the improved program is 23.4 m.Furthermore, 12 kinds of take-off running distances of a certain aircraft were computed when its engine thrust curve wasn't offered.The average relative error between computation result and actual running distances is 2.9%.The results indicate that the computation precision of the improved algorithm is higher than the former algorithm.
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Key words:
- airport engineering /
- runway length /
- take-off running distance /
- improvement algorithm
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表 1 滑跑距离检验数据
Table 1. Test data of running distance
机型 起飞质量/kg 程序计算结果/m 人工计算结果/m 飞机说明书所给数据/m 1 8 317 933 1 026 960 2 12 726 1 002 984 1 030 3 24 770 634 647 625 4 27 415 786 736 808 5 72 000 1 701 1 578 1 670 
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表 2 滑跑距离检验数据
Table 2. Test data of running distance
序号 风速/(m·s-1) 气温/℃ 气压/105Pa 跑道平均纵坡/‰ 起飞质量/103kg 程序计算的滑跑距离/m 实际测量的滑跑距离/m 绝对误差/m 相对误差/% 1 -2.7 -5.0 0.699 94 1.4 65 3 082 3 100 18 0.6 2 -4.0 -5.0 0.705 28 1.4 65 3 070 3 000 70 2.3 3 -3.5 -4.2 0.683 94 1.4 61 2 852 2 830 22 0.8 4 -1.9 -5.0 0.690 61 1.4 61 2 671 2 700 29 1.1 5 4.0 0.0 0.687 94 1.4 62 2 606 2 700 94 3.5 6 -1.4 -7.0 0.697 27 1.4 62 2 638 2 700 62 2.3 7 1.0 2.0 0.687 94 1.4 56 2 174 2 100 74 3.5 8 0.1 -3.0 0.695 94 1.4 64 2 885 2 950 65 2.2 9 -2.3 9.0 0.694 61 1.4 62 3 139 3 100 39 1.3 10 -2.3 8.0 0.694 61 1.4 54 2 208 2 400 192 8.0 11 0.0 16.6 0.962 59 1.1 60 1 342 1 390 48 3.5 12 2.0 22.3 0.965 25 -1.1 60 1 324 1 410 86 6.1
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表 3 气动数据插值节点
Table 3. Interpolation nodes of aerodynamics data
迎角/(°) 升力系数 阻力系数 0 0.460 0.054 2 0.620 0.060 4 0.800 0.070 6 0.970 0.084 8 1.166 0.102 10 1.320 0.126 12 1.420 0.156
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表 4 发动机瞬时推力插值节点
Table 4. Interpolation nodes of engine instantaneous thrusts
高度/m 马赫数 推力/N 高度/m 马赫数 推力/N 高度/m 马赫数 推力/N 高度/m 马赫数 推力/N 0 0.0 93 100 2 000 0.0 77 224 4 000 0.0 62 720 6 000 0.0 50 176 0 0.1 88 298 2 000 0.1 72 814 4 000 0.1 59 780 6 000 0.1 47 922 0 0.2 84 868 2 000 0.2 71 050 4 000 0.2 58 016 6 000 0.2 46 648 0 0.3 83 006 2 000 0.3 69 482 4 000 0.3 57 134 6 000 0.3 46 060 0 0.4 82 026 2 000 0.4 69 384 4 000 0.4 57 036 6 000 0.4 46 158
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