飞机气动估算及飞行性能计算-课程设计

1、 本科课程设计报告题 目 飞机气动估算及飞行性能计算学生姓名 班 级 日 期 目录气动特性估算11.1升力特性估算11.1.1外露翼升力估算11.1.2 机身升力的估算31.1.3 尾翼的升力估算51.1.4合升力线斜率的计算81.1.5临界马赫数的计算91.2 阻力特性的估算111.2.1全机摩擦阻力的估算111.2.2亚音速压差阻力的估算171.2.3亚声速升致阻力特性估算191.2.4超音速零升波阻估算201.2.5超声速升致阻力25飞机基本飞行性能计算372.1 平飞需用推力的计算372.1.1不同高度下的推力曲线图(15)402.1.2不同高度的马赫数分布432.1.3飞行包线图(1

2、6)442.2 定常上升性能442.2.1不同高度下的Vy-Ma（最大上升率）图（17）472.2.2绘制图求解不同飞行高度下的最大爬升角472.2.3升限的确定（读上图可得）482.3爬升时间计算492.3.1 亚音速等表速爬升492.3.2超音速等马赫数爬升502.3.3平飞加速段的求解方法50气动特性估算1.1升力特性估算飞机上的升力可表示为：其中： 升力系数 有： S 机翼参考面积 q 动压 1.1.1外露翼升力估算 （1）其中机翼的展弦比 =2.79m 翼展 l=11.7m 机翼的根梢比 =5.48，即 机翼面积 S=49.24机翼的表面为一梯形，由梯形面积计算公式有：S=可求得：

3、机身最大当量直径d=2.13m,外露机翼面积 =35.21,由几何关系有： 解之得=6.05所以，外露翼参数为：=4.65展弦比 公式 的函数关系可由下面图1确定： 图1:机翼升力线斜率计算图其中：外露翼根梢比 =4.65机翼相对厚度 c=5.1%尖梢比 =0.214由机翼的几何参数可知其前缘后掠角，弦线的后掠角可由下式得出：则 由 读第三幅图。查表时，近似取为1，在影响不大的区域，取线；在影响不大的区域，取与线性插值的结果；在两者交加区域取读取值的平均值。外露翼升力系数在考虑机身的影响后，可以写为：其中 修正系数 f=1.07 机身直径 d=2.13m 翼展l=11.7m 计算图表Ma或0.

4、42.3829390.01900.07410.62.080.01950.076050.81.560.0210.0819100.02420.094381.21.7246450.02210.086191.42.5474690.021080.0822121.63.2473990.0180.07021.83.8913240.01630.0635724.5033320.01510.058892.25.0949390.01360.053041.1.2 机身升力的估算机身升力主要由头部和尾部两部分组成，对于圆柱形状的机身，有： （*）其中 机身的升力线斜率 头部产生的升力线斜率 尾部收缩比 = 底部面积，尾

5、部形状为锥形，则底部面积为零，从而=0 机身面积，即尾部的最大面积 修正系数，取决于雷诺数、马赫数、尾部形状、尾翼布局等参数，其值可取0.150.20。此处，我们取=0.17 可按照下式查图2曲线得出： 图2： 具有锥形头部旋成体的头部升力计算曲线其中 为头部长细比，值为2.93 为机身圆柱部分长细比，值为3.94从而计算可得 =1.3447 进一步可得，再将其带入（*）式即可得机身的升力线斜率 另外，如果机身截面形状为椭圆形，则其升力线斜率按照圆柱形进行修正:其中 B： 机身最大截面的宽度 计算图表Ma或查表查表0.40.3128038020.03550.03550.03550.029550

6、.60.2730375430.03600.03600.03600.030050.80.2047781570.03700.03700.03700.03105100.04050.04050.04050.034551.20.2263907710.04600.04600.04600.040051.40.334401330.04800.04800.04800.042051.60.4262797270.04960.05040.0498760.0439261.80.5108064690.05040.05170.05084850.044898520.591143620.05170.05290.0521140.

7、0461642.20.668802660.05180.05380.052490.046541.1.3 尾翼的升力估算尾翼分为水平尾翼和垂直尾翼，只有水平尾翼产生升力。尾翼升力线斜率首先按单独机翼的升力线斜率估算方法,计算出单独尾翼的升力线斜率,再进行修正，因此，首先我们计算单独尾翼的的升力线斜率，过程如下：尾翼升力线斜率可以表示为以下参数的函数：其函数关系由之前图1可以查得。其中平尾参数为: 外露翼梯形比 相对厚度 C=3.62%尖梢比 =0.224 前缘后掠角 则 弦线的后掠角可由下式求出： 从而有 查上图1(b) 图1(c) 对两者进行线性插值即可得。查表时近似取为1，在影响不大的区域，取

8、线；在 影响不大的区域，取与线性插值的结果；在两者交加区域取读取值的平均值。Ma或b图c图插值结果0.42.6853890.0190.01780.01850.62.3440.02150.0190.0204580.81.7580.02250.02000.0212100.02650.02500.02581.21.9435420.02300.02250.0227921.42.8708020.02050.01900.0198751.63.6595690.01800.01800.0181.84.3852220.01530.01600.015725.0749090.01350.01370.01362.25

9、.7416040.01150.01200.011709尾翼的升力线斜率修正，主要修正下洗和阻滞。修正公式为：其中 按单独尾翼计算的升力线斜率 尾翼处的气流下洗角，近似认为等于机翼处的气流下洗角 气流阻滞系数，可根据尾翼布局按下表确定飞行器外形飞行器外形尾翼平面相对于机翼的位置Kw正常式（尾翼位于机翼后）尾翼安装在机身上，而且尾翼与机0.85翼平面重合0.85尾翼安装在机身上，但尾翼平面与机翼平面成45度或90度角0.9尾翼位于机身上面或下面，并离机身的距离为机身直径的一倍或以上1.0鸭式布局(前翼位于机翼之前)鸭式布局(前翼位于机翼之前)任意的1.0对于三角形机翼后气流下洗角的计算可以通过图3

10、由和计算，对于根梢比为无穷大的、后缘具有不大后掠角的机翼，可以采用同样方法确定。对于梯形机翼（1）产生的下洗角可以对三角形机翼的下洗进行修正： 不考虑机翼根梢比的下洗系数 A 尖梢比对下洗的影响系数，可通过图4确定 由单独机翼计算的参数 图3：确定三角形机翼后面气流下洗角的曲线（F4战斗机x可取为0.5）图4：确定参数A所用的曲线各参数随马赫数变化计算结果MaA0.436.50.870.950.6414880.0169070.636.50.870.950.7093810.0151560.836.50.870.950.735110.014315136.50.870.90.847530.01002

11、71.236.50.870.80.6655260.0194331.436.50.870.790.5730960.0216281.636.50.870.770.505890.0226721.836.50.870.760.4355180.022591236.50.870.740.3673360.0219332.236.50.870.720.3077130.0206631.1.4合升力线斜率的计算以上计算的各个部件的升力系数其参考面积均为各自的参考面积，例如机翼的参考面积为外露翼部分面积，机身的参考面积一般采用机身截面的面积，尾翼的参考面积为尾翼外露面积，这样为求得合力系数，必须对其参考面积进行转化

12、后叠加，其计算公式如下：（2）其中 外露翼面积 机身截面积 平尾外露面积 全翼面积 S代入公式（2）中计算得MaS0.40.029550.07410.01690735.213.576.649.240.0573950.60.030050.076050.01515635.213.576.649.240.0585910.80.031050.08190.01431535.213.576.649.240.06273410.034550.094380.01002735.213.576.649.240.0713371.20.040050.086190.01943335.213.576.649.240.067

13、141.40.042050.0822120.02162835.213.576.649.240.0647351.60.0439260.07020.02267235.213.576.649.240.0564211.80.04489850.063570.02259135.213.576.649.240.0517420.0461640.058890.02193335.213.576.649.240.0483972.20.046540.053040.02066335.213.576.649.240.0440711.1.5临界马赫数的计算飞机某一部件在局部马赫数超过1.0时，就会有波阻的存在，这个飞行状态

14、的马赫数称之为临界马赫数，计算飞机的波阻时，必须首先确定临界马赫数。确定临界马赫数后可以把流场分为亚声速、跨声速、超声速三个阶段，通常对于跨声速阶段的阻力难以进行估算，为了获得数据可以用图解法把亚声速和超声速进行光滑过渡而得到。机翼临界马赫数主要取决于机翼剖面形状、展弦比、后掠角等因素：其中 临界马赫数 机翼刨面的临界马赫数，通过图5，由机翼升力系数、相对厚度c和翼型最大厚度线的弦向位置所定 展弦比对临界马赫数的影响，由图6根据零升临界迎角查得 后掠角对临界马赫数的影响，由图6根据零升临界迎角查得。 图5 刨面临界马赫数与升力系数的关系机翼剖面的临界马赫数由机翼升力系数、相对厚度和翼型最大厚度

15、线的弦向位置所决定，以上参数已知即可确定临界马赫数。图6 展弦比与后掠角对临界马赫数影响曲线如果已知零升力时的临界马赫数、展弦比和后掠角便可通过曲线查出展弦比和后掠角对临界马赫数的影响。不同升力系数的临界马赫数0.10.7400.0680.8080.20.600.070.670.30.500.070.570.40.4300.070.50.50.3800.070.450.60.3300.070.41.2 阻力特性的估算阻力系数可以表示为零升阻力(摩擦阻力、压差阻力)和诱导阻力(升致阻力)两部分，其形式为： 无弯度机翼： 有弯度机翼：其中 零升阻力系数 A 诱导阻力因子 亚音速范围内，飞机的零升阻

16、力主要由表面摩擦阻力和气流分离引起的压差阻力组成。=1.1(+)其中 摩擦阻力系数 压差阻力系数1.2.1全机摩擦阻力的估算下面分别以亚音速和超音速情形进行讨论。全机摩擦阻力估算公式为：分别为机翼、机身、平尾、垂尾（立尾）的厚度修正系数分别为机身浸润面积和垂尾（立尾）面积分别为机翼、机身、平尾、垂尾（立尾）的摩擦系数，他们与表面附面层状态、沿表面压力分布梯度及表面粗糙情况有关，同时也与基于各部件特征长度的雷诺数有关。当飞机在大气中飞行时，基于各部件特征长度的飞行雷诺数通常是相当大的，加上由于工艺水平等原因，飞机表面不可能做到理想的光滑，因此可以把飞机附面层近似看成是全湍流附面层。对于光滑平板，

17、具有全湍流附面层的表面摩擦系数可以用下面的半经验公式表示： 其中，Re是基于各部件特征长度计算的雷诺数。对于机翼、机身、平尾、垂尾（立尾）的特征长度分别为气动弦长和当量直径，,取不同高度的标准大气参数值，计算。HMaa机翼cRe机翼平尾cRe平尾垂尾cRe垂尾机身cRe机身00.40.00001783401.2265.02470232991.711160272643.4432223137260.00001783401.2265.02705349481.711240408963.4448334706280.00001783401.2265.02

18、940465981.711320545283.4464446274200.00001783401.2265.021.18E+081.711400681603.4480557843220.00001783401.2265.021.41E+081.711480817913.4496669411240.00001783401.2265.021.65E+081.711560954233.441.13E+08260.00001783401.2265.021.88E+081.711641090553.4

19、41.29E+08280.00001783401.2265.022.12E+081.711721226873.441.45E+08200.00001783401.2265.022.35E+081.711801363193.441.61E+08220.00001783401.2265.022.59E+081.711881499513.441.77E+082.131.1E+0850.40.000016193200.7365.02292505691.71199696663.442004421526

20、0.000016193200.7365.02438758541.711149544993.4430066322280.000016193200.7365.02585011391.711199393323.4440088430200.000016193200.7365.02731264241.711249241663.4450110537220.000016193200.7365.02877517081.711299089993.4460132645240.000016193200.7365.

21、021.02E+081.711348938323.4470154752260.000016193200.7365.021.17E+081.711398786653.4480176860280.000016193200.7365.021.32E+081.711448634983.4490198967200.000016193200.7365.021.46E+081.711498483313.441E+08220.000016193200.7365.021.61E+081.71154833164

22、3.441.1E+082.136826104080.40.000015173080.5265.02214444341.71173090493.44146949912.1390989330.60.000015173080.5265.02321666511.711109635743.4422042486280.000015173080.5265.02428888681.711146180983.4429389981200.000015173080.5265.02536110851.711182726233.44367374772.13227473

23、331.20.000015173080.5265.02643333021.711219271473.4444084972240.000015173085.02750555191.711255816723.4451432467260.000015173085.02857777361.711292361963.4458779963280.000015173080.5265.02964999531.711328907213.4466127458200.000015173080.5265.021.0

24、7E+081.711365452463.4473474953220.000015173080.5265.021.18E+081.711401997703.44808224492.1350044132110.40.000014182950.3685.02152058561.71151827133.44104199492.1364518870.60.000014182950.3685.02228087841.71177740703.44156299242.1396778310.80.000014182950.3685.02304117121.711103654263.44

25、20839898200.000014182950.3685.02380146401.711129567833.4426049873220.000014182955.02456175681.711155481393.4431259848240.000014182950.3685.02532204961.711181394963.4436469822260.000014182950.3685.02608234251.711207308523.4441679797280.

26、000014182950.3685.02684263531.711233222093.4446889772200.000014182950.3685.02760292811.711259135663.4452099746220.000014182950.3685.02836322091.711285049223.44573097212.1335485379130.40.000014182950.2675.02111537461.71138016063.4476432052.1347325660.60.000014182950.2675.021

27、67306191.71157024083.44114648072.1370988480.80.000014182950.2675.02223074921.71176032113.44152864092.1394651311.00.000014182950.2675.02278843651.71195040143.4419108011220.000014182950.2675.02334612381.711114048173.4422929614240.000014182950.2675.02390381111.711133056193.442

28、6751216260.000014182950.2675.02446149841.711152064223.4430572818280.000014182950.2675.02501918581.711171072253.4434394420200.000014182950.2675.02557687311.711190080283.4438216023220.000014182950.2675.02613456041.711209088303.44420376252/p>

29、50.40.000014182950.3645.0281042201.71127622153.4455534892.1334386430.60.000014182950.3645.02121563301.71141433233.4483302342.1351579650.80.000014182950.3645.02162084401.71155244303.44111069792.1368772861.00.000014182950.1945.02202605501.71169055383.44138837242.1385966081.20.000014182950.1945.0224312

30、6601.71182866463.4416660468240.000014182950.1945.02283647701.71196677533.4419437213260.000014182950.1945.02324168801.711110488613.4422213958280.000014182950.1945.02364689901.711124299693.4424990702200.000014182955.02405211001.711138110763.442776744

31、7220.000014182950.1945.02445732101.711151921843.44305441922.1318912537170.40.000014182950.1945.0250546941.71117228253.4434637742.1321447210.60.000014182950.1945.0275820411.71125842373.4451956612.1332170810.80.000014182950.1945.02101093881.71134456503.4469275492.1342894411.00.00001418295

32、0.1945.02126367351.71143070623.4486594362.1353618021.20.000014182950.1215.02151640821.71151684753.44103913232.1364341621.40.000014182950.1215.02176914291.71160298873.44121232102.1375065231.60.000014182950.1215.02202187761.71168913003.44138550972.1385788831.80.000014182950.1215.02227461231.7117752712

33、3.44155869842.1396512432.00.000014182950.1215.02252734701.71186141253.4417318872220.000014182955.02278008171.71194755373.44190507592.1311795964200.40.000014182950.1215.0212529641.71125191093.4415597972.1315597970.60.000014182950.1215.02232367801.711467180143.44289271422.1323396950.80.00

34、0014182950.1215.02594588191.7111.2E+083.44740194532.1331195941.00.000014182950.1215.021.1E+081.7112.21E+083.441.37E+082.1338994921.20.000014182950.1215.021.75E+081.7113.51E+083.442.17E+082.1346793911.40.000014182950.0885.022.54E+081.7115.1E+083.443.16E+082.1354592891.60.000014182950.0885.023.47E+081

35、.7116.97E+083.444.32E+082.1362391881.80.000014182950.0885.024.54E+081.7119.13E+083.445.65E+082.1370190862.00.000014182950.0885.025.76E+081.7111.16E+093.447.17E+082.1377989842.20.000014182950.0885.027.12E+081.7111.43E+093.448.86E+082.138578883厚度修正系数的计算公式如下，其中考虑了马赫数对摩擦影响的修正其中 ： 翼型最大厚度线的弦向位置，无量纲翼型最大厚度线

36、的后掠角机身的厚度修正系数计算公式为:其中,机身长度,机身直径,解之得机身的浸润面积计算公式如下：其中 分别为头部、尾部、柱段长度 计算得 MaXccmaxc机翼0.40.40.05141.50.2558508540.60.40.05141.50.5308247170.80.40.05141.50.8909244210.4041.51.235924691.20.4041.51.7160038231.40.4041.52.2647614941.60.4041.52.8801027181.80.4041.53.56026657820.4041.54.3037397412.20.4041.55.10

37、9199179平尾0.40.280.036233.91670.2550915680.60.280.036233.91670.5292493940.80.280.036233.91670.88828043310.28033.91671.2718888761.20.28033.91671.7659378371.40.28033.91672.3306638141.60.28033.91672.9639108591.80.28033.91673.66386681520.28033.91674.4289743112.20.28033.91675.257871822垂尾0.40.350.036152.78

38、0.2376301520.60.350.036152.780.4930214460.80.350.036152.780.82747624910.35052.781.1642502181.20.35052.781.616488321.40.35052.782.1334221131.60.35052.782.7130781061.80.35052.783.35379750420.35052.784.0541547332.20.35052.784.812903493摩擦阻力系数的计算：HMa00.40.0023710.0027880.0025070.0026960.0080690.60.002236

39、0.002620.0023610.0025350.0087930.80.0021470.0025090.0022650.0024290.00993810.002080.0024270.0021940.0023510.0110591.20.0020290.0023630.0021380.0022890.012691.40.0019860.0023110.0020920.0022390.014561.60.0019510.0022670.0020540.0021970.016651.80.001920.0022290.0020210.0021610.01894720.0018930.0021960

40、.0019930.0021290.021442.20.0018690.0021660.0019670.00210.0241250.40.0025430.0030050.0026940.0029020.0087270.60.0023950.0028190.0025330.0027240.0094890.80.0022970.0026960.0024270.0026070.01070910.0022250.0026060.0023490.0025210.0119031.20.0021680.0025350.0022880.0024540.0136451.40.0021220.0024770.002

41、2380.0023990.0156441.60.0020820.0024290.0021960.0023520.0178781.80.0020480.0023870.0021590.0023120.02033320.002020.0023510.0021280.0022770.0229962.20.0019930.0023180.00210.0022470.0258680.40.0026660.003160.0028260.003050.0091680.60.0025080.002960.0026550.0028590.0099540.80.0024030.0028290.0025420.00

42、27340.01122210.0023260.0027320.0024580.0026420.0124641.20.0022660.0026570.0023930.002570.014281.40.0022160.0025950.002340.0025110.0163631.60.0021750.0025440.0022950.0024620.0186921.80.0021390.0024990.0022570.0024190.02125120.0021080.002460.0022230.0023820.0240282.20.002080.0024260.0021930.0023490.02

43、7012110.40.0028110.0033440.0029840.0032250.0096920.60.0026410.0031280.0027990.003020.0105060.80.0025290.0029870.0026780.0028850.01183210.0024460.0028830.0025880.0027860.013131.20.0023810.0028010.0025180.0027080.0150321.40.0023290.0027350.0024610.0026450.0172151.60.0022840.002680.0024130.0025920.0196

44、561.80.0022460.0026320.0023720.0025460.02233720.0022120.002590.0023360.0025060.0252472.20.0021830.0025530.0023040.0024710.028374130.40.0031070.0035240.0031370.0033960.0103220.60.0029520.0032920.0029390.0031750.0113010.80.002770.003140.0028090.003030.01276710.002650.0030280.0027130.0029240.0141951.20.002562