飞机气动估算及飞行性能计算课程设计报告

. .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班级日期目录气动特性估算11.1升力特性估算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5合升力线斜率的计算8临界马赫数的计算91.2 阻力特性的估算11全机摩擦阻力的估算11亚音速压差阻力的估算17亚声速升致阻力特性估算19超音速零升波阻估算20超声速升致阻力25飞机根本飞行性能计算372.1 平飞需用推力的计算37不同高度下的推力曲线图(15)40不同高度的马赫数分布43飞行包线图(16)442.2 定常上升性能44不同高度下的Vy-Ma最大上升率图1747绘制图求解不同飞行高度下的最大爬升角47升限确实定读上图可得482.3爬升时间计算492.3.1 亚音速等表速爬升49超音速等马赫数爬升50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 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机翼的外表为一梯形，由梯形面积计算公式有：S=可求得：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：那么 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0.42.3829390.01900.07410.62.080.01950.076050.81.560.0210.0819100.02420.094381.21.7246450.02210.086191.42.5474690.021080.0822121.63.2473990.0180.07021.83.8913240.01630.0635724.5033320.01510.058892.25.0949390.01360.053041.1.2 机身升力的估算机身升力主要由头部和尾部两局部组成，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，尾部形状为锥形，那么底部面积为零，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 为机身圆柱局部长细比，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，那么其升力线斜率按照圆柱形进展修正:其中 B： 机身最大截面的宽度 计算图表Ma或查表查表0.40.3128038020.03550.03550.03550.029550.60.2730375430.03600.03600.03600.030050.80.2047781570.03700.03700.03700.03105100.04050.04050.04050.034551.20.2263907710.04600.04600.04600.040051.40.334401330.04800.04800.04800.042051.60.4262797270.04960.05040.0498760.0439261.80.5108064690.05040.05170.05084850.044898520.591143620.05170.05290.0521140.0461642.20.668802660.05180.05380.052490.046541.1.3 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,再进展修正，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 那么 弦线的后掠角可由下式求出： 从而有查上图1(b) 图1(c) 对两者进展线性插值即可得。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。Ma或b图c图插值结果0.42.6853890.0190.01780.01850.62.3440.02150.0190.0204580.81.7580.02250.02000.0212100.02650.02500.02581.21.9435420.02300.02250.0227921.42.8708020.02050.01900.0198751.63.6595690.01800.01800.0181.84.3852220.01530.01600.015725.0749090.01350.01370.01362.25.7416040.01150.01200.011709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展修正： 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MaA0.436.50.870.950.6414880.0169070.636.50.870.950.7093810.0151560.836.50.870.950.735110.014315136.50.870.90.847530.0100271.236.50.870.80.6655260.0194331.436.50.870.790.5730960.0216281.636.50.870.770.505890.0226721.836.50.870.760.4355180.022591236.50.870.740.3673360.0219332.236.50.870.720.3077130.0206631.1.4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局部面积，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展转化后叠加，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MaS0.40.029550.07410.01690735.213.576.649.240.0573950.60.030050.076050.01515635.213.576.649.240.0585910.80.031050.08190.01431535.213.576.649.240.06273410.034550.094380.01002735.213.576.649.240.0713371.20.040050.086190.01943335.213.576.649.240.067141.40.042050.0822120.02162835.213.576.649.240.0647351.60.0439260.07020.02267235.213.576.649.240.0564211.80.04489850.063570.02259135.213.576.649.240.0517420.0461640.058890.02193335.213.576.649.240.0483972.20.046540.053040.02066335.213.576.649.240.0440711.1.5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展估算，为了获得数据可以用图解法把亚声速和超声速进展光滑过渡而得到。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线的弦向位置所决定，以上参数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)两局部，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 亚音速围，飞机的零升阻力主要由外表摩擦阻力和气流别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展讨论。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，他们与外表附面层状态、沿外表压力分布梯度及外表粗糙情况有关，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，飞机外表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，具有全湍流附面层的外表摩擦系数可以用下面的半经历公式表示： 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00.40.00001783401.2265.02470232991.711160272643.44322231372.13199521170.60.00001783401.2265.02705349481.711240408963.44483347062.13299281750.80.00001783401.2265.02940465981.711320545283.44644462742.13399042341.00.00001783401.2265.021.18E+081.711400681603.44805578432.13498802921.20.00001783401.2265.021.41E+081.711480817913.44966694112.13598563511.40.00001783401.2265.021.65E+081.711560954233.441.13E+082.13698324091.60.00001783401.2265.021.88E+081.711641090553.441.29E+082.13798084671.80.00001783401.2265.022.12E+081.711721226873.441.45E+082.13897845262.00.00001783401.2265.022.35E+081.711801363193.441.61E+082.13997605842.20.00001783401.2265.022.59E+081.711881499513.441.77E+082.131.1E+0850.40.000016193200.7365.02292505691.71199696663.44200442152.13124110980.60.000016193200.7365.02438758541.711149544993.44300663222.13186166470.80.000016193200.7365.02585011391.711199393323.44400884302.13248221961.00.000016193200.7365.02731264241.711249241663.44501105372.13310277461.20.000016193200.7365.02877517081.711299089993.44601326452.13372332951.40.000016193200.7365.021.02E+081.711348938323.44701547522.13434388441.60.000016193200.7365.021.17E+081.711398786653.44801768602.13496443931.80.000016193200.7365.021.32E+081.711448634983.44901989672.13558499422.00.000016193200.7365.021.46E+081.711498483313.441E+082.13620554912.20.000016193200.7365.021.61E+081.711548331643.441.1E+082.136826104080.40.000015173080.5265.02214444341.71173090493.44146949912.1390989330.60.000015173080.5265.02321666511.711109635743.44220424862.13136484000.80.000015173080.5265.02428888681.711146180983.44293899812.13181978661.00.000015173080.5265.02536110851.711182726233.44367374772.13227473331.20.000015173080.5265.02643333021.711219271473.44440849722.13272967991.40.000015173085.02750555191.711255816723.44514324672.13318462661.60.000015173085.02857777361.711292361963.44587799632.13363957331.80.000015173080.5265.02964999531.711328907213.44661274582.13409451992.00.000015173080.5265.021.07E+081.711365452463.44734749532.13454946662.20.000015173080.5265.021.18E+081.711401997703.44808224492.1350044132110.40.000014182950.3685.02152058561.71151827133.44104199492.1364518870.60.000014182950.3685.02228087841.71177740703.44156299242.1396778310.80.000014182950.3685.02304117121.711103654263.44208398982.13129037741.00.000014182950.3685.02380146401.711129567833.44260498732.13161297181.20.000014182955.02456175681.711155481393.44312598482.13193556611.40.000014182950.3685.02532204961.711181394963.44364698222.13225816051.60.000014182950.3685.02608234251.711207308523.44416797972.13258075491.80.000014182950.3685.02684263531.711233222093.44468897722.13290334922.00.000014182950.3685.02760292811.711259135663.44520997462.13322594362.20.000014182950.3685.02836322091.711285049223.44573097212.1335485379130.40.000014182950.2675.02111537461.71138016063.4476432052.1347325660.60.000014182950.2675.02167306191.71157024083.44114648072.1370988480.80.000014182950.2675.02223074921.71176032113.44152864092.1394651311.00.000014182950.2675.02278843651.71195040143.44191080112.13118314141.20.000014182950.2675.02334612381.711114048173.44229296142.13141976971.40.000014182950.2675.02390381111.711133056193.44267512162.13165639801.60.000014182950.2675.02446149841.711152064223.44305728182.13189302621.80.000014182950.2675.02501918581.711171072253.44343944202.13212965452.00.000014182950.2675.02557687311.711190080283.44382160232.13236628282.20.000014182950.2675.02613456041.711209088303.44420376252.1326029111150.40.000014182950.3645.0281042201.71127622153.4455534892.1334386430.60.000014182950.3645.02121563301.71141433233.4483302342.1351579650.80.000014182950.3645.02162084401.71155244303.44111069792.1368772861.00.000014182950.1945.02202605501.71169055383.44138837242.1385966081.20.000014182950.1945.02243126601.71182866463.44166604682.13103159291.40.000014182950.1945.02283647701.71196677533.44194372132.13120352511.60.000014182950.1945.02324168801.711110488613.44222139582.13137545731.80.000014182950.1945.02364689901.711124299693.44249907022.13154738942.00.000014182955.02405211001.711138110763.44277674472.13171932162.20.000014182950.1945.02445732101.711151921843.44305441922.1318912537170.40.000014182950.1945.0250546941.71117228253.4434637742.1321447210.60.000014182950.1945.0275820411.71125842373.4451956612.1332170810.80.000014182950.1945.02101093881.71134456503.4469275492.1342894411.00.000014182950.1945.02126367351.71143070623.4486594362.1353618021.20.000014182950.1215.02151640821.71151684753.44103913232.1364341621.40.000014182950.1215.02176914291.71160298873.44121232102.1375065231.60.000014182950.1215.02202187761.71168913003.44138550972.1385788831.80.000014182950.1215.02227461231.71177527123.44155869842.1396512432.00.000014182950.1215.02252734701.71186141253.44173188722.13107236042.20.000014182955.02278008171.71194755373.44190507592.1311795964200.40.000014182950.1215.0212529641.71125191093.4415597972.1315597970.60.000014182950.1215.02232367801.711467180143.44289271422.1323396950.80.000014182950.1215.02594588191.7111.2E+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+081.7116.97E+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0.40.40.05141.50.2558508540.60.40.05141.50.5308247170.80.40.05141.50.8909244210.4041.51.235924691.20.4041.51.7160038231.40.4041.52.2647614941.60.4041.52.8801027181.80.4041.53.56026657820.4041.54.3037397412.20.4041.55.109199179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0.40.350.036152.780.2376301520.60.350.036152.780.4930214460.80.350.036152.780.82747624910.35052.781.1642502181.20.35052.781.616488321.40.35052.782.1334221131.60.35052.782.7130781061.80.35052.783.35379750420.35052.784.0541547332.20.35052.784.812903493摩擦阻力系数的计算：HMa00.40.0023710.0027880.0025070.0026960.0080690.60.0022360.002620.0023610.0025350.0087930.80.0021470.0025090.0022650.0024290.00993810.002080.0024270.0021940.0023510.0110591.20.0020290.0023630.0021380.0022890.012691.40.0019860.0023110.0020920.0022390.014561.60.0019510.0022670.0020540.0021970.016651.80.001920.0022290.0020210.0021610.01894720.0018930.0021960.0019930.0021290.021442.20.0018690.0021660.0019670.00210.0241250.40.0025430.0030050.0026940.0029020.0087270.60.0023950.0028190.0025330.0027240.0094890.80.0022970.0026960.0024270.0026070.01070910.0022250.0026060.0023490.0025210.0119031.20.0021680.0025350.0022880.0024540.0136451.40.0021220.0024770.0022380.0023990.0156441.60.0020820.0024290.0021960.0023520.0178781.80.0020480.0023870.0021590.0023120.02033320.002020.0023510.0021280.0022770.0229962.20.0019930.0023180.00210.0022470.0258680.40.0026660.003160.0028260.003050.0091680.60.0025080.002960.0026550.0028590.0099540.80.0024030.0028290.0025420.0027340.01122210.0023260.0027320.0024580.0026420.0124641.20.0022660.0026570.0023930.002570.014281.40.0022160.0025950.002340.0025110.0163631.60.0021750.0025440.0022950.0024620.0186921.80.0021390.0024990.0022570.0024190.02125120.0021080.002460.0022230.0023820.0240282.20.002080.0024260.0021930.0023490.027012110.40.0028110.0033440.0029840.0032250.0096920.60.0026410.0031280.0027990.003020.0105060.80.0025290.0029870.0026780.0028850.01183210.0024460.0028830.0025880.0027860.013131.20.0023810.0028010.0025180.0027080.0150321.40.0023290.0027350.0024610.0026450.0172151.60.0022840.002680.0024130.0025920.0196561.80.0022460.0026320.0023720.0025460.02233720.0022120.002590.0023360.0025060.0252472.20.0021830.0025530.0023040.0024710.028374130.40.0031070.0035240.0031370.0033960.0103220.60.0029520.0032920.0029390.0031750.0113010.80.002770.003140.0028090.003030.01276710.002650.0030280.0027130.0029240.0141951.20.0025620.0029410.0026390.0028420.016291.40.0024930.0028710.0025780.0027740.0186851.60.0024370.0028110.0025270.0027170.0213591.80.0023890.002760.0024830.0026690.02429320.0023480.0027160.0024440.0026260.0274722.20.0023130.0026760.002410.0025890.030894150.40.0031070.0037230.0033060.0035850.0107660.60.0029120.0034730.0030930.0033470.0116340.80.0027830.0033090.0029540.0031910.01307210.0026890.0031890.0028520.0030780.0144821.20.0026150.0030960.0027720.0029890.0165581.40.0025550.003020.0027060.0029160.0189411.60.0025050.0029560.0026520.0028560.0216061.80.0024610.0029020.0026050.0028040.02453420.0024230.0028540.0025630.0027580.027712.20.0023890.0028120.0025270.0027180.031123170.40.0033580.0040470.003580.0038920.0116830.60.0031410.0037660.0033430.0036260.0125930.80.0029980.0035830.0031880.0034520.01412410.0028940.003450.0030740.0033250.0156271.20.0028120.0033460.0029850.0032270.0178481.40.0027460.0032610.0029130.0031460.0203981.60.002690.003190.0028520.0030790.023251.80.0026420.003130.00280.0030210.02638420.00260.0030770.0027550.002970.0297832.20.0025630.003030.0027150.0029260.033435200.40.0024580.0037830.004120.004120.0084210.60.0023170.0023730.0025480.0038320.0091660.80.0022230.0020750.0022210.0036450.01035210.0021540.0019090.0020370.0035080.0115121.20.0020990.0017950.0019140.0034020.0132031.40.0020550.001710.001820.0033150.0151421.60.0020210.0016430.0017470.0032430.0173091.80.0019850.0015890.0016880.0031810.01969120.0019570.0015420.0016380.0031270.0222762.20.0019320.0015030.0015950.0030790.0250551.2.2亚音速压差阻力的估算在计算压差阻力时，由于机翼及尾翼的压差阻力非常小，所以只考虑机身的压差阻力。飞机在超音速飞行时，压差阻力实际上就是波阻，所以不单独计算压差阻力。压差阻力可按照下式分为头部阻力、尾部阻力、底部阻力、附加阻力四局部。其中： 头部阻力系数，取决于头部长细比、马赫数，见以下图7图7 抛物线母线头部的阻力系数与马赫数的关系 尾部阻力系数，可通过以下图8由尾部长细比、收缩比、马赫数确定。由于纵坐标没有刻度，故此项可暂时忽略图8 直线上图和抛物线以下图母线尾部阻力系数计算曲线 底部阻力系数，通常超音速战斗机发动机安装在尾部，所以此项为0. 附加阻力系数，通常取0.0070.01，这里我们取 计算图表S0.4-0.02700.0093.5749.24-0.0