導(dǎo)彈總體設(shè)計(jì)《防空導(dǎo)彈主級燃料相對質(zhì)量因數(shù)計(jì)算》大作業(yè)

導(dǎo)彈總體設(shè)計(jì)《防空導(dǎo)彈主級燃料相對質(zhì)量因數(shù)計(jì)算》大作業(yè)班號：_________學(xué)號：_________姓名：_________一、要求：根據(jù)已知條件，采用數(shù)值積分法求解相對量運(yùn)動微分方程組，計(jì)算燃料相對質(zhì)量因數(shù)。綜合運(yùn)用積分、插值計(jì)算等計(jì)算方法，采用C、C++，或者M(jìn)atlab等語言的一種，編制計(jì)算程序。二、已知條件：1、分離條件：速度V=500m/s，時(shí)間t=3s，x方向位置x=674m，y方向位置y=329m，初始攻角，初始彈道傾角。2、氣動參數(shù)阻力因數(shù)插值表：（）2468101.50.04300.05110.06510.08470.11202.10.03600.04360.05580.07360.09732.70.03080.03720.04810.06410.08493.30.02650.03230.04190.05600.07464.00.02220.02720.03560.04780.0644升力因數(shù)斜率插值表：（）12468101.50.03020.03040.03060.03090.03110.03132.00.02790.02800.02840.02860.02880.02902.50.02610.02640.02670.02690.02720.02743.00.02470.02480.02510.02540.02570.02593.50.02260.02270.02310.02330.02360.02384.00.02090.02100.02130.02160.02190.0221注：以上攻角單位均為度。發(fā)動機(jī)參數(shù)：比沖Is=2156；重力加速度g=9.801；推重比；翼載。導(dǎo)引規(guī)律：三點(diǎn)法。目標(biāo)勻速直線等高迎頭飛行，，，（=14200m），（=32000m）（彈目斜距）大氣模型：參見教科書。三、計(jì)算思路①插值表的處理1.對于大氣參數(shù)密度ρ、聲速a，都是高度h的單值函數(shù)，本次計(jì)算采用最方便的線性插值，對于指定高度h，找出上下最接近的兩點(diǎn)h1,h2進(jìn)行計(jì)算。2.對于Cx，Cyα它由兩個(gè)參數(shù)決定，采用雙線性插值。具體算法如下：將Cx（α，Ma)看作是攻角和馬赫數(shù)的二元點(diǎn)函數(shù)Z（x，y)，則對于任意點(diǎn)p（a，b），找出距離a最近的點(diǎn)A（x1，y1）、B（x2，y2）、C（x3，y3）、D（x4，y4），如上圖示。先用P點(diǎn)的橫坐標(biāo)在x軸方向（A,B方向）上進(jìn)行第一次線性插值，計(jì)算出E點(diǎn)的值，同樣在C,D方向進(jìn)行第二次插值求出F點(diǎn)的值，最后在y軸方向（E，F(xiàn)方向）用縱坐標(biāo)進(jìn)行線性插值求出P點(diǎn)的函數(shù)值。②解方程組1.四階龍格庫塔公式：y(i+1)=y(i)+h*(K1+2*K2+2*K3+K4)/6K1=f(x(i),y(i))K2=f(x(i)+h/2,y(i)+hK1/2)K3=f(x(i)+h/2,y(i)+hK2/2)K4=f(x(i)+h,y(i)+hK3)2.三點(diǎn)法導(dǎo)引的相對量運(yùn)動微分方程組為：此方程組變量較多，但是只有方程1、方程2需要進(jìn)行復(fù)雜的求解運(yùn)算，其余的方程均可代入上一步的計(jì)算結(jié)果求得。以μ為自變量，初始μ=0，選定一個(gè)步長h，利用已知的初值條件，用龍格庫塔法解方程1、方程2，方程3~8可由1、2的結(jié)果代入計(jì)算求得，經(jīng)過多次運(yùn)算求解。具體步驟如下：已知初始參數(shù)g=9.801m/s^2，μ=0，Is=2156N*s/kg，P=2.2，p0=5880N/m^2，α0=1.5°，θ=26°，vt=vt0=420m/s，yt0=15000m，dt0=34200m，易得xt0=31569.39345，cotq0=xt0/yt0=2.10462623，h=0.001。1.利用大氣參數(shù)表計(jì)算出當(dāng)前高度y=y（h)（初值y0=329m）下的密度ρ,聲速a；2.利用當(dāng)前速度（初值v0=500m/s）和聲速解方程7計(jì)算出當(dāng)前馬赫數(shù)Ma；3.解方程3，4，得dx/du，dy/du；4.用龍格庫塔法解方程1，得dv/du；5.用龍格庫塔法解方程2，得dθ/du；6.將上述方程的結(jié)果代入方程5、6、8，解得α、q，t；7.用新值代替舊值重復(fù)1~6步驟，判斷y>=y0時(shí)，計(jì)算結(jié)束。四、計(jì)算結(jié)果擊中目標(biāo)時(shí)，μ=0.346，t=37.49648，x=16993.632，y=15058.591，v=849.348，θ=60.776°，α=5.439°，q=41.289°，xt=17080.872，Ma=2.873.五、C語言計(jì)算程序代碼#include<stdio.h>#include<string.h>#include<math.h>#definePI3.1415926535//圓周率π#defineh0.001//步長#definev0500.0//分離時(shí)導(dǎo)彈初速度v0單位：s#definet03.0//分離時(shí)刻t0，單位：s//#definex0674.0//#definey0329.0#definealpha01.5*PI/180//攻角α，單位：rad#definetheta026.0*PI/180//俯仰角θ，單位：rad#defineis2156.0//總沖Is,單位：N*s/kg#defineg9.801//重力加速度g,單位：m/s^2#defineP2.2//推重比P#definep05880.0//翼載p0，單位：N/m^2#definevt420.0//飛機(jī)速度vt，單位：m/s#defineyt015000.0//飛機(jī)初始縱坐標(biāo)yt，單位：m#definedt034200.0//彈目斜距Dt0，單位：m#definext031569.39345//飛機(jī)初始橫坐標(biāo)xt0，單位：mxt0=sqrt(dt0^2-(yt0-y0)^2)+x0#definecotq02.10462623//初始目標(biāo)對制導(dǎo)站的航向角的余切，cotq0=xt0/yt0;doubleinter_linear(doublex0,doublex1,doubley0,doubley1,doublex){//線性插值函數(shù)doublea0,a1,y;a0=(x-x1)/(x0-x1);a1=(x-x0)/(x1-x0);y=a0*y0+a1*y1;returny;}doubleinterp1(doublex[],doubley[],intn,doublea){//一維線性插值函數(shù)doublez;inti=0;for(i=0;i<(n-1);i++){if((a>=x[i])&&(a<=x[i+1]))break;//確定a的位置}z=inter_linear(x[i],x[i+1],y[i],y[i+1],a);returnz;}doubleinterp2(doublex[],doubley[],doublez[6][6],intm,intn,doublea,doubleb){//雙線性插值函數(shù)inti,j;doublew,w1,w2;for(i=0;i<(m-1);i++){//確定a在x軸的位置if((a>=x[i])&&(a<=x[i+1]))break;}for(j=0;j<(n-1);j++){//確定b在y軸的位置if((b>=y[j])&&(b<=y[j+1]))break;}if(a<x[0])i=0;//若給定的點(diǎn)超出范圍時(shí)，采用線性外推進(jìn)行插值elseif(a>x[m-1])i=m-1;if(b<y[0])j=0;elseif(b>y[n-1])j=n-1;w1=inter_linear(x[i],x[i+1],z[i][j],z[i+1][j],a);//在x軸方向進(jìn)行第一次插值w2=inter_linear(x[i],x[i+1],z[i][j+1],z[i+1][j+1],a);//在x軸方向進(jìn)行第二次插值w=inter_linear(y[j],y[j+1],w1,w2,b);//在y軸方向進(jìn)行插值returnw;}intmain(){//*****************************計(jì)算用到的參數(shù)**************************************doublecx,cya;//阻力系數(shù)Cx，升力系數(shù)斜率Cyαdoublealpha1[5]={2,4,6,8,10},ma1[5]={1.5,2.1,2.7,3.3,4.0};//Cx插值表中的α向量,Ma向量doublealpha2[6]={1,2,4,6,8,10},ma2[6]={1.5,2.0,2.5,3.0,3.5,4.0};//Cyα插值表中的α向量，Ma向量doublecx0[6][6]={{0.0430,0.0511,0.0651,0.0847,0.1120},\{0.0360,0.0436,0.0558,0.0736,0.0973},\{0.0308,0.0372,0.0481,0.0641,0.0849},\{0.0265,0.0323,0.0419,0.0560,0.0746},\{0.0222,0.0272,0.0356,0.0478,0.0644}};//Cx插值表doublecy0[6][6]={{0.0302,0.0304,0.0306,0.0309,0.0311,0.0313},\{0.0279,0.0280,0.0284,0.0286,0.0288,0.0290},\{0.0261,0.0264,0.0267,0.0269,0.0272,0.0274},\{0.0247,0.0248,0.0251,0.0254,0.0257,0.0259},\{0.0226,0.0227,0.0231,0.0233,0.0236,0.0238},\{0.0209,0.0210,0.0213,0.0216,0.0219,0.0221}};//Cyα插值表doubleyh[23]={0,1000,2000,3000,4000,5000,6000,7000,8000,\9000,10000,11000,12000,13000,14000,15000,\16000,17000,18000,19000,20000,21000,22000};//大氣高度y(h)doubleph[23]={1.22505,1.11168,1.00646,0.90913,0.81913,0.73612,0.65969,\0.58950,0.52517,0.46635,0.41270,0.36391,0.31083,0.26549,\0.22675,0.19367,0.16542,0.14128,0.12068,0.10307,0.08803,\0.07487,0.06373};//大氣密度表ρ(h)doubleah[23]={340.29,336.43,332.53,328.58,324.58,320.53,316.43,312.27,\308.06,303.79,299.46,295.07,295.07,295.07,295.07,295.07,\295.07,295.07,295.07,295.07,295.07,295.75,296.43};//大氣聲速表a(h)inti;doublep,a,q,cotq;doublex=674.0,y=329.0,v=v0,t=t0,u=0,alpha=alpha0,theta=theta0,ma,dr;doublex_2,y_2,v_2,theta_2,alpha_2;//x(n+1),y(n+1),v(n+1),θ(n+1),α(n+1)doublext=xt0;doubleKv1,Kv2,Kv3,Kv4;doubleKth1,Kth2,Kth3,Kth4;charstr[500];FILE*fp;fp=fopen("output.txt","w");//創(chuàng)建文件output.txtprintf("μtxyvθαqxtDrMa\n");sprintf(str,"μtxyvθαqxtDrMa\n");fputs(str,fp);//******************************開始計(jì)算*****************************************for(i=1;y<=yt0;i++){p=interp1(yh,ph,23,y);//從大氣密度表中用插值法得出當(dāng)前高度大氣的密度a=interp1(yh,ah,23,y);//從大氣聲速表中用插值法得出當(dāng)前高度大氣的聲速ma=v/a;//用當(dāng)前速度和聲速計(jì)算馬赫數(shù)Macx=interp2(ma1,alpha1,cx0,5,5,ma,alpha*180/PI);//當(dāng)前Ma,α下的Cxcya=interp2(ma2,alpha2,cy0,6,6,ma,alpha*180/PI);//當(dāng)前Ma,α下的CyαKv1=is/(1-u)-p*v*v*cx*is/2/P/p0/(1-u)-is/P*sin(theta);Kv2=is/(1-(u+h/2))-p*(v+h*Kv1/2)*(v+h*Kv1/2)*cx*is/2/P/\p0/(1-(u+h/2))-is/P*sin(theta);Kv3=is/(1-(u+h/2))-p*(v+h*Kv2/2)*(v+h*Kv2/2)*cx*is/2/P/\p0/(1-(u+h/2))-is/P*sin(theta);Kv4=is/(1-(u+h))-p*(v+h*Kv3)*(v+h*Kv3)*cx*is/2/P/\p0/(1-(u+h))-is/P*sin(theta);v_2=v+h*(Kv1+2*Kv2+2*Kv3+Kv4)/6;//龍格庫塔法計(jì)算方程1的v(n+1)y_2=y+h*is*v*sin(theta)/P/g;//利用方程3計(jì)算y(n+1)x_2=x+h*is*v*cos(theta)/P/g;//利用方程4計(jì)算x(n+1)Kth1=vt/yt0*(is/P/g+(is*v*v*sin(theta)/P/g-\y*Kv1)/v/v/sin(theta))/\(1+(cotq0-u*is*vt/P/g/yt0)/tan(theta));Kth2=vt/yt0*(is/P/g+(is*v*v*sin(theta+h*Kth1/2)/P/g-\y*Kv1)/v/v/sin(theta+h*Kth1/2))/\(1+(cotq0-(u+h/2)*is*vt/P/g/yt0)/tan(theta+h*Kth1/2));Kth3=vt/yt0*(is/P/g+(is*v*v*sin(theta+h*Kth2/2)/P/g-\y*Kv1)/v/v/sin(theta+h*Kth2/2))/\(1+(cotq0-(u+h/2)*is*vt/P/g/yt0)/tan(theta+h*Kth2/2));Kth4=vt/yt0*(is/P/g+(is*v*v*sin(theta+h*Kth3)/P/g-\y*Kv1)/v/v/sin(theta+h*Kth3))/\(1+(cotq0-(u+h)*is*vt/P/g/yt0)/tan(theta+h*Kth3));theta_2=theta+h*(Kth1+2*Kth2+2*Kth3+Kth4)/6;//龍格庫塔法計(jì)算方程2的θ(n+1)alpha_2=(v*Kth1+is*cos(theta)/P)/(57.3*p*v*v*cya*is/2/P/p0/(1-u)+is/(1-u));//利用方程5計(jì)算αcotq=cotq0-u*is*vt/P/g/yt0;//利用方程6計(jì)算cotqq=atan(1/cotq);//計(jì)算q，單位：radxt=cotq*yt0;//幾何關(guān)系cotq=xt/ytdr=sqrt((x-xt)*(x-xt)+(y-yt0)*(y-yt0));//利用方程7計(jì)算Drt=t0+u*is/P/g;//利用式(3-22)計(jì)算時(shí)間//t=t0+yt0*(cotq0-cotq)/vt;y=y_2;x=x_2;v=v_2;theta=theta_2;alpha=alpha_2;u=u+h;//******************************輸出當(dāng)前結(jié)果***************************************printf("%lf%2.6lf%5.6lf%5.6lf%3.6lf%2.6lf°%2.6lf°%lf°%5.6lf%5.6lf%lf\n",u,t,x,y,v,theta*180/PI,alpha*180/PI,q*180/PI,xt,dr,ma);if(fp!=NULL){sprintf(str,"%.3lf%2.3lf%5.3lf%5.3lf%3.3lf%2.3lf°%2.3lf°%.3lf°%5.3lf%5.3lf%.3lf\n",u,t,x,y,v,theta*180/PI,alpha*180/PI,q*180/PI,xt,dr,ma);fputs(str,fp);}//輸出結(jié)果到文件output.txt}fclose(fp);//關(guān)閉文件return0;}程序運(yùn)行結(jié)果如下：μtxyvθαqxtDrMa0.0013.000718.935350.916500.70426.060°1.774°25.414°31569.39334201.8071.4750.0023.100763.911372.910501.38226.120°1.771°25.444°31527.39834113.8831.4770.0033.200808.924394.982502.05926.180°1.771°25.474°31485.40234025.8991.4800.0043.300853.975417.130502.73726.240°1.771°25.503°31443.40633937.8561.4820.0053.400899.063439.355503.41526.301°1.770°25.533°31401.41133849.7551.4840.0063.500944.189461.659504.09426.361°1.770°25.563°31359.41533761.5971.4870.0073.600989.351484.040504.77326.422°1.770°25.593°31317.41933673.3801.4890.0083.7001034.551506.499505.45226.483°1.771°25.623°31275.42333585.1051.4920.0093.8001079.788529.036506.13126.544°1.771°25.653°31233.42833496.7721.4940.0103.9001125.061551.652506.81126.605°1.771°25.683°31191.43233408.3811.4960.0114.0001170.371574.347507.49126.667°1.771°25.713°31149.43633319.9321.4990.0124.1001215.717597.121508.17226.729°1.771°25.743°31107.44133231.4251.5010.0134.2001261.100619.975508.85326.790°1.771°25.774°31065.44533142.8601.5040.0144.3001306.519642.908509.53426.852°1.771°25.804°31023.44933054.2361.5060.0154.4001351.974665.921510.21626.914°1.772°25.834°30981.45332965.5551.5080.0164.5001397.464689.013510.89926.976°1.772°25.865°30939.45832876.8161.5110.0174.6001442.990712.187511.58127.039°1.772°25.895°30897.46232788.0191.5130.0184.7001488.552735.441512.26527.101°1.773°25.926°30855.46632699.1641.5160.0194.8001534.149758.775512.94827.164°1.773°25.957°30813.47132610.2511.5180.0204.9001579.782782.191513.63327.227°1.773°25.988°30771.47532521.2801.5200.0215.0001625.449805.688514.31727.290°1.774°26.018°30729.47932432.2521.5230.0225.1001671.152829.267515.00327.353°1.774°26.049°30687.48332343.1651.5250.0235.2001716.889852.928515.68827.417°1.775°26.080°30645.48832254.0201.5280.0245.3001762.661876.671516.37527.480°1.775°26.111°30603.49232164.8171.5300.0255.4001808.468900.497517.06227.544°1.776°26.142°30561.49632075.5561.5330.0265.5001854.308924.405517.74927.608°1.777°26.174°30519.50131986.2381.5350.0275.6001900.184948.396518.43827.672°1.777°26.205°30477.50531896.8611.5380.0285.7001946.093972.470519.12627.736°1.778°26.236°30435.50931807.4271.5400.0295.8001992.036996.628519.81627.801°1.779°26.268°30393.51331717.9341.5430.0305.9002038.0131020.870520.50627.866°1.779°26.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