Question

Problem 1: Draw the shapes of NACA 0035 and NACA 4435 airfoils using the formulas of 4-digit NACA airfoils. The results should include the profile data of the upper and lower surfaces together with figures. 1g1 Hint: you can either use worksheet like excel or build a short program of MATLAB, C++, etc. to generate the profile data of the upper surface and the lower surface.]

Answer 1

- I have used Matlab to solve this problem and also pasted the Ouput below . If in case you don't have MATLAB you can use octave which is open source

%%%%%%%%%%%%%%%%%%%%%Section1-Initializing%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all;
clc;
cla;

%%%%%%%%%%%%%%%%%%%%%Section2-Getting Inputs%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

prompt='The type of airfoil';
typeNACA=input(prompt,'s');

prompt='The number of gridpoints(typically between 50 and 1000)';
grdPts=input(prompt);

Mo=str2double(typeNACA(1));
Po=str2double(typeNACA(2));
To=str2double(typeNACA(3:4));

%%%%%%%%%%%%%%%%%%%%%Section3-Constants%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

a0=0.2969;
a1=-0.1260;
a2=-0.3516;
a3=0.2843;
a4=-0.1015;

%%%%%%%%%%%%%%%%%%%%%Section4-Actual values and Calculation%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

M=Mo/100;
P=Po/10;
T=To/100;

x=linspace(0,1,grdPts)';

yc=ones(grdPts,1);
dyc_dx=ones(grdPts,1);
theta=ones(grdPts,1);

for i =1:1:grdPts
if (x(i)>=0 && x(i)<=P)
yc(i)=(M/P^2)*((2*P*x(i))-x(i)^2);
dyc_dx(i)=((2*M)/(P^2))*(P-x(i));
  
elseif (x(i)>=P && x(i)<=1)
yc(i)=(M/(1-P)^2)*(1-(2*P)+(2*P*x(i))-x(i)^2);
dyc_dx(i)=((2*M)/((1-P)^2))*(P-x(i));
end
theta(i)=atan(dyc_dx(i));
end

  
%%%%%%%%%%%%%%%%%%%%%Section5-Thickness Calculation%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

yt=5*T.*((a0.*sqrt(x)+(a1.*x)+(a2.*x.^2)+(a3.*x.^3)+(a4.*x.^4)));

%%%%%%%%%%%%%%%%%%%%%Section5-Upper limit Calculation%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xu= x(:)-yt(:).*sin(theta);
yu= yc(:)+yt(:).*cos(theta);

%%%%%%%%%%%%%%%%%%%%%Section6-Upper limit Calculation%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xl= x(:)+yt(:).*sin(theta);
yl= yc(:)-yt(:).*cos(theta);

%%%%%%%%%%%%%%%%%%%%%Section7-Plotting the diagram%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

f1=figure(1);
hold on; grid on;
axis equal;
plot(xu,yu,'r-');
plot(xl,yl,'k-');

%%%%%%%%%%%%%%%%%%%%%Section8-Displaying the values%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Y=['| Upper Limit |','| Lower Limit |'];
disp(Y);
X=['||||xupper|','|||yupper|','|||xlower|','|||ylower|'];
disp(X);
Z=[xu,yu,xl,yl];
disp(Z);

Plot for 4435

0.4 0.3 0.2 0.1 -0.1 -0.2 0.3 04 0.5 0.6 0.8 0.9 02 0.30.4 0.1 0.7

The type of airfoil4435
The number of gridpoints(typically between 50 and 1000)100

XUPPER	YUPPER	X LOWER	Y LOWER
0	0	0	0
0.0005	0.0510	0.0197	-0.0470
0.0073	0.0719	0.0331	-0.0640
0.0152	0.0877	0.0454	-0.0760
0.0237	0.1007	0.0571	-0.0854
0.0326	0.1120	0.0684	-0.0931
0.0418	0.1220	0.0794	-0.0996
0.0513	0.1310	0.0901	-0.1052
0.0609	0.1391	0.1007	-0.1100
0.0708	0.1465	0.1111	-0.1142
0.0807	0.1532	0.1213	-0.1179
0.0908	0.1594	0.1314	-0.1212
0.1011	0.1651	0.1414	-0.1240
0.1114	0.1704	0.1513	-0.1265
0.1218	0.1753	0.1611	-0.1287
0.1322	0.1797	0.1708	-0.1306
0.1428	0.1838	0.1805	-0.1322
0.1534	0.1876	0.1901	-0.1336
0.1640	0.1910	0.1996	-0.1348
0.1748	0.1942	0.2091	-0.1358
0.1855	0.1971	0.2185	-0.1367
0.1963	0.1997	0.2279	-0.1373
0.2071	0.2020	0.2373	-0.1378
0.2180	0.2041	0.2467	-0.1381
0.2289	0.2059	0.2560	-0.1384
0.2398	0.2076	0.2653	-0.1384
0.2507	0.2090	0.2746	-0.1384
0.2616	0.2101	0.2838	-0.1382
0.2726	0.2111	0.2931	-0.1380
0.2836	0.2119	0.3023	-0.1376
0.2946	0.2125	0.3115	-0.1372
0.3055	0.2129	0.3207	-0.1367
0.3165	0.2131	0.3299	-0.1360
0.3275	0.2131	0.3391	-0.1354
0.3385	0.2130	0.3483	-0.1346
0.3495	0.2127	0.3576	-0.1338
0.3605	0.2122	0.3668	-0.1329
0.3715	0.2116	0.3760	-0.1319
0.3825	0.2108	0.3852	-0.1310
0.3934	0.2099	0.3945	-0.1299
0.4042	0.2088	0.4039	-0.1288
0.4147	0.2076	0.4136	-0.1277
0.4251	0.2063	0.4233	-0.1264
0.4356	0.2049	0.4331	-0.1251
0.4461	0.2034	0.4428	-0.1238
0.4565	0.2017	0.4526	-0.1224
0.4670	0.2000	0.4623	-0.1210
0.4774	0.1982	0.4721	-0.1194
0.4878	0.1963	0.4819	-0.1179
0.4982	0.1943	0.4917	-0.1163
0.5086	0.1922	0.5015	-0.1147
0.5190	0.1900	0.5113	-0.1130
0.5294	0.1878	0.5211	-0.1112
0.5398	0.1854	0.5309	-0.1095
0.5502	0.1830	0.5408	-0.1077
0.5605	0.1805	0.5506	-0.1059
0.5708	0.1779	0.5605	-0.1040
0.5812	0.1752	0.5703	-0.1021
0.5915	0.1725	0.5802	-0.1002
0.6018	0.1697	0.5901	-0.0982
0.6121	0.1668	0.6000	-0.0962
0.6224	0.1638	0.6100	-0.0942
0.6326	0.1608	0.6199	-0.0922
0.6429	0.1577	0.6299	-0.0901
0.6531	0.1545	0.6398	-0.0880
0.6633	0.1513	0.6498	-0.0859
0.6735	0.1480	0.6598	-0.0838
0.6837	0.1446	0.6698	-0.0816
0.6939	0.1412	0.6798	-0.0795
0.7041	0.1377	0.6899	-0.0773
0.7142	0.1341	0.6999	-0.0751
0.7243	0.1305	0.7100	-0.0729
0.7345	0.1268	0.7201	-0.0706
0.7445	0.1231	0.7302	-0.0684
0.7546	0.1192	0.7403	-0.0661
0.7647	0.1154	0.7505	-0.0638
0.7747	0.1114	0.7606	-0.0615
0.7848	0.1074	0.7708	-0.0592
0.7948	0.1034	0.7810	-0.0568
0.8048	0.0993	0.7912	-0.0545
0.8148	0.0951	0.8014	-0.0521
0.8247	0.0908	0.8117	-0.0497
0.8347	0.0865	0.8219	-0.0473
0.8446	0.0822	0.8322	-0.0449
0.8545	0.0777	0.8425	-0.0424
0.8644	0.0732	0.8528	-0.0400
0.8742	0.0687	0.8632	-0.0375
0.8841	0.0641	0.8735	-0.0350
0.8939	0.0594	0.8839	-0.0325
0.9037	0.0547	0.8943	-0.0300
0.9135	0.0499	0.9047	-0.0275
0.9232	0.0450	0.9152	-0.0249
0.9330	0.0401	0.9256	-0.0223
0.9427	0.0351	0.9361	-0.0197
0.9524	0.0300	0.9466	-0.0171
0.9620	0.0249	0.9572	-0.0145
0.9717	0.0197	0.9677	-0.0118
0.9813	0.0144	0.9783	-0.0091
0.9909	0.0091	0.9889	-0.0064
1.0005	0.0036	0.9995	-0.0036
0035

0035

0.2 0.15 0.1 0.05 -0.05 0.1 0.15 -0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

The type of airfoil0035
The number of gridpoints(typically between 50 and 1000)100

X UPPER	Y UPPER	X LOWER	Y LOWER
0.0101	0.0499	0.0101	-0.0499
0.0202	0.0691	0.0202	-0.0691
0.0303	0.0832	0.0303	-0.0832
0.0404	0.0946	0.0404	-0.0946
0.0505	0.1041	0.0505	-0.1041
0.0606	0.1124	0.0606	-0.1124
0.0707	0.1197	0.0707	-0.1197
0.0808	0.1261	0.0808	-0.1261
0.0909	0.1319	0.0909	-0.1319
0.1010	0.1371	0.1010	-0.1371
0.1111	0.1418	0.1111	-0.1418
0.1212	0.1460	0.1212	-0.1460
0.1313	0.1498	0.1313	-0.1498
0.1414	0.1532	0.1414	-0.1532
0.1515	0.1563	0.1515	-0.1563
0.1616	0.1591	0.1616	-0.1591
0.1717	0.1617	0.1717	-0.1617
0.1818	0.1639	0.1818	-0.1639
0.1919	0.1659	0.1919	-0.1659
0.2020	0.1677	0.2020	-0.1677
0.2121	0.1692	0.2121	-0.1692
0.2222	0.1706	0.2222	-0.1706
0.2323	0.1717	0.2323	-0.1717
0.2424	0.1727	0.2424	-0.1727
0.2525	0.1735	0.2525	-0.1735
0.2626	0.1741	0.2626	-0.1741
0.2727	0.1745	0.2727	-0.1745
0.2828	0.1749	0.2828	-0.1749
0.2929	0.1750	0.2929	-0.1750
0.3030	0.1750	0.3030	-0.1750
0.3131	0.1749	0.3131	-0.1749
0.3232	0.1747	0.3232	-0.1747
0.3333	0.1743	0.3333	-0.1743
0.3434	0.1739	0.3434	-0.1739
0.3535	0.1733	0.3535	-0.1733
0.3636	0.1726	0.3636	-0.1726
0.3737	0.1718	0.3737	-0.1718
0.3838	0.1709	0.3838	-0.1709
0.3939	0.1699	0.3939	-0.1699
0.4040	0.1688	0.4040	-0.1688
0.4141	0.1676	0.4141	-0.1676
0.4242	0.1664	0.4242	-0.1664
0.4343	0.1650	0.4343	-0.1650
0.4444	0.1636	0.4444	-0.1636
0.4545	0.1621	0.4545	-0.1621
0.4646	0.1605	0.4646	-0.1605
0.4747	0.1588	0.4747	-0.1588
0.4848	0.1571	0.4848	-0.1571
0.4949	0.1553	0.4949	-0.1553
0.5051	0.1535	0.5051	-0.1535
0.5152	0.1515	0.5152	-0.1515
0.5253	0.1496	0.5253	-0.1496
0.5354	0.1475	0.5354	-0.1475
0.5455	0.1454	0.5455	-0.1454
0.5556	0.1432	0.5556	-0.1432
0.5657	0.1410	0.5657	-0.1410
0.5758	0.1388	0.5758	-0.1388
0.5859	0.1364	0.5859	-0.1364
0.5960	0.1341	0.5960	-0.1341
0.6061	0.1316	0.6061	-0.1316
0.6162	0.1292	0.6162	-0.1292
0.6263	0.1266	0.6263	-0.1266
0.6364	0.1241	0.6364	-0.1241
0.6465	0.1215	0.6465	-0.1215
0.6566	0.1188	0.6566	-0.1188
0.6667	0.1161	0.6667	-0.1161
0.6768	0.1133	0.6768	-0.1133
0.6869	0.1106	0.6869	-0.1106
0.6970	0.1077	0.6970	-0.1077
0.7071	0.1048	0.7071	-0.1048
0.7172	0.1019	0.7172	-0.1019
0.7273	0.0990	0.7273	-0.0990
0.7374	0.0960	0.7374	-0.0960
0.7475	0.0929	0.7475	-0.0929
0.7576	0.0899	0.7576	-0.0899
0.7677	0.0867	0.7677	-0.0867
0.7778	0.0836	0.7778	-0.0836
0.7879	0.0804	0.7879	-0.0804
0.7980	0.0772	0.7980	-0.0772
0.8081	0.0739	0.8081	-0.0739
0.8182	0.0706	0.8182	-0.0706
0.8283	0.0672	0.8283	-0.0672
0.8384	0.0638	0.8384	-0.0638
0.8485	0.0604	0.8485	-0.0604
0.8586	0.0569	0.8586	-0.0569
0.8687	0.0534	0.8687	-0.0534
0.8788	0.0498	0.8788	-0.0498
0.8889	0.0462	0.8889	-0.0462
0.8990	0.0426	0.8990	-0.0426
0.9091	0.0389	0.9091	-0.0389
0.9192	0.0352	0.9192	-0.0352
0.9293	0.0314	0.9293	-0.0314
0.9394	0.0276	0.9394	-0.0276
0.9495	0.0237	0.9495	-0.0237
0.9596	0.0198	0.9596	-0.0198
0.9697	0.0158	0.9697	-0.0158
0.9798	0.0118	0.9798	-0.0118
0.9899	0.0078	0.9899	-0.0078
1.0000	0.0037	1.0000	-0.0037