AQM-91A wing and tail profiles



I've been studying the AQM-91 for a long time. The A&V scale model has wings with a strange profile, and I've long considered making new wing parts, preferably with 3D CAD and 3D printing. However I could not find information on the profiles used. Therefore I was happy to finally find a drawing that showed the wing and tail surfaces geometry, and the NACA profiles used. They are NACA 64A310 (mod), 64A306 (mod) and 64A007 (mod). For future 3D CAD work, I wanted to establish the profile coordinates. That turned out to be quite a bit of work and research, but I think the results are good.


Results

To start with the results: here are plots of the three profiles. The derivation and resulting coordinates are shown below.








NACA 6-series design method

The NACA 6-series airfoils were developed by means of conformal transformations, as described in NASA TM-4741 - Computer program to obtain ordinates for NACA airfoils and others references. I decided not to pursue this scientific way, but to use practical engineering approach instead, since this was more than adequate for the purpose. The webpage Thickness Function for NACA 6-Series Airfoils offers yet another method, but I did not use it.



NACA 64A thickness distributions

The coordinates for the (symmetrical) 64A006, 64A008 and 64A010 are taken from Abbott & Von Doenhoff, pages 354 to 356. Note that the footer on page 356 is not correct: it says 'NACA 643-018 Basic Thickness Distribution' but it is NACA 64A010. The NACA 6A-series airfoils have basically straight upper and lower lines aft of 80% chord, mostly for manufacturing reasons.

I checked whether the thickness distributions are simply scaled up, but the thickness ratios shows that there are small differences. The ratios also showed a peculiar ratio for 7.5 percent chord. A check in TN-1368 showed that the number 2.905 should be 2.805. The 64A007 data is linearly interpolated from 64A006 and 64A008, and thus the first result is found.

        64A006                 64A007        
      interpolated      
        64A008                 64A010                 ratio 006 vs 010                 ratio 008 vs 010        
0 0 0 0 0 - -
0.5 0.485 0.566 0.646 0.804 0.603 0.803
0.75 0.585 0.682 0.778 0.969 0.604 0.803
1.25 0.739 0.861 0.983 1.225 0.603 0.802
2.5 1.016 1.185 1.353 1.688 0.602 0.802
5 1.399 1.631 1.863 2.327 0.601 0.801
7.5 1.684 1.965 2.245 2.905 (2.805) 0.580 0.773
10 1.919 2.239 2.559 3.199 0.600 0.800
15 2.283 2.665 3.047 3.813 0.599 0.799
20 2.557 2.986 3.414 4.272 0.599 0.799
25 2.757 3.219 3.681 4.606 0.599 0.799
30 2.896 3.381 3.866 4.837 0.599 0.799
35 2.977 3.475 3.972 4.968 0.599 0.800
40 2.999 3.499 3.998 4.995 0.600 0.800
45 2.945 3.433 3.921 4.894 0.602 0.801
50 2.825 3.291 3.757 4.684 0.603 0.802
55 2.653 3.089 3.524 4.388 0.605 0.803
60 2.438 2.836 3.234 4.021 0.606 0.804
65 2.188 2.543 2.897 3.597 0.608 0.805
70 1.907 2.214 2.521 3.127 0.610 0.806
75 1.602 1.860 2.117 2.623 0.611 0.807
80 1.285 1.492 1.698 2.103 0.611 0.807
85 0.967 1.123 1.278 1.582 0.611 0.808
90 0.649 0.754 0.858 1.062 0.611 0.808
95 0.331 0.385 0.438 0.541 0.612 0.810
100 0.013 0.016 0.018 0.021 - -
LE radius 0.246 0.343 0.439 0.687 0.358 0.639


The NACA 64A camber line

I was puzzled by the question what camber line was used for the 64A family. Abbott & Von Doenhoff page 121 says: "When the mean-line designation is not given, it is understood that the uniform-load mean line (a=1.0) has been used". But the coordinates that I calculated with a = 1.0 did not match the NACA 64A210 and 64A410 data listed on pages 430 and 431. I then found the following in NACA TN-1368, page 2: 'A special mean line, designated the a = 0.8 (modified) mean line, has also been designed to maintain straight sides on the cambered sections". This indeed gave me matching coordinate data. One question remains for me: the a = 0.8 (modified) mean line is not perfectly straight for the last 20% chord, which is the whole idea behind the 6A series. The data below for the a = 0.8, a = 0.8 (modified) and a = 1.0 camber lines is taken from Abbott & Von Doenhoff, pages p402, 403 and 405. They represent the camber line for a design CL = 1, and are to be scaled according to the actual design CL.

                         a=0.8                 a=0.8 mod                 a=1.0        
                         yc                 dy/dx                 yc                 dy/dx                 yc                 dy/dx        
0 0 0 0 0
0.5 0.287 0.48535 0.281 0.47539 0.250 0.42120
0.75 0.404 0.44925 0.396 0.44004 0.350 0.38875
1.25 0.616 0.40359 0.603 0.39531 0.535 0.34770
2.5 1.077 0.34104 1.055 0.33404 0.930 0.29155
5 1.841 0.27718 1.803 0.27149 1.580 0.23430
7.5 2.483 0.23868 2.432 0.23378 2.120 0.19995
10 3.043 0.2105 2.981 0.20618 2.585 0.17485
15 3.985 0.16892 3.903 0.16546 3.365 0.13805
20 4.748 0.13734 4.651 0.13452 3.980 0.11030
25 5.367 0.11101 5.257 0.10873 4.475 0.08745
30 5.863 0.08775 5.742 0.08595 4.860 0.06745
35 6.248 0.06634 6.120 0.06498 5.150 0.04925
40 6.528 0.04601 6.394 0.04507 5.355 0.03225
45 6.709 0.02613 6.571 0.02559 5.475 0.01595
50 6.790 0.00620 6.651 0.00607 5.515 0
55 6.770 -0.01433 6.631 -0.01404 5.475 -0.01595
60 6.644 -0.03611 6.508 -0.03537 5.355 -0.03225
65 6.405 -0.06010 6.274 -0.05887 5.150 -0.04925
70 6.037 -0.0879 5.913 -0.0861 4.860 -0.06745
75 5.514 -0.12311 5.401 -0.12058 4.475 -0.08745
80 4.771 -0.18412 4.673 -0.18034 3.980 -0.11030
85 3.683 -0.23921 3.607 -0.23430 3.365 -0.13805
90 2.435 -0.25583 2.452 -0.24521 2.585 -0.17485
95 1.163 -0.24904 1.226 -0.24521 1.58 -0.23430
100 0 -0.20385 0 -0.24521 0


NACA 64A410 check calculation

To check the method, the NACA 64A410 profile coordinates were calculated using the NACA 64A010 thickness distribution, combined with the a = 0.8 (modified) camber line scaled down to 40%, using the equations on page 113 of Abbott & Von Doenhoff. The small differences with the NACA 64A410 coordinates (listed on page 431 of Abbott & Von Doenhoff) are most likely rounding errors, slide rule vs computer. The large differences for 7.5% chord are again the result of the 2.805 vs 2.905 error, as reported above.

64A010     a=0.8 mod     a=0.8 mod (40%)     64A410 calculated     64A410 A & vD p431     deltas
x y y dy/dx y dy/dx x upper y upper x lower y lower x upper y upper x lower y lower
   0         0                0                            0.000     0.000     0.000     0.000     0.000     0.000     0.000     0.000     0.000     0.000     0.000     0.000     0.000     0.000  
0.5 0.804 0.281 0.47539 0.112 0.190 0.350 0.902 0.650 -0.677 0.350 0.902 0.650 -0.678 0.000 0.000 0.000 0.001
0.75 0.969 0.396 0.44004 0.158 0.176 0.582 1.113 0.918 -0.796 0.582 1.112 0.918 -0.796 0.000 0.001 0.000 0.000
1.25 1.225 0.603 0.39531 0.241 0.158 1.059 1.451 1.441 -0.969 1.059 1.451 1.441 -0.969 0.000 0.000 0.000 0.000
2.5 1.688 1.055 0.33404 0.422 0.134 2.276 2.095 2.724 -1.251 2.276 2.095 2.724 -1.251 0.000 0.000 0.000 0.000
5 2.327 1.803 0.27149 0.721 0.109 4.749 3.035 5.251 -1.592 4.749 3.034 5.251 -1.592 0.000 0.001 0.000 0.000
7.5 2.805 2.432 0.23378 0.973 0.094 7.239 3.766 7.761 -1.820 7.230 3.865 7.770 -1.919 0.009 -0.099 -0.009 0.099
10 3.199 2.981 0.20618 1.192 0.082 9.737 4.381 10.263 -1.996 9.737 4.380 10.263 -1.996 0.000 0.001 0.000 0.000
15 3.813 3.903 0.16546 1.561 0.066 14.748 5.366 15.252 -2.243 14.748 5.366 15.252 -2.244 0.000 0.000 0.000 0.001
20 4.272 4.651 0.13452 1.860 0.054 19.770 6.126 20.230 -2.405 19.770 6.126 20.230 -2.406 0.000 0.000 0.000 0.001
25 4.606 5.257 0.10873 2.103 0.043 24.800 6.704 25.200 -2.499 24.800 6.705 25.200 -2.499 0.000 -0.001 0.000 0.000
30 4.837 5.742 0.08595 2.297 0.034 29.834 7.131 30.166 -2.537 29.834 7.131 30.166 -2.537 0.000 0.000 0.000 0.000
35 4.968 6.12 0.06498 2.448 0.026 34.871 7.414 35.129 -2.518 34.871 7.414 35.129 -2.518 0.000 0.000 0.000 0.000
40 4.995 6.394 0.04507 2.558 0.018 39.910 7.552 40.090 -2.437 39.910 7.552 40.090 -2.436 0.000 0.000 0.000 -0.001
45 4.894 6.571 0.02559 2.628 0.010 44.950 7.522 45.050 -2.265 44.950 7.522 45.050 -2.266 0.000 0.000 0.000 0.001
50 4.684 6.651 0.00607 2.660 0.002 49.989 7.344 50.011 -2.024 49.989 7.344 50.011 -2.024 0.000 0.000 0.000 0.000
55 4.388 6.631 -0.01404 2.652 -0.006 55.025 7.040 54.975 -1.736 55.025 7.040 54.975 -1.736 0.000 0.000 0.000 0.000
60 4.021 6.508 -0.03537 2.603 -0.014 60.057 6.624 59.943 -1.417 60.057 6.624 59.943 -1.418 0.000 0.000 0.000 0.001
65 3.597 6.274 -0.05887 2.510 -0.024 65.085 6.106 64.915 -1.086 65.085 6.106 64.915 -1.086 0.000 0.000 0.000 0.000
70 3.127 5.913 -0.0861 2.365 -0.034 70.108 5.490 69.892 -0.760 70.108 5.490 69.892 -0.760 0.000 0.000 0.000 0.000
75 2.623 5.401 -0.12058 2.160 -0.048 75.126 4.780 74.874 -0.460 75.126 4.780 74.874 -0.460 0.000 0.000 0.000 0.000
80 2.103 4.673 -0.18034 1.869 -0.072 80.151 3.967 79.849 -0.228 80.151 3.967 79.849 -0.229 0.000 0.000 0.000 0.001
85 1.582 3.607 -0.2343 1.443 -0.094 85.148 3.018 84.852 -0.132 85.148 3.018 84.852 -0.132 0.000 0.000 0.000 0.000
90 1.062 2.452 -0.24521 0.981 -0.098 90.104 2.038 89.896 -0.076 90.104 2.038 89.896 -0.076 0.000 0.000 0.000 0.000
95 0.541 1.226 -0.24521 0.490 -0.098 95.053 1.029 94.947 -0.048 95.053 1.028 94.947 -0.048 0.000 0.001 0.000 0.000
100 0.021 0 -0.24521 0.000 -0.098 100.002 0.021 99.998 -0.021 100.000 0.021 100.000 -0.021 0.002 0.000 -0.002 0.000


NACA 64A306 calculation

Now the method has been verified, NACA 64A306 profile coordinates were calculated using the NACA 64A006 thickness distribution, combined with the a = 0.8 (modified) camber line scaled down to 30%.

64A006     a=0.8 mod     a=0.8 mod (30%)     64A306 calculated
x y y dy/dx y dy/dx x upper y upper x lower y lower
   0         0                0                            0.000     0.000     0.000     0.000     0.000     0.000  
0.5 0.485 0.281 0.47539 0.084 0.143 0.432 0.564 0.568 -0.396
0.75 0.585 0.396 0.44004 0.119 0.132 0.673 0.699 0.827 -0.461
1.25 0.739 0.603 0.39531 0.181 0.119 1.163 0.915 1.337 -0.553
2.5 1.016 1.055 0.33404 0.317 0.100 2.399 1.327 2.601 -0.694
5 1.399 1.803 0.27149 0.541 0.081 4.886 1.935 5.114 -0.853
7.5 1.684 2.432 0.23378 0.730 0.070 7.382 2.409 7.618 -0.950
10 1.919 2.981 0.20618 0.894 0.062 9.882 2.810 10.118 -1.021
15 2.283 3.903 0.16546 1.171 0.050 14.887 3.451 15.113 -1.109
20 2.557 4.651 0.13452 1.395 0.040 19.897 3.950 20.103 -1.160
25 2.757 5.257 0.10873 1.577 0.033 24.910 4.333 25.090 -1.178
30 2.896 5.742 0.08595 1.723 0.026 29.925 4.618 30.075 -1.172
35 2.977 6.12 0.06498 1.836 0.019 34.942 4.812 35.058 -1.140
40 2.999 6.394 0.04507 1.918 0.014 39.959 4.917 40.041 -1.081
45 2.945 6.571 0.02559 1.971 0.008 44.977 4.916 45.023 -0.974
50 2.825 6.651 0.00607 1.995 0.002 49.995 4.820 50.005 -0.830
55 2.653 6.631 -0.01404 1.989 -0.004 55.011 4.642 54.989 -0.664
60 2.438 6.508 -0.03537 1.952 -0.011 60.026 4.390 59.974 -0.485
65 2.188 6.274 -0.05887 1.882 -0.018 65.039 4.070 64.961 -0.305
70 1.907 5.913 -0.0861 1.774 -0.026 70.049 3.680 69.951 -0.132
75 1.602 5.401 -0.12058 1.620 -0.036 75.058 3.221 74.942 0.019
80 1.285 4.673 -0.18034 1.402 -0.054 80.069 2.685 79.931 0.119
85 0.967 3.607 -0.2343 1.082 -0.070 85.068 2.047 84.932 0.117
90 0.649 2.452 -0.24521 0.736 -0.074 90.048 1.383 89.952 0.088
95 0.331 1.226 -0.24521 0.368 -0.074 95.024 0.698 94.976 0.038
100 0.013 0 -0.24521 0.000 -0.074 100.001 0.013 99.999 -0.013


NACA 64A310 calculation

NACA 64A310 profile coordinates were calculated using the NACA 64A010 thickness distribution, combined with the a = 0.8 (modified) camber line scaled down to 30%.

64A010     a=0.8 mod     a=0.8 mod (30%)     64A310 calculated
x y y dy/dx y dy/dx x upper y upper x lower y lower
   0         0                0                            0.000     0.000     0.000     0.000     0.000     0.000  
0.5 0.804 0.281 0.47539 0.084 0.143 0.386 0.880 0.614 -0.712
0.75 0.969 0.396 0.44004 0.119 0.132 0.623 1.079 0.877 -0.842
1.25 1.225 0.603 0.39531 0.181 0.119 1.106 1.397 1.394 -1.036
2.5 1.688 1.055 0.33404 0.317 0.100 2.332 1.996 2.668 -1.363
5 2.327 1.803 0.27149 0.541 0.081 4.811 2.860 5.189 -1.778
7.5 2.805 2.432 0.23378 0.730 0.070 7.304 3.528 7.696 -2.069
10 3.199 2.981 0.20618 0.894 0.062 9.803 4.087 10.197 -2.299
15 3.813 3.903 0.16546 1.171 0.050 14.811 4.979 15.189 -2.637
20 4.272 4.651 0.13452 1.395 0.040 19.828 5.664 20.172 -2.873
25 4.606 5.257 0.10873 1.577 0.033 24.850 6.181 25.150 -3.026
30 4.837 5.742 0.08595 1.723 0.026 29.875 6.558 30.125 -3.113
35 4.968 6.12 0.06498 1.836 0.019 34.903 6.803 35.097 -3.131
40 4.995 6.394 0.04507 1.918 0.014 39.932 6.913 40.068 -3.076
45 4.894 6.571 0.02559 1.971 0.008 44.962 6.865 45.038 -2.923
50 4.684 6.651 0.00607 1.995 0.002 49.991 6.679 50.009 -2.689
55 4.388 6.631 -0.01404 1.989 -0.004 55.018 6.377 54.982 -2.399
60 4.021 6.508 -0.03537 1.952 -0.011 60.043 5.973 59.957 -2.068
65 3.597 6.274 -0.05887 1.882 -0.018 65.064 5.479 64.936 -1.714
70 3.127 5.913 -0.0861 1.774 -0.026 70.081 4.900 69.919 -1.352
75 2.623 5.401 -0.12058 1.620 -0.036 75.095 4.242 74.905 -1.001
80 2.103 4.673 -0.18034 1.402 -0.054 80.114 3.502 79.886 -0.698
85 1.582 3.607 -0.2343 1.082 -0.070 85.111 2.660 84.889 -0.496
90 1.062 2.452 -0.24521 0.736 -0.074 90.078 1.795 89.922 -0.324
95 0.541 1.226 -0.24521 0.368 -0.074 95.040 0.907 94.960 -0.172
100 0.021 0 -0.24521 0.000 -0.074 100.002 0.021 99.998 -0.021




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