Corvair Test Results

Analysis of Loads on the Pietenpol Air Camper Wing Attach Fittings

Since I have modified the wing attach fittings on my Pietenpol Air Camper I became concerned about the forces acting on those fittings. Specifically, I wanted to know what forces were acting on the fittings at the cabane struts since I have modified these fittings for the folding wing, and at the lift strut fittings since I am using a “V” strut configuration instead of the parallel configuration on the plans. To do this you first need to determine the lift distribution spanwise along the wing. Many aerodynamics texts will tell you that the lift distribution along a rectangular planform wing like that of the Air Camper takes the form of an ellipse. This is because of the loss of lift at the wing tips. What I could not find however was what proportions to use for the ellipse. An ellipse can vary in shape from a near circle to a near line. I reasoned that the proportions of the ellipse should follow the aspect ratio of the wing. This logic agrees with what we know, that high aspect ratio wings, like in sailplanes, are more efficient than lower aspect ratio wings, like in the Air Camper. So, we can now determine the lift distribution of the Air Camper as a 5 by 29 ellipse. If my calculus skills were better I could probably use an equation to determine the actual lift values along the wing, but it’s been too many years, so I had to resort to the spreadsheet at the end of this paper. The formula for a 5 by 29 ellipse is shown below.

With the lift distribution now known, the next thing to figure out is how do these forces affect the fittings? There are probably other ways to get the answer, but for me the easiest is to look at the effects of torque. Let’s look at some examples of how this works. In the first example we have two points, A and B, 10 feet apart, with a weightless (theoretical) board lying across them. We put a 50 lb weight directly over point B.

Now it may seem a bit obvious that point B has 50 lbs and point A has 0, but let’s see how we can show it using torque. Using point A as a pivot point we get a 50 lb weight on a 10 foot arm giving a torque of 500 ft lbs (10 ft x 50 lbs). Working backwards from what we just did we take 500 ft lbs divided by 10 feet to show that there is a force of 50 lbs at point B. Not too useful in this example, but it shows the concept. Conversely, if we take point B as the pivot point we see that there is 0 lbs weight at point A, 10 feet away. Therefore the torque is 0 and there is no force at point A. Let’s look at another configuration. We will use the same setup as in the previous example, but this time we will reposition the 50 lb weight to the center of the board, 5 feet from each end point.

This again may seem obvious that each point, A and B, will feel a 25 lb force, but let’s use the torque calculations once again. Using either point as the pivot point you get 50 lbs at a distance of 5 feet for 250 ft lbs of torque. 250 ft lbs pushing on the opposite point, 10 feet away gives a force of 25 lbs. Very simple so far, but now let’s add another weight and cantilever the board like on a wing spar.

Looking at the torque about point A you get 100 lbs at 0 feet away for 0 torque, plus 50 lbs 20 feet away for 1000 ft lbs and a total of 1000 ft lbs. 1000 ft lbs pushing down on point B, 10 feet away, puts 100 lbs force at point B. Using point B as the pivot point we get 100 lbs at 10 feet for 1000 ft lbs, minus 50 lbs at 10 feet in the other direction for 500 ft lbs resulting in a torque of 500 ft lbs. This torque of 500 ft lbs pushing down on point A 10 feet away gives a force of 50 lbs at point A. Cool!

Now let’s apply this same technique to the Air Camper wing. Using the cabane fitting as the pivot point we can calculate the total torque as the sum of each individual torque value along the wing. The spreadsheet at the end of this paper shows the lift at each inch along the wing as a percentage of the total lift. It also calculates the torque at each inch by multiplying the lift times the distance from the pivot. Summing these numbers all the way to the wing tip gives 51.74 inch lbs. Applying this torque to the lift strut fitting at a distance of 72 inches gives a force of 0.719 lbs. Using the lift strut as the pivot point we calculate the individual torque values in both directions from this point, (as we did fir point B above) and then sum them to get the total torque of 7.69 inch lbs. Applying this to the cabane strut fitting 72 inches away we get 0.107 lbs force at the cabane. To get the total force on the cabane we must add the sum of lift on the center section which is 0.174 giving a total cabane force of 0.281 lbs. But we’re not quite done. The force of torque is perpendicular to a radial line from the pivot point, or in this case perpendicular to the spar. But, the lift strut is not perpendicular to the spar. It angles back to the fuselage and this angle causes more force on the lift strut. To get the force on the lift strut we must determine the distance of a line that is perpendicular to the lift strut and goes through the cabane fitting. In the case of my Air Camper modification that distance is 36 inches, or half of the distance from the pivot point to the wing strut fitting. Therefore the force on the wing strut fitting is doubled from 0.719 to 1.437 lbs. We almost have it now. We just need to determine how much the lift distribution varies from the front to the rear spar cordwise. On the Air Camper wing both spars are located fairly well far forward. The center if lift on an airfoil is also located somewhat forward. Therefore, to simplify the calculations I will assume that the spars share the equally share the lift loads. So, we divide the force on the cabane fittings in two, with half for the front cabane fitting and half for the rear. We do the same for the lift strut fittings that attach the lift struts to the wing. But, because my modification uses a “V” strut we must use the full lift strut force for the lower end of the struts. The table below shows the forces for the three fittings as percentages of total lift, and for an 1100 lb aircraft at 1, 2, and 3 Gs. I also calculated the forces on the fittings of a plans built Air Camper, and for my Kolb MKII.

Loads on Fittings for 1100 lb Aircraft, Folding Wing

G Load	Cabane Fitting	Lift Strut Fitting at Wing	Lift Strut Fitting at Fuselage
%	0.141	0.719	1.437
1	77	395	791
2	155	791	1581
3	232	1186	2372

Loads on Fittings for 1100 lb Aircraft, Original Wing

G Load	Cabane Fitting	Lift Strut Fitting at Wing	Lift Strut Fitting at Fuselage
%	0.130	0.734	0.734
1	72	404	404
2	143	807	807
3	215	1211	1211

Loads on Fittings for 800 lb Kolb MKII

G Load	Fuselage Fitting	Lift Strut Fitting at Wing	Lift Strut Fitting at Fuselage
%	0.196	2.02	0.734
1	78	808	808
2	157	1616	1616
3	235	2424	2424

So what have I learned? Well, I see that my four foot center section puts more load on the cabane struts and less on the lift struts than the plans built two foot center section would. No surprise. I see that the highest stress point is where the lift struts attach to the fuselage. I had already known this, and I had doubled the fuselage cross strap at the attach point from 1 x 1/16 to 1 x 1/8. The pivoting fitting that I am using at the fuselage attach point is rated for 3200 lbs, or 4 Gs. Perhaps the thing that surprised me the most was the amount of force on the light weight fittings on my Kolb. If the Kolb fittings can handle the loads, then I am very confident I the fittings on the Air Camper.

Air Camper Wing Lift Distribution and Torque Values

station	lift	%	Lift Strut	Cabane
0	30	0.007292
1	29.9995	0.007292
2	29.99802	0.007291
3	29.99554	0.007291
4	29.99207	0.00729
5	29.98761	0.007289
6	29.98216	0.007288
7	29.97571	0.007286
8	29.96827	0.007284
9	29.95984	0.007282
10	29.95041	0.00728
11	29.93999	0.007277
12	29.92857	0.007275
13	29.91615	0.007272
14	29.90274	0.007268
15	29.88832	0.007265
16	29.8729	0.007261
17	29.85647	0.007257
18	29.83905	0.007253
19	29.82061	0.007248
20	29.80116	0.007244
21	29.78071	0.007239
22	29.75924	0.007233
23	29.73676	0.007228
24	29.71326	0.007222	0	0.520004
25	29.68873	0.007216	0.007216	0.512359
26	29.66319	0.00721	0.01442	0.504708
27	29.63662	0.007204	0.021611	0.497052
28	29.60903	0.007197	0.028788	0.489392
29	29.5804	0.00719	0.03595	0.481729
30	29.55074	0.007183	0.043097	0.474063
31	29.52004	0.007175	0.050227	0.466396
32	29.4883	0.007168	0.057341	0.458727
33	29.45552	0.00716	0.064437	0.451057
34	29.4217	0.007151	0.071514	0.443388
35	29.38682	0.007143	0.078572	0.435719
36	29.35088	0.007134	0.08561	0.428052
37	29.31389	0.007125	0.092628	0.420387
38	29.27584	0.007116	0.099623	0.412726
39	29.23672	0.007106	0.106597	0.405068
40	29.19653	0.007097	0.113547	0.397414
41	29.15527	0.007087	0.120473	0.389766
42	29.11293	0.007076	0.127374	0.382123
43	29.0695	0.007066	0.13425	0.374488
44	29.02498	0.007055	0.1411	0.366859
45	28.97937	0.007044	0.147922	0.359239
46	28.93266	0.007033	0.154716	0.351627
47	28.88484	0.007021	0.161481	0.344025
48	28.83592	0.007009	0.168217	0.336433
49	28.78588	0.006997	0.174922	0.328853
50	28.73471	0.006984	0.181595	0.321284
51	28.68242	0.006972	0.188236	0.313727
52	28.629	0.006959	0.194845	0.306184
53	28.57443	0.006945	0.201419	0.298655
54	28.51872	0.006932	0.207958	0.291141
55	28.46186	0.006918	0.214461	0.283642
56	28.40383	0.006904	0.220928	0.27616
57	28.34464	0.00689	0.227357	0.268695
58	28.28427	0.006875	0.233748	0.261248
59	28.22272	0.00686	0.240099	0.253819
60	28.15998	0.006845	0.24641	0.24641
61	28.09604	0.006829	0.25268	0.239022
62	28.0309	0.006813	0.258908	0.231654
63	27.96454	0.006797	0.265092	0.224308
64	27.89696	0.006781	0.271232	0.216986
65	27.82814	0.006764	0.277327	0.209686
66	27.75809	0.006747	0.283376	0.202411
67	27.68678	0.00673	0.289378	0.195162
68	27.61421	0.006712	0.295331	0.187938
69	27.54037	0.006694	0.301236	0.180741
70	27.46525	0.006676	0.30709	0.173573
71	27.38884	0.006657	0.312893	0.166432
72	27.31113	0.006638	0.318643	0.159322
73	27.2321	0.006619	0.324341	0.152242
74	27.15175	0.0066	0.329983	0.145193
75	27.07006	0.00658	0.33557	0.138176
76	26.98703	0.00656	0.341101	0.131193
77	26.90263	0.006539	0.346573	0.124243
78	26.81686	0.006518	0.351986	0.117329
79	26.7297	0.006497	0.357339	0.11045
80	26.64114	0.006476	0.362631	0.103609
81	26.55116	0.006454	0.36786	0.096805
82	26.45976	0.006431	0.373025	0.090041
83	26.36691	0.006409	0.378125	0.083316
84	26.2726	0.006386	0.383159	0.076632
85	26.17682	0.006363	0.388124	0.06999
86	26.07955	0.006339	0.393021	0.06339
87	25.98076	0.006315	0.397847	0.056835
88	25.88045	0.006291	0.402602	0.050325
89	25.7786	0.006266	0.407283	0.043861
90	25.67519	0.006241	0.41189	0.037445
91	25.57019	0.006215	0.416421	0.031076
92	25.4636	0.006189	0.420875	0.024757
93	25.35538	0.006163	0.425249	0.018489
94	25.24552	0.006136	0.429543	0.012273
95	25.134	0.006109	0.433755	0.006109
96	25.0208	0.006082	0.437883	0
97	24.90589	0.006054	0.441925	-0.00605
98	24.78924	0.006025	0.445881	-0.01205
99	24.67084	0.005997	0.449748	-0.01799
100	24.55066	0.005967	0.453525	-0.02387
101	24.42867	0.005938	0.457209	-0.02969
102	24.30484	0.005908	0.460799	-0.03545
103	24.17915	0.005877	0.464293	-0.04114
104	24.05157	0.005846	0.467689	-0.04677
105	23.92206	0.005815	0.470986	-0.05233
106	23.7906	0.005783	0.47418	-0.05783
107	23.65716	0.00575	0.477271	-0.06325
108	23.52169	0.005717	0.480255	-0.06861
109	23.38417	0.005684	0.483131	-0.07389
110	23.24455	0.00565	0.485896	-0.0791
111	23.1028	0.005616	0.488549	-0.08423
112	22.95889	0.005581	0.491086	-0.08929
113	22.81276	0.005545	0.493505	-0.09427
114	22.66438	0.005509	0.495805	-0.09916
115	22.5137	0.005472	0.497981	-0.10397
116	22.36068	0.005435	0.500031	-0.1087
117	22.20526	0.005397	0.501953	-0.11334
118	22.0474	0.005359	0.503743	-0.1179
119	21.88705	0.00532	0.5054	-0.12236
120	21.72414	0.00528	0.506918	-0.12673
121	21.55862	0.00524	0.508296	-0.131
122	21.39043	0.005199	0.50953	-0.13518
123	21.21951	0.005158	0.510616	-0.13926
124	21.04579	0.005116	0.511551	-0.14323
125	20.86919	0.005073	0.512332	-0.14711
126	20.68966	0.005029	0.512953	-0.15087
127	20.5071	0.004985	0.513411	-0.15452
128	20.32144	0.004939	0.513703	-0.15806
129	20.13259	0.004894	0.513822	-0.16149
130	19.94046	0.004847	0.513766	-0.16479
131	19.74496	0.004799	0.513528	-0.16798
132	19.54598	0.004751	0.513104	-0.17103
133	19.34341	0.004702	0.512488	-0.17396
134	19.13715	0.004652	0.511675	-0.17676
135	18.92708	0.004601	0.510659	-0.17942
136	18.71305	0.004549	0.509433	-0.18194
137	18.49495	0.004495	0.507991	-0.18432
138	18.27261	0.004441	0.506325	-0.18654
139	18.04589	0.004386	0.504429	-0.18861
140	17.81461	0.00433	0.502294	-0.19053
141	17.5786	0.004273	0.499913	-0.19227
142	17.33766	0.004214	0.497275	-0.19385
143	17.09159	0.004154	0.494372	-0.19526
144	16.84016	0.004093	0.491192	-0.19648
145	16.58312	0.004031	0.487726	-0.19751
146	16.32022	0.003967	0.483961	-0.19834
147	16.05116	0.003901	0.479883	-0.19898
148	15.77563	0.003835	0.47548	-0.19939
149	15.49328	0.003766	0.470736	-0.19959
150	15.20373	0.003696	0.465634	-0.19956
151	14.90657	0.003623	0.460156	-0.19928
152	14.60132	0.003549	0.454283	-0.19875
153	14.28748	0.003473	0.447991	-0.19795
154	13.96445	0.003394	0.441257	-0.19687
155	13.6316	0.003313	0.434052	-0.19549
156	13.28817	0.00323	0.426347	-0.19379
157	12.93333	0.003144	0.418106	-0.19176
158	12.56612	0.003054	0.409289	-0.18937
159	12.1854	0.002962	0.39985	-0.1866
160	11.78988	0.002866	0.389738	-0.18341
161	11.378	0.002766	0.378888	-0.17976
162	10.94794	0.002661	0.367228	-0.17563
163	10.49744	0.002552	0.354668	-0.17096
164	10.02375	0.002436	0.341101	-0.16568
165	9.523424	0.002315	0.32639	-0.15972
166	8.992003	0.002186	0.310362	-0.153
167	8.423609	0.002047	0.292791	-0.14537
168	7.810174	0.001898	0.273368	-0.13668
169	7.140096	0.001736	0.25165	-0.12669
170	6.395599	0.001555	0.226965	-0.11504
171	5.546796	0.001348	0.198191	-0.10112
172	4.535499	0.001102	0.163159	-0.08378
173	3.211713	0.000781	0.116318	-0.06011
174	0	0	0