Preliminary Wing Design

If we use the formula for stalling speed as a base we can easily calculate a ... to 19.8 on the "C" scale we will read 47 directly below on the "D" scale. This is our ...
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Preliminary Wing Design By W. Rowland Murray, EAA 8341 1732 So. Carmelina Ave., Los Angeles 25, Calif.

OF THE first things to be done in designing an O NEairplane is the determination of the area of the wing

which is dictated by the desired landing speed — to all practical purposes the stalling speed. We must start with the gross weight of our proposed airplane and perhaps the best way to estimate this is to multiply the horsepower of our engine by a reasonable number of pounds for each horsepower. By checking the power loading of known airplanes we decide this figure should be between 10 and 20 Ibs./hp as a figure higher than this could give us too poor a climb while a lower figure would give a higher performance than we need for our airplane. We decide on 15 lbs./ hp and with our 65 hp engine we have an allowable gross weight of 975 lbs. Checking known airplanes we find this to be a reasonable figure for our type so we settle on this figure. If we use the formula for stalling speed as a base we can easily calculate a number of things if we remember our wing will lift one weight, no more, no less, at ono angle of attack at a given speed. If we increase the weight one pound we will either have to change the speed or the angle of attack to compensate for it. If we change the angle of attack the slightest amount we will have to change the weight or the velocity. It must all balance out. From this we can see our formula will apply to any speed, not just the stalling speed, so we will use V instead of the usual VB. A change of density or temperature will also

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change the performance of our wing so we will use Standard Atmosphere as our base (sea level density and a temperature of 59 deg. F.), which allows us to disregard these factors. There are a number of things that also will affect our answers but our calculations should be within 5 percent or so which should be close enough for our purpose. Anyone wishing to correct for Reynolds' number, aspect ratio, etc., can get the information from any good book on aerodynamics. The formula we will use for landing speed says the stalling speed is equal to 19.8 times the square root of the wing loading divided by the lift coefficient. V (or Vs) = 19.8

(in mph)

V is the speed we have chosen and can be used for any velocity by changing W/S or C,. W is the weight in pounds and S is the wing area in square feet. C, is the lift coefficient obtained from the wing section data. At first glance this may look like a rather long and tedious job, but if we use a 10 in. slide rule for our work it will be easy and rapid. A 25c rule from the dime store will do as well as a $20.00 one so we have no problem here. As a starter we will try a wing loading of, say, 9 lb./ft.2 which will give us a wing area of 975/9 or about 108 ft.2.

From our wing section graph we find the top of the lift curve gives us a C, max of about 1.6. Now if we put the 1.6 on the "B" scale in line with the 9 on the "A" scale (using both left hand scales in this case) and drop down to 19.8 on the "C" scale we will read 47 directly below on the "D" scale. This is our answer V = 47 mph. Now perhaps we think this is a little too fast a landing speed for one of our skill and decide 35 mph would be about right. Starting with 35 mph and doing the work backwards we will get a W/S of about 5 lbs./ft.2. In other words our wing loading is equal to 2

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Q:

S 19.8 ' C, Our wing area in this case will be 975/5 = 195 ft.2. This is a very large wing and it might be noted that we have increased our wing area by 195 — 108 = 87 ft.2 in order to get a decrease of 12 mph in our landing speed. This is too great a penalty to pay so we will probably try

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another loading or area, perhaps 120 ft.2. Th?re is almo ,t Ld

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40

5

8

10 15 20 ANGLE OF ATTACK CAT W/S= ? LBS/FT*

JANUARY 1965

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always a wind that will cut down our landing speed so perhaps 47 mph is not much too great for us anyway. Using our slide rule we can read off the C, we will need for a certain W/S and V. From the C, we can get the angle of attack from our wing section data. We can calculate the velocity needed to lift our load at different angles of attack. The results of these calculations can be plotted in a similar manner to that shown in the accompanying graph — in this case the mph has been plotted against the angle of attack and the W/A is 9 lbs./ft.2. It should be noted that when C, is less than 1 the W/S on the right "A" scale is used until the velocity reaches 100 mph after which we go again to the left "A" scale but this time we use the right "B" scale for our C,. A