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Flying Knights Newsletter

2000 First Quarter

Previous Page               Page 6                  Beginning

Cont. from Page 5
        We can assume that our plane in level flight is flying with an optimum Thrust Coefficient of about ‘one’. Because the prop is twisted, it will be about the same all along the length of the prop. This leaves us with the rest of the equation.
Mass density of air.
        The mass density of the air is the same as it was for the other equations. This numerical value is (.0024/2). 
The prop area. 
       If the prop were a rectangle, the area would simply be the ‘diameter' times the ‘width’. It's not. We lose some in the center and some at the tip.

 However, it's safe to assume that the actual area is about 60 - 70% of the rectangular area.
       Calculus would give an exact value but this is only a hobby. We’ll just take the 60% value and run.
       For our example, let’s use a 10 x 8 prop. The width is 7/8". The diameter is 10" so the area is 8.75 sq. in.
       60% of this is 5.25 sq. in. Naturally, we need this in sq-ft. (what else!), so we need to divide by 144. This gives us 0.034 sq-ft.
The prop speed
       This is not as hard as it seems. First we need to take the circumference of the propeller arc. Multiply our 10" prop length by Pi (3.14), which gives us 31.4 in. Once again, we need this in feet, so divide by 12. This gives us 2.61 ft.
       Now all we have to know is how many times the prop rotates in a second.
       This is easy. Its just the RPM divided by 60. For 10,000 RPM, that's 167 rps.

        Each revolution is 2.6 ft. Our prop speed is simply 167 times 2.6 (rev's x distance) or 436 ft. per sec.
        By the way, that's 229 m.p.h.! No wonder that baby will cut your fingers off.
        Thrust = .0012 x .0364 sq-ft x (436 fps) squared. This gives 8.3 lbs of thrust.
        Of course that wasn't the question. We wanted to know what RPM we need in order to fly our Sig. Cadet at 30 MPH. That's where the drag was 2 lbs.
        That's the thrust we must provide. How fast must our prop go to generate 2 lbs of thrust?
        We need to re-arrange our equation as follows:
Velocity = Sq. root of (Thrust / (.0012 x Area)).
        So for 2 lbs. of thrust we have: Sq. root of (2 /(.0012 x .0364 sq. ft.).
        This gives us a prop speed of 214 ft /sec. Divide this by the circumference of the prop (2.61 ft) and we get 81.9 revolutions per second.
        Multiplying by 60 gives us 4919 RPM. Our prop must turn at 5000 RPM.

More speed, More Drag, More RPM
        We also found that at 40 mph our drag increased to 3.5 lbs. Let’s see fast our prop has to rotate to maintain this faster speed.
        Apply the same equation again for 3.5 lbs.
        The answer: 283 ft/sec. Dividing again by 2.6 ft gives 108.4 rps. Multiplying by 60 we get 6507 RPM. That’s an increase of 1500 RPM.
        We now have equations (actually forms of the same equation) for Lift, Drag and Thrust. By making some rather simple measurements on our model, we can determine many of the model's flight characteristics.
       This is especially handy if the model is one of our own design or we are going to modify the model in some way.
       Sometimes a small change will affect the flight behavior in a big way. It would be nice to know before we make the change.