Cont. from Page 5We 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.
| 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