Force of the prop

[murphey]

I'm doing short explanation about prop safety for Young Eagles. Let's not get into the discussion of foot-pounds (rotational force) vs pounds (linear force), nor include the lateral motion the prop travels. Let's assume the airplane is stationary. I want to make sure I've got the right numbers & calculations. And let's not go past 1 or 2 decimal digits.

weight of prop: 34.5 pounds
length: 76 in or 1 blade is 38 in.
revs: 2700 revs/minute (rpm)

Distance the end of the blade travels in 1 revolution:
38 * PI = 38 * 3.14159 = 119.4 in = 9.95 ft.

Distance the end of the blade travels in 1 minute:
119.4 * 2700 = 322,380 in
or
322,380 in/min divided by 12 = 26,865 ft
or
26,865 ft/min divided by 5280 ft = 5.09 statute miles

How far in 1 hour?
5.09 sm/min * 60 min = 305.4 miles

Calculating the torque (rotational force) involves vector algabra so let's simplify. Assume a linear motion, that the 34.5 pound prop is being thrown at you at a speed of 305.4 mph, how hard is it going to hit you? Better yet, do you want to get in the way of ANYTHING going 305.4 mph?

Solution: Stay away from propellers!!!!

 

[Jim Logajan]

I'm doing short explanation about prop safety for Young Eagles. Let's not get into the discussion of foot-pounds (rotational force) vs pounds (linear force), nor include the lateral motion the prop travels. Let's assume the airplane is stationary. I want to make sure I've got the right numbers & calculations. And let's not go past 1 or 2 decimal digits.

weight of prop: 34.5 pounds
length: 76 in or 1 blade is 38 in.
revs: 2700 revs/minute (rpm)

Idling and taxiing rarely require RPMs above 1500. Static RPM at max power is rarely above 2400 for most small planes. If the airplane is stationary, perhaps use 650 RPM?

Distance the end of the blade travels in 1 revolution:
38 * PI = 38 * 3.14159 = 119.4 in = 9.95 ft.

Thorpe already caught this error.
C = 2*R*pi = D*pi

So C = 76*3.1 = 236 in = 19.7 ft

Distance the end of the blade travels in 1 minute:
119.4 * 2700 = 322,380 in
or
322,380 in/min divided by 12 = 26,865 ft
or
26,865 ft/min divided by 5280 ft = 5.09 statute miles

How far in 1 hour?
5.09 sm/min * 60 min = 305.4 miles

Calculating the torque (rotational force) involves vector algabra so let's simplify. Assume a linear motion, that the 34.5 pound prop is being thrown at you at a speed of 305.4 mph, how hard is it going to hit you? Better yet, do you want to get in the way of ANYTHING going 305.4 mph?

Solution: Stay away from propellers!!!!

In the end you didn't figure out the force it was going to hit you, just that the speed is awfully fast. I'd suggest a different approach using the definition that relates energy, force, and distance (E = F*D), dividing both sides by time to yield this equation:

engine_power = force_on_blade * speed_of_blade
(P = F*V)

For simplicity of demonstration explain that to compute prop speed you'll just use a circumference with a radius half the blade radius.

The rest is left as an exercise for the student....