Centripetal Acceleration calculation help

[nautica]

a) calculate the centipetal acc at the tip of a 4.00 m long helicopter blade that rotates at 300 rpm.

300 rpm = 31.42 rad/s = w

Centrip Acc = rw^2

Ac = (3.41 rad/s)^2 * 4 m

Ac = 3948.87 m/s^2

b)compare linear speed of the tip with the speed of sound which is 340 m/s

v=rw

v = 4m * (31.42 rad/sec) = 125.28 m/s

So the blades are slower than the speed of sound.

This does not sound right to me I figured the blades would be faster - but maybe just not at the tip?

Thanks
Nautica

 

[arcnets]

OK up to here, I think...

Originally posted by nautica
Ac = 3948.87 m/s^2

But how do you arrive at this figure? - Seems much too large to me...

v=rw
v = 4m * (31.42 rad/sec) = 125.28 m/s
So the blades are slower than the speed of sound.
This does not sound right to me I figured the blades would be faster - but maybe just not at the tip?

IMO, your math is correct here. Not sure, but I think helicopters have been around since the 1920's or so, when no aircraft engineer was even close to handling supersonic speeds... Still those machines worked, didn't they? Another thing, I believe it's not possible to move supersonic with any propeller-driven aircraft because the blades are just not allowed to move supersonic - turbulence & friction would lead to destruction... Just compare a helicopter's sound to that of a whiplash (where the tip does reach supersonic) - it's very different, much smoother isn't it? ... Enough for now.

 

[nautica]

Sorry, it was a typo, should have been 31.42

Thanks
Nautica