The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.59 m and 0.98 m, respectively. The respective rotational speeds are 456 rev/min and 4143 rev/min. Calculate the speeds of the tips of both rotors.
main rotor:
tail rotor:
Compare these speeds with the speed of sound, 343 m/s.
vmain rotor / vsound
vtail rotor / vsound
speedtip= w*r where w=2PI*rev/min*1min/60sec (what does PI mean?)
pi = 3.1416
They provide the formula to use. Just do the calculations and compare the results to the sound speed.
Show your work if you need further assistance.
To calculate the speed of the tips of both rotors, we can use the formula v = w * r, where v is the speed of the tip, w is the angular velocity in radians per second, and r is the radius of the rotor.
First, let's calculate the angular velocity w for both rotors using the rotational speeds given in revolutions per minute (rev/min). We'll convert the rotational speeds to radians per second:
w = (2 * π * rev/min) * (1 min/60 sec)
Now, let's calculate the speed of the main rotor tip:
Angular velocity of the main rotor (wmain rotor) = (2 * π * 456 rev/min) * (1 min/60 sec)
Next, we calculate the speed of the tail rotor tip:
Angular velocity of the tail rotor (wtail rotor) = (2 * π * 4143 rev/min) * (1 min/60 sec)
The next step is to calculate the speed of the tip for each rotor using the formula v = w * r. We'll use the given diameters of the rotors as the radius (r):
Speed of the main rotor tip (vmain rotor) = wmain rotor * 7.59 m
Speed of the tail rotor tip (vtail rotor) = wtail rotor * 0.98 m
Finally, to compare these speeds with the speed of sound (343 m/s), divide the speed of each rotor tip by the speed of sound:
vmain rotor / vsound = vmain rotor / 343 m/s
vtail rotor / vsound = vtail rotor / 343 m/s
And that's how you calculate the speeds of the tips of both rotors and compare them with the speed of sound!