Here are some calculations regarding the amount of energy and power required to "spin-up" a clutch assembly.
Assumptions:
Clutch radius = 4"; clutch weight = 10 pounds (convert pounds to poundals for calculations).
Moment of inertia is close to that for a uniform flat disk (not clutch disk).
Rev limit = 8000 rpm, or 133 revolutions per second, rps.
Kinetic Energy = 0.5 * I * (w)^2, where I is the moment of inertia and w is the angular velocity (radians/sec),
and where I = 0.5 * m * (r)^2, where m is the mass ( m = weight/g ), and r is the radius. g = 32.1 ft/sec^2.
Therefore, KE = 6092 foot-pounds = 11.1 horsepower seconds. (Energy) (This could be expressed in watt-hrs.)
If the clutch is spun-up in 2 seconds, the Power required is 11.1 / 2 = 5.5 hp.
If it takes 5 seconds, 2.2 hp; 10 seconds, 1.1 hp; 20 seconds, 0.55 hp. ( KE / time = power; 550 ft-lbs/sec = 1 hp )
Each horsepower is jealously guarded by every racecar driver, especially in H/P.
Treat the flywheel in a separate calculation, due to its different diameter.
If an aluminum flywheel weighs 7 pounds, its radius is 6", and the net moment of inertia is near 0.6 * m * (r)^2 (considering the starter ring gear at the outer radius), then the Power required for spin-up is about 53% of that required for the clutch. If spin-up takes 5 seconds, the clutch AND flywheel absorb about 3.3 hp; if 2 seconds, 8 hp.
Since the engine, clutch, and flywheel spin-up much more quickly in first gear, as compared to other gears, the power consumed by the rotational inertia of these components significantly reduces the net power available for vehicle acceleration.
Charlie Tolman
