Light weight flywheel - good idea?

[DavidNJ]

Originally Posted by mylesdw

Go on then, put me out of my misery! What have I done wrong:

We have a 40 lb flywheel 11" in diameter at 800 rpm,

Rotational mass (I)= 0.5 * m * r^2

so

I = 2420 = 0.5 * 40 * 11^2

Energy = 0.5 * I * w^2

so

774400000 = 0.5 * 5280 * 800^2

We also have a 2800 lb car travelling at 5 mph,

to make a comparison we need to convert mph to inches per minute

v = 5 / 60 * 63359 = 5280

Energy = 0.5 * m * v^2

39028528010 = 0.5 * 2800 * 5280^2

My energies are a factor of 50 apart!

Units,units, units...

Your inertia is in lb*in². It is 16.8 lb*ft².

However, your rotational speed should be in radians/second not revolutions/min. That is a factor of 377.

So you energy becomes 1/2 * 16.8 lb*ft² * (800/(60*2*pi) rad/sec)². This equals 1800 lbf-ft.

At 5mph your car is traveling 7.33 ft/sec. So your equation is 1/2 * 2800 lb * (7.33 ft/sec)² which equals 2340 lbf*ft.

The 40# figure is a little light. 45-50# is probably closer.

[PDUB]

It's been a long time since physics class, but recall that the formulas in play here are based on the mass of an object (the m in the formula). The US measure of mass (unit) is the slug (short for "sluggishness??").

Pounds are a measure of force... the force due to gravity on the flywheel or car in this case (acceleration due to gravity is 32.2 ft/s^2 in US units).

Additionally, r is for radius, rather than diameter, d.

Correct me if I am wrong, but it looks like it should be:

I = kmr^2, where k is the inertial constant (1/2 for a uniform rotating disk).

= 0.5[(40lb)/(32.2ft/s^2)][5.5in/(12in/ft)]^2 = 0.5(1.24slug)(0.45833ft)^2 = 0.13045 slug-ft^2


KE = 0.5(I)(w)^2, where w = angular velocity = (800 rev/m)(2*pi rads/rev)/(60s/m) = 83.77 rad/s

= 0.5(0.13045 slug-ft^2)(83.77rad/s)^2 = 457.78ft-lb = 620 J

For the car:

KE = 0.5mv^2 = 0.5(2800/32.2)(7.33)^2 = 2338 ft-lb = 3169.8 J

It is pretty late, so this could be in error ... I will try to look it over again during the daylight hours

Otherwise, let me know if you find problems.

Thanks