I was looking at stationary bikes and the resistance methods they use. The flywheel caught my attention. If I had a 50# flywheel for instance and I wanted to calculate how much energy it would take to get it to a given rpm would I base this on the rotational speed at the center of mass? I have no idea how to figure out the amount of power needed to maintain that speed. Would this be based entirely on drag co-efficient?
I will give an actual example, I don’t understand it very well so I may not present the problem correctly. I am thinking of something similar to a centrifugal governor. The xample I am going to give may not be practical to actually build but it seems to fit my problem well. Suppose I had a wheel 30" diameter. It had any amount of hollow spokes lets just say 4. The was a 1# steel ball inside of each spoke. . This ball had the magical ability to float freely inside of the hollow spoke and form a perfect seal to the sides. It was built with all the air on top of the ball when the ball was resting at the axel. No matter what none of the air on top of the ball would ever go to the other side of the ball. The wheel starts to turn and centrical; force starts to send the ball outward creating pressure on one side of the ball and a vacuum on the other side. Would the person be turning the wheel experience those forces? or just the forces of the ball being further out on the wheel. Now compare this to a spring with the weight being pulled back to the axel. would the spring slow the wheel faster and be experienced as resistance?
The concept you’re looking for is mass moment of inertia:
For a given RPM, a flywheel with greater moment of inertia will contain more kinetic energy than one with a lesser moment of inertia.
Weight is a factor in the moment of inertia of a flywheel, but so is the placement of that weight. A flywheel that places most of that weight in a large-diameter ring will have a larger moment of inertia than one that packs it all into a small-diameter solid disk.
Formulas exist for calculating the mass moment of inertia for various shapes:
Assuming you’ve got a simple solid disk of material, you could calculate its moment of inertia as Iz, = m*r2 (see “thin, solid disk of radius r and mass m” from the above list). You can then calculate the kinetic energy of such a flywheel as:
E = 0.5 * I *ω2
Where:
E is the kinetic energy of the flywheel in joules
I is the moment of inertia of the disk, in units of kg*m2
ω is the rotational speed of the wheel in radians per second (1 revolution = 6.28 radians)
A stationary bike’s flywheel doesn’t offer the rider any resistance unless it is accelerating. If you want to dissipate energy at a constant speed, then you need some kind of friction brake, eddy current brake, or aero brake.
The movement of the balls away from the axis of rotation of the wheel would increase its moment of inertia. For a given amount of kinetic energy, in the system, such movement would tend to cause the wheel to decelerate, but of course that centrifugal movement would only occur as the wheel actually accelerates. The net effect is that the person attempting to accelerate the wheel would find it harder to accelerate than one in which the balls were stuck close to the axis of rotation.
Correct. The bike I have ridden uses the flywheel to smooth out the peddling. You tighten a strap around the flywheel to increase the effort.
What if it was built like a centrifugal governor. Where springs opposing the spinning weights would control the resistance. The amount of spring tension pulling the weights back to center would be the resistance?
If the flywheel is spinning at a steady speed, then those spring-loaded weights would be sprung out to a constant radius, and the flywheel would have a constant inertia (this would be a different inertia than at some other speed). There wouldn’t be any resistance for the rider unless he tried to accelerate, at which point the wheel would offer more resistance than a simple solid flywheel (because the weights would move toward the rim, increasing inertia and increasing the amount of kinetic energy input required for that higher speed).
The fitness industry is always looking for forms of resistance that might improve on existing forms. Thats why the questions.
Here is what is confusing me. While I am accelerating, I am throwing the weights out toward the outer limit of their radius. To do this I have to use the centrifugal force of the weights to overcome the spring tension allowing the to move outward. The spring tension would remain constant as long as the speed was the same. Would I not be constantly trying to overcome the springs in order to maintain that speed?
Thanks, I think I have it now, I was having a problem wrapping my brain around it.