[jyl]

Thanks. Here is the problem I am trying to solve. It isn't a practical project, just a mental hobby thing. There is a concept, I am trying to figure out if the physics would work.

The concept (which is not my idea, I don't take credit) is a wheel that contains an internal hollow channel, that is annular, circling the circumference of the wheel. Inside the channel, there is a weight. The weight can slide frictionlessly around the channel. There is some unspecified "mechanism" that allows the weight to be driven around the channel by applying force to the wheel (imagine a gear, or a solenoid). Set the vehicle on the ground, facing to your right, with the weight at 3 o'clock. The gravity pushes the weight down (clockwise) in the channel. Use the drive mechanism to hold the weight at 3 o'clock. The reaction force on the wheel will rotate the wheel clockwise and propel the vehicle forward. Relative to the wheel, the weight will be rotating counterclockwise. Relative to the vehicle, the weight will be stationary.

The vehicle weighs 85 kg (bicycle + rider). The weight weighs 2 kg. Radius of the wheel is 35 cm.

My initial reaction was that this drive system will produce very little force, just gravity force on a 2 kg mass, call it 20 N. I considered it essentially like a mass (the weight) hanging from a pulley, connected by the string to another mass (the vehicle). Hence the set-up I described in the original post. I calculated the force would only be able to propel the vehicle up a 1.3 degree slope.

The person who proposed the concept pointed out that the drive system would work as a primary drive on flat road, and as an auxiliary drive on inclines. On flat road, even 20 N will accelerate the vehicle from a dead stop. It is only a small acceleration, but since it is sustained, the vehicle will get to reasonable speeds before too long. On an incline, you would use another force (pedaling) as your primary power source to get the vehicle going, and the drive system provides additional force. He also said that the power provided by the drive system will increase as the vehicle accelerates. The claim is that by the time the vehicle is going a reasonable speed (10 m/s) the drive system is providing 200 watts of power (20 N x 10 m/s) which is actually a lot, relative to the primary power source (an average cyclist can only pedal at a 200 watts for an hour).

I am having trouble grasping this intuitively. I can't grasp how a constant force of 20 N can produce ever-increasing power with increasing velocity, if the acceleration is due or partly due to another force.

The other thing is, I am starting to doubt my initial assumption that holding the weight at 3 o'clock produces a constant force of 20 N on the rim. With the wheel at rest, it does. But when the wheel is rotating fast?

Again, please ignore the practical aspects of this concept (what sort of mechanism? what friction? what happens when the mechanism is turned off while the vehicle is in motion? what effect on steering?). At this point, I am trying to understand the basic workings of the conceptual design. And, no, there's no intention of making a commercial product of this.