machin wrote:... I think using energy to explain it is worth a try at least!
Look here man, you are confused, and clearly not confident in what you are putting across. I am done with that a long time ago. Simple little physics that you are using cannot explain what is taking place. The system is accelerating, and the acceleration isn't even linear or constant, so it's above anything that you are going to post.
What you pose about conservation of energy puts you on the right track, but you veered off after that.
Try this on for size,:
Torque = I * alpha, alpha being angular acceleration, I for for a disk like a wheel or gear is 1/2 mass x radius squared. ok? that's not going to change.
This is how the energy comes in:
K.E. = 1/2 * I * angualar velocity squared.
differentiating with respect to time would give you:
Torque x angular velocity = power.
With that said, multiple gears afford flexibility in acceleration becuase they can manipulate the torque, regardless of the characteristics of the power source.
This is simple theory.
You increase torque you increase acceleration, that's the idea behind the gearbox. The power characteristics doesn't matter; constant power or not.
I can't help you any more.
You can't tell me anything new about gearbox design, let's just leave it at that.