Motorcycle: Flywheel mass and rear wheel torque

[Alwaysmore2learn]

TL;DR Summary

Flywheel mass and rear wheel torque

Hello, I made this account to ask this question that I’ve been loosing sleep over.

My question is say you have 2 identical motorcycles the engine the exact same and everything the only difference is the mass of the flywheel one bikes engine has a flywheel twice the mass as the other will the torque at the rear wheel of the one with the heavier flywheel be lower?

My thinking is force from the engine is used to accelerate the flywheel so there will be less torque at the rear wheel compared to the one with the lighter flywheel. My knowledge in physics is lacking in simply just a motorcycle obsessed being who enjoys the physics of motorcycles, but can someone please give me a answer and explain to me what’s going on?

I know that the engine with the heavier fly wheel will accelerate slower and that it will store energy in the form of inertia but I simply want to know if the torque at rear wheel will be different thank you guys for taking the time to read this and hopefully answer my questions in detail I can’t tell you how many hours of thought I’ve put into it.

 

[Baluncore]

Welcome to PF.

It all depends on the acceleration. When the bike accelerates there will be less torque available at the drive wheel because more energy must be diverted to accelerate the heavier flywheel.

If traveling at a fixed speed, energy will go to overcome wind resistance and friction. No energy is needed to keep a flywheel of any weight spinning at a fixed speed.

 

[jack action]

The basis for this is Newton's second law of motion, $T=I\alpha$ in its rotational form.

Let's say you have a flywheel with inertia $I_f$ and angular acceleration $\alpha_f$. There is a torque $T_e$ coming for the engine and a torque $T_w$ coming from the wheel. Then:
$$T_e - T_w = I_f\alpha_f$$
Or:
$$T_e = T_w + I_f\alpha_f$$
So if you are going at a constant velocity (even considering at rest), as soon it will accelerate against the wheel reactive torque, you will need a greater torque coming from the engine as you suspected.

As @Baluncore said, if the velocity is constant, $\alpha_f$ is $0$, therefore the wheel torque and the engine torque are opposite and equal.

But if the wheel torque is increasing (say, the motorcycle begins to go up a hill) and the flywheel is decelerating, then $\alpha_f$ becomes negative and the engine torque needed is less the the wheel torque. This is when the energy stored in the flywheel during the acceleration is released.

Also, on a moving vehicle, the simple weight addition of the flywheel adds to the total mass of the vehicle, therefore increasing the vehicle's linear inertia ($m$ in $F=ma$). This will also contribute to affect the acceleration of the whole vehicle.

 

[Lnewqban]

...
I know that the engine with the heavier fly wheel will accelerate slower and that it will store energy in the form of inertia but I simply want to know if the torque at rear wheel will be different thank you guys for taking the time to read this and hopefully answer my questions in detail I can’t tell you how many hours of thought I’ve put into it.

The torque or rearward force applied on the rear contact patch should be the same for both flywheels.
There is a direct link between the expanding force in the combustion chamber and the rear wheel (think of the gears and sprockets as a lever of same length for both cases).
The ability of that torque to accelerate the bike will be restrained by the reduced rotational speed of the rear wheel, in the case of the heavier flywheel (think of same engine having to accelerate a bike with greater rotational and linear inertias).