- #1

Shune2001

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Iâ€™m in need to solve a problem in physics, which might be easy for you but it is not for me as my background in physics is not good.

I have a bike (drawn in simulation platform) with a flywheel connected to the crank (or shaft). The flywheel is not always fixed (or engaged) with the crank, it sometimes engages and others disengages with/from the crank via electrical clutch, and ofcourse there is gear between the flywheel and the crank.

I need to calculate:

1- Cycling total power (includes the effect of the flywheel while engagement/disengagement)

2- The power of the flywheel only (when it engages/disengages) to understand the effect of the flywheel on the total cycling power.

Now, due to simulation constraints, I donâ€™t have a sensor to measure the forces of the legs on the pedals, nor I want to derive it mathematically (for complexity); therefore, I used the following method:

First I calculated the torque on the crank through:

Torque = Crank Acceleration * Inertia of the bike and the humanoid (I can get these values from the program)

Then, I calculated the power as:

Power= Torque * Crank Angular Velocity (rad/s)

Is this method correct to calculate the total cycling power including the effect of the flywheel on the crank during engagement and disengagement? Or do I need to add the inertia of the flywheel to the equation of the torque while the flywheel is engaged? Or do I need to calculate separately the power of the flywheel and add it to the equation of power mentioned above ?

Concerning the second request, The power of the flywheel only, I know that the work done by the shaft on the flywheel is equal to the difference in the kinetic energy of the flywheel

Work= Â½ * Inertia_Flywheel * Angular_Velocity_Flywheel(2) - Â½ * Inertia_Flywheel * Angular_Velocity_Flywheel(1)

Then take the derivative of the work to get the power of the flywheel.

What Iâ€™m confused about is the angular velocity(1), angular velocity(2) and the derivative to get the power:

For example, if the flywheel engages with the crank for 5 seconds (or 5 samples), should I say that Angular_Velocity(1) of the flywheel is the one before or at the time of engagement ? and Angular velocity(2) is the one at time= 5 seconds(when disengaged) ? then the derivative is the difference between the two values ? or I need to divide by 5 to get the derivative ? or should I calculate the work at engagement and the work at disengagement and take the derivative (the difference) between the two values ? like:

W_eng= Â½ * Inertia_Flywheel * Angular_Velocity_Flywheel(2) - Â½ * Inertia_Flywheel * Angular_Velocity_Flywheel(1)

Where: Angular_Velocity_Flywheel(2) is the velocity after engagement,

Angular_Velocity_Flywheel(1) is the velocity before engagement

W_diseng= Â½ * Inertia_Flywheel * Angular_Velocity_Flywheel(4) - Â½ * Inertia_Flywheel * Angular_Velocity_Flywheel(3)

Where: Angular_Velocity_Flywheel(4) is the velocity after disengagement,

Angular_Velocity_Flywheel(3) is the velocity before disengagement

Then

Flywheel power = W_diseng â€“ W_eng ?

Iâ€™m really confused and need your help..

Many thanks

Shune