- #1
Shune2001
- 4
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Dear Friends
I’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 don’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= ½ * Inertia_Flywheel * Angular_Velocity_Flywheel(2) - ½ * Inertia_Flywheel * Angular_Velocity_Flywheel(1)
Then take the derivative of the work to get the power of the flywheel.
What I’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= ½ * Inertia_Flywheel * Angular_Velocity_Flywheel(2) - ½ * 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= ½ * Inertia_Flywheel * Angular_Velocity_Flywheel(4) - ½ * 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 – W_eng ?
I’m really confused and need your help..
Many thanks
Shune
I’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 don’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= ½ * Inertia_Flywheel * Angular_Velocity_Flywheel(2) - ½ * Inertia_Flywheel * Angular_Velocity_Flywheel(1)
Then take the derivative of the work to get the power of the flywheel.
What I’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= ½ * Inertia_Flywheel * Angular_Velocity_Flywheel(2) - ½ * 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= ½ * Inertia_Flywheel * Angular_Velocity_Flywheel(4) - ½ * 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 – W_eng ?
I’m really confused and need your help..
Many thanks
Shune