Torque Calculation with Total Load of 100 Kg
Hello, I have a bicycle with a total load of 100 kg. I need to calculate the starting torque necessary to propel the bicycle, taking into account either the wheel or the pedal (crank), and considering the rolling friction. Could you please provide a numerical explanation?
Answer:
To calculate the torque needed to start a bicycle, we first need to find the force needed to overcome the rolling resistance (rolling friction), and then apply it to the relevant distance (the radius of the wheel for wheel torque, or the length of the pedal crank for crank torque).
Let's start with calculating the force required to overcome rolling resistance:
Force due to rolling resistance:
Rolling resistance is a force that resists the motion of a body rolling on a surface. It is calculated by multiplying the rolling resistance coefficient (usually denoted by Crr) of the surface by the normal force (which is the weight of the bicycle plus the rider).
For simplicity, let's assume the coefficient of rolling resistance for a typical bicycle tire on asphalt is approximately 0.005. The weight (which is the mass times gravity) of the bicycle and the rider combined is 100 kg, and we'll take the acceleration due to gravity to be approximately 9.81 m/s².
Therefore, the rolling resistance force Frr would be:
Frr = Crr mass gravity
Frr = 0.005 100 kg 9.81 m/s²
Frr = 4.905 Newtons
Torque on the wheel:
Torque is the force applied to an object that causes it to rotate, and it's calculated by multiplying the force by the distance from the point of application of the force to the axis of rotation (in this case, the radius of the wheel).
Let's assume the wheel has a radius of 0.35 m (which is roughly the radius of a typical 700c road bike wheel).
The torque T on the wheel would then be:
T = Frr * r
T = 4.905 N * 0.35 m
T = 1.72 Nm
Torque on the pedal (crank):
To calculate the torque on the pedal (or crank), we have to consider the gear ratio as well, because the force exerted on the wheel is transmitted through the bicycle's gear system to the pedal.
The gear ratio is the ratio of the number of teeth on the chainring (front gears, connected to the pedals) to the number of teeth on the rear gear (connected to the wheel).
Let's assume a gear ratio of 3 (which would be reasonable for a bike on a flat surface). The force at the pedal is the force at the wheel divided by this gear ratio.
Let's also assume the length of the pedal crank is 0.17 m.
The force Fp at the pedal would be:
Fp = Frr / gear ratio
Fp = 4.905 N / 3
Fp = 1.635 N
The torque Tp at the pedal would then be:
Tp = Fp * crank length
Tp = 1.635 N * 0.17 m
Tp = 0.278 Nm
Which means, in this scenario, to start the bicycle, you would need to apply a torque of 1.72 Nm on the wheel or 0.278 Nm on the pedal.
Please note that these calculations are an oversimplification and many factors, such as air resistance, the efficiency of the bicycle's drive train, the slope of the road, and the starting inertia, have not been taken into account.