Calculate Torque for Acceleration: 4-Wheel Car with 1000kg Mass & 12m/s Velocity

[michael7777]

I wasnt sure where to post my question. Here goes:

I have a car with 4 wheels and one motor.
The motor drives an axle connected to the back wheels.
The total mass of the car is 1000kg
Each wheel weighs 20kg and is a solid cylinder
The effective frictional force is 0.2
The radius of the wheel is 0.5m
The radius of the axle is 0.05m


If I would like to accelerate at 12m/s from rest:
What is the required torque on each wheel?
What is the required motor torque?

Here is my lame solution which I think is pretty incorrect:
F = ma * m/g + um
Fwheel = (ma * m/g + um) / 4
Twheel =( (ma * m/g + um) / 4 ) * radius
Twheel = ( (1000*12 * 1000/9.8 + 0.2*1000) / 4 ) * 0.5
Twheel = 153086.2 Nm
Tmotor = 4*Twheel = 612344.9 Nm

I think maybe you need Io = (MR^2) / 2
But i don't know

 

[michael7777]

I found a really good website which went a long way in answering my question:

http://www.lastufka.net/lab/cars/why/pit.htm

 

[Moetasim]

how to apply it to the problem

I would approach this problem by first defining the variables and equations needed to calculate torque for acceleration.

Torque, denoted as "T", is defined as the product of force and the distance from the pivot point to the point where the force is applied. In this case, the pivot point would be the center of the wheel and the force would be the frictional force between the wheels and the ground.

The equation for torque is T = F x d, where F is the force and d is the distance. We can also use the equation T = I x alpha, where I is the moment of inertia and alpha is the angular acceleration.

To calculate the required torque on each wheel, we need to first calculate the force acting on each wheel. This can be done by using Newton's second law, F = ma, where m is the mass of the car and a is the acceleration. In this case, the acceleration is 12m/s^2. So, the force acting on each wheel is F = (1000kg)(12m/s^2) = 12000N.

Next, we need to calculate the distance from the pivot point to where the force is applied. This can be done by using the radius of the wheel, which is 0.5m. So, the torque on each wheel would be T = (12000N)(0.5m) = 6000Nm.

To calculate the required motor torque, we need to consider the fact that the motor is connected to the axle, which has a smaller radius than the wheel. This means that the torque required at the motor would be greater than the torque required at the wheel. We can calculate the torque at the motor by using the equation T = I x alpha, where I is the moment of inertia and alpha is the angular acceleration.

The moment of inertia, denoted as "I", is a measure of an object's resistance to changes in rotational motion. For a solid cylinder, the moment of inertia is given by I = (1/2)mr^2, where m is the mass and r is the radius. In this case, the mass of each wheel is 20kg and the radius is 0.5m. So, the moment of inertia for each wheel is I = (1/2)(20kg)(0.5m)^2 = 2.5kgm^2.