# Apply impulse to a wheel creates constant acceleration?

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1. Mar 21, 2015

### Lucas Borsatto

Hello!

Well, I am in trouble with this question for some time. I am making a simulator with autonomous cars and its movement is done applying constant impulses to the wheel. My question is: if the vehicle is in the intertia state and I start to apply this impulses, the vehicle will assume a constant acceleration?
In my simulation, the vehicle begins with progressive increases in acceleration and only after some time the acceleration keep constant. But I know that it is a perfect system because when I set 0 impulse after some time, the velocity keep constant.
This can occur due to the moment of inertia of the wheel ?

2. Mar 21, 2015

### gsal

What do you mean by "0 impulse"...are you saying that with no force applied you get perpetual motion? i.e., the car moving at constant speed? I don't know about that...is there friction or drag in your system?

3. Mar 21, 2015

### Staff: Mentor

The inertia of the wheel would be insignificant. You are applying a series of uniformly-spaced-in-time impulses of fixed magnitude to a vehicle, then its acceleration should be constant if there is no friction or drag. Unless you are producing wheel-spin?

Last edited: Mar 21, 2015
4. Mar 21, 2015

### Lucas Borsatto

Yes yes, when I set 0 force to impulse, the vehicle gets constant velocity. But the system itself is not important actually. The important is the physics behind it, because if it is wrong I would fix it.
The question is: When I apply an impulse with X force constantly to a wheel, it will get constant acceleration?
I guess we can assume that it is a momentum, once the impulse is constantly applied, am I right?

5. Mar 21, 2015

### Lucas Borsatto

Yes, the wheel will spin with the application of the impulse. But the wheel do not start with a spin, if it is what you mean.

Last edited: Mar 21, 2015
6. Mar 21, 2015

### Staff: Mentor

The wheel couples the energy to the vehicle. The wheel responds according to the dictates of the vehicle mass, unless it loses traction.

A force is not an impulse. An impulse is a steady force applied for a fixed duration of time.

7. Mar 21, 2015

### Lucas Borsatto

Actually the system have a friction in the wheel, but I think it is a little tricky, once it work only to make the vehicle move and then, when I put the 0 impulse, the vehicle get constant velocity. Reformulating the question: is possible a wheel spin and move with a constant acceleration applying impulses with X value?

8. Mar 21, 2015

### Staff: Mentor

That indicates a complete absence of friction and drag losses.

I think you may not be implementing the regular series of impulses that you think you are.

Those impulses are coupled to the vehicle, so it should exhibit a fixed acceleration.

9. Mar 23, 2015

### CWatters

There are a lot of possible answers..

1) If the car is "ideal" (no friction or drag) then:

* Applying constant torque to the wheel will cause a constant acceleration.
* If you apply pulses of torque you would get constant acceleration during the pulse and constant velocity between the pulses.

or

2) If the car is non-ideal then what happens depends on the magnitude of the torque...

If the torque is large enough to overcome losses then...
* Applying constant torque to the wheel may cause constant acceleration. It depends how the losses are modelled - are they constant or proportional to velocity or ??. Real cars typically accelerate up to a certain speed and then travel at constant velocity.
* If you apply pulses of torque you may get constant acceleration during the pulse and constant deceleration between the pulses. Again it may depend on how the losses are modelled.

If the torque averages less than the losses then the car either won't move, or it may maintain constant velocity, or it may slow down. Again it may depend on how the losses are modelled.

If the wheel spins(slips) the problem is a lot more complicated. For example why does it ever stop slipping?

10. Mar 28, 2015

### Lucas Borsatto

Well, I have discovered that the system is "ideal", but the impulses are applied between intervals. So, by you guys explained to me here, I suppose that it explains the why the acceleration increase over time, and only after some time the acceleration is constant , right?

11. Mar 28, 2015

### Staff: Mentor

I think you should provide some graphs to illustrate what is concerning you. We might be able to better understand the problem if you can demonstrate with actual graphs.