A vehicle has two wheels rolling at different speeds. What forces act on the vehicle as it follows a curved trajectory ?

[isni]

This is not homework, it's a problem I came across while trying to model differential braking for my flight simulator. I cannot really see what force pushes the vehicle horizontally and I would really appreciate a detailed explaination.

 

[Aurelius120]

If they are performing pure rolling, the velocity of COM of the wheels will be different that causes the curved trajectory.

 

[isni]

what you say makes a lot of sense, but it doesn't explain what im mostly interested in, what forces are applied to the vehicle, as a whole, that makes it follow this curved trajectory. There has to be a horizontal force in there and I cannot figure out where it's coming from

 

[jack action]

You should have a friction force pointing towards the left at the front axle and another one pointing right at the rear axle. If the moments are in equilibrium, the vehicle will go forward. (Vertically in your drawing.)

If the sideway static friction forces of your wheels can be broken (sliding), your vehicle will rotate about the COM (or some other point if the moments of the sideway forces are not equal and opposite), changing the direction of your forces. So as the vehicle still seems to go "forward", the newly rotated vehicle's frame moves sideways with respect to the ground.

 

[Aurelius120]

You should have a friction force pointing towards the left at the front axle and another one pointing right at the rear axle. If the moments are in equilibrium, the vehicle will go forward. (Vertically in your drawing.)

If the sideway static friction forces of your wheels can be broken (sliding), your vehicle will rotate about the COM (or some other point if the moments of the sideway forces are not equal and opposite), changing the direction of your forces. So as the vehicle still seems to go "forward", the newly rotated vehicle's frame moves sideways with respect to the ground.

But if the two wheels connected by an axle , is the internal force that forces them to remain together, tension?

 

[DaveC426913]

But if the two wheels connected by an axle , is the internal force that forces them to remain together, tension?

Wait. You are not suggesting the two wheels are locked together via the axle? You are allowing them to rotate independently, yes?

We're not talking 1964 Buick Skylark with solid axle suspension are we?

 

[jbriggs444]

Wait. You are not suggesting the two wheels are locked together via the axle? You are allowing them to rotate independently, yes?

One easy arrangement would be a solid drive axle (no differential) attached rigidly to the wheels. One wheel with radius $2r$ on the left and one wheel with radius $r$ on the right.

Probably not a Michelin XGV size 75R-14.

 

[Aurelius120]

Wait. You are not suggesting the two wheels are locked together via the axle? You are allowing them to rotate independently, yes?

We're not talking 1964 Buick Skylark with solid axle suspension are we?
View attachment 346818

I thought if the velocity of COM of both the wheels is different, it can be treated as rod whose ends have different velocities causing the rod to rotate. It is analogous to that, Right?
Something similar to this except velocity(v) in place of acceleration and axis of rotation outside the both wheels

OR in this question:

Then tension is the internal force in the rod

 

[jbriggs444]

I thought if the velocity of COM of both the wheels is different, it can be treated as rod whose ends have different velocities causing the rod to rotate. It is analogous to that, Right?

"Cause"?

If the rod has ends that move at different velocities then the rod will be rotating. But that is correlation, not causation.

If the rod is "rigid" then it will retain its size and shape regardless of the pattern of external forces that is encountered. In practice, "rigid" means that small deformations result in large restoring stresses so that size and shape are approximately preserved.

 

[Lnewqban]

This is not homework, it's a problem I came across while trying to model differential braking for my flight simulator. I cannot really see what force pushes the vehicle horizontally and I would really appreciate a detailed explaination.

Flight simulator dealing with 4-wheel vehicle?

What is the driving force?
What makes the shown angular velocities different?
How the mentioned differential braking works in this specific case?

 

[berkeman]

Flight simulator dealing with 4-wheel vehicle?

You beat me to it!!

 

[jack action]

But if the two wheels connected by an axle , is the internal force that forces them to remain together, tension?

If both wheels are connected, one wheel will slip for sure while on different path lengths.

You can have different friction forces on the same axle. Imagine one wheel on asphalt and another one on ice: One has traction, and the other has almost nothing. Worst case scenario, imagine one wheel off the ground: both wheels turn at the same angular velocity but one offers no resistance at all from friction.