What is the best tank's width ?

[oracid]

What is the best tank's width ?
As you know, I am interested in tank.
During my tests, I found that the more the tank's width was big, the less the track goes out of his lane during a turn on a spot.
I have the intuition that when the track follows a large circle, the friction caused by ripage is less.
I guess this is because of the shorter distance of the extremities of the track and the perimeter of the circle.
But how to prove it? I will like to make a video on the subject, but I have not done great studies and I'm afraid to say stupid things.
Could someone explain this without too much math?
Thank you in advance.

[AVCampos]

Hmm, without any formal training on the subject, I'd say that, at its longitudinal centre, the influence of track width is related to the different linear velocities required for the innermost and outermost edges: given that on each side there's a single track, therefore with a constant linear velocity, there's always going to be some slippage, and here having good adherence (via, for example, your rubber inserts) is a disadvantage.

The more spread apart the tracks are, the less difference there is between the inner and outer edges of each track, so the effect should be reduced.

[oracid]

I'm not sure I understand your answer.
I think that for a given tank, rotation on the spot is easier when its width is larger.

[AVCampos]

You're not alone, I have a natural knack for not being able to explain things clearly.

What I mean is that, in a curve (including the vehicle spinning on itself), the two edges of a tread behave like the wheels of a regular car going in a curve: the innermost edge will go on a shorter trajectory than the outermost edge. So, a tread is like a car that doesn't have a differential, in that its edges always move at the same speed: one or both will necessarily slip on the ground.

Still considering a tracked vehicle spinning on itself (so the centre of rotation coincides with the centre of the vehicle), the larger the distance between treads, the larger the radius of the curve each tread describes, so there will be less speed difference between the two edges of the tread, and therefore less slippage.

For a wider tread and a fixed turning radius (i.e. fixed distance between treads), the difference between the radius of the innermost edge and outermost edge will be greater, and so will the slippage.

It'd be simpler to explain with a diagram, but so far I don't have the time to do one...

[oracid]

Ok, I understand what you mean.
But simplify the problem and consider a thread has no width and it is a line.
In this case, I think there is less friction when the tank is wider.
No ?

[AVCampos]

Yes, I believe so. Considering the two vehicle width (impossible) extremes, zero and infinite...

The tracks of a zero-width vehicle end up like a longitudinal line. Thus, rotating it should produce maximum friction at the tips and zero at the middle.

If you have an infinite-width vehicle, the treads' length ends up essentially zero, which corresponds to two points, one for each tread. Rotating them should have zero friction in total.

So, interpolating to real-world widths, I'd say that slippage is proportional to the ratio between tread length and vehicle width: greater for long and narrow vehicles, lesser for short and wide vehicles.

A particular case of this is two-wheeled vehicles in a Segway-like configuration (eventually with an auxiliary caster for balance): these wheels approximate to zero-length treads (as a wheel ideally has a single point of contact with the ground), which lead to the zero friction we know.

[oracid]

Thank you for your patience to solve my nightmare...

[AVCampos]

No problem! That's what we're here for.