Wheels, Tyres and Traction

During a friendly sumo competition we discussed the merits of various Lego^® wheels for traction power (well... for sumo this is rather pushing power!). Here are the results of a measurement campaign I did afterwards.

Test method

I built a simple vehicle, powered by two motors and heavily geared down so that only adherence on ground limits pulling power (wheels do slip). Various wheels and treads can easily be attached to 4 or 6 driven shafts. A small electronics scale, attached on the vehicle at one end and fixed to ground at the other end, is used as a dynamometer.
 

More wheels ?

Is it effective to add more wheels to pull more? Solid friction laws says no, and this is clearly demonstrated in the table below. Once wheels are slipping, traction per wheel is Tw = K x Ww where Ww is weight per wheel and K a constant depending on tyre and ground materials. If vehicle weight is fixed (unused wheels were stacked on top, total weight here was 465g), increasing wheel number decrease weight per wheel, keeping vehicle traction constant.
Large motorcycle wheels are used in this test (2903 + 2902 tyres).

Of course this applies only on a solid, reasonably even ground. More wheels may be needed to spread load on a larger surface (mud, sand...), but to maintain pulling capability as many of them as possible should be driven.
 

More weight ?

As implied in previous experiment, a heavier vehicle has proportionaly greater pulling capability. This can be seen in the curves below.

At first I used motorcycle wheels, but their large diameter resulted in too much strain on the gear train and I broke an old-style 24 tooth gear (new type ones are sturdier).  

More speed ?

I also tried to see if wheel rotation speed had an influence on traction. Varying motors supply voltage between 2.5V and 10V shows only a very slight increase in traction power.

Wheels comparison

The wheels and tyres were tested on different surfaces. Charts below shows friction coefficient (Traction / vehicle weight) and are sorted by decreasing average efficiency.

NOTE: Because wheel diameter is different, scale attachment was adjusted to remain as close to ground as possible. But some variation remained that may have influenced the results. So take these results with a grain of salt !

	Short hair carpet
	Abrasive back of tile
	Varnished, shiny tile
	Matt tile
	Raw plywood