Toe Compliance Control - Toe Base

We have a seen a lot of teams show up with a rear suspension like the one in this picture –

What I am specifically pointing out is the method of toe control in the rear. There are 2 control arms and the upper one what looks like an implementation of a revolute joint through a bushing. This works in theory but practically there is bound to be compliance in the joint. This is not only form the compliance from the bushing but also from the compliance that arises out of having a tiny toe base.

The definition of the toe base of the vehicle is varied but in general it is the length of the moment arm of that opposes the re-aligning torque that the tyre produces. In this above picture it is the length of the cylindrical section at the outer end of the control arm. This is clearly small as is a definite ‘No No’ for a Formula Student car. The suspension must have a toe link.

In a more conventional suspension system there is a toe bar that prevents the rear suspension from steering. Here the toe base can be more clearly defined as the perpendicular distance of the point where the toe arm meets the upright from the king pin axis. The diagram clearly demonstrates this –

It is important for the toe base to be large. The compliance (or the ‘play’) in the suspension system dramatically reduces as the toe base becomes bigger. This can be simply illustrated by this simple thought experiment. Support you have a spherical bearing with 1 mm of compliance in it. Note: 1 mm compliance is chosen for ease of calculation, if you really have a bearing with 1mm compliance you must throw it away. This compliance will translate to the wheel being compliant when turned in the top view of the car. Here is a plot of the compliance in the wheel in degrees vs the toe base length.

The graph clearly illustrates the importance of having a large toe base. Simply having the toe link will NOT do. The suspension in the next picture will be compliant of this reason.

Rear toe compliance on a Formula Student vehicle will make it handle like a super-market trolley and will lose points in design. Which is why it finds second place in Pat’s “Seven Deadly Sins of FS Design” 

Moral of the story : Toe compliance is evil. Evil can be fought with larger toe-base. Hero wins only with a larger toe base, a little like this one -

This blog post is originally written for the Formula Student India website and has been cross posted from here.