In a spin

Revisiting the perennially complicated problem of tuning the differential

- DANNY NOWLAN

One of the most important, yet most often forgotten, set-up items in engineering a racecar is the differential. The reason it is so important is it plays a critical role in both power delivery and car handling. Ignore both at your peril.

A couple of years ago I addressed this matter at length, but recently received a great question on what your ballpark differential wheel speeds should be. That offered a perfect opportunity to re-visit this important chassis engineering topic.

The principal problem we have with the differential is we have two wheels moving at different speeds, as illustrated in Figure 1.

The reason tuning the differential is such a mess is that for a given forward speed, V, and a given yaw rate, r, because the wheels are separated by a track, t, we have the inside wheel velocity at V-t.r/2 and the outside wheel velocity at V+t.r/2.

Making an already tricky situation worse is the fact the differential was never truly engineered. It just sort of happened. As a consequence of this, there are many different types, including locked, open, Torsen and the many variants of our old friend, the limited-slip differential.

Now, what also must be considered is the mid-corner condition in racing where both the inside and outside of the tyre have wildly different traction and cornering conditions. This is illustrated in Figure 2.

As can be seen from Figure 2, the traction circle radius is much greater on the outside tyre then it is on the inside tyre. So, if we apply exactly the same slip ratio to both the inside and outside tyre, the differential will turn the car quite forcefully. A driver of the calibre of the likes of Lewis Hamilton / Ayrton Senna / Michael Schumacher could probably handle this, but most racecar drivers won’t.