Best way i think of axle stiffness is "Rate of Lift"
The stiffer the axle the easier it is for the Castor angle to lift the inside rear wheel and the more direct the response.
It will then also Set the inside rear wheel down quicker as you unwind the steering lock.
A softer axle slows the rate at which the inside wheel lifts in relation to the castor angle on the front, but tends to hold the wheel up in the air for a little longer once steering lock is unwound.
But then you have to think about the outside wheel and how that reacts. as a very soft axle will allow a full contact patch as it flexes more. whereas a hard will make the it tip and slip. But go too soft with a lot of grip and you end up with a pogo stick ;-) Go too hard and it slides around and won't dig in.
but this all depends on the grip level on track and how the driver drives.
As the other two people said. Its a black art. The more you think about it the more complex it becomes....Then you miss an apex or braking point and that axle change to find 1/100th was pointless
;-)
You usually find theres more time in POWER and Driving than other stuff. Spend on POWER and Tuition then the chassis part becomes easier ;-)
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