In a way, it's probably easier to begin with what DI isn't;
It isn't anything to do with your tyres (apart from what they weigh!)
It isn't anything to do with wheel geometry or alignment
It isn't anything to do with spring rates, suspension ratios or damper values
It isn't anything to do with suspension type or layout
It isn't anything to do with whether a car understeers or oversteers
It's all to do with where mass is on the vehicle, relative to the front and rear axles. The only way to change it is to move mass around - if you remove mass uniformly, you don't change DI, it's only changing the distribution that counts.
The calculation of DI comes down to an equation that looks a bit like K^2/ab.
k is the appropriate radius of gyration,
a is the longitudinal distance from the front axle to the c of g
b is the longitudinal distance from the c of g to the rear axle.
All of this can be projected into the plane of the road - there's no need to consider the height of anything, and so lowering a car can't change the DI significantly.
I say significantly, because there is a second order effect, because owing to the suspension geometry, the longitunal position of the wheel contacts will change by a tiny amount as the vehicle is lowered, but, this is a tiny effect compared with the lengths of a and b - even going from full bump to full rebound isn't going to change the product ab by much.
One non-mathematical way to consider DI is to imagine the car parked over a painted line on an ice rink. The line passes along the centreline of the car, directly under the centre of the front axle, and out, directly under the centre of the rear axle.
If you now imagine a hammer hitting the passenger side front hub, knocking the front of the car towards the driving side.
So, when the car comes to rest, a plumb bob that is dropped from the middle of the front axle will lie to the driver's side of the line in the ice.
If the DI is one, a similar plumb bob dropped from the middle of the rear axle will coincide with the line. In other words, a sudden change in sideforce (and hence slip angle) at the front axle results in no change at the rear axle.
For DI greater than 1, the rear axles plumb bob would be towards the driver's side of the line, and for less than 1, to the passenger side.
The only things missing from my rough description is that the car would really be travelling forwards.
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This principle can also be applied in other planes.
For example, using the same formulation but using the radius of gyration in the pitch angle direction can tell you how the vehicle responds to a sudden bump on the front axle.
Another example - consider a driven live axle, and a simple beam dead axle, the two are kinematically similar, but, because of the weight of the diff in the middle, have a completely different DI. In this respect, having an beam axle with a DI of 1 is as close as you can get to independence with that set-up.
