Milliken and Milliken question

[browney]

Hi,
I was wondering if anybody was able to explain a derivation/simplification in Milliken and Milliken that I am having trouble with (I was hoping some like minded people here had been through it!!)?

In equation 5.2, the for the direct acceleration term (ay = Vr + 'v dot'), 'v dot' is simplified to V*Beta (Vehicle velocity multiplied by vehicle slip angle).

I have read the text a few times and I can't understand what is being done here.

I'd really appreciate any help!

[Greg Locock]

You missed a dot. v dot is the rate of change of lateral velocity, and he's assumed V is constant. v~V*beta, so v dot= V*beta dot

In English rate of change of lateral velocity equals vehicle speed times rate of change of vehicle slip angle.

As you might imagine it's a fairly small proportion of ay in typical scenarios, unless you are drifting or losing the back end. beta dot is a noisy measurement in reality.

The final line ay=V*(r+beta dot) boils down to lateral acceleration= vehicle velocity*(yaw rate+rate of change of vehicle slip angle). So if you haven't got a Corevit then one way to get beta would be to integrate betadot, (ay/V)-r all of which you can measure with traditional instrumentation. Beta is handy, it tells you what your rear tires are up to.

[browney]

Thanks,

I wasn't clear on why this is a component of acceleration (the centripetal component is obvious).

I can imagine it is due to the rate of the reduction of radius caused by the rate of change in the vehicle slip angle?

[Greg Locock]

Yes I think so since v=DR using D notation and so vdot=D2R