Milliken and Milliken question

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browney
1
Joined: Sun Apr 15, 2012 9:13 am

Milliken and Milliken question

Post by browney » Thu Apr 20, 2017 1:53 pm

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
145
Joined: Fri Jun 29, 2012 11:48 pm

Re: Milliken and Milliken question

Post by Greg Locock » Thu Apr 20, 2017 7:43 pm

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
1
Joined: Sun Apr 15, 2012 9:13 am

Re: Milliken and Milliken question

Post by browney » Sat Apr 22, 2017 8:16 am

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
145
Joined: Fri Jun 29, 2012 11:48 pm

Re: Milliken and Milliken question

Post by Greg Locock » Sat Apr 22, 2017 11:52 pm

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