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Roll Gradient/Stiffness

Roll Gradient/Stiffness

Roll Gradient/Stiffness

I'm a little confused about the roll gradient equation given by Milliken in Race Car Vehicle Dynamics.  A simplified version is at the bottom of p586, and the complete version including some derivition is found on pages 681-682.  

My question came about when I was correlating some real world data to the output of the equation, and was out by a factor of 10.  Milliken's equation states the result in rad/g, however I believe the acceleration units shouldn't be normalized to g's?  So for example, if I'm working in metric units, the result should be rad/ms-2?

The force due to the lateral acceleration is F=MAy, with M being the unsprung mass, and Ay being the lateral acceleration (actual acceleration, not g's).  This creates a moment about the roll axis which is H distance below the CG: Moment = FH = MAyH.  So, if we have roll stiffness K in Nm/deg, then Moment/K = MAyH/K, so deg/Ay = MH/K.  At no stage is Ay normalized to arrive at this equation.

Have I missed something obvious?

RE: Roll Gradient/Stiffness

If you're not solving for roll gradient normalized to lateral g's why would you expect your answers to numerically match them?

I hope this isn't what it sounds suspiciously like . . . and I suspect that your answers aren't "out" by exactly 10.0 either.


RE: Roll Gradient/Stiffness

One of the hardest things I've found about the Milliken book is his non-standard use of symbols (at least from my experience).

When Milliken says ay, he means the acceleration due to gravity.

When Milliken says Ay, he means ay/g.

His use of symbols is listed on the inside of the front cover.

RE: Roll Gradient/Stiffness

Edit of previous post:

ay is lateral acceleration, not acceleration due to gravity.

I should never post before my first cup of coffee.

RE: Roll Gradient/Stiffness

True, the units used in each equation do vary a bit from section to section, but if you read each example properly they are internally consistent, or, at least, I haven't found any significant errors.

Perhaps you can't plug and chug like you can from a textbook. I'm not convinced that is a bad thing.



Greg Locock

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RE: Roll Gradient/Stiffness

Agreed, you are forced to question the origin of every term in every equation and check the units.  You have to go through the book with your brain engaged.  I guess that is why I am chewing my way through this book so slowly.

RE: Roll Gradient/Stiffness

Just curious (I haven't read the Milliken book and don't know alot about vehicle dynamics), but why do you only look at the unsprung mass when calculating lateral loads?  Are you only interested in frequencies above the 1-2 hertz body natural frequencies?

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