RCVD p.146 Equation

[CWA]

Hi guys, I have a rather specific question. As titled, it's with regards to an equation in Milliken's Race Car Vehicle Dynamics book, on Page 146; Equation 5.2.

ay = Vr + V. (the dot is supposed to be on top..)

I understand that Vr comes from V^2/R, because r = V/R. But the second term on the right side is what confuses me.

I've read the explanation but still just can't get my head around this idea that there is more that contributes to ay than just centrifugal force due to path curvature.

The text says that this second term is due to direct lateral acceleration; how does that differ from centrifugal force? And in which directions are these different force components both positive?

If anyone can help shed any light on this, perhaps describe things in a different way; I'd be very grateful.

[BillCobb]

Vehicles can spin (turn) and they can sideslip (move sideways without turning. So these are the terms representing turning and sideslipping.

Driving on a closed course demands the simultaneous control by induced moments of a displacement constraint using velocity generated forces and moments.

[Dash]

That is taking into effect transient effects. Please continue reading the rest of pg 146 and I think it does a pretty good job explaining it. ( regurgitating the example in my own words below ).

Pretend you are going around a corner at steady state on a surface with mu = 1 . Halfway around the corner there is a patch of ice you drive over ( or insert other variable ). At the instant you hit the patch of ice mu changes to a very small number, and the radius of curvature you follow changes. This change in curvature will give you that second term.

[Edward M. Kasprzak]

I'll say the same thing Bill Cobb said, just in a different way. The "v_dot" term is for the lateral translation of the car. The Bicycle Model car has two translational and one rotational degree of freedom. It's free to translate longitudinally (u) and laterally (v), and rotate in yaw (r). Combine the two translations and then, as Bill Cobb said, you have sideslip.

RCVD Chapter 5 simplifies the discussion by assuming a constant u (or V), which leaves a two DOF system (v and r).

[slicktop]

I find the small angle assumption V=u to be confusing. Where is the turn center located in fig. 5.16? Is it perpendicular to V or is it perpendicular to sqrt(V^2 + v^2)? Or can it be either?

[Dash]

It is assuming that the vehicle slip angle is at a small angle. The cosine of a small angle is close to one. Example. Cos(10deg) = 0.985 which is basically equal to 1 just to simplify the calculation.

Also, I believe it is perpendicular to V, which would also basically be perpendicular to u or parallel to v since it is using the small angle assumption