Re: steering force

[Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>]

Thanks to those who helped. The analogy JohnD
suggested (sticks pushing in different directions,
according to orientations of wheels) is very useful.
I did refer to a boat (on a shallow pond) but instead
of a sail it had two people with long sticks pushing
against the bottom.
Ludwik Kowalski

I asked:
In preparing for tomorrow's lecture I am again
having a difficulty with explaining the mechanism
by which the centripetal force starts acting on the car
(on its wheels) when the steering wheel is turned.

I draw two pictures. On the first picture the planes of all
four wheels are parallel, in the second the planes of the
front wheels are at an angle, for example, 20 degrees,
with respect to the planes of the back wheels. The back
wheels are still oriented as they were when the car was
moving forward along the straight line. The front wheels,
however, are now oriented to make sure the car is turning
to the left.

I am supposed to say that the centripetal force is provided
by the road; it is a familiar static friction force. But this is
not enough; something essential is missing to make this
acceptable. Am I the only one who is bothered by this?

The sidewise force would not appear (ideally), if all four
wheels were suddenly locked, no matter what their
orientations are. I am thinking about a situation in which
wheels are locked when the car is in the air, for example,
when going too quickly over the top of a hill. The sidewise
force (to the left on my picture) appears only when wheels
are rolling. Therefore, rotation of wheels should be an
essential element of my explanation. But I am not able
to generate such explanation. Please help.

On Sunday, Nov 9, 2003, John S. Denker wrote:

> On 11/09/2003 09:12 PM, Ludwik Kowalski wrote:
> > I am supposed to say that the force is provided by the road;
> > it is a familiar static friction force.
>
> I like to call it quasi-static.  Details
>    http://www.av8n.com/physics/car-go.htm#sec-rolling-friction
>
> > But this is not enough; something essential is missing to make
> > this acceptable.
>
> Indeed yes, there is more to the story.
>
> > The sidewise force would not appear (ideally), if all four wheels
> > were suddenly locked, no matter what their orientations are.
>
> If I understand the question, that's not where the
> answer lies.
>
> The magic of steering comes in part from quasi-static
> rolling friction, but there's more to the story.  In
> particular, if the "tires" were rolling *freely* like
> the ball in a ball-point pen, there would be plenty
> of quasi-static rolling friction, but no steering.
>
> So we need to think also about what goes on at the
> *bearing* at the axle.  That is what allows a proper
> wheel to roll freely in one direction, while exerting
> forces of constraint in the other direction.
>
> If you want to analyze the bearing, it is an
> interesting but not entirely elementary exercise.
> For students who don't yet know how to analyze the
> dynamics of a car in a turn, analyzing the bearing
> is not appropriate.  It would be better to just
> say that the bearing is designed to create forces
> of constraint that allow the wheel to roll in the
> "good" direction but not in the cross-direction.
>
> We note in passing that it didn't have to be that
> way;  consider a disk penetrated (through its
> center) by an axis that is mis-aligned with the
> axis-of-symmetry.  The result will be a wobbly
> wheel.  Not good.  This illustrates that you
> can't take wheels for granted ... rather you must
> engineer them to do what you want.