Re: L2-"Negotiating" a curve.

[brian whatcott <inet@INTELLISYS.NET>]

Without providing a complete 'why' answer in the favored format,
 here are some observations of the turning forces on vehicles.

When a steerable wheel turns left, it develops a force roughly perpendicular
 to its direction. This force may be visualized by placing two smooth thick
plastic sheets together and running the steerable wheel(s) over the sandwich.
 The upper sheet is displaced away from the turning direction.

   The wheel does not in fact move in the direction in which it is pointing.
 There is normally a slip angle, greater for radials as I recall than for
old fashioned cross plies. This slip angle is associated with the side force.

 Front wheel drive cars earn a superior rating on ice, because they conserve
 the small margin of traction to use the slip angle between wheel 'heading'
and wheel 'track' for turning force needed to hold a curved track, without
the need to devote some of the available traction to a greater slip angle
needed to
1) convert long axis thrust into wheel 'heading'
2) convert wheel heading to wheel track.

If still more of the available traction is devoted to braking, then turning
force is even less available.

Brian Whatcott


At 22:38 11/3/99 -0500, you wrote:
> ... a tricycle without
> pedals.... a large equilateral triangle,
> the view from above. Two wheels at the base (back side
> where the pushing force is applied) and one wheel at the
> top (where the steering column is).
>
> The axis of the back wheels is parallel to x and the planes
> of all three wheels are parallel to y. ... The
> platform moves in the y
> direction, the speed is constant because the sum of four
> external forces is zero. The forces are:
>
> Fp (my push along the y axis),
> Fr (rolling friction on the back right wheel),
> Fl (rolling friction on the back left wheel) and
> Ff (rolling friction on the front wheel).
>
> The magnitudes of the three rolling friction forces are
> identical; they are equal to Fp/3.
>
> It is easy to make the free body diagram in this case.
> One force along y and three forces along the -y. I am
> assuming the tricycle is a rigid body (except for tires)
> and that the mass of each wheel is negligibly small.
>
> Now the front wheel is turned to the left. Why does
> the net force, directed to the left, appear? ...
> Ludwik Kowalski
>
> Mark Sylvester (referring to a four wheel vehicle) wrote:
>
> > I guess the front wheels will have a static friction force acting on them,
>
> > perpendicular to their rolling direction. The unbalanced component must
> > be strictly centripetal for uniform circular motion of the trolley, so I
> > deduce that the tangential part of this static friction force, acting
> > backwards, must be balanced by the pusher, for constant speed. This
> > suggests that, yes, you have to push in order to turn at constant speed.
> > But what about energy? The KE of the trolley is unchanged and there's
> > no sliding, yet you are doing work pushing in the tangential direction.
> > Hmmm.... maybe turning is not so simple. Can it be that you do
> > something other than just pushing tangentially? ......