Re: Photograph

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

Brian, I have no problem with your modification of my explanation,
which, admittedly was a bit hasty and not as clear as I would have
liked it to be. Of course, in the case of the toy cars, there is no
steering going on, so any instability that gets started because the
rear wheels are slipping while the front ones are not cannot be
corrected by steering the front wheels as is possible (but difficult)
with a real car.

Hugh

> At 13:40 10/29/00 -0400, Hugh set the lamp swinging while
>  he related an interesting story, and then he continued:
> > ///
> > A nice classroom demonstration of stability (and the close
> > relationship between static friction and rolling friction) is to take
> > two (large--6-8 inches long, so they can easily be seen) toy cars and
> > put them on an inclined plane. Tape the front axle on one and the
> > rear axle on the other, so that the taped wheels don't turn. Then get
> > the class to guess which car will roll straight down the ramp and
> > which won't. My experience has been that most students will guess
> > that the one with the taped rear wheels will be stable and the other
> > one will not be.
> >
> > They are quite surprised when the opposite proves to be the case. The
> > explanation is that once the rear wheels are locked, they are
> > providing less of a retarding force than the front wheels, and so any
> > misalignment of the front and rear wheels will cause the car to start
> > spinning about a vertical axis unstably, so that the small
> > perturbation gets magnified. This illustrates why two features of
> > many modern cars, front-wheel drive and anti-lock brakes are
> > extremely helpful in keeping cars under control in reduced friction
> > situations.
> >
> > Hugh
> > --
> >
> > Hugh Haskell
> > <mailto://haskell@ncssm.edu>
> > <mailto://hhaskell@mindspring.com>
>
>
> I was not completely comfortable with the explanation for
> the non intuitive observation on car stability that Hugh describes.
>
> In the two cases,
>
> first the front wheels slip.
> There is a force at the front wheels opposing the car's movement
>  at 180 degrees to the movement. Any perturbation in yaw meets
> a correcting moment from the rear wheels and a small pro yaw moment
> from the front.
> It's reasonable to accept that the former is bigger than the latter.
>
> second, the rear wheels slip.
>  The front wheels may steer into the yaw to oppose it, so there is
> sideways translation. This is a dynamic effect.
> But if the front wheels are not steered, they provide a pro-yaw
> sideforce, while the rear wheels simply provide a force at
> 180 degrees to the car's movement.
>
> But then I look again at Hugh's explanation, and I see that I
> am balking only at the word 'retarding' force - which I would
> replace with sidewards force (provided by a rolling tire) -
> sidewards to the vehicle's direction in fact.
>
> Brian
>
> brian whatcott <inet@intellisys.net>  Altus OK
>                 Eureka!

--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
have to..
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