Re: .Bernoulli and curve balls.

[palmer@sfu.ca (Leigh Palmer)]

> The argument referred to a physical situation in which one side of a
> round spinning object is causing the airflow to become turbulent
> while it remains laminar on the other side. The nature of the ball is
> immaterial as long as the forces involved are the same. Stitches
> cause the airflow to become turbulent at a different velocity and as
> they rotate around, can cause the direction of the Magnus force to
> change. The latter does not happen with a smooth ball. The same
> physics applies to a fast ball as well -- if the ball's translational
> velocity is high enough, it is almost impossible to make it curve
> very much. This is partly due to the smaller time of flight but
> mostly due to a reduction in the Magnus force due to turbulent flow.
> The physical effect is the same as that which causes a reversal of
> the sign of the force for balls with more uniform surfaces. The
> physical principle is more generally applicable than for that
> specific example -- it is not a whole new day.

No, but it is a whole new regime. If the relevant length is the width
of the seam then the onset of turbulence is at a relative speed less
than one tenth as great, and my previous protestations about long term
stability of the phenomenon for a real curve ball apply *a fortiori*.

I don't see why you are fighting this. Isn't it clear? I know that it
doesn't involve the Bernoulli equation, but nonetheless the physics is
done; it is well known territory.

> Do not misquote -- the argument is not wrong, the functional form of
> the Magnus force near the transition to turbulent flow is wrong IN
> DETAIL. However, though the real function is not a simple
> superposition of low- and high-velocity limits, it must ultimately
> reduce to those limits in the appropriate cases. Therefore, though
> Adair's function should not give the correct QUANTITIVE force, it
> does provide an adequate tool for QUALITATIVE reasoning.

I apologize again for the truncation, especially since it appears that
I did miss your point. I am used to quantitative reasoning. Is the
Adair argument off by a factor of two? Ten? Or maybe as far off as the
greenhouse effect is from explaining the heating of greenhouses?

That was a rhetorical question, of course. If you have no quantitative
answer wait until I have had a chance to look at the book, perhaps
next week. (I have two midterm exams to give this week.)

> We do this all the time. Do you use (mu) N for the frictional force?
> It too is wrong in detail and gives quantitive predictions that do
> not work in even the most rudimentary physics lab. Friction, too, is
> a very complicated problem that likely would require a supercomputer
> to solve it correctly (if then). This does not prevent us from using
> an idealized situation for qualitative reasoning, simply because it
> makes the analysis tractable and because it highlights a particular
> and relevant physical relationship. This simple form for friction
> does have the correct qualitative behavior (friction does depend on
> the magnitude of the contact force between two surfaces) and
> therefore provides a tool for reasoning about general behavior, even
> though if you try to use it for quantitative analysis you get
> blatantly wrong results. This will have to suffice until you get
> your grant to do a supercomputer analysis of curve balls (real soon
> now, I hope -- it would be interesting).

I'm scarcely the right person to work on such a problem. The linear
model of surface friction is widely applicable (that means it applies
well in many circumstances) and yields quantitatively correct results
(that means +/- 20% in this case) for them. If you are talking about
doing school laboratory exercises and looking up coefficients of
friction for, say, "hardened oak on cast iron" in a textbook, then of
course you are correct in your disdain for the model. That is not the
manner in which it is applied and in which it is useful. I ask: is
the simple model Adair advances likely to be correct in the same
segree?

> Some people have even won Nobel prizes for doing things that were
> arguably wrong but were near enough right to enable useful analysis
> to be performed.

Example? Was it known at the time it was done that the analysis was
incorrect, as is the case here?

> It is interesting to note, however, that the same "faulty" wind
> tunnel tests give the correct results for a spinning baseball. Are
> they only invalid for smooth balls? If the calculation is at variance
> with experimental observation, likely the calculation is the one
> which is wrong.
>
> The spin rate of a typical ball decreases by something on the order
> of 20% per second. This varies somewhat with the speed of the
> ball but for a 60 mph curve ball, which will cross the plate in about
> half a second, it isn't very much change. Spin rates are about 1600
> rpm and so decrease to around 1400 rpm.

Useful numbers. Were these known and emulated at the time of the wind
tunnel measurements, or were the measurements done in the manner I
suggeted, with constant speeds?

Leigh