Re: [Phys-l] football orientation in flight

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

Thanks for keeping the discussion going.  Here is the original question
from the student, submitted with his permission:
========================================
Professor Schnick,

When a quarterback throws a long, arcing pass the point of the football
is intially upwards but at the end of its path the front points
downward.  Is the front pushed down because of Bernoulli's principle?  I
don't think that the rotation of the football is the primary cause
because when I throw the ball straight upwards the same effect does not
happen.

-Eric

Eric T. Holland
Saint Anselm College Class of 2009
100 Saint Anselm Drive Box 0909
Manchester, NH 03102-1310
========================================
> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
> Sent: Thursday, May 22, 2008 9:08 AM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] football orientation in flight
>
> On 05/22/2008 05:00 AM, Jeffrey Schnick wrote:
> > Does this work?  (Discussed as viewed by the thrower.)  The ball is
> > spinning clockwise meaning it has forward directed angular momentum.
>
> Or, equivalently, we could just say the angular momentum bivector
> is clockwise as viewed by the thrower ... so we don't need to
> mess with angular momentum vectors or the right-hand rule.
>
> > As
> > it arrives at the top of its flight it has a positive angle of
attack.
> OK.
>
> > This results in some circulation
>
> Does that mean circulation around the roll axis (i.e. spin axis)
> or circulation around the pitch axis?  I'm assuming the latter.

Around the pitch axis.

> > which means the air acquires some
> > rightward angular momentum.
>
> Probably not.  Most fluid dynamics treats the air as irrotational,
> which means vortices can only be created in pairs.  When airfoil
> starts to produce circulation it sheds a _starting vortex_ equal
> and opposite to the bound vortex.
>   http://www.av8n.com/how/htm/airfoils.html#fig-trailing

Are we agreed that the effect would not occur if the ball was moving
through vacuum?  If so, then for this fluid dynamics problem, it is not
okay to treat the air as irrotational.  The angular momentum of the ball
is changing during flight.  By conservation of momentum, it must be
exchanging angular momentum with the air.

> As a separate argument leading to the same conclusion, if you throw
> (or kick) a football /without/ any spin-stabilization but with an
> angle of attack, little or no torque is observed.  

How can you tell?  I have never seen a football launched point first
into the air in the direction of travel with no change in orientation
whatsoever.  Also, if there is very little rotation, the response to
torque would be different that in the case of the spinning football so
if the football was in an orientation for which there is significant
circulation, it might quickly change to one for which there is little to
no circulation.

> If the torque
> depends on angle of attack, the same lack of torque would occur
> in the spinning case.  (This is a problem because you would need
> a lot of torque in order to change the spin axis in the spinning
> case.)
This is a problem if your are right about the lack of torque for the
same angle of attack in the case of a non-spinning ball.  Wish I could
go outside and launch a 65 yard pass, point first, with no spin right
now.  I think punters do sometimes get the football to tumble forward
during the latter half of flight but I am not confident in my memories
of my observations and the tumbling may be due to a small initial
angular momentum about the pitch axis.
> >  This means the ball gains some leftward
> > angular moment which, with its big roughly forward angular momentum,
> > means it yaws left.  This results in some leftward lift and its
> > associated circulation which means the air acquires some upward
angular
> > momentum.  This means the ball gains some downward angular momentum
> > which, with its big roughly forward angular momentum means it
pitches
> > downward.
It keeps pitching downward, overshooting its mark, then it acquires some
downward lift (oxymoronically) and its associated circulation which
means the air acquires some leftward angular acceleration.  This means
the ball gains some rightward angular acceleration which makes it yaw
right until it is pointing in the direction of its velocity.  By this
time the ball is at a point in its trajectory for which the pitch angle
is correct and the process stops until the ball reaches a point in the
trajectory for at which the current pitch represents an upward angle of
attack.  Then the process begins all over again.  (Okay, of course it
doesn't occur stepwise.  The point is, the changing nature of the torque
due to the changing direction of the velocity of the center of mass of
the ball means that this is not a recipe for ordinary precession.  It
does suggest that there is some wobble, and I think that there is some
observable wobble, but the wobble is not symmetric with respect to the
velocity vector and the overall effect in a half cycle is to bring the
axis closer to the new direction of the velocity of the center of mass.
In fact, I think I have seen a ball that started out with noticeable
wobble, lose some of that wobble in flight.  (Does this really happen?)
> Even if we hypothetically accept the air-acquires-angular-momentum
> part of the argument, this part says it pitches down only after it
> has yawed left.  This is a recipe for precession or wobble of the
> axis _around_ the forward direction, without bringing the axis any
> closer _to_ the forward direction.
>
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