Re: Rex cornering overview (from T. rex mechanix)

[ngear@gvtc.com]

Betty wrote:

>Human athletes turn during a full-out run using method #2, method #3 and
>method #5-primarily 2.  In competition most arenas are not banked, and
>are mighty smooth so speeds are higher than possible cross-country...

Referring to body rotation due to:
>> 1) Some action by the tail:  
>> 2) Wide-stepping:  
>> 3) Banking:  
>> 4) Two-foot torque to ground:  
>> 5) One-foot torque to ground:

Okay, it looks like I should have elaborated on something here.  In order to
impart torque to a body, you must have a couple.  You have a couple whenever
there are two forces (or components of forces) acting in opposite directions
at some distance from one another.  The torque couple in each of the above
is as follows:

1 Tail action:  Never could find the couple.
2 Wide-stepping:  Since the feet are at some side displacement, there will
be a torque couple whenever the feet impart a change of velocity from what
the body would have experienced otherwise.  More on this in a bit.
3 Banking:  As can be seen in the wobble rotor, the couple in the banking
effect comes of points on different sides of the body "surfing" the sine
wave in opposite directions.
4 Two-foot torque:  One foot pushes one way and the other foot pushes the
opposite way.
5 One foot torque:  One side of the foot pushes one way and the other side
pushes the opposite way.

The greater the difference in force, and/or the greater the distance between
the forces, the faster the rotational acceleration.

Now, as to Betty's comments.  There are two different couples human athletes
can experience with regard to #2.  One is when a foot is displaced to the
side and it is trying to change the velocity of the body.  This couple has
two flavors: thrust vs. inertia, or braking vs. inertia (from a physics
point of view, the principle for each is the same).  In both these cases,
displacing the foot to the side of the center of gravity causes a sideways
acceleration resulting in a net change of direction.  In the case of thrust
vs. inertia, the rotation is in the correct direction and will face the
athlete into the new net direction.  An example of this action can be found
when football players both launch and turn simultaneously.  In the case of
braking vs. inertia, the rotation is in the wrong direction, and will result
in the athlete having to run sideways--which is generally not a good thing.
However, there is a second couple of consequence to humans here.  Remember I
said a change of velocity *from what the body would have experienced
otherwise.*  Runners run through air, which constantly acts to retard their
motion, so you will have a torque couple for any runner maintaining a
constant speed whenever the center of the retarding force is offset to one
side of the feet--which is what happens when a runner banks around a turn.
(So this couple would be thrust vs. drag.)  

So Betty is correct that human runners can use couples 2, 3, and 5.  
   The effect of 3 (banking effect), as I mentioned before, is always
present with any body that experiences a change of axis, but the effect is
not large.  In the case of a runner traveling 15 mph around a 100 ft. radius
turn on a track, the banking effect would contribute almost six degrees
rotation around a 180 degree turn.  (Or .07 rpm--roughly four times the
speed of an hour hand).
   The effect of 2 (stepping wide) would apply in thrust vs. inertia in any
event that required a simultaneous quick start and turn, but thrust vs.
inertia would not apply to running at sustained speed.  The case of thrust
vs. drag, however, would certainly apply in the case of the runner rounding
the bend on a running track, and probably between 10 and 15 percent of the
drag would be translated into rotational torque in the above example.  But
now our runner has the opposite problem of rex.  This runner only needed to
impart 2 rpm rotational velocity at the very beginning of this turn, and
because this is a constant radius turn, no change in rotational velocity
would have been required until the completion of the turn.  But the thrust
vs. drag effect is acting to accelerate the rotation of the runner
throughout the entire turn, so this athlete will have to continuously impart
foot-torque to the ground around the turn to counteract this effect.
Fortunately, the tortional forces involved in all of these are pretty
trivial and probably would not be noticed at all by the runner.

Okay, wrestling this topic back to rex, what about those aerodynamic forces?
Could thrust vs. drag (due to air resistance) have made a significant
contribution to rotation?  My suspicion is that the air-drag to mass ratio
would have been very small, so I would expect this effect to be quite small.
I would prefer, of course, to be able to work out the actual numbers, but
unfortunately, to do the numbers I'd need three things.  I'd need to know
what air-drag a rex experienced at a given speed (which would be tough to
figure, because surface friction would have dominated over compressive
drag--the opposite of what we experience--and surface friction is a great
deal more complex than compressive drag), I'd need to know the center of the
drag, and I'd need to know how far the rex was banked over in a turn--for
which I would need to know the radius of the turn, for which I would need to
know the rotational velocity.  Since the effect on rotational velocity is
the very thing I am trying to figure, you can see the problem with that last
one.

One final point is that, although thrust vs. drag might have added something
to rotation, it could not have helped arrest rotation at the conclusion of
the turn.

Anyone know a good aerodynamicist?

Nicholas