Re: Up Hill or Down

[David LeBlanc <dleblanc@mindspring.com>]

At 08:31 PM 1/10/00 EST, Tivers@aol.com wrote:
>In a message dated 1/10/00 3:28:45 PM Pacific Standard Time,
dfletche@gte.net 
>writes:

><< If the horse's back remains level, the center of gravity will not change. 
> But bringing the hind legs forward changes the relative load on the fore and
> hinds in favor of the hinds. Don't confuse these two. David worked out the
> math. But it was not a change in CG, but a change in support location (the
> assumption in that math was that the back remained level relative to
> gravity - lower in relation to the slope). If the horse does not lower his
> back (with respect to the slope) then the horse tilts forward with respect
> to gravity and the CG will shift forward.>

>Well, you're on to the next question already. We still don't have a 
>definitive statement from the horseman-observer that a horse standing on a 
>sloping plane, nose down, receives more weight on the forelegs--before any 
>contortions take place. Once that is established, simply, without any 
>formularific obfucation, 

If the horse remains parallel to the ground, the load distribution won't
change.  It is a simple, provable fact.  If you're incapable of dealing
with high school algebra and trigonometry, then you won't be able to
confirm or deny this.  It's not a matter of opinion, and discussing it is
about as useful as debating whether the acceleration due to gravity at the
earth's surface is 9.8 meters per second square.  If you can do algebra and
trig, then just try to follow the statics lesson I gave you.  Draw it out
on a piece of paper and work the math.

>then we can proceed to the second assertion, that 
>the horse is capable of countering the effects of gravity by crouching lower 
>behind, as, it is said, by moving his rear legs forward--that is moving mass 
>forward, underneath his body. 

You obviously do not understand what I wrote.  I tried my best to describe
it in a way that anyone with a basic education could follow, but e-mail
doesn't make a great chalkboard.  There is no 'countering the effects of
gravity', or changing the laws of physics.  That's a ridiculous notion, and
the fact that you brought it up shows me that either you just don't have
the math background to follow simple algebra (not an insult - lots of
people don't, and the state of math education is sorely lacking - I've
taught algebra to college students), or I'm not explaining it in a way that
you can understand.  Let's review, and see if maybe you can follow it this
time:

1) The sum of the forces acting on an object in each direction must balance
out, or it will accelerate.  This is known as Newton's law, and is where
the story about the apple came from.

2) The offset at which a force acts times the force is known as the moment
(or leverage).  If something isn't going to spin around either a hinge
point or its center of gravity, all these have to balance out, too.  You
can observe this by getting on a see-saw with someone who doesn't weigh the
same as you - one of you has to sit further in than the other.

Now, the first point says that the horse has to carry all of its load on
some combination of the front and back legs.  Pretty simple conclusion.
However, this part alone doesn't tell us what the distribution is going to
be.  The second equation is needed to find the answer - 9th grade algebra
tells you that if you have 2 unknowns, you need 2 equations.  What changes
here is that how much of the load ends up on which end of the horse is
determined by WHERE THE ANIMAL PUTS ITS FEET.  If it puts its legs straight
down, the load is 60-40 front to back.  If it puts them all 4 together in a
small spot, then the load is going to be very close to 50-50.  If it brings
its hind legs in so that they contact the ground closer to the center of
gravity than the fore legs do, then the hind legs will carry more of the
weight.  If it puts its rear legs directly under its center of gravity, it
can do neat dressage tricks, and takes all the load on the rear legs.

If you can't follow this, then I'd refer you to "Vector Mechanics for
Engineers : Statics and Dynamics", by Beer and Russell.  It's an excellent
text.  I've spent many, many hours with an earlier edition, and got an 'A'
in the class.  It also seems to be getting good reviews from readers at
Amazon.com.


David LeBlanc
dleblanc@mindspring.com


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