Re: RC: Re: Re: Up Hill or Down

[David LeBlanc <dleblanc@mindspring.com>]

At 09:25 AM 1/12/00 EST, Tivers@aol.com wrote:
>Here is the beginning of a conversation with James Rooney on the subject. 
>
><< Yes and no, Tom. There is no change in the total vertical weight or the
> percentage weight on fore and hind. There is an increase of force parallel
> to the ground - a braking or decelerating force going downhill and an
> accelerating force going uphill. Stress means force per unit area, and you
> are really talking about total force and not unit force.
> So going up and down hill does increase horizontal but not vertical force.
> Same thing applies to the standing horse on an incline. As the angle of the
> incline increases there must be more horizontally directed force to
> maintain its position. Okay? Jim
 
> At 08:32 PM 01/11/2000 EST, you wrote:

>Ok, my error is in the words "carrying more weight"?  Weight being vertical 
>force. What the incline does is change the direction of force vectors--going 
>downhill throws more force at the forelegs, but not more "weight". Is that 
>correct?

One of the assumptions I made when figuring the numbers was that the ground
was reasonably soft, and that the horse's hooves would dig in enough to
flatten.  Under this assumption, even though the horse's body might be
tilted, the hooves are supported by a surface that is flat.  With most of
the soils I've seen on trails that were very steep, this is a pretty
reasonable assumption.  If the ride is on a road, it isn't likely to be all
that steep - for example a 15% grade means you get 15 ft rise for every 100
ft, and we usually consider that a fairly steep grade for vehicles - this
works out to about a 10 degree slope.

If you change that assumption, and say that the horse's hooves can't dig
into the surface (say hard clay or pavement), now there is going to be a
force parallel to the ground that acts upon the hoof.  You can take any
element of a system and look at it from the standpoint of force and moment
balance, so you could do that just for a hoof, a whole leg, or the entire
horse.  If you have forces acting in more than one direction, then you have
to balance those, too.  Note that forces along both the vertical and
horizontal enter into the moment balance.  This does cause the load to
shift towards the front, but again, the placement of the legs with respect
to the center of gravity is still going to have a strong effect.  Whether
that causes a higher load in the foreleg than while standing on flat ground
is going to depend on where the horse puts its legs (and how much it lowers
its CG by dropping its butt).  Having a rider in the picture changes this
part quite a lot, as the rider can very easily shift their CG back and
forth quite a bit, and isn't a negligible part of the overall load.  If the
rider leans back (you have to), you're bringing the overall CG back and
down - both of which tend to decrease loading on the front.  Whether the
saddle has a tail crupper, how tight the girth is, and how well the saddle
fits the horse, as well as how much the horse compensates by lowering their
butt all impact what the rider's weight shift is going to do to the loading
on the horse's legs.  

So the horse dropping its butt is going to help it in this situation in a
lot of different ways - makes the rider come forward less, reduces the
extra load in the front to offset the moment from the horizontal (with
respect to the ground), and shifts the vertical loads rearward.  I don't
have time this morning to run the numbers, and I really ought to go measure
a horse to figure the actual leg length to body length - plus I'd need to
guess at where the CG sits vertically.  If the horse responds to the change
by just leaning back a little, that can be used to offset the horizontal
moment, too - the further the front support is from the CG, the more
effectively it counteracts the horizontal forces, and the more of the
vertical forces are shifted to the rear.

Short answer is that it depends.  Depends on where the horse puts their
legs, and what sort of footing you're on.  You can't just say more load
ends up in the front, since it depends on a lot of factors.  It would make
a good exam problem to figure out exactly how it all works out.

Now when a horse is moving, the picture gets a lot more complex.  Any time
you have motion to consider, you not only have to balance forces and
moments, but you also have to balance momentum and energy (which you figure
depends on what is more convenient - certain types of problems are a lot
easier figuring it one way than the other - energy is usually best, because
of conservation of energy - and energy isn't directional).

If you look at the energy balance of something moving, you've got 3 factors
- wind resistance (probably not a big deal to a typical horse - they're
naturally well-designed from an aerodynamic standpoint - though the rider
isn't), the amount of energy absorbed by the ground (for a car, this would
be rolling resistance), and that's going to be a strong function of the
soil - this is why a race on sandy ground is so much harder on the horse.
Lastly, you've got change in potential energy.  If a horse is trotting
downhill, and isn't trying to apply the brakes, then it is trading off
potential energy against the other 2 factors, and is actually doing less
work than it is on level ground.  Less work means lower dynamic stresses in
the legs.  If we're assuming a trot, it is also probably a good assumption
that the horse isn't trying to slow down by much, and the butt probably
doesn't drop by much - in this case, the animal is going to have about the
same distribution front to back as on flat ground.

As soon as the animal tries to slow down, then you get much higher loads.
If it is a really steep hill, in reality, you're probably not going
straight down it, but are dealing with switchbacks.  In this case, trotting
isn't an option, and the horse is probably going to try to get each foot
solidly under it before it moves the next one - in that case, we're almost
back to the static situation.

Lastly, all this 'rocket science' does is help us quantify and explain what
we observe.  The trick is to closely observe what is going on in the real
world and see how that correlates.  Heidi tells us that the horses
typically end up with more injuries to the rear from downhills than they do
to the forelegs.  If her observation holds in general, then I'd strongly
suspect that the rear legs end up with higher loads overall.

What would be an interesting study would be to put special shoes with
stress sensors on a horse, make them do different things, and record the data.


David LeBlanc
dleblanc@mindspring.com


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