Bad Math...and Physics (was Physiology of Weight)

[guest@endurance.net]

K S SWIGART   katswig@earthlink.net


Truman Prevatt said:

> Work required is directly proportional to mass - that's high
> school physics. It takes twice the work to carry a 220 pound
> rider than it does a 110 pound rider.

The problem with the math/physics of this is that it does not take into
consideration the fact that the horse must expend work moving its own
weight in addition to the rider's weight.  So...assuming the same wieight
horse (an absurd assumption, but I will make it anyway for the sake of
argument) of approx 900 lbs (I suspect that most endurance horses are
around this weight, but I have one that weighs only 600 lbs and some
people have ones that weight over 1200 lbs), then the total weight carried
varies between 1010 and 1120 so the difference in total weight carried (of
which work is a function) is 11% more not 100%.

So, if you are going to do that kind of math, make sure that you are doing
math with the right numbers.

However, while it might be high school physics that says that work done is
directly proportional to mass, this only holds true as long as
acceleration is held constant.

Even discounting that horses change their speed across the ground, during
the course of single stride the total mass of the horse (body and rider
together) is constantly accelerating and decelerating depending on which
one, how many of the feet the horse has on the ground as well as where
under its mass the horse puts its feet during the course of its stride
(e.g. just how much "extension" does the horse use).  The physics
associated with this is unlikely to be covered in a high school physics
class because, among other reasons, the math starts to become REALLY ugly.

I don't mind the concept of using basic mechanical physics (f=ma) to
discuss the amount of work done by endurance horses; however, if you are
going to do it, it would be wise to understand that the relationship
between work done and load carried is MUCH more complicated than dividing
rider weights into each other.  Doing so is not even a good way of getting
a close approximation.

And it begs the question entirely of how horse and/or rider weight affects
the team's capacity to do work.

kat
Orange County, Calif.