Ridecamp: Re: [RC] Mad Science

This is making an assumption that all horses are shaped the same.  Mass is
directly proportional to volume. So the key is the ratio of  the  surface
area to volume. This ratio changes depending on shape. For example if I take
a basketball and fill it full of water (the water used to measure the volume).
The surface area of this is fixed no matter the shape the basketball is in
as long as I don't stretch it. Now I can push on the basket ball and push
out half the water so there is now half the volume but the surface area is
still the same. So the ratio of surface area to volume has doubled. In fact
I can make the volume of the basketball arbitrarily small which makes the
ratio of the surface area arbitrary large. 

Of course a horse is not a basketball - else you'd never find a saddle to
fit him and he'd keep rolling out of bed, but if you look at the trunk it
pretty much is a cylinder. The same for the neck. Horses are built differently.
You have your round sturdy horses. A lot of people I know call these "mountain
horses." You have your thin, slab side horses with very deep heart girth
- usually with a high wither. You have everything in between. 

The volume of a cylinder is the arc length of the perimeter times the length.
For grins I took the sturdy horse to be basically a round cylinder and the
cross section of the second horse to be an ellipse ( elongated circle).  An
ellipse is specified by two lengths. The first is the longest length through
the middle (major axis) and the second is the length through the center at
right angles to the major axis (minor axis). I now measured two of my horses
to get the proportions of these values. They were about 2 to 1.  So I used
that in the calculation. Turns out that if you take a circular cylinder and
an elliptic cylinder of the same volume the elliptic cylinder will have more
surface area. You can show mathematically that the cylinder of finite length
that minimizes the surface are to volume ratio is a circular cylinder. Any
other shape of the perimeter will produce a larger ratio. 

With the 2 to 1 proportions I used the ratio surface area to volume of the
elliptic cylinder is 10% greater than that of the circular cylinder. 

So while this is a first order analysis, the key is the ability to cool is
very dependent on the shape of the horse. It may well turn out that a 16-1
hand 1000 slab side horse can cool just as fast as a 14-2 hand 850 pound
"sturdy built" horse based on the larger surface area to volume ratio as
determined by the shape. 

Truman

Susan Garlinghouse wrote:
> > I've been told by several ride vets that it's the ratio of body mass to
> > surface area. The determining factor tends not to be the amount of energy
> > produced by the animal but, it's ability to keep the body cool. A horse
> >     
> being
> > 15 hands tall and weighing 1200 pounds will probably have the same surface
> > area of a horse 14.2 at 850 pounds.
> >       
>
> Nope.  The 1200 lb horse has a body surface area of 6.817 square meters, or
> .00568 square meters of cooling area per pound of body mass.  The 850 pound
> horse has a body surface area of 5.411 square meters, or .00636 square
> meters per pound of body mass.   All other things being equal, the smaller
> horse is 12% more efficient at cooling himself, and in all likelihood, has
> less heat to dissipate to begin with.
>
>  Another factor in the equation is the
> > type of muscle that predominately composes the horses anatomy.
> >         
>
> True, but if you're referring to the Tevis data, 95% of the horses had 50%
> or more Arabian blood, generally of very similar muscle fiber type
> populations, so that was effectively cancelled out as a variability.
>
> Susan G
>
>