<% appTitle="Ridecamp Archives" %> Ridecamp: Re: [RC] Mad Science
Ridecamp@Endurance.Net

[Archives Index]   [Date Index]   [Thread Index]   [Author Index]   [Subject Index]
Current to Wed Jul 23 17:30:54 GMT 2003
  • Next by Date: Re: [RC] Mad Science
  • - Rides 2 Far
  • Prev by Date: [RC] Endurance Awards
  • - Diane

    Re: [RC] Mad Science - Truman Prevatt


    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