Re: Mechanical, chemical and heat energy

[Truman Prevatt <truman.prevatt@netsrq.com>]

Niccolai when is the last time you saw a horse that looks like a
basketball!  A horse is not sperhical.  A spherer is the minimal surface
for a fixed volumn in three space - the surface that minimizes the
surface are for a fixed volumn.  I would believe that the reason one
does not see many living objects that are spheres is that they would fry
from the inablability to remove heat. 

Most horses have large "flat" areas - the neck, the side, the side of
the hind legs, etc.   One can truely get into this mathematically if one
wants but unless you can write the equations and solve them then
quantative and geometrical arguments will have to do.  The 25% os a
gross approximation and of course you are correct that mass is directly
related to volumn.  The basic point is when the mass - or volumn -
increases so does the surface area, given a fixed mass density.  Yoo are
right it may be 10 to 15% instead of 25% depending of the shape of the
horse.  

At any point the larger horse of the same shape will have additional
surface in which to dissipate heat.  

The convservation on enerery at the cellular level implies that the
amount of energy to produce the required machanical energy is turned
into mechanical energy is equal to the amont of mechanical energy
required plus the loss in heat energy plus the system overhead energy. 
Chemical to mechanical conversion is not perfect and heat results. 
Since energy is conserved then either this energy is lost to the
environment or it is absorbed by the system, the horse.  The horse can
only absorbe a finite amount of heat before it croaks.  

When the larger system is considered to include the external enviroment,
then the ambiant physical conditions must be considered which include
the temp and the air's ability to support the conversion of sweat to
water vapor thus removing heat from the horse.  The realtive humidity is
the measure of the air's ability to take on additional water vapor.  At
100% the air is saturated and it cannot accept additional vapor so there
is no cooling.  However there is a secondary method of cooling in this
case. When the horse takes air in its lunges the temp of the air is
raised and the relative humidity is decreased - the air will hold
additional water.  Then water mosture is turned into vapor in the lungs
and cools.  But again a larger horse - all else being equal will have
larger lungs so more area for which water to vaporize and additional
cooling.

I am not sure what you mean by a damped system.  I would have described
it as an controlled system with the controls trying to keep the vital
metabolic parameters in a very narrow range.  

I would agreed that you might be able to decouple the rider from the
horse, i.e. simiply take the extra weight as belonging to the horse if
the rider weight was a small precentage of the horses weight and didn't
significantly - what ever the hell that means - the basic properties of
the horse. For example if the center of mass of the horse was not
perturbed by any significant amount then you are probably correct.  If
you put a person that weights 25% of the weight of the horse then I
believe that more care needs to be taken.  A six foot 100 kg rider will
significantly perturb the location of the center of mass of the system
and hence will perturb the state of the system when compaired to the
"unperturbed system of the 500 kg horse".

The only way to find out is write the equations of montion for both and
solve them.  A fairly nontrivial task if I must say.

Truman

Niccolai Murphy wrote:
> 
> I should know better than to get into this with a methematician!
> 
> Regarding surface area, not strictly true. Weight is proportional to
> volume which would be a approimated by a cubic function of some
> notional dimension (especially if we are discussing a spehrical
> horse). Whereas surface area would be approximated by a square
> function of that same dimension. So a lighter horse should have a
> higher surface area to weight ratio than a heavier horse.
> 
> Also, energy is conserved if you take the boundary of the experiment
> far enough away from the horse. If you draw the boundaries around the
> horse than energy is lost from the system, as you say in the form of
> heat, noise, etc. The horse itself must be a highly damped system
> leading to huge damping losses in the form of heat. If damping is a
> function of the product of force and velocity then the heavier horse
> without payload would tend to loose more than the smaller horse. So it
> interesting to see that the rider weight seems to be represented by an
> uncoupled equation.
> 


-- 
Truman Prevatt
Mystic “The Horse from Hell” Storm
Rocket a.k.a. Mr. Misty
Jordy a.k.a. Bridger (when he is good)
Danson Flame - hey dad I'm well now and ready to go!

Brooksville, FL