Re: Mechanical, chemical and heat energy

[Niccolai Murphy <niccolai_m@yahoo.com>]

---Truman Prevatt <truman.prevatt@netsrq.com> wrote:
>
> 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. 
 
No they are not spherical but can be approximated into a number of
basic shapes, cylinders for barrel and limbs, ellipse for neck and an
ovoid for the head. In most cases you are down to a radius and length
or at least a mjor and minor axis. So the equations still hold true,
you can't get around them with a bit of arm waving. Compensation for
the decrease in surface area to weight ratio is generally species
specific, hence the large ears on the African elephant and so forth. I
think we agree on that part so on to the next...

Footnote... I thought most animals were not sperical because they
couldn't stop themselves fro rolling out of bed otherwise.

> 
> 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.  

Yes, 10 or 15% sounds like it might be but right. However if we
consider the unloaded horse and if we consider the system of the horse
alone, then the heat generated by the horse through damping losses in
the mechanism, we could in general approximate the heat generated to
the weight of the horse. Damping approximates to the product of force
and velocity. With force prportional to weight and velocity held
constant that leaves the heavier guy with more heat to loose.

The mechanism of damping I'm assuming here is the damping in muscle,
skeleton and joints. All quite wastefull, why didn't nature invent the
wheel and paved roads?

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

True, but will also have more heat to disipate.
 
> 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.  

I agree with this only if you count frictional losses in your system
overhead. I think that these losses are very high in all of us, and
get greater with age.

> 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 agree that there is a beautiful control loop in a horse. Consider.
From a energy consumption point of view damping is very important in a
mechanical system controlled or otherwise. If you clap a horse on the
rump (with a few noticable exceptions, I'm tempted to say Arabs here
but that wouldn't be PC so I'll say my TWH mare) it will not go
bouncing off the walls forever. It will deform slightly where you
impacted it and the muscle/fat will bounce back once and the come to
rest. QED... Damping. There's tons of it in the system and just as
well too. I'm sure the control loop minimizes the losses as far as
possible. I think you have considered heat only from chemical sources
and not mechanical ones too.

> 
> 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.
> 

Well we could try, as a first approxmation consider two spheres, with
masses M1 and M2, S for displacement then, stick dot S into the
damping term and dot dot S into the forcing function.... by the time
we are done we could design the ultimate saddle pad!






==
Nicco Murphy - Poway, San Diego, CA


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