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Re: formula for energy expenditure

Yeah, right, no problem. . . . .we'll just figure this little dude up
right quick here!!!!!

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Hiya,

A bunch of people have been asking me lately about replacing the
calories burned by the horse during a ride and I thought everyone might
be interested in seeing a nifty formula that was published in the
journals from Pagan and Hintz (both widely respected) that pretty
accurately calculates the calories expended by a horse during exercise.
This is the formula that is much more accurate than the formulae
currently used in the NRC books to calculate energy required for work
above maintenance levels.

It's interesting, if nothing else, to see the calories required for an
average horse to cover 50 miles---a 900 lb horse carrying a 165 lb rider
and covering 50 miles in 6 hours actual riding time burns up 18.3
Mcals.  The same horse carrying a 210 lb rider and covering the same
fifty miles in four hours would burn 26 Mcals.  A 1000-lb thoroughbred
carrying 112 pounds and running a mile in two minutes (sorry, Tom, I
don't know average times for a mile) would burn 4.6 Mcals in just two
minutes, which is pretty damn impressive considering he's providing
almost all of that energy in the form of glucose (endurance horses get
at least a large portion of their energy requirements from fats, which
are in greater supply.)  And since feed efficiency is only around 60%
efficient for a typical ration (that means that only 60% of the calories
ingested actually get utilized in energy production, the rest is burned
in metabolism or lost heat, etc), that means that you would have to feed
30.5, 7.7 and 43.4 Mcals, respectively, to make up the energy burned
during that ride.  Incredible, considering that the same horse would
only use 13.4 Mcals a day for daily maintenance.  Another good argument
for making sure your horse is in good body condition before you start a
heavy ride season---he's going to need those extra stores of fat!

(And, by the way, please don't take this as a recommendation to try to
feed back those calories right after the ride, or we'll all going to
have a whole lot of colicky, foundering horses).  

Anyway, here's the formula.  The engineers and math whizzes on the list
can take it and run with it.  For the rest of us, below are directions
on how to actually get useable numbers.  Again, this is just for fun,
not an indication that anyone should make major changes to their horse's
diet...unless you're riding 50 miles every weekend, only providing 10
lbs of hay a day and scratching your head as to why ol' Flash is looking
a little peaky. :-D

The formula is: Y = e (superscript)3.20 + .0065x; where x is the speed
is meters/minute, and Y equals the calories expended per kg per minute.

Here's how to actually get an answer if you're not a math genius---you
will need a calculators that does logarithms, natural logs, etc, just
the cheapy kind they give out at the gas station won't do it.

First you need to calculate the average speed ("x")you're traveling at. 
It's okay if you change speed alot, the formula still works.  Figure out
how many miles you traveled and how long it took you to get there. 
Convert the miles to meters by multiplying miles times 1609.35 (the
number of meters in a mile).  Fifty miles is 80,467.5 meters.  Divide
this number by how many minutes you took getting there.  This will give
you your average speed in meters per minute.  For example, if you took
six hours to travel fifty miles than x= 80,467.35 divided by 360 =
223.54 meters/min.

Multiply x by .0065 and add 3.20.  For example, 223.54 times .0065, plus
3.2 equals 4.65.  If you have a memory function on the calculator, put
this number into the memory, or at least write it down.

Find on the calculator the inverse function for the natural log.  The
primary function on the caculator button will say "LN", and the
inverse/2nd function will have an "e" with an "x" superscript.  Take the
number you just calculated above (in the example, the 4.65), push the
2nd function key, and then the LN key to get the inverse function.  In
the above example, the result would be 104.89.  This number is the
number of calories your horse is burning PER minute, PER kilogram of
weight getting moved down the trail.  This is "Y".  Put this number into
memory or write it down.

To calculate the total expenditure of energy, you need to know the
kilograms.  Take your horse's weight in pounds and add the number of
pounds he's carrying in rider and tack weight.  For example, a 900 pound
horse carrying 165 pounds of rider and tack totals1065 pounds.  Divide
this number by 2.2 to convert to kilograms. 1065 pounds equals 484
kilograms.

Take the number of kilograms and multiply it by the Y number you
calculated above, and then calculate THAT number by the minutes you were
riding.  In the on-going example, if you took six hours to do a 50 mile
ride, you rode for 360 minutes.  So the total expenditure of calories
was 18,650,000 calories.

To convert this number into units you're more familiar with, divide this
number by 1,000,000 (one million) to give you Mcals, or by 1000 to give
Kcals, the unit most people are thinking of when they think calories, as
in "that piece of cake is 500 calories".

Divide the number of Mcals by .60.  For example, 18.65 Mcal divided by
.60 equals 31.08 Mcals.  This is the number of extra caolries you would
have to actually feed just to replace the calories burned during this
ride, IF you wanted to maintain weight---remember, the horse has already
supplied the energy he needed from fat stores, as well as a small amount
from what he ate during the ride.  Hopefully, if you're competing, then
you are already feeding more than just a flake of hay.  Just to give a
general idea, you would have to feed 20 pounds of corn to supply the
18.65 Mcals, or about 15 cups of vegetable oil, or 23 pounds of oats. 
So if you're competing alot, you might use this formula to give you just
a general idea of how many extra calories you need to be providing in
the daily ration (obviously, you would spread the extra calories over a
number of days, and make sure the horse keeps exercising, so you don't
run into azoturia problems).  If you don't provide enough calories, the
horse isn't going to drop dead or his ears fall off, he's just going to
lose weight throughout the season, which IS eventually going to affect
his performance.

This formula seemed to be pretty accurate in the study, but probably is
only a rough estimate for endurance horses that will be expending more
or less energy depending on factors like terrain, temperature, the skill
of the rider and individual factors like temperament, keeping qualities,
type of feed provided and feed efficiency factors.  But for those riders
that like knowing the details of what's going on, this formula might be
something interesting for you to keep around just for grins.

Seeya,

Susan Garlinghouse

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