## Thursday, January 01, 1998

### Formula for Energy Expenditure - Susan Garlinghouse

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 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.

Susan Garlinghouse