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I need help finding an equation that the Navy's Physical Readiness Program Office (PRIMS) keeps unpublished for some unexplainable reason and will not share after numorous requests. Anyways, luckily, I have access to a calculator where I can input two variables ( weight, calories burnt) and it returns the equivalent run time. There are two fitness events which require this machine to run-time equation, those are stationary bike and ellipticals. The elliptical equation was simple to recreate in javascript because I found a PDF explaining the conversion. This is shown below, however, the conversion for the stationary bike is what I can't find.

The equation to convert elliptical calories burnt into a run-time goes like this:

  1. Conduct a 12-min ET bout.
  2. Obtain the machine calorie report, while correcting for machine bias: a. Add 0 kcal for bouts on the Lifefitness 9500 HR. b. Add 20 kcal for bouts on Nautilus Model E9 16. c. Add 7 kcal for bouts on Precor Model EFX 556.
  3. Divide the calorie report from Step 2 by 12 to get energy production rate in kcal/min.
  4. Multiply the test subject’s weight in pounds by 1.09 to determine the total energy required to run 1.5 mi.
  5. Divide the result of Step 4 by the result of Step 3 to obtain the raw run time estimate in a decimal format.
  6. Multiply the decimal portion of Step 5 by 60 to convert it to seconds. The result is the raw run time estimate expressed as min:sec.
  7. Obtain the run time equivalent for the ET bout by adding 1:08 min for a male test subject or 2:15 for a female test subject.
  8. Use the run test standards in the PRT instruction to convert the run time equivalent to a PRT score.

The above shows an expanded version of the equation: Raw Run Time Estimate = (13.08*Weight)/Machine Calorie Report , plus 68 (1:08,mm:ss) or 135 (2:15,mm:ss) to correct for gender bias.

The above was taken from http://www.dtic.mil/dtic/tr/fulltext/u2/a462116.pdf

The equation to convert statinary bike calories burnt into a run-time goes like this: ? ? ? ? ?

This is where I am stuck.

In the case anyone is wondering what the purpose for this conversion is, it's two part: 1) curiosity, and 2) the last part of a IOS/Android/Windows phonegap application that I am making available to Sailors for free.

Thanks, I'm not the greatest a math, I can produce tables of the produced run time, weight, and calorie varibles if necessary.

Kane Schutzman
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  • I'm not asking anyone to solve this for me though I wouldn't complain, if someone could get me on the right path that would be helpful. – Kane Schutzman Feb 04 '14 at 19:06
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    If I were attempting to solve this problem, I would create tables of runtime with corresponding weight/calorie variables. Then, I would use some interpolation/curve fitting method to find a best-fit polynomial, and see if there's a pattern in common... (Just an idea.) – apnorton Feb 04 '14 at 19:10
  • Thank you anorton, I will be looking into your suggestion shortly. – Kane Schutzman Feb 04 '14 at 19:33

4 Answers4

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If you log into PRIMS and click on the "help" tab, there is a bike/elliptical calculator that will convert the calories you burned into your run time. There is also a calculator that will determine your overall score based on the numbers you enter (as goals). In case anyway is looking at this and needs to know where to find a calculator.

Kristin
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If you have tables with $m$ columns, $n$ rows, and you have a column whose value you are trying to match for general inputs, you can use regression techniques. The easiest would be linear regression, which will give you the best fit straight line to the data. Note that if the formula they use is not linear it will do a poor job. You will want to generate the fit using a set of data, and then test it against a different set of data. If a linear model does not work try fitting the data with the lowest order polynomial you can. Excel has tools that will do this automatically.

kleineg
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  • Also note that the function the Navy uses is of two variables. So, a typical linear regression fit might not be enough--some strategic pattern-matching/guesswork may be needed. ;) – apnorton Feb 04 '14 at 19:46
  • Well, starting to build the tables - so far I can at least say that the step 7 for elliptical is the same as for the bike conversion, so at least the gender bias correction is exactly the same. – Kane Schutzman Feb 04 '14 at 21:06
  • thanks for your comments I tried up voting but I don't have the necessary reputation. – Kane Schutzman Feb 14 '14 at 23:49
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for females: (6.296+4.087*(weight/calories)+1.77) for males: (6.296+4.087*(weight/calories))

Kane Schutzman
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With a little research I actually found that the fomula is:

Males: 6.296+(4.087*[Weight in lb]))/Calories)

Females: 6.296+(4.087*[Weight in lb]))/Calories) + 1.77

I have not yet profed the female with parenthies, but male actually comes out wrong if you try deviding the Weight by calories first.

Jean Verkempinck
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