Help with a Frost Bite Time Equation

**boynejs** · 02-11-2016, 06:59 AM

I have the following equation...

Frost Time = ((-24.5 x ((0.667 x (wind x 8/5)) +4.8)) + 2111) x (-4.8 - ((temperature -32) x 5/9))^-1.668

wind = cell x4
temperature = cell y4

I came up with the following equation...

SUM(-24.5*(SUM(0.667*(X$4*(8/5)))+4.8),2111) *sum ((-4.8,-((Y$3-32)*(5/9)))^-1.668)

but I keep getting the error #NUM!

Can anyone point out my error?

Thanks!

Jeff

**sourabhg98** · 02-11-2016, 07:14 AM

Try this-

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**boynejs** · 02-11-2016, 07:25 AM

Thanks for getting back to me. I still get the same error. I figured it has to do with the negative exponent.

Jeff

**sourabhg98** · 02-11-2016, 07:32 AM

But I am not getting any error.
Can you attach a sample workbook?

**MrShorty** · 02-11-2016, 11:09 AM

I figured it has to do with the negative exponent.

Sort of. It isn't so much the negative exponent that causes a problem, but the fractional (.688) part of the exponent. And even that is not a universal problem. It is only a problem when the "base" is a negative number. So Excel can calculate 5^-1.688 just fine, but it will fail to calculate (-5)^1.688.

Looking at this with my engineering background, I see a temperature term where you a) convert your temperature from Fahrenheit to Celsius (which can be positive or negative), then b) add a constant and c) raise that to a fractional power. IMO, the easiest solution is to use an absolute temperature scale (Kelvin rather than Celsius) that can never give a negative number. Since Kelvin=Celsius+273.15, it should be relatively simple algebra to adjust that part of the formula to use K rather than C. That's how I would do it.

On edit: I looked closer, and that will not fix it. On closer inspection, that temperature term will be negative whenever t in C is > -4.8 C. Is there a restriction on the use of the equation to temperatures <= -4.8 C? Because it looks like there should be such a limit. Is there a different equation that should be used at warmer temperatures?