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## ASTUTE READER NOTICES: CONVERSION OF RCF TO RPM IS UNCLEAR

I think there might be an error in the equation for converting RCF to rpm on page 140 of the second edition, hardcover.

Should the equation be:

rpm= (RCF / (r x 1.118 x 10^-6))^1/2

because the radius is measured in mm?

E. D.

Dear E. D.

Thank you for pointing out the issue.  You are correct.  The difference has to do with the units of radius.

If you look around, you will find that there is no convention for whether to report the radius of the rotor in mm or cm.  Unfortunately, I didn’t make it clear that there are two versions in common use, and that they are both in the book specifically to show that.  On page 139, it is written out correctly for mm, and it states explicitly that I mean radius in mm.  On page 140, I switched to cm, with only a parenthetical comment that I had done that.  I really should make that more obvious.  When using cm, the exponent is –5, when using mm the exponent is –6.

One way to think about it is to imagine measuring the rotor in mm, now imagine measuring the exact same rotor in cm.  The second measurement is going to be the first measurement divided by 10.  But the RCF hasn’t changed.  To take that “divide by 10” into account, therefore, you need to multiply the answer by 10, or you won’t get the same RCF.  That “multiply by 10” gets folded into the constant so the exponent becomes 10^-5.