Anybody have any idea what to do when you have two forms of the same equation, using the same variables and numbers for those variables so that one checks the other, only they don't give the same answers? Case in point, the calculation for inductance of a single-layer air-core inductor using the diameter/length of that coil and number of turns, and it's counterpart to calculate the number of turns in that coil given the inductance and diameter/length. Very simple and straightforward, only I get different answeres from the two. What could I be doing wrong? I have measured and remeasured the length of the coil, and done the same with the diameter, even going to the point of wrapping ten loops of wire around it before removing same and measuring/dividing first by ten and then by pi to make sure I was being accurate. Still, I get inconsistant answeres from the two equations, these being L=d^2*n^2/(18d + 40 l) and (sqrtL*18d+40l)/d. The first tells me 8.35 microhenries with a diameter of 1.75 and 9.5 turns, but the second then tells me 7.9 turns with the same diameter and a length calculated by the number of turns that will fit in an inch ( .04 inches for #24 plastic coated copper wire). I even ran all this through a different calculator. And both of these equations come from the ARRL handbook (p 6.22 of the 2004 edition), so I have to trust them... Am I just stupid? What is going on here? I feel like an idiot, and am probably going to find out I am right, but I need to know... What am I doing wrong?
Many thanks for any help. Even insults are welcome, so long as you care to share why you are insulting me. :)
Dave