I am trying to figure out how to solve for the amount of $n$ turns in a spiral when I have given the inner radius, the total length of the spiral, and the distance between each coil. The spiral is spinning outwards and the distance between each arm stays constant. I tried using archimedes spiral equation and try to solve for $n$ however I keep getting stuck and unable to solve the equation. If you want to try out with my numbers I have $R_i=25, L=250, b=6$ (distance between each spiral).
My final goal is to write an equation in excel that I can change the 3 parameters I gave above and it will give out the number of turns for the spiral.
Thank you!