This little program calculates how far above the fork crown brake
bolt a rack deck needs to be set to not foul the front wheel.
usage: deck2bolt HTA(degrees) A-C(mm) RAKE(mm) MIN-CLEARANCE(mm)
(min-clearance is the vertical distance from the axle to the top
of the wheel + however much room you might want for fender clearance.
It is probably ridiculous to have it be larger than a-c, but you
might want to flare the front end of a fender up for some sort of
aesthetic reason.)
Basically, it rotates the min-clearance back to match HTA, then
tells you min-clearance * ( 1 - cos(hta) ) (min-clearance is rotated
back to make the hypoteneuse of a right triangle, then I subtract
the back wall of that triangle {cos(hta)} from original min-clearance
and what's left is how much above the crown bolt hole the deck needs
to be to clear the wheel.
This simple calculation is made slightly more complicated by fork
rake -- a raked fork has an effective hta that's larger than the
actual hta. That's a simple equation as well; asin(rake/a-c).
So what this program does is returns
m-c * ( 1 - cos(hta + asin(rake/a-c)) )
with some stupid sanity checking where it refuses to calculate if
either a-c or m-c is less than 100mm. It does NOT sanity check
for m-c > a-c, so you can go to town with wheels that are much
larger than the fork will accept.