FPA
Yes there is a formula , actually two.
First, if you don't have a chart with the FPA, % gradient and gradient , then you will have to find the gradient (grad) of the required FPA. To do that you find the SIN of the angle then multiply that # by 6076 (the number of feet in one N.M.) This will give you the "gradient". e.g Enter 3 degrees and press the SIN button. You will get 0.052335956. (This numner by the way IS the % Grad - 5.2%)
Next multiply that # by 6076 - result = 317.99 or 318 ft down for every one N.M. forward. That is the Grad.
Now for the second formula : The Grad. (318) can now be multiplied by the distance in N.M. to get height to lose i.e. aircraft height above the airport. Now you can divide the height to lose in feet by either a). the Grad to find the distance in N.M. or b). the distance in N.M. to get the Grad.
EXAMPLE : Say you would like to start down from the 10 nm fix from the threshold on an angle of 3.3 degrees. Runway threshold elevation 700 ft. asl. Where do you start the descent?
First formula:
Press 3.3, press SIN = 0.05756 (% Grad = 5.7%) X 6076 = 349.7 or 350. This is the Gradient.
Second formula:
350 X 10 = 3500 feet - height to loose.
To find the aircraft altitude, add 3500+700+50 = 4250 ft.
(50 is the threshold crossing height)
So at 4250 ft at 10.3 n.m. from the threshold (thats .3 of a nm before 10) you would pull the FPA knob and set -3.3.
You can work another way. Say you want to maintain a 3000 ft altitude for the same airport above so now you want to find out at what DISTANCE to start down for 3.3 degrees.
Start with 3000 ft minus 700, minus 50 to get height to lose = 2250 ft. Divide 2250 by 350 Grad = 6.4 n.m.
So at 6.7nm pull and set -3.3 degrees on the FPA knob and slide down the "glide slope".
Here are the numbers for the FPA's recommended for JET aircraft.
FPA 3.0 %Grad 5.2 Grad 318
" 3.1 " 5.4 " 329
" 3.2 " 5.6 " 340
" 3.3 " 5.8 " 350
" 3.4 " 5.9 " 361
" 3.5 " 6.1 " 372
" 3.6 " 6.3 " 382
" 3.7 " 6.5 " 393
Check them out for yourself on a sientific calc using the formulae above.
i.e. Grad=SIN of angle X 6076
Height to lose = Grad X Dist
Dist = Height divided by Grad
Grad = Height divided by Dist
Angle = Grad divided by 6076 Inv SIN
Hope that will answer your question.