Runway Point of Intercept
 

Depends, ILS or PAPI?

3 degrees is near enough to 5 % or 1:20, for small distances so, from wherever you want to start the calculations, the horizontal distance to run to intercept is 20 times the height loss required.

Depending on your assumptions and project, you may also have to account for the issue of the MEHT. You might be seeing 2 reds/2 whites from the FD but the gear on a 737 will have a very different threshold crossing height to a 747.

From a design perspective:

ILS: GPA through the TCH to the ASBL. The RDH needs to be calculated to that the wheel glidepath does not go lower than 6m screen height at the threshold. The standard from ILS GP to wheel GP is 5.8m (denoted as 'H' or in this example 'W'). If the aircraft using the runway have a greater H than 5.8m, the GPA must be adjusted. Quite a few aircraft, especially the longer versions have upwards of 8m H. Depending on SOP, there may be an add for flair.
https://cimg0.ibsrv.net/gimg/pprune....9045509467.jpg
example of H and H1 values

PAPI: GPA through the TCH to the ASBL. The difference here is that the PAPI is set with the aiming point, given eye height MEHT The AIM point is set using the GPA, TCH and eye height H1. The same minimum screen height WTH applies at the threshold of 6m

https://cimg3.ibsrv.net/gimg/pprune....24d6788e13.jpg
https://cimg0.ibsrv.net/gimg/pprune....6da5e14584.jpg

What - 50m for a handlebar moustache?

Good one Smythe: GPA, TCH, ASBL, RDH, H/W, MEHT, H1, WTH, EWH.

What's ASBL?

Approach Surface Baseline, ASBL is the baseline using the elevation at the threshold. It assumes the world is flat at that elevation. (at least for design purposes)

https://cimg0.ibsrv.net/gimg/pprune....bed9fd2371.jpg