Throw Distance for a Target Beam Pool
The inverse of the lighting-beam tile: the throw distance a fixture needs to cast a target beam (pool) diameter, throw = D / (2 x tan(beam angle / 2)). A 20 degree fixture makes a 10.6 ft pool from a 30 ft throw; a wider 40 degree beam reaches the same pool from just 14.5 ft. Answers 'how far to hang it for an X-foot pool' instead of the pool at one throw. Geometry only - the illuminance still falls with the square of the throw (check the level with lighting-beam). The fixture cut sheet governs.
Formula and source
throw = target_pool_diameter / (2 x tan(beam angle / 2)); the inverse of beam_diameter = 2 x throw x tan(beam angle / 2).
First-principles theatrical photometry - the beam-spread geometry the form fixture photometric charts (manufacturer cut sheets) publish, solved for the throw, by name; public domain.
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