NavList:

Not quite celestial, but certainly navigation related with the same principles.  I have great respect for the knowledge base here so asking for some thoughts/references/guidence.

I got into this by degrees.  Just to explain.  I am trying now to establish a best accurate range estimation to a specific target at a known probobly shallow angle of elevation above the sea surface. Specifically an emergency flare. It's the classic lighthouse approximation, but more transient and farther away.

If I can relate quickly how/why I got to this point. without trying one's patience:

I was comparing 25mm aerial flares &12 Ga aerial flares.  25mm burn 7 seconds, reach 375' @33,000 candela.  12 ga burn 7 seconds, reach 500' feet @ 16,000 candela.  To add a third for fun parachute flares go 1150' burn 40 seconds @ 30,000 candela.

I won't bore with details, but nominal range, actual range, etc tables quickly show double the candela only adds a few miles.  Twice as bright is nothing like twice as far.  I was coming to the conclusion in limited visibility the 25 mm wins by adding a couple miles of potential observation due to increased  intesity,  but in near perfect visibility, the 12ga wins on account of the fact it is still visible, reaches higher altitude, and thus can be seen by a more distant vessel.  

Obviously if your expense account can afford it, parachutes are the best. 12 Ga dominates nowadays. I've been trying to restock my own 25's for two months, and they are backordered.

I started thinking about rescue coordination: trying to figure out what the situation would look like to the rescue ship.  Using classic sq rt He formulas both gun fired aerial flares limit out in the 22-26 mile  range from a horizon viewpoint.  Farther if the viewer is elevated.

So here the practical questions I ended up at:

1.    If it goes 500' or 375' and I'm say 18 miles away, how far above my horizon will it be, will it attract attention?  How high will  it appear on the horizon by dip and refraction, vs pure trig, which leaves an insignificant fractional angle?  Clearly if its very low, it will be visible less time, and it can get lost in clutter/background lights, etc. lets say it goes 500' but at my distance its first 300+' is out of my sight, I only see the upper part of the trajectory, so how high will it appear to the observer? Is it really visible at all at those altitudes. 

2.   If I am the spotting ship, and I see a flare on the distant horizon, I can quickly estimate angle by use of fingers held horizontally (if no actual self measure and test, 2 degrees per finger is often used), or some other means. I'll likely miss the first but might see it so I can plot the second or third if fired at intervals. 

The critical reason this is important is I can:.

1. Establish my exact or DR position. (GPS age now so precise is easy)

2. Establish my best estimate of the true bearing to the target. Most mariners want bearings in true/corrected form: Can Dead Men Vote Twice at Elections?  (Compass, deviation, variation, add EAST.)

3. Use the estimated angle/elevation for a guesstimate range.  If it hangs a long time, its a parachute.  If it arcs, you can figure a 12 or 25, most often a 12 nowadays.  So assume it peaked between 375 - 500' (at least common USA flares).

so, now I stand a chance of relaying accurate info to search plotters/rescuers. Up here in the cold north atlantic, a good plot can be life or death based on minutes of in-water exposure.

My solution would be:   I know my height above water as observer (for dip), I guessed an approximate angular elevation (say one finger 2 degrees). I identified the type as parachute vs projectile. I observed/recorded its true bearing to my exact present position.

Now anyone can plot my position, a line of position to target, and estimate a distance of say xx - xx based on elevation. . 

That gives us the best chance of finding the mariner in distress quickly.  We run the line and most probable range block first with our first on-scene asset, before extending our pattern. Understanding how high it appears might also help a decison as to what to fire first if you become the one doing the firing. It is possible if you are first on scene you use your flares to lead other assets with which you have limited communication.

I hope that all makes sense. 

Might clear up in my head after some sleep, but wonderin if anyone has some input/thoughts on best way vs approximations/compromises.

MC