If a human eye can detect a single candle flame at anywhere from 15 to 30 miles,
That is apocryphal and easily shown to be incorrect.
If you were correct then you should complain to your congressman about all the money the Coast Guard has wasted putting those big powerful lamps in lighthouses when they could have saved billions of dollars by just using a birthday cake candle (O.K. two birthday cake candles for redundancy.) As I posted before, running lights on the largest ships are visible at three nautical miles. To make sure that the running lights comply with that requirement the government wrote specific regulations that specify the required lamp intensity for running lights. To achieve 3 NM visibility requires a lamp intensity of 12 candellas (11.77 candles, let's call it 12 candles too.) The regulations also require a 0.9 candella (candle) lamp to achieve visibility at 1 NM. So, either you are right, that one candle can be seen at 30 miles or the government is right that one candle is only visible at about one nautical mile, my money is on the government's engineers on this one. If you want to be exact, 0.9 candella is 0.88 candles. Since the intensity of the light is attenuated at the square of the distance, it takes a lamp four times brighter to be visible at only twice the distance, one candle would be visible at 1.06 NM. Since the power required increases at the square of the distance, to be visible at 30 NM it would take 30^2 x 0.88 candles which is 792 candles so you are only short by 791 candles. If you want to do the rest of the math you will find out that this produces a light intensity at the eye of 0.000000024 foot-candles which your research will show is the minimum amount of light your eye can detect. Here is the actual regulation:
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Title 33: Navigation and Navigable Waters
PART 84—ANNEX I: POSITIONING AND TECHNICAL DETAILS OF LIGHTS AND SHAPES
§ 84.15 Intensity of lights.
(a) The minimum luminous intensity of lights shall be calculated by using the formula:
I=3.43×106 ×T×D2 ×K−D
where I is luminous intensity in candelas under service conditions,
T is threshold factor 2×10−7lux,
D is range of visibility (luminous range) of the light in nautical miles,
K is atmospheric transmissivity. For prescribed lights the value of K shall be 0.8, corresponding to a meteorological visibility of approximately 13 nautical miles.
(b) A selection of figures derived from the formula is given in Table 84.15(b):
Table 84.15(b)
Range of visibility (luminous range) of light in nautical miles D Minimum luminous intensity of light in candelas for K=0.8 I
1 0.9
2 4.3
3 12
4 27
5 52
6 94
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I also pointed out before that the running lights are designed to shine the light out towards the horizon an ithey do this by using fresnel lenses that refracts the light that would be emitted at a high angle and bends it to go out towards the horizon so no light would shine up into the sky for Amelia to see. These steamships lights are designed to send the light out in a narrow 10° band in the range of 5° below the horizon to 5° above horizon. Lights for sailing ships cover a larger vertical range because sailing ships heal over so the greater vertical range in needed to make sure that the light is always visible from the horizon. Neither the Ontario nor the Myrtlebank were sailing ship. The government also has a specific regulation governing the vertical range of the running lights and here it is:
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§ 84.19 Vertical sectors.
(a) The vertical sectors of electric lights as fitted, with the exception of lights on sailing vessels underway and on unmanned barges, shall ensure that:
(1) At least the required minimum intensity is maintained at all angles from 5 degrees above to 5 degrees below the horizontal;
(2) At least 60 percent of the required minimum intensity is maintained from 7.5 degrees above to 7.5 degrees below the horizontal.
(b) In the case of sailing vessels underway the vertical sectors of electric lights as fitted shall ensure that:
(1) At least the required minimum intensity is maintained at all angles from 5 degrees above to 5 degrees below the horizontal;
(2) At least 50 percent of the required minimum intensity is maintained from 25 degrees above to 25 degrees below the horizontal.
(c) In the case of unmanned barges the minimum required intensity of electric lights as fitted shall be maintained on the horizontal.
(d) In the case of lights other than electric lights these specifications shall be met as closely as possible
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Obviously these are the current versions of these regulations but they have not changed in any large way since the '30s.
gl