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Frank - I'm interested in where the 3438 figure for using the sextant as a
rangefinder comes from.

> Rommel John Miller, you wrote:
> "I am sure every steward knows where to find the answer."
> Indeed. But do you trust the answer that they bring you? There's no
> downside for that steward if the answer is just a guess. I certainly agree
> that the captain of the vessel will provide a reliable answer if available
> because captains take pride in their vessels, and numbers like this matter
> --if the captain has time for such matters.
> You added:
> "Algebra and geometry can find the height of buildings with formulae,
> therefore finding the answer can be had of your dip on the boat deck, one
> might think"
> Oh yes, there are lots of mathematically "clever" ways to do it. But in
> the real world, where the Internet is close at hand (maybe *actually in
> your hand*), it is generally easiest, most efficient, and most accurate to
> locate a photo of the vessel and, based on its length, also acquired
> online, measure the height of your observing location directly. If there
> are no photos online, then take one yourself from a few vessel-lengths
> away while in port.
> For a mathematically clever method, drop a rock (the crew, and possibly
> the Harbor Patrol, will be upset, but do it anyway). Time the fall of the
> rock from your observing height until it hits the water to a fraction of a
> second, perhaps using a video or audio recording feature on a smartphone
> to get tenth-of-second accuracy. Take the number of seconds, multiply by
> 4, and that gives the dip directly in minutes of arc. This works because
> ballistic fall time and dip of the horizon are both proportional to the
> square root of the height. Example: if a rock, or other small dense
> object, takes 1.5 seconds to reach the water, then the dip is 6'. If it
> takes 3.0 seconds, then the dip is 12'.
> For another mathematically clever method, use your sextant as a range
> finder. You need to calibrate this, but just once in the life of the
> instrument. Then lean over the side of the vessel from your observing
> height and look at the waterline beneath you, or look at some object, like
> a buoy, in the water close to the vessel (I recommend you tie a lanyard to
> your sextant before you lean over the side with it!). Line up the direct
> and reflected images just as you would for an index correction with the
> sea horizon and read off the angle. This will be an "off arc" angle
> assuming the normal index error is zero. For a typical sextant,
> specifically an Astra IIIB, the relationship will be:
>   Height(in feet) = 750 / angle(in minutes of arc).
> So if the "index error"-like angle of the waterline is, for example, 15
> minutes of arc, then the height of eye is 50 feet. Note that you should
> zero out the normal index error or correct for it as usual after you
> measure the angle. This angle can be measured with decent accuracy, but
> you should do the calculation for values +/- 0.5' just to be sure you
> recognize the possible range. For this case of 15' observed, the height of
> eye might be between 48 feet and 52 feet implying that the dip correction
> could be 6.7 to 7.0 minutes of arc. Given other uncertainties, this is
> really quite good and a useful measure of dip. Just don't drop your
> sextant...
> Frank Reed
> PS: The number 750 in the range finder rule can be estimated for other
> sextants by measuring the distance between the two lines of sight of the
> instrument when it's set to zero. If that's three inches, let's say, then
> you divide by 12 to convert to feet and multiply by 3438. The result, 860,
> is the factor in the numerator of the rule. If the distance is 2.6 inches,
> then you get the 750 factor for the Astra sextant. It's better to try it
> out empirically by actual ranging measurements (a backyard activity), but
> you can get a good approximation before you start by looking at the
> distance between the lines of sight on the sextant.
>
> [plain text auto-generated]
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