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Old 20-03-2022, 06:09   #1
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Distance off lighthouse

page 84.The Practical Pilot Leonard Eyges.D=60H/A°.How can that be?H is height of lighhouse on chart.
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Old 20-03-2022, 07:26   #2
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Re: Distance off lighthouse

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page 84.The Practical Pilot Leonard Eyges.D=60H/A°.How can that be?H is height of lighhouse on chart.
Vertical sextant angle
The triangle can be described in terms of H, α and Distance:

Distance = H / tan(α)

Vertical sextant angles: math
where, the angle is in radians (0—2π) and both height and distance are in metres.

The relations between radians and degrees is:
α = A * π / 180
with “A” being the same angle in degrees.
To describe angle A in minutes total, then A * 60 = a, thus α = (a / 60) * (π / 180). So, α = a / 3438, “a” being the angle in arc minutes.
Fact: tan(x) = x, if angle x is small.
Resulting in (with π = 3.14): Distance (m)= H * 3438 / a

Furthermore, distance in Nautical Miles = distance in meters / 1852.
Voilà, a very practical equation:
Distance = 1.856 * H / a
It contains just two approximations, both of neglitible influence. First, we left out the tan function and second we used 3.14 for π.
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Old 20-03-2022, 10:01   #3
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Re: Distance off lighthouse

Tan (1*) is approximately 1/60.
For angles near 1*:
60H /A* is approximately D
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Old 20-03-2022, 14:46   #4
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Re: Distance off lighthouse

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Originally Posted by copaco View Post
page 84.The Practical Pilot Leonard Eyges.D=60H/A°.How can that be?H is height of lighhouse on chart.
For angles less than about 10°, 1° subtends 1 unit of height for every 100 unit of distance.
So I° subtends 1ft at 100ft.

1 nautical mile = approx 6000 feet.
So at 1NM, 1° will subtend 60 feet ( 6000/100)
IOW,

it's 60ft per degree at 1NM,
it's 30ft per degree at 0.5NM
it's 120ft per degree at 2NM
...
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Old 20-03-2022, 14:48   #5
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Re: Distance off lighthouse

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If you actually quoted what you are asking about, people who don't have that book could probaby explain it.


Yeah I’m a bit lost here missing some details
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Old 20-03-2022, 14:53   #6
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Re: Distance off lighthouse

Adelie answered to my satisfaction.
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