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Re: short horizon Hs correction
From: Thomas Schmidt
Date: 2000 May 23, 8:04 AM
From: Thomas Schmidt
Date: 2000 May 23, 8:04 AM
Frank Dinkelaar wrote:
> In regards to the attachment (navigation formulas) send by Ed Kitchin
> the formula in #1 of the great circle course
> it seems to me it looks like this
> cos D = abs(sinL1 - sinL2) - abs(cosL1 x cosL2 x cos Dlo)
> it would save me many hours of experimenting if somebody
> could confirm or send me the formula in a clearer form.
> thanks
According to my textbook on spherical geometry, the distance D
along a great circle between two points at latitudes L1 and L2
and with the difference in longitude DLo between them is
cos(D) = sin(L1)*sin(L2) + cos(L1)*cos(L2)*cos(DLo)
We may test this with the example given for mid-latitude sailing,
where it's stated that the great-circle distance between
L1 = 41 deg 26 min N Lo1 = 71 deg 23 min W
and
L2 = 32 deg 22 min N Lo2 = 64 deg 39 min W
DLo = 6 deg 44 min
is 632.2 miles:
cos(D) = 0.66175 * 0.53534 + 0.74973 * 0.84464 * 0.99310
= 0.98314
D = arccos(0.98314) = 10.536 deg = 632.2 nm, as expected.
(Note that since D is relatively small, cos(D) is close to 1
and therefore it may be more practical to apply Formula #11
in this case, especially if you use tables or a slide rule.
The above formula is still valid, though).
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Thomas Schmidt e-mail: schmidt@hoki.ibp.fhg.de
