# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: short horizon Hs correction
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).

--
-------------------------------------------------------------------
Thomas Schmidt                  e-mail:     schmidt@hoki.ibp.fhg.de
```
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