# NavList:

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

**Re: Non-graphical way to solve a wind triangle**

**From:**Frank Reed

**Date:**2020 May 11, 20:39 -0700

Equations as posted by Greg:

"CORRECTION ANGLE = ASIN(((DRIFT X SIN(SET-TC))/STW)

SOG=SQRT((STW2 + DRIFT2) - (((2 X STW) X DRIFT) X COS(TC - SET + CORRECTION ANGLE)))"

I was hoping someone else would deal with this, but no luck. I'll take a stab at it.

First, I'm going to make one change in the internal terminology here and replace "CORRECTION ANGLE" by plain old 'A' (for angle, if you like). And just for notational aesthetics, I'll replace "big fat X" for multiply with a mid-dot: A X B becomes A **·** B. Next it's clear that Greg or his source have gone crazy with parentheses. Almost none of the parentheses pairs are necessary thanks to simple order of operations rules and commutativity of multiplication. Changes so far:

A = asin[drift·sin(set - tc) / stw],

sog = sqrt[stw2 + drift2 - 2**·**stw**·**drift**·**cos(tc - set + A)].

Now even without getting into the underlying geometry of this, it's clear that the second equation is a representation of the plane trigonometry law of cosines:

c^{2} = a^{2} + b^{2} - 2·a·b·cos θ.

See it?

And therefore those 2's following stw and drift and really exponents -- squares. So finally:

**A = asin[drift·sin(set - tc) / stw],sog = sqrt[stw ^{2} + drift^{2} - 2·stw·drift·cos(tc - set + A)].**

*set*and

*drift*are obvious enough terms. And I suppose

*tc*is "true course",

*stw*is "spreed true wind" (or true wind speed), and

*sog*is "speed over ground". Yes?

Clockwork Mapping / ReedNavigation.com

Conanicut Island USA