Haversine

[pabrides]

Ever wonder why we still see haversine tables in some navigation books?  Me too, until I read this article about them:

https://plus.maths.org/content/lost-lovely-haversine

The main point is this:

"The reason why the haversine function has come out of fashion is that with the help of calculators and computers it’s easy enough to work out the distance straight from formula (2). That’s why you don’t find a haversine button on your average calculator. "

Here is a quote from another pub describing haversine as it relates to the Gunter versed sine line :

"The scale title V * S means versed sines, but it does not reflect our current versine which equals (1 -cosine). It actually represents, in modern terminology, the logarithm of (1 -haversine), or 1/2 (1 + cosine). The haversine function (half-versed-sine) was introduced for computational reasons in the formula that calculates the angular distance between two arbitrary points on the globe. This formula could be calculated between the NUM, the SIN and the V * S scales on the Gunter rule."

So that's pretty much why we have haversine tables.  If you've never used the haversine table give it a try... you'll get a good feel for what our forefather navigators went through to chart their ships. Where once about every navigator knew the meaning of haversine, now you can consider yourself a member of a select few who still do :)

Cheers

[P.Rutherford]

Haversines have been very useful especially with the Doniol method.  CelNav and Lou worked this stuff out a while back.

https://thenauticalalmanac.com/Forum/sho...ght=doniol

In calculating distance between 2 points on a sphere here's the formula I use;

Distance = 90 – Sin-1(sin(Destination latitude) x sin(Your present latitude) + cos(Destination latitude) x cos(Your present latitude) x cos(Difference in longitude between Your Location and Destination Location)

Multiply answer by 60 to get Nautical miles.   If you look at the formula closely you'll recognize it as quite similar to the Hc formula but uses destination latitude and present latitude for declination and present latitude.

It's simple....like radar.

Paul