Derivation of The Haversine Formula
Derivation of The Haversine Formula
Derivation of The Haversine Formula
P = Local Hour Angle.LHA ( Celestial longitude! Measured 0 to 360. When the sun crosses the Greenwich
meridian at Noon its Hour angle is Zero/360, an observer in longitude 30 west would have a Local Hour Angle
of 330 at that time.)
Longitude by Chronometer using haversine formula No 5 and logarithms.(Traditional method)
hav LHA(Local Hour Angle) = hav ZX (Zenith Distance) + hav(Latitude +/- declination) x sec Lat x sec.Dec
Dead reckoning Latitude (A best estimate of where we are at the time) = 05 52.0 North
Declination of the sun (Tabulated in the Nautical Almanac)
= 0327.0 South
Latitude + Declination (Lat is North, Dec is South so we add)
= 0919.0
True Altitude (Of the sun. Measured by sextant and corrected for hight of eye, parallax etc) = 3631.0
9000.0
ZX( Zenith Distance) = 53 29.0
Natural hav ZX 53 29.0 = 0.20247
Natural hav L+D 0919.0 = 0.00660
Natural hav
= 0.19587
LAT 05 52.0
DEC 0327.0
LHA
D. Long
47 49
Latitude A 17 22
Latitude B 4008
We can then use another form of the formula to get an initial course to steer. This is usually calculated twice
daily and course adjustments made accordingly.
Hope this is enough! Its not used much these days because of Global positioning systems. GPS. Which can do
great circles for us. It is still a requirement to know however.
XXXXXXX Dad.