Planning a leg
nav logflight planninggreat circle distance and bearingwind triangleETE calculation
Two waypoints to a heading and a time: great circle distance and bearing, the compass correction, the wind triangle, and the time en route.
Great Circle Distance (Haversine)
The shortest distance between two points on a sphere, from their latitudes and longitudes. Sinnott's haversine form, which keeps its precision on short legs where the older law-of-cosines version loses it.
Initial Great Circle Bearing
The course at the moment of departure along the great circle to a destination, measured clockwise from true north. It is the starting bearing only — on any track but a meridian or the equator it changes the whole way.
Compass to True Heading (Variation and Deviation)
The TVMDC chain in one line: a compass heading corrected by deviation for the ship's own iron and by variation for the earth's field, giving the true heading a chart is drawn in. East corrections are positive and are added going this way.
Wind Correction Angle
How far off the desired track to point the nose so the wind carries you along it instead of off it. Only the crosswind component matters: the along-track part of the wind changes the speed, never the heading.
Wind Triangle Ground Speed
What the aircraft is actually making over the ground once the wind has had its say: true airspeed, wind speed, and the angle between the wind and the intended track. The E6B's whole reason for existing.
Estimated Time En Route
Distance divided by ground speed. Trivial arithmetic, and the single most common place a navigation plan goes wrong, because the speed put into it is so often the airspeed or the log speed rather than the speed actually made good.
How they fit together
Every nav log ever filled in runs this order, whether the aircraft is a Cessna or the vessel is a yacht. Haversine and initial bearing come out of the same two latitude and longitude pairs and answer how far and which way. The word initial in the second one is doing real work: a great circle track is the shortest path but it is not a constant heading, and the bearing changes continuously along it. Fly the initial bearing all the way across the North Atlantic and you arrive somewhere else. Over a hundred miles the difference is negligible and nobody cares; over a thousand it is the whole reason waypoints exist.
Compass to true heading is where paperwork meets the instrument, and it is the step beginners reverse. The chart and the two formulas above are in true; the compass in front of you is not, because magnetic north is somewhere else and the metal around the instrument moves it again. Variation is the earth's error and lives on the chart; deviation is the aircraft's own error and lives on a card taped beside the compass. The old mnemonic still earns its keep — east is least, west is best — meaning easterly variation is subtracted going from true to magnetic. Get the sign backwards and you are off by twice the variation, which in parts of Canada is over 30°.
The last three are the wind. Wind correction angle is how far to crab into it, and it is applied to the heading while the course stays where the chart drew it — the aeroplane points one way and travels another, and confusing the two is how a track drifts. Ground speed from the same wind triangle is what the clock actually responds to, and it is worth noticing that a crosswind costs you speed even with no headwind component at all, because part of your airspeed is spent holding the crab. Time en route then divides distance by ground speed, and it is the number the fuel plan is built on, so run it with the real ground speed rather than the true airspeed. A 20-knot headwind on a 100-knot aeroplane is 25% more time in the air and 25% more fuel, and the return leg does not give it back.