Velocity Made Good (VMG) Calculator: Point or Foot, Time to the Mark and Laylines

How it works

VMG = boat speed × cos(true wind angle + leeway) · VMC = boat speed × cos(angle off the course to the mark) · break-even speed = best VMG ÷ cos(angle) · time = distance ÷ (VMG + tidal stream) · distance sailed = distance ÷ cos(angle) · layline offset = distance × tan(angle)

A sailboat cannot sail straight into the wind, so its progress toward a windward mark is the part of its speed that points up the wind: boat speed times the cosine of the true wind angle. Pointing higher shrinks the angle but costs speed; footing off adds speed but sends more of it sideways. The best angle is where speed × cos(angle) peaks, which is what a polar diagram’s upwind and downwind targets give for each wind strength. Downwind the same arithmetic explains why most boats reach at 140–165° and gybe rather than sail dead downwind. The calculator compares two angle and speed options and shows how much better the winner is. It also gives the break-even speed the other option would need at its angle, so you know whether footing or pointing can pay. Switch to VMC to measure progress toward a mark that is not straight up or down the wind; the angle is then measured off the direct course. Under More options, leeway widens the upwind track, a tidal stream along the course adds to or subtracts from progress over the ground, and a time loss per tack or gybe is added to the leg time. The layline is the line from which one tack or gybe fetches the mark. You reach it when the mark bears twice your wind angle (plus leeway) off the bow. Use true wind angles and speeds through the water; apparent angles are much tighter and would overstate VMG.

Worked example

Pointing at 42° true at 6.2 kt gives 6.2 × cos 42° = 4.61 kt VMG; footing to 50° at 6.8 kt gives 6.8 × cos 50° = 4.37 kt, so pointing is 5% better. To match it at 50° the boat would need 4.61 ÷ cos 50° = 7.17 kt, 0.37 kt more than it makes. A mark 5 NM dead upwind takes 1 h 5 min, sailing 6.73 NM through the water (35% extra) with tacks 84° apart, and the laylines are 4.50 NM either side of the start. Footing would take 3.5 min longer.

Sources: Velocity made good — Wikipedia · Katamarans.com VMG tool (VMG = SOG × cos(½ tacking angle), leeway) · Satsig Clipper 70 VMG calculator (best upwind and downwind VMG angles from polars)

Frequently asked questions