Velocity made good calculator
A sailing boat cannot sail into the wind, so progress upwind is boat speed times the cosine of the angle to the wind.
kt
nm
kt
Velocity made good
4.607kt
- VMG at the wider angle
- 4.371 kt
- Better option
- 1 The closer angle is faster to windward
- Time to make the distance
- 2:10:13
- Distance actually sailed
- 13.46 nm
- Total tacking angle
- 84.0 degrees
- Time saved over the alternative
- 0:07:03
Show the working
- Boat speed = 6.2
- True wind angle = 42
- Distance to windward = 10
- Speed at a wider angle = 6.8
- That wider angle = 50
- Velocity made good = 6.2 * cos(rad(42)) = 4.6075
- VMG at the wider angle = 6.8 * cos(rad(50)) = 4.370 96
- Better option = 4.6075 >= 4.370 96 ? 1 : 2 = 1
- time_hours = 4.6075 > 0 ? 10 / 4.6075 : 0 = 2.170 38
- alt_time_hours = 4.370 96 > 0 ? 10 / 4.370 96 : 0 = 2.287 83
- Distance actually sailed = cos(rad(42)) > 0 ? 10 / cos(rad(42)) : 0 = 13.4563
- Time to make the distance = 2.170 38 * 3600 = 7813.35
- Time saved over the alternative = (2.287 83 - 2.170 38) * 3600 = 422.834
- Total tacking angle = 42 * 2 = 84
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
The formula
- VMG = boat speed x cos(true wind angle)
Pointing higher is not always faster. The optimum is where the product of speed and cosine peaks, which is what a polar diagram shows.
The same arithmetic applies downwind, where sailing deep costs speed and sailing hot costs distance.