This page pairs a historical triangular sail profile with a deliberately limited lift-only equation. It does not calculate drag, drive, heel, trim, righting moment, reefing or boat performance.
Leg-of-mutton Sail Interactive Calculator
Vary luff, foot, wind speed, entered lift coefficient and the angle of the lift vector from the displayed parallel axis. The result is a first-order lift-only estimate; its two mathematical components are not boat drive or heel predictions.
Equation Used
- The sail planform is treated as a right triangle with area L B / 2.
- Air density is fixed at 1.225 kg/m3 and the entered coefficient is applied uniformly.
- The force inset is separate from the side-profile drawing; drag, sheeting, aspect ratio, mast bend, hull motion, drive, heel and stability are excluded.
This is a lift-only equation screen with declared mathematical axes; drag and boat response are outside its scope.
Triangular profile and lift-only screen
Hiscox item 760 shows a triangular leg-of-mutton sail attached along a mast and boom. The profile animation changes only an illustrative belly highlight; it does not solve cloth shape or trim.
The separate vector panel applies the standard lift equation to a flat triangular planform area. The lift estimate is then resolved along two labelled mathematical axes. Those axes are not asserted to be boat-forward and boat-lateral directions.
Use as an equation illustration
The calculator can show how entered area, wind speed and lift coefficient change a first-order lift magnitude, and how one vector resolves into two components relative to a chosen axis.
It cannot select a sail or rig, predict boat speed, reefing, trim, heel, righting moment, balance or structural loads.
Lift-only equation and declared axes
The area is A=LB/2 for the entered right-triangle planform. Beta is the angle drawn from the panel's parallel reference axis to the lift vector, so Lparallel=Lift cos(beta) and Llateral=Lift sin(beta).
No drag coefficient is entered or calculated. These are mathematical components of lift only, not net aerodynamic drive or heel forces.
Worked lift-only example
For luff 6 m and foot 3 m, area is 9 m². At 12 knots (6.17 m/s), rho=1.225 kg/m³ and entered CL=1.0, the first-order lift estimate is about 210 N. At beta=55° it resolves to about 121 N parallel-axis and 172 N lateral-axis.
This example does not include drag or any hull, rig, stability or performance calculation.
Model boundary
A real sail's coefficient and force direction depend on three-dimensional shape, angle of attack, Reynolds number, aspect ratio, twist, sheeting, mast and rig interaction, unsteady wind and hull motion. The page provides none of those models.
Do not interpret the component labels as drive, heel, righting moment, reefing threshold or safe rig load.
Sources
- Hiscox, Mechanical Movements, item 760: historical triangular sail profile.
- NASA Glenn, Lift Equation: supports Lift=CL(rho V²/2)A and identifies the required variables; it does not turn lift alone into net boat drive or heel.
Lift-screen questions
Is the displayed lift the total aerodynamic force?
No. Drag is omitted, so the result is a lift-only estimate.
Is beta the apparent-wind angle off the bow?
No. Beta is defined only between the displayed parallel axis and lift vector.
Does the lateral component predict heel?
No. The calculator has no centre of effort, hull, ballast or righting-moment model.
Can this result set reefing or rig dimensions?
No. Those decisions require vessel-specific design data and operating guidance.
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