Dellenbaugh Angle & Ballast Ratio Calculator (Sailboat Stiffness, Heel vs Wind, When to Reef)
Judge how stiff or tender a sailboat is: the Dellenbaugh angle from sail area, heeling arm, displacement and metacentric height, the ballast ratio, the righting moment per degree, the estimated heel angle at each wind speed and the wind at which to take the first reef.
How it works
Dellenbaugh angle = SA (ft²) × heeling arm (ft) × 1 lb/ft² ÷ RM₁ = 57.3 × SA × HA ÷ [displacement (lb) × GM (ft)] · RM₁ = Δ × GM × sin 1° · ballast ratio = ballast ÷ displacement · heel ∝ wind², normalised to ≈ 17 kt at the Dellenbaugh angle; reef wind = 17 × √(reef heel ÷ DA) · SA/D = SA ÷ (Δ ÷ 64)^(2/3)
Designers compare how stiff sailboats are with the Dellenbaugh angle: the heel a boat takes when a standard wind pressure of one pound per square foot acts on her upwind sail area at the height of the heeling arm, resisted by the righting moment from displacement and metacentric height. Under about 15 degrees is a stiff boat, over 20 a tender one. Because heeling force grows with the square of wind speed, that one number also gives a heel-versus-wind curve and therefore a sensible reefing wind. The ballast ratio is a companion figure: it says less about initial stiffness than about how much the keel will fight to bring her back from a knockdown.
Worked example
A 35 ft cruiser of 15,000 lb with 5,800 lb of ballast (39% ballast ratio), 640 ft² upwind, a 24 ft heeling arm and GM of 3.5 ft has a heeling moment of 640 × 24 = 15,360 ft·lb at 1 lb/ft² against a righting moment of about 916 ft·lb per degree, so a Dellenbaugh angle of about 16.8° — a moderate cruiser-racer. Twenty degrees of heel arrives at about 19 knots apparent, so that is the first-reef wind; after reefing, the second reef comes near 22 knots.
Frequently asked questions
How do I find GM?
From the designer's stability data, or by an inclining test: move a known weight a known distance across the deck and measure the heel — GM = (w × d) ÷ (Δ × tan θ). Typical cruising monohulls are 3–4 ft; multihulls are far higher and are not assessed with this formula.
What heeling arm should I use?
The vertical distance from the centre of effort of the upwind sail plan to the centre of lateral resistance of the underbody. A quick estimate is 0.39 × I (foretriangle height) plus the freeboard plus about half the draft; design offices compute it from the sail plan drawing.
Is a higher ballast ratio always better?
For ultimate stability and recovery from a knockdown, yes, but it costs weight and speed, and low-slung bulb keels achieve the same righting moment with less ballast. Compare boats using ballast ratio together with the capsize screening formula and the limit of positive stability.
Related calculators
Boating figures are planning estimates based on published rules of thumb and standards (USCG, ABYC, manufacturer tables). Your boat's capacity plate, builder documentation and local regulations govern; conditions at sea vary.