A full-rigged brig carries square sails on both its foremast and mainmast, with a fore-and-aft spanker aft. The yards support the square sails across the vessel; the spanker uses a different arrangement of spars. Explore that sail plan here, then compare how two specified transverse force components act ahead of and behind an assumed turning reference.
Full-rigged Brig Interactive Calculator
Enter two force magnitudes, their distances ahead of and behind the reference point, and their common angle to the vessel’s centerline. The calculator compares yaw moments; it does not predict sail forces or rudder settings.
Equation Used
The two forces act toward the same leeward side on opposite sides of the reference point. This deliberately simplified comparison uses perpendicular components and fixed lever arms. The aft moment is positive here. Real sail forces, the hull’s hydrodynamic response, heel, leeway and rudder forces are not calculated. No rudder angle follows from these inputs.
Reading a brig’s sail plan
The foremast stands toward the bow and the mainmast farther aft. Each carries horizontal yards with square sails beneath them. “Square” describes how the sail is rigged across the vessel, rather than requiring a mathematically square outline. A gaff and boom support the fore-and-aft spanker behind the mainmast. Headsails extend forward toward the bowsprit.
The drawing separates the two stacks of square sails and the aft spanker. It is a simplified generic rig, not a measured plan of a particular ship. Its sails and hull do not change size when a force input changes. Moving markers on the separate force diagram show the assumed force direction; they do not represent measured wind, vessel speed or a sailing maneuver.
A rig used for history and sail training
The U.S. Brig Niagara at the Erie Maritime Museum provides a documented example of a two-masted square-rigged vessel. The museum describes its role as Oliver Hazard Perry’s relief flagship at the Battle of Lake Erie. Its modern educational role makes the arrangement of spars and rigging accessible to visitors and trainees.
A brig’s two square-rigged masts distinguish its basic arrangement from a fore-and-aft schooner. Historical rig names have variations, so a particular vessel’s sail plan is the better reference for its detailed arrangement. A snow rig carries its aft trysail on a small additional mast immediately behind the mainmast.
Two forces and their yaw moments
A force produces a moment equal to force times perpendicular distance from its line of action to the reference point. Here the fore and aft positions lie on the vessel centerline, at distances a and b. Each force is assumed to act at the same angle theta to that centerline. Its transverse component is F sin(theta).
The forward magnitude is M_forward = F_forward sin(theta) a. The aft magnitude is M_aft = F_aft sin(theta) b. The two transverse forces point to the same side, but their positions ahead of and behind the reference give opposite turning effects. The displayed net moment is M_aft − M_forward. Inputs are newtons and metres; dividing by 1000 gives kN m.
The normalized difference is 200(M_aft − M_forward)/(M_aft + M_forward). Zero means equal opposed moments, not an absence of side force. One nonzero moment alone gives +200% or −200%. If both are zero, this percentage is undefined and shows a dash.
The common angle multiplies both moments equally, so changing it changes their magnitudes but not their normalized difference. This is a consequence of the assumed model, not a claim that a real brig’s helm balance is independent of wind angle.
Example: unequal forces, equal moments
At the defaults, the forward force is 10,000 N acting 4 m ahead of the reference. The aft force is 4,000 N acting 10 m behind it. At 60°, their transverse components are about 8,660 N and 3,464 N. Both moments are therefore about 34.64 kN m, giving zero net moment and 0% difference.
Increasing the aft force to 5,000 N gives about 43.30 kN m aft, leaving +8.66 kN m net and a normalized difference of about +22.2%. These numbers describe the specified two-force system. They do not determine the vessel’s turning rate, heading, stability or required rudder angle.
From a force diagram to a real vessel
Actual sail forces depend on apparent wind, sail shape, trim and interactions between sails. Their points of action move with the sail configuration. The hull, keel and rudder contribute forces and moments of their own. Treating all forward sail force as one resultant at one fixed arm is an assumption for this exercise, not a description of every square sail on a brig.
Weather helm describes a tendency to turn toward the wind; lee helm is a tendency to turn away. The aft-positive convention illustrates the corresponding turning sense when both transverse forces act to leeward. It does not diagnose either condition aboard a real vessel. Vessel-specific stability information and operating procedures are needed for decisions about sail handling and rigging loads.
Frequently asked questions
What makes the vessel a full-rigged brig?
It has two masts carrying square sails, with a fore-and-aft spanker aft of the mainmast. The drawing also shows headsails toward the bowsprit.
Why can unequal forces give equal yaw moments?
A smaller force acting through a longer perpendicular lever arm can balance a larger force with a shorter arm. At the defaults, 10,000 N times 4 m equals 4,000 N times 10 m before their common sine factor is applied.
Does zero net moment mean the vessel is stationary?
No. It means the two assumed moments cancel. The two transverse forces can still produce a net side force; vessel motion is not solved.
Why does changing force angle leave the percentage unchanged?
The same sine factor multiplies both moments in this model and cancels in their normalized ratio. Real sails need not share a common force direction or fixed force magnitudes.
Can I use the result to set the rudder?
No. Rudder force depends on water flow, rudder geometry and angle, and its lever arm. None of those is supplied by this calculator.
Why does the difference sometimes show 200%?
The difference is divided by the mean of the two moment magnitudes. With one nonzero moment and one zero moment, that definition produces a magnitude of 200%; it is not a percentage efficiency.
Is the force angle the true wind angle?
No. It is the direction of the entered force resultant relative to the centerline. A sail’s resultant force is not generally aligned with the incoming wind.
Are the dimensions in the drawing a build plan?
No. The rig is schematic, and the force diagram scales the selected arms for illustration. It does not specify spars, rigging tensions, safe sail area or vessel stability.
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