Science of the Spreader
by Bruce Krohn
Editor’s preface –
Have you ever wondered why all those wires, ropes, rods, poles, and stuff are attached to a sailboat mast? Some of them are for controlling the sails, but others are essential for the mast to do its job of holding the sails without the whole thing falling down on your head. The mast and its rigging – the shrouds that go up the mast, the spreader poles that hold them out from the mast, the stays that hold and sometimes adjust the mast fore-and-aft, and all the pieces of hardware connected to the rigging – are part of a system that lets the boat go from Point A to Point B without rig failure (if properly maintained and used!) and without having to have a mast so heavy as to threaten the boat's stability. The rig makes the mast stronger so that the mast doesn't fail but instead can withstand the powerful loads of wind-filled sails. The mast and rig transmit forces to the hull, allowing the boat to sail over the bounding main.  Pat Byrnes
------
The simplest mast system is an unstayed mast where any side force is almost entirely a sheer force on the mast. The only compression force on the mast is the weight of the rig. The sheer force on the mast is translated to a compression force on the deck at the partners and a shear force on the sole at the shoe. However, this takes a rather sub-stantial mast to carry much sail. To reduce weight and windage  aloft, stays are added. A stayed mast trades sheer force for a
tension force on the shrouds, a compression force on the mast,
and a combined tension and sheer force on the chain plates.
The sum total of the tension and compression forces involved
can be calculated based solely on the mast base- to chain
plate distance and the height of the shroud attachment points.
There is a practical limit. The force on the fittings that attach the stays to the mast is a function of the reciprocal of the sine of the angle that the stays make as they meet the mast. As this angle narrows, the sine of this angle goes to zero and the function, (and force), goes to infinity. A minimum of about 12 degrees is the current limit for readily available hardware. On a boat with a typical 5 foot distance from chain plate to mast base, the upper shroud attachment point can be no higher than about 24 feet without violating this “12 degree rule”. One way to have a tall mast and narrow beam, but not violate this rule is to use spreaders to artificially increase this angle.
The spreaders also take tension from the outer shrouds, convert it to compression, and transfer it to the mast. This imposes a bending force on the mast at the base of the spreaders. (Note that the spreaders are intended to be entirely in compression which is why they should exactly bisect the angle they make with the outer shrouds, i.e. the spreaders should point slightly up). To counteract this bending force, lower shrouds are attached to the mast just below the spreader bases and run to chain plates. All shrouds are subject to the 12 degree rule so a really tall mast may have a series of spreaders and lowers. The addition of lower shrouds, and possibly separate chain plates, helps divide and distribute the total tension load between several shrouds and fittings.
Spreaders can also be swept forward, or more commonly aft, to help control fore-and-aft bending in the middle of the mast. The chain plates, of course, must also be offset fore or aft to do this. Although spreaders do increase the angle the shrouds make to the mast and drain some tension from the outer shrouds, they do not, in any way, alter the basic tension and compression forces as calculated using just the height of the stayed portion of the mast and the width of the chain plate base. Any tension drained off the outer shrouds by the spreaders will show up in the lowers.
The spreader length is also important because this influences the amount of bending force imposed on the middle of a mast. If the spreaders are too long, they have too much leverage and will over bend the mast for a given load. If they are too short, they will not transfer enough force to counter the load imposed by the lower shrouds.
In general, the length of the spreaders is set by the designer based on the specified mast section and the anticipated wind load on the sail plan.