Legal Disclaimer: I am not a structural or marine engineer. And I've seen my fair share of home-brew failures. Use this information only as a guide to help understand the factors that figure into mast stress. Don't change the rig from what the designer provided unless you've thought about what can go wrong. And if you're not sure about your scantlings, you should consult a professional engineer to verify that that they will provide the necessary margin of safety. Finally, if you think you might want to do some boat designing, I recommend that you read "Gougeon Brothers on Boat Building" (on-line at the West Systems website) and buy a copy of Dave Gerr's "Elements of Boat Strength" (International Marine, 2000).
Finally, REALITY!
In Part 1 we figured out how much a mast will theoretically bend (and break?) under load. But does it?
First, a quick summary to highlight some of the conclusions if you skipped the math...
[1] The pressure on the sail is equal to the wind speed, in knots, times itself, times 0.005. At a wind speed of 10 knots, for example, you can figure on (10 x 10 x 0.005 =) 0.5 pound of pressure for every square foot of sail area.
[2] Doubling wind speed increases the pressure on the sail by a factor of four; tripling the wind speed increases the pressure by a factor of nine. Therefore, if that 10 knot breeze gusts up to 20 knots, the pressure on the sail would increase from 0.5 to 2 pounds of pressure per square foot of sail area. Of course, this assumes that you don't luff the sail.
[3] To keep a small boat level, the torque (force times distance) generated by sail pressure must equal the torque generated by the keel, or by hiking out. A 100-SF sail can apply a force of up to 200 pounds in a 20 knot gust. If the sail's center of effort is 5 feet above the waterline, that sounds like 1,000 foot-pounds of torque that could possibly cause a small boat with a centerboard to capsize.
[4] The amount of torque that it takes to bend and ultimately break a mast is dependent on the dimensions and the material used to build the mast. Aluminum -- or carbon fiber -- is not necessarily the best material. It all depends...
Sail maker Stuart Hopkins, of Dabbler Sails, measures mast bend to design and tweak a sail. The following procedure to measure spar bend is based on his "Determining Spar Bending," (www.dabblersails.com/blog/blog.pl?type=show&id=43&pic_id=4)...He doesn't talk about breaking a spar, but his methodology might let you evaluate a mast for "ultimate strength before you get out on the water.
First, support the mast at the tip and where it passes through the partners. Support gaffs and lug, gunter, or lateen yards and booms (the the sail is not loose-footed) at their ends. As shown above, the force of the wind, in pounds per square foot, is given by 0.005 times the wind speed squared in knots. For example, a wind speed of 10 knots is equal to a pressure of (10 x 10 x 0.005 =) 0.5 pounds per square foot.
Next, apply a weight (such as water, which weighs 8.3 pounds per gallon) equal to this pressure to the spar, assuming that the sail's center-of-effort is approximately in middle of the spar. Hang the weight from the midpoint of the spar (for masts and gaffs) or from the halyard attachment point (for lug, gunter, and lateen yards).
According to Hopkins, to get the correct bend the proper load to the spar is the product of the wind pressure times the area of the sail, using the following rule of thumb based on the type of rig. The factors he uses are:
- 1/2 of the sail area for masts carrying Bermudian, gaff, or sprit sails;
- 1/2 of the sail area for the gaff and boom on a lateen sail; and
- 1/3 of the sail area for gaffs and lug or gunter yards
Hopkins gives an example: measure the bend of an unstayed mast carrying a 100-SF Bermudian sail in 10 knots of wind, using water as the load.
Since the sail is Bermudian, the sail area (100 SF) used for the load calculation is reduced by half, to 50 SF. The pressure at 10 knots of wind is 0.5 psf, so the load to be applied is (50 SF x 0.5 psf) 25 pounds. Water weighs about 8 pounds per gallon, so we need (25 pounds/8 pounds per gallon) 3 gallons of water. Therefore, the bend of a 100-SF Bermudan sail in 10 knots of wind on an unstayed mast requires 3 gallons of water attached to the midpoint between the mast partner and the tip.
Once the spar is weighted down, measure the deflection using a string line fixed between the partner and mast tip. If the spar is rectangular, the wider, stiffer section (fore-aft section) should be in vertical axis. Imagine the sail pressure bending the mast top back.
To evaluate the spar deflection at higher wind speeds, adjust the load's weight, or the volume of the water. For example, to evaluate the mast bend with the same sail at 20 knots, increase the load by a factor of four. For the 100-SF Bermudian sail example, increase the volume of water from 3 to 12 gallons, or approximately 100 pounds of load. When I run these tests, I use old weightlifting weights instead of water (12 gallons would take a mighty big bucket, but you can hang successive weights on the spar -- just watch your toes).
Want to test your home-made unstayed mast? Clamp the end up to the mast partner to something stable (a boat trailer or truck tailgate) and start hanging weights on the mast at the sail's center-of-effort height. I would use the full pressure weight for this test, instead of derating it for measuring the mast bend. For example, use 200 pounds of load for the 100-SF Bermudian sail in a 20-knot puff (and about 450 pounds if you think you'll see a 30-knot gust). The problem will be finding enough weights -- how about using some cinder blocks? If you can careen your boat, I think you could also test the mast partner (or a tabernacle) and the mast using the hanging weight technique. Next time I build a small boat and rig, I'm going to try it and see.
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