by Paul Goodwin - US4061 - September 1990
Revised February 2010 - Paul Goodwin
This article will explain how to measure mast stiffness, how to plot the stiffness, and provides the stiffness of several different masts that the author has tested. In addition, a target stiffness is recommended for people that are not sure how to tune their wood mast.
The critical area of stiffness is below the hounds, since most bending occurs midway between the hounds and base. When the mainsheet is first pulled in (on the starting line), the mast has a smooth bend along its full length. This bend is primarily caused by leech tension in the sail. As the boat picks up speed, increasing pressure on the sail causes the tension in the sidestay and forestay to increase. The rigging tension pulls down on the hounds, forcing the mast to bend be- cause of the increased compression. As the mast bend increases, the distance between the tip of the mast and the back of the boom decreases, which reduces the leech tension. As the boat approaches top speed, the tip of the mast actually straightens out, and almost all of the bend is below the hounds. Look carefully at a picture of a DN under sail to see this effect (the May, 1990 Newsletter has some good examples).
Since the mast is bending due to compression, small changes in stiffness can have a large effect on how easily the mast bends in puffs. This is similar to measuring batten stiffness by pushing the batten down on a bathroom scale. Once the batten is out of column, it continues to bend with very little increase in load.
The article by John R. Jombock on plank bend measurements (Demystifying Plank Stiffness - January 1990 Newsletter) suggests using a single weight to determine the stiffness of a plank. While this is technically correct, use at least three weights. This gives four data points, allowing a plot of load vs. deflection. Calculating stiffness from this plot provides greater accuracy than a single point measurement.
You will need three calibrated (accurately measured) weights of approximately 40 lb each, and a dial indicator for measuring deflection. Barbell weights work well, and are available at most sporting goods stores. A dial indicator has the precision required for accurate results, and tool stores sell them for a reasonable price (frequently less than $20). A dial indicator which has a range of 1" can make measurements of over 1" by resetting it after each 1" of travel. many" different styles of base are available for holding the dial indicator.
Make both side to side measurements and fore/aft measurements. Use 11' between supports to find the stiffness in the critical area below the hounds. You should also make measurements with 15' between supports, which will help determine how limber the tip is. This gives four stiffness curves for each mast, and allows for reasonable accuracy when comparing masts.
The supports for the mast must be very strong so there is no movement when adding weights. Sawhorses make good supports, but be sure they do not rock or shift when the weights are added. Putting a roller under one end to eliminate any friction will help in getting consistent, accurate results.
To measure the stiffness below the hounds, set the inside edges of the supports 11 ' apart (see figure 1).
Set the mast on the supports, about 2" from the base of the mast, clamp the mast to one of the" supports so it does not rotate when the weights are added (see figure 2).
Hang the weights halfway between the supports. Set the dial indicator over the middle of the mast, with the tip close to the point where the weights are applied. Be sure to put any clamps or fixtures used for hanging the weights on the mast before setting the dial indicator.
Making the measurements
Set the dial indicator to "0". (This is the first data point to lbs, 0 inches). Add one weight to the mast. Write down the weight and the reading from the dial indicator. Add another weight and write down the new reading. If you run out of travel on the dial indicator, reset it to "0" before adding more weight. Keep making measurements until all of the weights have been added. It should not be necessary to use more than 120 Lbs if your measurements are accurate.
Plot the results on graph paper as shown in figure 3a. If your measurements have been perfect, then a straight line will pass through all of the points. If the points are not on a straight line, then check your measurements. If the points fall above and below a straight line, then check the weights for accuracy, and use extra care when reading the dial indicator. If the points are on a curve, then check the supports for movement or bending when adding the weights.
Figure 3a - Measurements at 11 feet
Once the accuracy of your measurements are satisfactory, repeat in the fore/aft direction. Then move the supports to 15', and run another set of deflection measurements (see figure 3b). Keep two charts, one with the 11' measurements, and the other with the 15' measurements. Make comparisons by adding the plots from different masts.
Figure 3b - Measurements at 15 feet
Figures 3a and 3b show plots of the mast deflection taken on a Kenyon 2040 wing mast, a Norton wing, and on a wood mast. The Norton is one of the softer masts (from 1986). Table 1 shows the spring rate derived from these.curves (as suggested by John Jombock).
The measurements in figures 3a and 3b were made with 20 lb weights. Notice how close all of the measurement points are to a straight line. No mast starts out limber and becomes stiff, or vice versa (except in the case of a mast with a wood stick inside for support). So look for measurement errors if you plot your results and the points do not fall on a straight line.
Comparing different masts
When looking at figurea 3a and 3b, the lower a line is on the graph, the stiffer the mast is. This rule shows that the Kenyon mast is stiffer than the Norton on all curves. Also, all of the masts are stiffer fore and aft than side to side.
Looking at the plots more carefully, the side to side curves show the effect of tapering above the hound. In the top graph (measured below the hounds), the increase in stiffness between the wood mast, the Norton, and the Kenyon is almost equal. In the bottom graph (measured from tip to base), the difference between the wood mast and the Norton is much greater than the difference between the Norton and the Kenyon. This is because the tip of the wood mast is very soft.
People building wood masts can use these methods to compare the stiffness of their own masts. The wood mast in figure 3 is a mast which has been very fast, but is quite limber. A mast this flexible can be difficult to sail in light wind, and requires sheeting out in heavy air to prevent over bending.
If you have never sailed a wood mast before, then try using a stiffness close to the Norton wing below the hounds. If you're comfortable with a softer mast, then try a stiffness similar to the wood mast in figures 3a and 3b.
Many wood masts which have been going fast are stiff fore and aft (stiffer than a Norton wing), and limber side to side (5 - 10% more limber than a Norton wing). The stiffness in the tapered section above the hounds has been hard to understand, with masts going fast with either a stiff or flexible tip.
One problem with a soft, tapered mast tip is that it reduces leech tension. This flattens the head of the sail and reduces power, particularly at low speeds- to compensate for this, many people use sails with more luff curve above the hounds . A wood mast could have no taper and the same stiffness as the Norton wing. This mast should sail like a Norton, but not break so easily.
Notice that all of the masts are at least 3 times as stiff fore and aft as they are side to side. If a mast is not stiff enough fore and aft, then it will not rotate very well when tacking. This can be demonstrated by sheeting the sail in (not to tight) and rotating the mast. A good mast will snap back and forth from tack to tack. A mast without enough fore and aft stiffness will not snap across, and will be more likely to rotate to the wrong tack in puffs.
One note of caution when tuning wood masts. Adding carbon fiber tows on the outside of a mast provides a fast, easy, and inexpensive way to increase stiffness. However, the stiffness will increase for several days after applying the carbon fiber. Therefore, add enough carbon fiber to bring the stiffness to a level slightly less than desired. Then make the final stiffness measurements after allowing a week or more for full curing of the epoxy.
This article answers some of the questions that sailors have asked about measuring mast stiffness. It should also encourage more people to make accurate measurements of mast stiffness. The techniques described here may sound too technical and complex, but the results are worth the effort. After completing the initial setup, stiffness can be measured in about 1/2 hour per mast. Transferring the urements onto a graph requires about 15 minutes, and provides a permanent record of mast stiffness.