A Foolproof Method for Tillering Bows

by Dick Baugh (Dec. 28, 2003)

The purpose of this article is to present a simple, systematic method for checking the tiller (evenness of bending) and draw weight of a wooden bow before you even string it. This is a quantitative method of doing what an experienced bowyer does in a very subjective, qualitative way. Initially the traditional wood bowyer uses his/her skill and experience to shape the bow limbs to the approximate size, erring on the side of too heavy. The bowyer then strings the bow, looks at the shape and scrapes or rasps away some wood where it looks too stiff. Next the bowyer tests the draw weight, pulling to the desired weight at, for example, only 16 inches instead of the desired 28. More wood is scraped off until the bow pulls the desired weight at the desired draw length. The tillering is checked after every removal of wood. An experienced bowyer can make a bow from seasoned log to shootable weapon in less than an hour, but how many hours did it take him/her to acquire the expertise?

One of my personal challenges in the study and practice of traditional Stone Age skills is to apply modern scientific analysis methods to crafts of our Stone Age ancestors. The objectives are to gain a deeper understanding of our ancestors and to develop easier methods for doing some of their crafts without the long and tedious learning process they must have gone through. This article is not a treatise on making wooden bows, but instead, a new way of achieving the desired results. I hope this new tillering method will lead to better bowmaking for all of you.

As the son of a very good amateur magician I learned at a very early age that human senses are very easily deceived. Therefore, I have always doubted my ability to tiller a bow for even bending by eyeball alone. This is particularly difficult for "character" bows with snaky limbs. How do you compare the bending in the two limbs of a bow when one of them has a natural bend in it and the other is straight? It is easy. You don't even have to put a string on the bow. You simply clamp the bow in a horizontal position so one limb of the bow doesn't move; hang a known weight from the tip of the other limb and note how far it deflects. Do the same for the other limb. It shouldn't matter if one limb initially has some extra curve. The limbs had better bend the same amount. You check for uniformly varying stiffness along the limb by clamping all but the outermost 1/2 of each limb, suspending the weight and measuring the deflection. The deflection of the outer half limb should be from 1/4 to 1/3 of the entire limb. The setup I use is shown in Figure 1. One can also determine the draw weight of the bow by seeing how far the weight makes the bow tips deflect. You can do all this before you ever put a string on the bow. There are three quantities that can be checked this way. Do the two limbs bend equally? Is the stiffness tapered uniformly and similarly in the two limbs? What is the draw weight going to be? The devil is, of course, in the details.

Lets Look at the Details:

A "reasonable" design rule for a bow is to have the working part of the bow limbs bend in circular arcs (constant radius of curvature). We also know, thanks to the pioneering work compiled in "Archery, the Technical Side" in the 1950's, that for maximum efficiency the working parts of a bow limb should be equally stressed. In order to achieve these goals with a straight limbed bow make the limbs with constant thickness and a width that tapers uniformly from the innermost to the outermost part of the bow limb. We also must have the two limbs well balanced in stiffness. When one limb is "snaky" we still want its stiffness to vary linearly from the innermost to the outermost part.

The amount the tip deflects depends on the weight you hang from the bow tip, the length of the bow and the draw weight. If you increase the hanging weight by a factor of two, the deflection will increase by the same factor. If you measure the deflection on a 50 pound bow of a given length then the deflection for a 40 pound bow of the same length will be 50/40 greater. Is it obvious that it won't depend on the type of wood you use? The limbs must also have equal deflections.

The results of the calculations, Table 1, are normalized for a one pound weight hung from the tip, draw weights at 28 inches of 40, 50 and 60 pounds and a 7 inch fistmele. Since a one pound weight would give a small and consequently inaccurate deflection you should use a heavier weight and multiply the number in the table by the number of pounds you are hanging. The table was based on some computer calculation and then checked experimentally against the following bows:

1. 61 inch California Bay bow pulling 44 lb. at 28 inches by Tim Baker.

2. 64 inch Osage bow pulling 48 lb. at 28 inches by Jim Hamm.

3. 78 inch Pecan bow pulling 56 lb. at 28 inches.

4. 48 inch sinew backed Black Locust bow pulling 32 lb. at 20 inches made by the author.

5. 63 inch Red Oak bow pulling 56 lb. at 28 inches.

When one limb of the 61 inch California Bay bow was clamped and the 6.5 pound weight suspended from the nock, the deflection was 2.275 inches. When the inner half of the limb was clamped and the 6.5 pound weight suspended from the nock, the deflection was .61 inches. Figures 2 and 3 show the results. According to Table 1, hanging a 6.5 pound weight from the tip of a 60 inch bow pulling 44 pounds should give a deflection of .40 X 6.5 X 40/44 = 2.36 inches.

This compares favorably with the actual measurement (2.275 inches). The other bow deflections also agreed quite well
with the calculations.

Table 1. Tip deflection per pound for bows of different lengths and draw weights.

Note that a 48 inch bow deflects more than a longer bow for the same draw weight. This is to be expected because the limbs of the shorter bow have to bend more in order to draw a 28 inch arrow. In the interest of simplicity, the table only includes results for a 28 inch draw length. For the same draw weight at a 27 inch draw length all the deflections would be increased by a factor of 28/27. For other draw lengths and weights go figure.

Using the Table to Build a Bow:

Assume that you want to build a 66 inch bow pulling 50 pounds at 28 inches and you are using a 2 liter beverage container weighing 4.3 pounds as a test weight. Each limb should deflect .30 X 4.3 = 1.29 inches. The outer 1/2 of each limb should deflect 1.29 X 1/4 = .32 inches.

1. Rough out the bow to its approximate dimensions. Pay attention to all the caveats in the book entitled, The Traditional Bowyer's Bible.

2. Compare the measured deflection of the outer half of each limb with .32 inches as shown in Figure 2.

Clamp horizontally all but the upper half of the top limb of the example bow rigidly to a table. Mark the vertical position of the tip. Suspend the weight from the tip and measure how far down the tip deflects. Do the same for the bottom half of the lower limb. The two measurements should agree within 5%. This tells you that the stiffness of the ends of the bow are well balanced and appropriate for the desired draw weight.

3. Compare the measured deflection of the entire limb with 1.29 inches as shown in Figure 3. Clamp horizontally the lower limb so that only the top limb of the example bow can deflect. Mark the vertical position of the tip. Suspend the weight from the tip and measure how far down the tip deflects. Do the same for the lower limb. The two measurements should again agree within 5%. This tells you that the stiffness of the limbs of the bow are well balanced.

4. Remove wood from the bow limbs gradually until they are balanced, have uniform stiffness, and deflect the required amount. If you took off too much wood then apply a backing of flax, hemp or sinew. When the deflections are close to the desired amount put a string on and see how it shoots.

Conclusion:

This method is foolproof, not idiot-proof. You still have to use all the rules of good bowyery. This method takes a lot of the guesswork out of tillering and obtaining the proper draw weight .

Sources of Known Weight:

Using a one pound weight for this test would result in very small deflection and consequent inaccuracy. A heavier weight and bigger deflection improves the accuracy. I use a steel block that has been accurately weight at 6.50 pounds. A full plastic two liter carbonated beverage container weighs almost exactly four pounds 5 ounces. This is a convenient weight to use. If you want to use something else as a weight and don't have a way to measure it then take whatever you want to use to the local grocery store and use their scale.

References:

The Traditional Bowyer's Bible from Bois d'Arc Press, POB 233, Azle, TX 76020. I never get tired of reading these three volumes.

Archery, the Technical Side, Hickman and Nagler, editors.

Figure 1. The workbench, clamp, 6.5 pound weight, and piece of cardboard used to indicate the deflection of the outer half of a bow limb.

Figure 2. A closeup of the deflection of the outer half of the limb.

Figure 3. Deflection of the entire limb. Two marks representing the deflection of the outer half are visible in the upper left corner.

Figures 1, 2, and 3 have not been included in this article. We are urging you to join the Society of Primitive Technology (SPT). This article will be published with Figures 1, 2, and 3 in the next "Bulletin of Primitive Technology #27". To join, see their website or phone (208) 359-2400.

E-mail your comments to "Richard A. Baugh" at richardbaugh@att.net