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More about the elliptical bow
Part 2 of 2

If a slight approach towards the trapezoidal section is desired, the corners of the back of the bow may be rounded more than those of the belly. If a more distinct trend towards the trapezoidal is desired for the purpose of securing still higher cast, that is, greater pull per weight of limb, the back may be narrowed up about 10 or 15 per cent from the dimeFig. 3A. It will be noted on inspecting this figure that the bent form of limb used is within ½" of the circular form. It is a cause of continual astonishment that so little variation from the true circular form which Dr. Klopsteg advocates makes such a radical change in the distribution of the cross-sectional dimen-sions. This very slight divergence almost completely eliminates the instability at the ends caused by the thickness being greater than the width when the circular type is used, and gives a shape of limb which so distinctly avoids the tendency towards wide shoulders near the handle. For example, the 40 pound bow (B-50 in Table I and in Figure 3A) has a maximum width of limb of 1.35 inches. The same weight bow, if built to the circular arc of 28½" radius would have a width of 1.75", a thickness of .57" over the full length of the limb and it would have its thickness greater than its width for the last six or seven inches next to the nocks.

All bows are practically rigid in the 2 or 3 inches next to the nocks and that feature, together with some of the known advantages obtained thereby lead to the thought that the ends should be recurved. This can be done, using the dimensions given above without changing the bent shape of the bow materially, but requiring higher stringing or longer draw. I have found that recurving the ends of a bow built according to the above dimensions, on a 1½" or even a 2" radius, does not change the bent form of the bow and adds definitely to its cast. I do not know whether this increase of cast is desirable for target purposes or not, but it is certainly desirable for flight duty. I have a feeling that these recurved tips by reason of their instability, that is, their tendency to turn side-wise, exaggerate variations in the nature of the string release and introduce sidewise errors in the arrow or make unduly burdensome the care required in releasing. Whether this tendency outweighs the advantage of lighter pull at full draw, is probably a question of personal experience. I have been rather hesitant about using target bows with recurved ends, although I know that some of the best shots have used them successfully.

Questions have frequently been asked as to how to lay out the ellipse to check whether the proper shape is being obtained and perhaps correct for some soft spot in the wood. The 19.3 x 25.3 ellipse used in Table I and Figure 3A can be easily laid out by taking a straight edge and measuring from one end, A, distances of 25,3 inches to point B, and 19.3 inches to point C. Now, if the point B is caused to travel along the vertical or 19.3 axis of the attached figure or a similar full scale figure and the point C is caused to travel along the horizontal axis, marked 25.3 inches, the point A will trace out the ellipse. This can be done in full scale very accurately.

I trust that the above will automatically answer some of the questions that have been loading up my mail.