As a start Table No. 2 has been prepared showing the universal spine number of several of the specimens listed in Table No. 1, in comparison with various kinds of wood whose weights and modulus of elasticity are listed in Publication No. 46 of the U. S. Department of Agriculture. This table again shows why Port Orford, Norway Pine and Spruce are used so extensively for arrows. The universal spine number shows the same relative listing of the various materials as the rating number "N" does. So if the archer finds it too difficult to compute the universal spine number he can prepare a table of rating numbers similar to table No. 1 from his own tests and at least get a comparison of the materials he has on hand. If the length of the dowel is made 29¼", the distance between supports 28 inches, the weight suspended from the dowel 2 pounds and if the deflection obtained is expressed in inches and the weight of the dowel in grains then the rating number
|N = DW2||(3)|
can also be compared directly with the materials listed in Table No. 1.
The chances are that no material will be found with a spine rating number much better than the Spruce listed as No. 1. It would be interesting to compare a large assortment of materials from various sources and see just how low the spine rating numbers will go, keeping in mind that the lower the number the better the spine.
|TABLE No. 2|
|Comparison of Universal Spine No.|
|No.|| Kind of|
| Source of|
| Wt. per|
| Modulus of |
|1||Spruce||No. 1 of Table 1||27.1||2,280,000||32.3|
|2||Sitka Spruce||No. 2 of Table 1||24.7||1,830,000||33.3|
|3||P. O. Cedar||No. 4 of Table 1||29.2||2,380,000||35.8|
|4||Norway Pine||No. 10 of Table 1||29.7||2,030,000||43.5|
|6||Bamboo||No. 16 of Table 1||51.5||5,500,000||48.4|
|8||Com. Birch||No. 17 of Table 1||36.7||2,480,000||54.2|
|9||West. Red Ced.||Montana||22.0||886,000||55.0|
|17||Yew||No. 23 of Table 1||37.5||1,340,000||105.0|
|20||Lemonwood||No. 24 of Table 1||54.5||2,150,000||138.0|
|21||Osage||No. 25 of Table 1||60.0||1,530,000||236.0|
Spine, of course, does not tell the complete story of a material for arrows.
Such properties as ease of working the material, resistance to warping in a wide range of temperature, straightness of grain, uniformity of the material, etc., all have to be considered in selecting arrow material. However, none of these properties affect the flight of an arrow directly and are only secondary considerations in the selection of material. Also, there are archers who claim that too great a stiffness in the arrow can be as harmful for certain weight bows as too little. There are others who don't even attempt to match target arrows by stiffness but use a shooting machine. No doubt they are correct in their contentions since in the final analysis grouping arrows in the gold is the primary object. However, this is a question of stiffness rather than spine and stiffness can be varied by changing the diameter of the arrow. In other words if a certain stiffness of an arrow is required for a particular weight bow, this stiffness can be obtained by a change in the size of the arrow rather than by a change in the spine number. Therefore, in selecting a suitable arrow material even these archers have to give thought to spine.
In any event a spine number as determined above will give a proper combination of all the mechanical and physical properties of a material affecting the flight of an arrow, and this number as has been shown above can be readily determined by anyone.
In all the above work the derivations of the various equations have been purposely omitted. The writer will gladly furnish anyone a copy of the proof and derivation of all the equations used if so required thru the Archery Review. If any archer should find it difficult to compute the rating number "N" or Universal Spine Number "S" from his own tests the writer or one of the archer's mathematically inclined friends will, I am sure, be glad to assist in such computation if given all the necessary data.
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