Cable length dynamics by adding twists to cable

[LPOP]

Hi,

I am an avid archer and am about to begin making my own strings for myself and others compound bows.

I am searching for a formula to help me calculate the appropriate length of string material needed to build a string that will equal a certain length after pre stretching and adding twist to it. I am hoping to eliminate trial and error and have a formula that will give me a near perfect length of bow string each time, regardless of the required length of cable needed for a particular bow.

To make a string; one wraps a single strand from a spool in a continuous loop onto the posts of a string jig, of which there are two posts. The posts of the jig are set to a particular length i.e 50 inches. A typical bow string will have 18 strands of string filament wrapped around the jig posts or 9 strands on each side of the posts. After the ends of the string is tied off to the bundle to prevent slippage, the string is then put under 300# of tension for a specific time. The non recoverable elongation of this string is approximately .005 percent after this procedure. Then twist are added to the string in order to promote stability to the shooting system. Typically; this is anywhere between one twist for every two to three inches of finished cable; one twist equals 360 degrees of rotation.

Now, adding twists to a string or string bundle will shorten the string and pre stretching will slightly but permanently increase its length. So, it is necessary to anticipate these factors and add extra length to the string for twisting and subtract a bit for the non recoverable elongation.

I don't know how much a string will shorten per twist but I imagine that it is directly related to the diameter of the fiber and or the total diameter and the end to end length of the completed string. The diameter of the string material can vary but the one that i use is .014" and the diameter of a completed bow string contains 18 cross sections of this size string.

What formula would tell me how much additional length is needed to give a string the proper length after stretching and twisting?

Thank you.

 

[eljose79]

Hello,

I understand your desire to have a formula that can accurately predict the length of a bow string after pre-stretching and adding twists. While there are many factors that can affect the final length of a bow string, there are a few key variables that can be used to develop a formula for your specific needs.

Firstly, the amount of stretch that occurs during the pre-stretching process will depend on the material used for the string and the amount of tension applied. This can vary depending on the specific material and the manufacturer's recommendations, so it may be necessary to do some testing to determine the exact amount of stretch that occurs for your specific string material and tension.

Secondly, the amount of shortening that occurs with each twist will depend on the diameter of the string material and the total number of twists added. As you mentioned, the diameter of your string material is .014 inches and there are 18 cross sections of this material in a completed bow string. This information, along with the number of twists you typically add, can be used to calculate the amount of shortening per twist.

A formula that could be used to calculate the additional length needed for twisting and pre-stretching could look something like this:

Additional Length = (Stretch Factor x Original Length) + (Twist Factor x Number of Twists x Diameter of String Material x Number of Cross Sections)

The stretch factor and twist factor would be determined through testing, as mentioned above. It may also be helpful to add a small margin of error to this formula to account for any additional factors that may affect the final length of the string.

I hope this helps you in your string-making process. As always, it is important to continue testing and refining your formula to ensure accuracy and consistency. Good luck with your project!