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Archery Analytics Archery Analytics

Arrow and Bow Tuning using the natural oscillation frequency method

A good match between bow and arrow is given if the natural oscillation frequency of the arrow is adjusted to the acceleration time in the bow.

oscillating arrow

An arrow is called stiff if it has got a relatively high natural oscillation frequency. A stiff arrow requires a short acceleration time in the bow, hence, a stronger bow. An arrow is called soft if it has got a relatively low natural oscillation frequency. A soft arrow requires a longer acceleration time.

The computation of these frequencies may help you in answering the following questions

  • Do my arrows fit my bow?
  • Which arrows optimally fit my bow? (spine, tip weight, shaft length, ...)
  • What options do I have to make my arrows fit my bow?

Remark: This tool can help you to identify issues, select arrows and give you some advise on how to change settings. However, it is not intended as a replacement for a proper bow tuning, see e.g. our white paper on tuning and data analysis. Other aspects such as how the release exactly behaves and the details of the draw-force curve do have a significant influence as well. Please also note that this tool will produce correct results only within the range of typical recurve bow parameters.

Computing an arrow's natural oscillation frequency

Arrow parameters

Spine of the arrow shaft as number (360 ... 1000)


Length of the arrow shaft


Specific weight of the arrow shaft. Take a bare arrow shaft, measure the weight and divide the weight by the length of the shaft. Example: 15 grams/ 74cm = 0.2027 grams/cm


Weight of the arrow head


Weight of the nock (including insert/pin)


Weight of the fledges (altogether)


This is the distance from the string to the fletches at their maximum width. Typically 4-6 cm (2-3 in).

Bow parameters

The effective draw length is the distance the string is pulled. You can measure it as the distance between the tip of a nocked-in arrow and the clicker edge (resp. the position where a clicker edge would be).



Draw weight at draw length


%

efficiency of energy transfer to arrow (typically 80%)

Optionally, you can provide your own intermediate points for draw length vs. draw weight, such as 20 cm / 15 lbs. This will increase the accuracy of the frequency computation. Please use the same units as for the draw length and draw weight above.




Intermediate point #1 (optional)

Intermediate point #2 (optional)

Intermediate point #3 (optional)

Results

no results computed yet

Measuring an arrow's natural oscillation frequency

If you have got your arrows at hand, you can measure the natural oscillation frequency quite easily. Just follow these steps:

  • Use an app for tuning musical instruments, such as gStrings. Or use this app which will give you a faster measurement but with a slightly lower accuracy Spectroid
  • Hold your arrow with the tip down and between 2 fingers. Start with a holding position of about 15 cm (6 in) below the nock.
  • Slightly push the arrow shaft against the edge of a table and feel the vibration in your fingers holding the arrow.
  • Vary the position of your fingers up and down in order to find the position where the arrow vibration is strongest (this position is called the vibration node, see also image at the top).
  • Now hit the arrow shaft a bit harder to the edge and quickly hold the middle of the shaft in close proximity to the mic of the device running the tuning app.
  • Read the natural oscillation frequency (in Hertz, Hz) and compare it to your bow's required oscillation frequency.
  • If the arrow's frequency is more than 3 Hz too high, the arrow is too stiff. Conversely, if it is more than 3 Hz too low, the arrow is too soft.
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