alvinhilario

Introduction

This code is meant to explore the relationships between different arrow and bow variables such as Arrow Length, Arrow GPI, Arrow Spine, Arrow Component weight, etc. and the Bow Poundage with one critical assumption/restraint:

That there is an optimal Point Weight for a given Arrow Length, Arrow Spine, Bow Poundage, and Bow IBO, because an arrow is similar to a mass+spring system and there's a sweet spot between under and over spined arrow setups. Ideally, this optimal point weight should make it easier to get a bullet hole with bare shaft paper tuning right from the get go assuming your rest, cams, and D-loop are where they're supposed to be.

The method for determining an Arrow Manufacturer's recommended Spine for a given Bow IBO, Bow Poundage, Arrow Length, and Point Weight confusing, much varied between brands, and do not offer a high resolution nor intuitively visual interface to explore arrow dynamics.

Although one could make a far underspined or far overspined arrow setup, paper tune to get a bullet hole, and still have a successful hunt, I'm more interested in geeking out and providing a tool for fellow archers and hunters.

These values aren't meant to be exact, but it should get you directionally where you want to go, and in the ballpark.

Example and Quick Takeaways

Below is an example where I compare two options for a 200 spine arrow for my PSE Mach 34 with an IBO of 335 FPS, and 71# draw at 29" draw length. Specifically a higher FOC (shout out to the Ranch Fairy and Dr. Ashby) and Weight option, the Sirius Orion in Blue, and an ultra fast option, the Victory RIP XV in Orange. Here's some takeaways:

• The Orion has a higher Optimal Point Weight, Total Arrow Mass @ 547gr, and FOC @ 18.39%, almost considered Extreme FOC
• The Orion maintains Speed (FPS), Momentum and Kinetic Energy over distance better
• To venture into the 600-700gr and >20% FOC regime, I'd need to drop down to between a 50-60# draw. This would have marginal impact on momentum, but take around a minus 30-50 fps hit, increase of 30-60ms time to target at 20yd, and dip from the Extreme Game Animal Kinetic Energy territory to Large Game Animals.
• The Victory RIP XV, saves about 130ms time to target at 60yd, and starts in the Large Game Animal territory at 60yd right off the bat at 70# draw

FOC Color Band Legend

• Red - Normal FOC <12%
• Light Blue - High FOC 12-19%
• Medium Blue - Extreme FOC 19-30%
• Dark Blue - Ultra Extreme FOC >30%

Kinetic Energy Color Band Legend

• Red - Small Game - 25ft lbs, <34J
• Light Blue - Medium - Deer 25-41ft lbs, 35-56J
• Medium Blue - Large - Elk 41-65ft lbs, 56-88J
• Dark Blue - Extreme - Moose 65+ft lbs, >88J

Assumptions

From the analysis of various Arrow Spine charts from popular arrow manufacturer's, I've derived the following equation that calculates the Optimal Point Weight given the Bow IBO, Bow Poundage, Arrow Length, and Arrow Spine

• Nominal Starting Point Weight is 150 grains
• Assume Relationship between Nominal Starting Point Weight and Effective Poundage is 25:5 (From manufacturers)
• IBO to Poundage Slope is 0.252
• IBO to Poundage Intercept is -81.8
• Will also be using a default Drag Coefficient of 2, but feel free to play around with it

Linear Regression parameters derived from various arrow manufacturer spine charts. See below for plots

• aggregateRegValuesSlopeSlope = -0.001
• aggregateRegValuesSlopeIntercept = -0.174
• aggregateRegValuesIntSlope = -3.885
• aggregateRegValuesIntIntercept = 237.637

References

• Ashby Reports (2019). Terminal Arrow Performance Update. View Report
• Meyer, H.O. (2015). Applications of Physics to Archery. View Paper

Support This Tool

If you find this arrow calculator helpful and would like to support its continued development, please consider making a donation. Your support helps me maintain and improve this tool for the archery community.

Donate via PayPal Donate via Venmo: @Alvin-Hilario

View on GitHub