Crossbow Arrow Drop Calculator

Disclaimer

This is an up-to-date version of Steven A. Jackson's archery ballistics calculator, slightly tweaked to be particularly useful to crossbow users. Some irrelevant factors are taken out of the formulas, such as whether the arrow has feather fletchings (highly unlikely) or plastic vanes. Some common defaults are loaded as well.

For a more detailed explanation, check the notes below the calculator.

Distance (yards)Drop (inches)Arrow Speed (FPS)Kinetic Energy (ft/lbs)Momentum (lb/sec)
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Notes

These calculations are based on the notable publication "Exterior Ballistics of Bows and Arrows" by W.J. Rheingans. It focuses on determining the maximum shooting range that can be achieved with arrows of different designs. What happens after an arrow leaves the crossbow depends on a couple of factors:

  • The initial speed of the arrow
  • The arrow weight
  • The amount of friction during the arrow flying through the air

It might be worth noting that the original study deals with an extra variable: the speed and direction of the wind.

But since its main interest is getting the projectile as far as possible, it is safe to ignore. The main focus of most crossbow shooters is actually hitting a target - whether it is a game animal or a dummy target. This is not to say that wind doesn't affect the accuracy (because it does!), but it has no place in a calculator as we cannot predict or measure it on the field or create a meaningful simulation model.

Advanced settings

The purpose of the optional advanced settings of the calculator is to determine the amount of resistance the arrow gets from the air. This is where the details of the arrow design come into play.

Please note that these are optional and there are some common/average default values loaded so you don't have to set those explicitly if you are not ready to dig that deep at the moment.

The way to calculate said resistance is by measuring the surface area of the arrow and including the shape of certain arrow parts (tips and fletchings) into the equation.

Our calculator assumes an arrow with a bullet-like shape of the tip and plastic vanes as these correspond to virtually all products on the market today.

The surface area of the arrow consists of the shaft (that's why we need its length and external diameter) and both sides of each vane.

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