Category Archives: Math

Notes about valves and flow rates

Comparing valves for compressed gases can be difficult for several reasons. Even if you are familiar with how valve performance is specified, you can easily make mistakes. Valve performance is specified in several different sloppy and confusing ways, almost always in non-metric units. The worst part is that valve performance can be specified in obvious […]

Nerf Engineering notes

I’ve started organizing my writings and thoughts on Nerf ballistics into a set of notes (link corrected). Readers of my blog might be interested. For the moment my notes are very rough and incomplete. I’ll update the PDF as I make changes. I’d appreciate any feedback, especially corrections and ideas. Edit (2012-10-02): I’ve removed the […]

Solving the point mass model of a dart’s trajectory, part two

I wrote a technical paper about solving these equations and made some conclusions for design. I have fully solved the flat-fire case given that the x velocity stays above a certain number (and it generally will). (Original link broken: My newer notes contain that paper and more.) The take-home message is pretty simple: Keep kinetic […]

boltsniper’s optimal barrel length formula

Whenever there is a thread about one of the holy grails of Nerf ballistics, an equation for the barrel length that maximizes performance, someone is bound to mention the results of some tests boltsniper did in 2005 when he was designing the FAR. boltsniper, for the uninitiated, is one of the few engineers in the […]

Solving the point mass model of a dart’s trajectory, part one

This blog post is relatively math heavy and it serves mostly as notes for my own use. I will assume some familiarity with differential calculus and ordinary differential equations. I also will assume some familiarity with the basic equations that govern the motion of Nerf darts after they leave the barrel. Yesterday I had an […]

Approximate expansion diameter of latex tubing

I previously wrote about how to estimate the expansion diameter of latex tubing, but I made no measurements to verify that the formula I suggested, where is the unexpanded inner diameter of the tube and is the unexpanded tube wall thickness, was accurate. Back in 2010, I made some measurements for tests that were aborted […]