I help out with refereeing a Live Action Roleplay System, in which NERF blasters are used to simulate guns. Modifying those NERF blasters to deliver foam over longer distances is allowed and outright encouraged, because making a terrifying foam dart blaster is hilarious fun. Eye protection is also not mandatory, and people don't really want to leave site covered in bruises, so we need a power limit in place.

None of the above paragraph can be changed - simple solutions like "make eye protection mandatory" or "stop modifying NERF blasters" are not usable.

The NERF Rival projectile is a foam ball, roughly 1 inch in diameter:

A NERF Rival ball

They're really expensive, especially when you need to supply an army. Various third-party manufacturers produce small foam balls of the same diameter but at a lower price, so we want to allow participants to buy them and use them. Unfortunately, third-party rounds are often firmer than the official NERF projectile, and some manufacturers produce projectiles of inconsistent quality, meaning that they hurt more when they hit the target, presumably because they deliver more kinetic energy.

We want to allow as many third-party ammo types as possible so that our participants can be well-supplied, and so that if one supplier stops operating we've got plenty of places to get more, and we also want a simple testing procedure so that participants can reproduce the experiment in their own homes, and so that we can bring the setup to a camp site without lots of specialised and expensive kit.

What experiment can we set up to measure the kinetic energy delivered to a target by a small foam projectile?

  • $\begingroup$ It is not difficult to set up a ballistic pendulum: en.wikipedia.org/wiki/Ballistic_pendulum $\endgroup$
    – user137289
    Commented Feb 4, 2018 at 9:16
  • 1
    $\begingroup$ @Pieter, that looks like a great solution! Firing the projectile from a known blaster into a specialised pendulum at close range should be fairly reliable. $\endgroup$
    – ymbirtt
    Commented Feb 4, 2018 at 9:18

1 Answer 1


The Drop Test

I'm self-answering this, not to share my results, but to present one solution that I'v come up with that should give us reasonable results. I'm afraid I stopped studying mechanics about 10 years ago, so I don't know how valid my premise actually is.


The projectile will never penetrate the target (hopefully!). When the projectile strikes the target, some quantity of energy is transferred into the target, some negligible quantity is transferred into the environment, and the rest is used to deform the projectile. If a solid target is used, which will not deform from the impact, then all the energy that is not used to deform the projectile will be transferred into the target, then back into the projectile when it bounces.

Experimental Setup

A transparent persepex tube of diameter slightly larger than the projectile is secured to a wooden block. A hole is drilled through the tube at height $h_0$, and a toothpick is inserted. A line is marked around the tube at height $h_1$.

A diagram of the experimental setup

To test a projectile, it is inserted into the open end of the tube such that it rests on the toothpick. The toothpick is quickly removed from the tube, allowing the projectile to drop. A user observes the projectile's first bounce. A projectile that completely clears the line at $h_1$ is too firm, and is therefore unsafe.


$h_0$ can be set to any arbitrary value. $h_1$ can be computed by a slightly more complex setup, in which a microphone is placed at the bottom of the tube, in the wooden block. The time in between impacts can be used to compute $h_1$ with some quick maths. Repeated experimentation can be used to find an $h_1$ that is acceptable.


This is not foolproof. By dropping a few different balls onto my desk, I've found that the official NERF balls bounce more than both a softer third-party ball and a firmer third-party ball. I don't understand why this would be the case.


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