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Swiss Shooting Range Over a Wall and a Highway?

Functions & Equations

A unique Swiss shooting range where shooters fire over a protective wall

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Start here β€” this is the source that inspired this exploration.

Introduction

At a shooting range in Switzerland, competitors fire over a protective wall that separates the firing line from the target area. The wall height, the distance to the targets, and the bullet's trajectory all have to line up so rounds clear the wall safely and still land on target. Treating the bullet's path as a simple quadratic β€” no air resistance β€” gives a clean model of launch angle, velocity and range, but real bullets lose energy to drag over distance. Part of this exploration is finding where that idealised model is good enough, and where it would give a false sense of the safety margin.

Guiding Questions
  • The range fires over a wall and a road. What path does a bullet's drop follow over distance?
  • Model the trajectory with a quadratic: what launch angles clear the wall but still hit the target area?
  • Find the safe envelope of angles and speeds. How much margin does the design have?
  • What changes for a longer range or a higher wall? Could you design the geometry yourself?
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Key Mathematical Concepts
Optimization Trigonometry Projectile Motion Quadratic Functions Parametric Equations
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