The Algorithmic Beauty of the Trebuchet

On the physics and mechanics of a medieval trebuchet, a type of catapult, its design, working and optimization through improved simulation and mathematical analysis.

A screenshot of Trebstar

# Trebuchet Mechanics.

is a free manuscript that provides an extensive description of the mechanics of trebuchets. It starts with elementary black-box and "see-saw" models, and builds gradually to the full model that includes a sliding, constrained sling. Geometry, physics, detailed derivation of equations. Energetics; definition of efficiency; tips on design; analysis of the finger mechanism; a monte carlo design method. Plenty of material for the mathematically inclined, but also lots of insight for the guy that just wants tips on efficient designs and to explore how to make his design perform efficiently.

Download it for free here. An Adobe Acrobat (PDF) file; 1.3 MB.

TrebStar Simulator Application

Trebstar is a free app that allows you to compute the range and range efficiency for your design. Input the parameters for the treb, and watch the animation. It allows propped, hinged counterweights, includes the constrained, sliding sling, and gives the range, range efficiency of the design. Various plots and tables allow one to examine the effect of variations in the trebuchet design on the efficiency, range, and forces exerted on the parts of the mechanism.

Some Features of Trebstar Simulator

  1. An optimum sling length search for the trebuchet is included, greatly easing your search for an optimum design.
  2. A CW diagram plots the position of the CW as a function of time. How straight is the fall of the CW? Does it matter?
  3. Range efficiencies with and without the beam as an energy source are both shown.
  4. Trebstar provides a table of 15 variables as a function of time, enabling you to make up your own plots of just about any combination of variables. It gives the kinetic and potential energies of the parts as a function of time and as a function of beam rotational velocity, etc.
  5. The maximum force on the axle normalized to the weight of the CW is shown, to be used in calculating a safe diameter of the axle.
  6. Nonuniform beams are handled by input of the radius of gyration and the center of mass of the beam.
  7. Defaults for the parameters may be saved, so variations on a nominal design can be readily made.
  8. One can more systematically explore the parameters by using a text input file to generate multiple runs, and save the results to a text file.
  9. It has lots of help files attached. Read the help files!

TrebStar should be particularly useful for those elementary physics/science classes that are studying energies and forces. Plots of these as a function of time or configuration parameters can be used as a basis for a variety of projects in the classroom. What things other than range efficiency can be used to determine how good a design is?

The Free Macintosh System X, intel Version of Trebstar

For System 10.6, thru 10.12 (Snow Leopard to Sierra)

Download here

This is a .zip file, 2 MB.

The Free PC, Windows 10 Version of Trebstar

Download here

This is a .zip file, 3.1 MB.


Both of these versions will warn you that you are downloading an application from the internet, which can be dangerous because of malware and viruses. I have checked both versions for viruses, and perhaps you should too. These warnings can be easily skirted in both platforms. On the Mac, go to the System’s preferences/security and privacy file and check the box allowing the download to proceed. There is something similar on the PC side. You may have to deal with similar warnings from your antiVirus application.

Will It Break?


"Will It Break?" is a manuscript for serious trebuchet builders that will help you to design and construct your dream. It provides methods for understanding and predicting the forces and stresses in your design during the hurl. Includes easy-to-use formulas for choosing dimensions and materials for all of the parts. Is the axle diameter large enough? Is the CW box strong enough? Will the beam break? How about the sling and the sling release prong? Forces tending to break the truss.

It includes a discussion of the forces acting on all the parts, their handy scaling rules, and many completely worked examples. Provides easy guidance for the novice, and leads for the experts. Tips to improve the safety of your operation. This is a sequel to my popular, free "Trebuchet Mechanics" manuscript, and has a more "practical" emphasis. 42 pages, 21 figures.

# Will It Break?.

Other material about Trebuchet Mechanics

My Own Trebuchet!

This babie throws bowling balls. Over the trees!

Shumie bowling It works!

Onager Physics


# "Onager Physics?" is another free manuscript that analyzes the physics of the Onager (Mangonel). It concentrates on the properties of the rope bundle, or skein, that generates the torque on the beam, but has some more general remarks on the scaling properties, efficiency and energetics as well. Download the file Onager Physics.

This site was created by Donald B. Siano