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. Last Modified on Jan. 24, 2006.

A screenshot of MacTreb*4.05

TrebStar is here!

A Mac Application for Simulating a Trebuchet

MacTreb*4.05 allows one 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. For fixed CWs too.

New in Version 4.05

An optimum sling length search for the trebuchet is included, greatly easing your search for an optimum design.
CW diagram plots position of CW as a function of time. How straight is the fall of the CW? Does it matter?
Range efficiencies with and without the beam as an energy source are both shown.
Now 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. The kinetic and potential energies as a function of time. as a function of beam rotational velocity, etc.
The maximum force on the axle normalized to the weight of the CW is shown, to be used in obtaining a safe diameter of the axle.
Calculations of the radius of gyration and the center of mass of the beam are more user friendly.
The beam of the trebuchet may be tapered, and a point mass added to it, permitting designs of fixed counterweight trebs.
Defaults for the parameters may be saved, so variations on a nominal design can be readily made.
Various other small improvements in layout and bugs killed
One can now more systematically explore the parameters by using a text input file to generate multiple runs, and save the results to a text file.

TrebStar4.05 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?

To get a fully functioning program, you need to pay a small fee for a serial number. The unregistered version does not allow for sling optimization. The CW path screen and the output tables are also disabled for any but the first throw after start-up.

The Macintosh System X Version

Download MacTrebX here. This is Stuffit .sit self extracting archive; 1.1 Meg.

New on Jan. 24, 2006. Equivalent to Version 4.05 for PowerPC Macs, system 9 and less.

The Macintosh PPC Version

Download MacTreb*4.05 here. This is Stuffit Classic ver. 1.6 self extracting archive; 1.0 M

New on New on April 4, 2002. Version 4.05 for PowerPC Macs.
MacTreb was written in RealBasic 4.0--a new programming language for the Mac that is great for this sort of project.

The Windows Version

Virtually the identical features as MacTreb*4.05. Written once, compiled for both platforms with the click of a checkbox! Goodby Visual Basic.

Download WinTrebStar4 here. This is a zipped file using winzip ver 7; 496 k

Download version compatible with Windows XP WinTrebStarXP here. This is a zipped file using Stuffit Deluxe ver 10; 1.1 Meg.

Payment Options

Please use the Kagi service to pay $15 securely by credit card or for non-US currencies.

Onager Physics

"Onager Physics?" is a free manuscript that analyzes the physics of the Onager by elementary methods. 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.New on April 4, 2002. Fixes an error in the dimensional analysis of previous versions.

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.

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?" is now available the following way: Go to the Kagi service to pay $18 by credit card. Kagi also accepts checks and non-US currencies, and is a secure site. Then I'll send you the manuscript electronically within three days. Easy...

Trebuchet Mechanics.

An extensive description of the mechanics of trebuchets that 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; the PDG Treb. Uses three variables (the angles defining the configuration), five lengths and three masses as parameters specifying the design to arrive at three simultaneous differential equations that are solved numerically to give the motion during the throw. Plenty of material for the mathematically inclined, but also lots of insight for the guy that just wants tips on efficient designs. Now includes a discussion of the non-uniform beam.

Download it here. New on April 4, 2002 An Adobe Acrobat (PDF) file; 388 k.

Don't have Adobe Acrobat Reader? Then go get it here. Well worth the download--easy to do, easy to use, and an important helper application.

Wackiest Trebuchet of the Week

Weird and wonderful: see the oddest treb yet described--it actually hurls!

Other material about Trebuchet Mechanics

An animation
A mathematica program
A trebuchet javascript calculator
A fortran montecarlo simulator

Top Trebuchet Sites:

All links updated as of Jan. 24, 2006

To purchase a model of a trebuchet or an onager, you can't do better than Ron Tom's site!

Center for Historical Technology--a Medieval center in Denmark with very large trebuchets and other machines. A museum devoted to uncovering the old technologies. I visited here last year and had a really great time, thanks to my host Peter Vemming. A great site!
Ron Toms' page with The International Registry of Hurlers, the people thrower design and the Catapult Bulletin Board. And more... Wonderful site.
Team Tormentum
Grey Company Trebuchet has lots of links. Terrific site!

My new Trebuchet! Torrisilly, Lout'nberg, Shumer and Feinstein, and other kooks who want to reduce citizens to the era of pre-gunpowder weaponry should take a look. My second effort to construct a potent weapon of mass distruction is illustrated here! When will they get around to banning these too? This babie throws bowling balls. Over the trees!
It works!