The Algorithmic Beauty of the
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
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; 388 k.
TrebStar Simulator Application
Trebstar 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.
Some Features of Trebstar
- An optimum sling length search for the trebuchet is
included, greatly easing your search for an optimum
- 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?
- Range efficiencies with and without the beam as an
energy source are both shown.
- 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.
- 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.
- Nonuniform beams are handled by input of the radius
of gyration and the center of mass of the beam.
- Defaults for the parameters may be saved, so
variations on a nominal design can be readily made.
- 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.
- It has lots of help files attached. Read the help
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 Windows Version of TrebStar Simulator
Virtually the identical features as MacTreb. Works in Windows 7.0 too.
Download version also compatible with Windows XP:
This is a zipped file using Stuffit Deluxe ver 10; 1.1
The Free Macintosh System X, intel Version of Trebstar
For 10.6, 10.7, and 10.8 (Snow Leopard, Lion, and Mountain Lion)
Now here This is a .zip file, 1.8 MB.
The Free Macintosh System X (Pre 10.6) Version of
Download MacTrebX here. This is Stuffit .sit
self extracting archive; 1.1 Meg.
MacTreb was written in RealBasic
Payment Options for TrebStar
The above free, unregistered versions of TrebStar will
show the results of throws from your input parameters,
including the range and efficiency but does not show
tables of forces and energies tables except for the
first throw. It also does not allow for sling
optimization and does not show the CW path.
For a fully functioning version of TrebStar, you need
to pay a small fee for a serial number.
service to pay $15 securely by credit card or for
non-US currencies. Or use paypal:
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?" is also available for $18 from the
kagi site mentioned above. Or use paypal:
- An animation
- A mathematica program
- A fortran montecarlo simulator
My Own Trebuchet!
This babie throws bowling balls. Over the trees!
"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
This site was
created by Donald B. Siano
I appreciate your
mail, comments, and suggestions