This work was conducted in an attempt to understand the mechanical stresses inside the beam of an existing trebuchet (the Renfrew trebuchet). After several years of uusage this beam broke but the cause was initially not known.

The developed code (strictly javascript using the canvas-capability of HTML 5) simulates a trebuchet with a hinged counter-weight and a projectile which slides initially inside a horizontal shute with friction present. Classical F=m*a considerations lead to a set of three second order differential equations which are solved numerically using a 4th order Runge-Kutta method. Following the motion of all the parts of the trebuchet we are able to conduct a stress analysis (only for the Renfrew treb).

As a first check on our calculations we used conservation of energy.

Secondly, by setting the mass of the projectile to near zero we are
able to simulate a classical double pendulum and successfully compared
our results to the results of the simulator available at
http://complexity.stanford.edu/blog/double-pendulum-simulation

The input for the
Standford simulator is somewhat restrictive but you can enter there

Θ_{1}=90 ω_{1}=0 mass_{1}=20 length=25

Θ_{2}=90 ω_{2}=0 mass_{2}=15 length=18

and click on
to provide our program with
the corresponding input.

Finally, a javascript-based trebuchet simulator is available
at http://www.virtualtrebuchet.com/. You can enter there the input values of the Renfrew-trebuchet with
the following exceptions :

Projectile Diameter : 0.1 m

Pivot to Arm CG : +0.2 m

Inertia of Arm : 539.3 kg m^2 (they require central moment of intertia)

Release angle : 39.0 (what my program gets) for given sling finger angle

As a result you should get from them a flight time of 6.231 s, a distance of
132.591 m and a release velocity of 37.045 m/s.

My simulation produces a flight time of 6.26737 s, a distance of 136.2 m
and a release velocity of 35.6 m/s. Note that my simulation does not
include air resistance, but their's does.

Zig Herzog; hgnherzog@yahoo.com Last revised: 07/22/15