The swinging counterweight trebuchet. On internal forces

TL;DR

This paper derives explicit formulas for internal forces in a swinging counterweight trebuchet based on known motion parameters, aiding in structural analysis and design optimization.

Contribution

It provides new explicit expressions for internal forces in a trebuchet using known angular coordinates and their derivatives, enabling better structural assessment.

Findings

Formulas for internal forces derived explicitly

Comparison of dynamic and static forces at shot initiation

Illustrative results for a specific trebuchet

Abstract

The forces that act internally in a trebuchet as it delivers a shot depend on the motions of throwing arm, counterweight and sling. These motions are considered known experimentally or theoretically and given in the form of time-dependent angular coordinates. Explicit expressions in terms of these coordinates and their derivatives to second order are derived for the internal forces. The forces that act immediately after a shot is initiated can be extracted from the equations of motion without solving them, and they are compared with static forces just prior to initiation. Required strengths of the different parts of a trebuchet depend on the internal forces, which also determine sliding friction losses. Illustrative results are given for a specific trebuchet.