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The swinging counterweight trebuchet. On internal friction

E Horsdal

Abstract

Mechanical energy is lost to friction during a shot with a trebuchet. The losses are mainly due to sliding friction at the bearings for the throwing arm and at the hinge for the swinging counterweight, but the aerodynamic force on the sling also contributes. Generalized forces for these sliding and aerodynamic frictions are derived and included in the equations for the internal movement of the engine. The equations are solved by the use of perturbation theory and calculated losses are compared with results from an experimental engine of small dimensions. Scaling to full-size trebuchets is discussed.

The swinging counterweight trebuchet. On internal friction

Abstract

Mechanical energy is lost to friction during a shot with a trebuchet. The losses are mainly due to sliding friction at the bearings for the throwing arm and at the hinge for the swinging counterweight, but the aerodynamic force on the sling also contributes. Generalized forces for these sliding and aerodynamic frictions are derived and included in the equations for the internal movement of the engine. The equations are solved by the use of perturbation theory and calculated losses are compared with results from an experimental engine of small dimensions. Scaling to full-size trebuchets is discussed.
Paper Structure (20 sections, 27 equations, 7 figures, 7 tables)

This paper contains 20 sections, 27 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. The trebuchet and friction
  3. Dissipation functions $\mathcal{F}$ and generalized forces $\mathcal{R}$
  4. Sliding friction
  5. Aerodynamic friction
  6. Equations of internal movement with friction
  7. Results and comparison with experiment
  8. Convergence of iterative procedure
  9. Rates of mechanical energy loss
  10. Loss of mechanical energy and efficiency
  11. Loss of range
  12. Discussion and scaling
  13. Scaling of equations of motion
  14. Strengths of shafts and throwing arm
  15. Scaling at constant $S_{\mathrm{shaft}}$
  16. ...and 5 more sections

Figures (7)

  • Figure 1: Trebuchet. Height of pivot is $H=L_1\cos\theta_i$.
  • Figure 2: Reaction force $F_R$ at fulcrum in units of $Mg$.
  • Figure 3: Range $R$ in vacuum vs release time.
  • Figure 4: a) Reaction forces at pivot and hinge. b) Aerodynamic force on sling.
  • Figure 5: Powers at fulcrum, hinge and sling until release for maximum range.
  • ...and 2 more figures