Motviktsslungans dynamik : En analys av medeltida konstruktionsråd för mekaniskt artilleri
This Master’s thesis analyses the dynamics of the medieval counterweight lever engine, or
, a type of mechanical artillery. The purpose is to study the differences between different types of these machines, and see if computer simulations can be used to validate preserved advice on construction. Simulations include machines with a fixed counterweight, a hinged counterweight and a combination of both counterweights.
Due to the almost complete lack of archaeological finds and insufficient historical source material there are still, after more than a century of research, many unanswered questions concerning the design and performance of these machines.
The present study is based on an analysis by Jahsman (2004). A more detailed mathematical model employing Coulomb-friction is used. The dimensioning of the arm and the analysis of the loads are more detailed in order to give the arm more representative qualities and in order to easier notice deficiencies in the selected principles of dimensioning and design choices. Force and moment equations describing the movements of each machine are set up and solved numerically in MATLAB. For simulations without friction the equations are solved explicitly with DE-solver
ode23/45 and including friction implicitly with ode15i
. The arm is dimen-sioned with regard to bending, tension and shear. The three types of counterweight engine are optimized with regard to efficiency and maximum range per total arm length. Initially, mass-less arms without friction are examined, followed by the introduction of a physical arm, dissi-pation effects, and finally a physical counterweight.
In accordance with medieval sources the machine with a hinged counterweight exhibits a longer range, for a given size. The reason is primarily the long counterweight arm of opti-mized machines, giving high initial potential energy. At the same time, it is assumed that the greater friction losses in bearings and the more rapidly fluctuating forces in the machine du-ring the throw contribute to a lower precision. The medieval arm proportion of 1:4.45 with a hinged counterweight is confirmed as a favourable proportion in terms of efficiency for the standard arm used. Even lower arm ratios, mentioned in medieval sources, are in the simu-lations only optimal for more well-balanced arms, arms with a fixed or a combination of counterweights, or arms with a hinged counterweight mass at least 100 times greater than that of the projectiles
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