The double-pendulum aspect ofStaff sling staff-slingSling dynamicsDynamics is shown to enhance its performancePerformance. The onagers, with and without slingSling, are analyzed and their performances predicted. The roles of these and other horizontal-axisAxis engines in ancient siegeSiege warfare are discussed. Onagers are compared with ballistas, and the eventual dominance of onagers in the late Roman Army is described. An explanation of the general observation that siegeSiege engines were more effective at short rangeRange is provided. The historyHistory, Historian and significance of traction trebuchets are presented. TwoBenchmark “benchmark” traction trebuchets are analyzed and their performancesLaunch speed (launch speedSpeed, rangeRange, efficiencyEfficiency) predicted and compared (with each other and with the performancePerformance capabilities claimed of ancient machines). It is shown for traction machines that the many and various engineEngine parameters need to be chosen carefully to optimize performancePerformance. CounterweightCounterweight (CW) trebuchets are introduced and their origins speculated upon. The performances of two varieties ofCounterweight (CW) CW trebuchets (fixed CW and swinging CW) are derived and compared with each other and with theTraction trebuchet traction trebuchetTrebuchet. The historicalHistorical reenactment spread and evolutionEvolution of trebuchets is given, and their effectiveness as the most powerful mechanicalMechanical warWar machines is emphasized.