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were no interactions with the surroundings, a body could move without propulsion, as in outer space). Most propulsive systems aim at moving a body over land or through a fluid at constant speed, but all propulsive systems need to accelerate the body at some stage. The power required to propel a body of mass m (e.g. a car) may be expressed as: with: Wtotal Waccel Wclimb Wroll Wfluid-drag W mav, W mgvcos, W c mgvcos, W (17.8) c A 1v3 (17.9) D F 2 accel climb roll R fluid-drag where a is the acceleration applied, v the actual speed, the slope of climbing, cR a tyre-rolling coefficient (typically 10-2), cD a fluid-drag coefficient (typically of order 1, but may drop to 0.1 for streamlined bodies), AF the frontal area projected by the body in the direction of motion, and the density of the fluid medium. The idealisation of a long rope being hauled in absence of any other interaction may be a good propulsion paradigm; because of force reciprocity, propulsion may be thought both as a pushing the environment (the rope, in the example) to the rear, and as pulling (the rope) from the front. As a first model, for a constant-mass vehicle, the momentum balance in the direction of motion may be writtenas mxTD,mbeingthemassofthebody, x push on the rope example) and D the drag force resisting the motion (friction with the rope, frictional and pressure drag in a fluid, etc.). For these vehicles, the drag can be measured by towing at constant speed, and the thrust by breaking. For steady motion at speed v, the energy dissipated just by the motion is Dv=Tv, and a propulsion efficiency may be defined to compare this energy with the energy p Tv Wshaft Notice that all engines consume more energy that what they supply: electrical engines, elastic engines, etc., but particularly thermal engines, where this internal energy conversion efficiency, e, is of the order of 30% to 50% (in electric motors it may be typically 95%). Most propulsion systems may be considered in this way just power plants that apply a torque, M, to a its acceleration, T the thrust force (pull or (because it is usually through a shaft), in the way: (shaft-propeller efficiency) (17.10) supplied by the engine that cause the motion, Wshaft shaft at a certain rotation speed, , producing a power Wshaft coupled to the propeller itself, which may be the friction wheels in land vehicles, or the pressure- reaction blade-propeller in sea and air vehicles. But there are some propulsion systems based on the change of momentum of a working fluid, notably rockets, jet-engines and water jets, which have inlets and outlets through which some fluid flow. The momentum balance for an open system is (5.2): =M. The shaft then is mechanically d openings dm mvF F (v e pAn) (17.11) dtVA edteeePDF Image | THERMAL MACHINES AND HEAT ENGINES
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