Appendix B - Propulsion primer, performance, parameters and units.



The Propulsion Principle


[273] The thrust of all flight propulsion systems comes from the same principle reaction-as expressed by Newton's second law of motion:


force = mass . acceleration


In the case of airplanes flying through air, boats moving across the water, or rockets flying in the atmosphere or outside it, the reaction principle can be expressed in the equivalent forms:


force = rate of change of momentum, or

force = mass flow rate . change in fluid velocity.


The airscrew or propeller, the boat propeller, the jet engine that swallows atmospheric air operation, and the rocket engine that carries its oxidizer as well as fuel, all use the reaction principle. If you have stood at the stern of a boat under power, for example, and observed the wake, you have seen that the wake moves faster than the adjacent water, which is a visual indication of the change in fluid velocity.


Flight propulsion systems vary in the relative amounts of mass flow rates and changes in fluid velocity, as illustrated diagrammatically by figure 63. Assume, for comparison purposes, that the three types of vehicles are moving horizontally through the atmosphere at the same flight speed, designated by V, and that all are producing the same propulsive thrust, designated as F. Let us now examine, on a relative basis, the amount of fluid mass affected-and the velocity given to it. On this relative basis, the propeller affects the largest air mass but gives it the lowest increase in velocity. The....


graph of atainable airspeed vs time

[274] Fig. 61. Growth of aircraft speed. (Adapted from NACA figure, 1953.)


graph contrasting aircraft speed with thrust and drag requirements

Fig. 62. Aircraft thrust requirements increase with speed. (Adapted from NACA figure. 1953.)

illustration of propulsion formulas for propeller, turbojet/ramjet and rockets

[275] Fig. 63. Propulsion principle is the same for propeller. turbojet. ramjet, and rocket. F = thrust (assumed same for all in comparison): m = mass flow of working fluid (air or exhaust gas) ; VJ = exhaust gas velocity; VO= flight velocity. (NACA figure, 1953.)


....turbojet and ramjet engines affect a smaller mass of air than the propeller, but give the air a much higher velocity. The rocket, carrying its own working fluid as fuel and oxidizer, does not accelerate air but for the same thrust, ejects the smallest amount of fluid mass at the highest velocity.


Since both the propeller and air-consuming jet engines must accelerate the air they fly through to produce thrust, it follows that their thrust depends upon flight velocity. For the propeller, the limitation begins to show when its tip approaches the speed of sound in the air (340 m/s at sea level; 295 in/ s at 10700 m altitude). In the mid-1930s, an airplane speed of 805 km/ hr (224 m/ s) was attainable only in power dives and there was uncertainty over whether full power on the engine speeded up the dive or slowed it down. For the air-consuming jet engine, the momentum drag of the incoming air increases with flight speed and when flight speed equals the exhaust jet speed, thrust falls to zero. The rocket, on the other hand, carries all of its working fluid and its jet thrust is independent of flight speed, in or out of the atmosphere. These relationships are illustrated qualitatively by figure 64.