Thrust maximum

Figure 6-10. Maximum thrust loads with pressure upsets at the compressor discharge.

Maximum thrust is attained when Pe = P0 and a is made small, then... 

H0 can be calculated from the propellant composition, but He must be obtained by successive approximation, assuming that the final state of the exhaust gases is known. For present purposes, it is sufficient to note that H0 — He correlates well with the heat of explosion of the solid explosive. In order to obtain the maximum thrust from a rocket it is therefore necessary to achieve the highest combustion temperature, but also necessary to produce gases with the lowest mean molecular weight. 

The maximum thrust is obtained atp = p , i. e., when the pressure at the nozzle exit is equal to the ambient pressure. 

As shown by Eq. (1.65), the maximum thrust F , is obtained when at a given specific heat raho of the combustion gas ... 

When the nozzle expansion ratio becomes infinity, the pressure ratio pjpa also becomes infinity. The maximum thrust coefficient Cp then becomes... 

Referring to Fig. 1.3, the momentum entering the air-intake is given by rhj> and that exiting from the nozzle is given by (m -i- m v. The thmst created by the momentum change is fundamentally represented by Eq. (1.62). When the air-intake and the nozzle attached to the ducted rocket are designed to obtain maximum thrust efficiency, the pressures at the front end of the air-intake and at the aft end of the nozzle become Pa = Pi = Pr> and then Eq. (1.62) is represented by... 

The combustion temperature in a gas generator is maximized at the stoichiometric mixture of 8 = 5. The specific impulse increases with increasing e (fuel-lean mixture). However, the thrust decreases as e is increased. The maximum thrust is obtained at the stoichiometric mixture ratio. It is evident that L increases with increasing b- The I p of a pyrolant containing 1b(0-2) is 1100 s and its T)-is about 1600 K at e = 20. 

Since the thrust reaches a maximum value when pe = pa, a well designed rocket exhaust nozzle should exhaust gases at an exit pressure nearly or exactly equal to the ambient pressure. Near the point of maximum thrust the second term in the thrust equation (Eq. n. A. 9.) is like a small correction term. Thus it is appropriate to define another parameter, the effective velocity c, whose significance will be examined in more detail ... 

If the effect of mixture ratio upon the characteristic velocity and thrust coefficient is examined, additional information is gained over that obtained from consideration of the specific impulse alone. Since the characteristic velocity bears the same dependence upon combustion temperature and molecular weight as does the specific impulse, the optimum characteristic velocity and optimum specific impulse would be expected and are observed to occur at approximately the same mixture ratio, see figure V. A. 6. The failure of these two performance parameters, c andcF. to have maximum values at the same propellant mixture ratio is traceable to their differing dependencies upon the specific heat ratio. The same effect is reflected in the dependency of the thrust coefficient upon the mixture ratio. For optimum expansion and a fixed pressure ratio across the nozzle, the thrust coefficient depends only upon the specific heat ratio. The dependence of the specific heat upon the mixture ratio in turn results in a dependence of the thrust coefficient upon the mixture ratio. Since thrust coefficient increases with decreasing specific heat ratio for a fixed pressure ratio, the maximum thrust coefficient should occur at the mixture ratio of maximum specific heat. The specific heat of the products increases both with temperature and with complexity of the product species. The maximum specific heat is found near the stoichiometric mixture ratio. For equilibrium expansion the specific heat also includes the effect of exothermic recombinations. This later effect is a maximum at the condition of maximum dissociation in the chamber which similarly occurs at the maximum combustion temperature or near the stoichiometric mixture ratio. 

Since the air pressure decreases with increasing flight altitude, at constant nozzle diameter, the total thrust increases with increasing flight altitude. This increase can correspond to approximately 10 to 30 % of the total thrust depending on the rocket. The maximum thrust is reached in vacuo. The so-called effective ejection velocity ceff (of the combustion gases) is defined as the ratio between the thrust and the mass flux (dm / dt) ... 

If the nozzle is designed so that a is relatively small and pe = po (the condition of maximum thrust), then Eq. (41) becomes... 

Near-equilibrium flow conditions generally yield the maximum thrust for rocket propulsion, because partial recombination of the dissociated atoms, as the temperature falls, releases additional kinetic energy. On the other hand, when the rocket engine is considered for high temperature chemical processing, it is invariably desirable to freeze the composition attained in the combustion chamber. From both theoretical and practical standpoints, it is not always possible to predetermine the flow conditions in the De Laval nozzle as the foregoing discussion indicates,... 

Oxygen, in the form of LOX, is widely used as the oxidizing agent in many kinds of rockets and missiles. As an example, the huge external fuel tank required to lift the space shnttle into space holds 145,000 gal (550,000 1) of liquid oxygen and 390,000 gal (1,500,000 1) hydrogen. When these two elements react in the shuttle s main engines, they provide a maximum thrust of 512,000 lb (232,000 kg). 

Results are shown for expander half angles ranging from 10° to 50° (Note that the expander angle exhibiting the maximum thrust production does not directly coincide with the minimum subsonic layer thickness. This is a direct result of the competing effects of viscous forces and micro-nozzle geometry. The optimum expander angle is the result of this trade-off)... 

A mixture that bums at the highest possible temperature to provide maximum thrust... 

Engines maximum thrust Pratt Whitney PW4062 63,30 71 General Electric CF6-80C2B7F 3 kg 9 kg ... 

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