Total thrust jet velocity specific impulce.

All rocket engines produce a total thrust force which is the sum of a momentum thrust resulting from the acceleration of the exhaust gas and a pressure thrust arising from the difference in pressure between the exhaust gas at the nozzle exit and the surrounding air. The total thrust is the maximum for a given rocket engine when the pressure thrust is zero that is when the exhaust pressure is the same as the ambient pressure. For other than these conditions, the nozzle overexpands or undeerexpands the gas stream with resulting loss in efficiency. Because a ballistic missiles rises through the atmosphere during the period of propulsion, the ambient pressure varies. Ideal expansion conditions cannot be realized, and the design of the rocket engine has to be optimized to allow for the effects of incorrect expansion during part of the propulsion period.

A rocket engine thus consists of a combustion chamber in which the propellants are burned to produce a high-temperature gas, and an exhaust nozzle through which the gas is expanded and accelerated. The convergent-divergent form of the nozzle, needed to give a supersonic exhaust, produces subsonic flow up to the narrowest section, known as the throat, and supersonic flow beyond that section.

The jet velocity of a rocket engine is the velocity at which the gases are discharged from the nozzle. The momentum thrust is proportional to this jet velocity and the mass flawing from the nozzle. The jet velocity proportional to the temperature of the gas inside the combustion chamber and inversely proportional to the mean molecular weight of the products of combustion. Propellants rich in hydrogen and other light elements are thus advantageous because they lead to allow mean molecular weight of the exhaust gas.

The jet velocity is also dependent upon the ratio of the specific heats of the gas and the thermodynamic efficiency of the process of expansion through the exhaust nozzle. The effective exhaust velocity takes the pressure thrust into account is calculated from the total thrust and the mass flow.

The mass flow rate from a nozzle is proportional to the combustion and the nozzle throat area.

The thrust developed by a rocket engine is calculated in terms of the chamber pressure, the nozzle throat area, and a term known as the thrust coefficient. This latter is a function of the nozzle expansion ratio, the specific heat ratio for the exhaust gases, and the external pressure.

The characteristic velocity is proportional to the chamber pressure, the nozzle throat area, and inversely proportional to the mass flow through the nozzle. It is a measure of propellant performance. For example, the characteristic velocity is the combustion chamber pressure required to give unit mass flow for unit nozzle throat area for the propellant used.

The specific impulse of a rocket engine is the thrust per unit weight flow rate.

Liquid and solid propellant units. Liquid, solid and composite propellants.

There are four basic components of a liquid rocket engine propulsion system; the propellant tanks which are usually integral with the structure of the missile contain the propellants before their injection into the combustion chamber. The four engine components are the feed system which is used to move the propellants from their storage tanks into the combustion chamber, the thrust chamber where the propellants are burned and the expelled at high velocity, a control system which starts, stops, and controls operation of the engine, and auxiliary devices such as means to deflect the jet to change the direction of the thrust vector.

In the turbopump group, there is a turbine, an oxidizer pump, and a fuel pump. Impulse turbines are generally used because, for the desired ranges, they are simpler in design and weigh less per unit horsepower. The working fluid from the gas generator passes through the turbine nozzles where its enthalpy is converted into kinetic energy. The turbine wheel and blades accept the high-velocity gas and the impulse rotates the wheel. The turbine is designed with reference not only to the power level of its operation, but also to the efficiency of the turbine itself. This latter depends upon the velocity of the working fluid, the speed of the blades, the number of stages, and any gears that may be employed. The exhaust nozzle from the turbine has to be designed so that the power output remains constant with altitude that is despite changes in ambient pressure as the vehicle rises through the atmosphere. The two pumps are most often of the centrifugal type because this is both efficient and economical in weight and volume. The pumps must be capable of handling large flows at high pressures, without trapping gases in the pump. Usually the design has an impeller that rotates within a casing to accelerate the fluid to a high velocity at the periphery of the impeller. Then the fluid passes into a volume and diffuser which converts the fluid’s kinetic energy into pressure energy. The pumps must be designed for a given flow discharge rate and output head. This is governed by the required combustion chamber pressure drop through the cooling system and valves and in the injectors. Other impotent parameters in pump design include the impeller up speed and the amount of internal and external leakages. The inlet also has to be established be reference to the suction head required and available to the cavitations problems.

The hot working fluid for the turbine of the turbopump comes from a gas generator which can be a “cold” type generator using monopropellants, or a “hot” generator using the combustion of the combustion of the main propellants of the missile system. A gas-pressurized system uses a separate propellant supply whereas a feed system used the same propellants as the main rocket engine. A solid- propellant system burns solid propellants to supply the turbine gas. In all these systems, the governing factor is the permissible temperatures of the evolved gases when they enter the turbine. Fuel-rich mixtures are often used to keep the gases at an acceptable temperature.

Fig. 5 shows a cutaway view of a typical liquid- propellant rocket engine for an IRBM. This illustration shows the gas generator and the gas turbine. The gearbox is used to connect the turbine shaft to the propellant pumps. On each pump is a helical impeller which reduces cavitation, and a centrifugal pump which gives the high-pressure output. From the pumps the propellants pass through main control valves to the thrust chamber. They are injected through injectors into the combustion chamber where they burn. Expansion to supersonic velocity takes place through the convergent-divergent expansion nozzle. The thrust chamber is cooled by the passage of fuel through the many tubes which make up its walls.

With the constant appearance of new chemicals and new low-molecular weight polymers, the versatility in formulating improved propellant fuels will continue to increase.

Radical improvement is expected in the specific impulse (thrust per unit weight) and in the attainment of the desired burning rate.

The mechanical properties of a propellant are measures of its ability to maintain the integrity of the grain. Therefore, elastic and tensile properties and storage and aging characteristics are vital. Cracking of the propellant grain prior to or during flight of a rocket because of poor mechanical properties may cause a malfunction that would render a rocket useless.

For solid- propellant rocket engine the propellant contains both fuel and is housed in the combustion chamber. Design of the charge shape and the way in which it burns gives control as rate which the surface of the propellant recedes in a direction normal to the surface which is exposed to the hot gas. This burning rate depends upon the chamber pressure and temperature.

There are two main types of solid-propellant rockets. The restricted burning rocket burns its propellant like a cigarette from one end only and has the other surfaces of the propellant coated with an inhibitor which restricts burning. An unrestricted burning rocket allows the propellant to burn on several surfaces which are shaped to give the required thrust characteristics.

Typical grain shapes are shown in Fig. 6. A tubular grain produces a progressive thrust, that is, the thrust progressively increases as the period of burning advances. A double-anchor grain produces a regressive thrust, a rod and tube, and a star grain give neutral thrust, a multifin grain produces a dual thrust, high thrust immediately on ignition followed by a period of low constant thrust.

There are two types of propellants used in solid- propellant rocket engines, one is known as a double-base propellant and the other is a composite propellant. The former consists of nitroglycerine and nitrocellulose whereas the latter uses a granular oxidizer such as ammonium perchlorate mixed with some organic fuel such as synthetic rubber.

The basic conventional propellant combination used in the missile has been liquid oxygen and rocket fuel, which is essentially kerosene. These are relatively cheap propellants costing about to cents per pound for the fuel and less than one cent per pound for the liquid oxygen. Moreover this combination gives a good performance, a specific impulse at altitude of approximately 350 seconds. Storable liquid- propellant combinations give similar performance but have not yet been used extensively. Future improvements may yield an increase in performance to about 450 seconds specific impulse for high-energy propellant combinations, and to about 400 seconds for storable propellants. These latter will probably find increasing use in ballistic missiles because of their great advantages of reducing the problems of logistic and last propellant loading. Storable propellants are propellants which can be stored within the missile without evaporation or without chemical decomposition of either the propellant or the tank. They thus make the missile ready for immediate firing at all times, and have obvious strategic advantages. Engines designed for conventional liquid oxygen/ RP propellants. Conversion is straight forward and relatively inexpensive. A common modern storable propellant combination uses nitrogen tetroxide as the oxidizer and hydrazine as the fuel.

Today, composite propellants are composed essentially of three main components: the oxidizer, the metallic fuel, and the fuel binder. Replacement of one or all three of these chemicals by materials haying a much higher energy content will lead propellants of improved performance on the basic of thermodynamic calculations. These calculations indicate that we can, by the use of more energetic oxidizers, light metals, and new fuel binders containing fluorine that have not yet been synthesized, produce propellants with specific impulses 20 to 25 cent higher than the existing theoretical specific impulse available today. Some of these new chemicals do yet exist, and we have no assurance of when they will be synthesized, when they will became available, and whether or not they will result in the propellant mechanical properties required to fulfill the existing needs. The use of these ingredients may present some serious problems. These materials must be synthesized and their chemistry understood. If they react with other materials in a propellant, they must be protected either by a metal or a plastic coating, and some of these materials are extremely reactive. Finally, these materials must be used in a propellant formulation and the propellant must be evaluated.

Economic calculations will help to select only those propellants that slow both technical improvements and cost reductions for the intended use. These calculations show that today’s propellants are to beat, and future solid composite propellants of high energy may have limited applications because of costs. Solid propellants will have new competition either from liquid or hybrid (combination liquid and solid) propellants in various applications. These too may have economic advantages over the future ultrahigh energy solid propellants.