In this chapter, we examine propellant budget, performance of multiple or complete rocket propulsion systems, designs of liquid propellant rocket engines with pressurized or with turbopump (TP) feed systems, engine controls, engine calibration, system integration, and system optimization. Some content also applies to solid propellant motors and hybrid propulsion systems.

11.1 PROPELLANT BUDGET

In all liquid propellant rocket engines the amount of propellant inserted into the vehicle tanks is always somewhat greater than the nominal amount of propellant needed to accomplish the intended mission. The extra propellant is needed for purposes other than providing thrust (e.g., for auxiliary functions like valve actuation), to compensate for changes from engine to engine (such as dimensional tolerances causing slight changes in flow), for uncertainties of engine construction and for minor variations in the flight plan. A propellant budget represents the sum of all the propellant utilization categories and losses in an engine—11 are identified below. Such a budget defines how much propellant has to be loaded and is aimed at minimizing the amounts of extra propellant.

1. Enough propellant must be available for achieving the required vehicle velocity increase and any nominal set of attitude control maneuvers for the specified application of the entire flight vehicle or stage. The nominal velocity increment is defined from a system analysis and mission optimization calculations based on Eqs. 4–19 or 4–20 and 4–35. When there are alternative flight paths or missions for the same vehicle, the mission with the most propellant consumption, such as one with higher drag or different orbit or the highest total impulse, is selected. Mission‐required propellants constitute by far the largest portion of the total propellant loaded into the vehicle tanks.
2. In TP systems using a gas generator cycle, a small portion of the overall propellant is used by the gas generator. It operates at lower flame temperatures and different mixture ratios than the thrust chamber; this causes a slight change to the overall mixture ratio on the propellants flowing from the tanks, as shown later in Eqs. 11–3 and 11–5.
3. In a rocket propulsion system with thrust vector control (TVC), such as a swiveling thrust chamber or nozzle, the thrust vector may rotate by a few degrees; this causes a slight decrease in the axial thrust that reduces the vehicle velocity increment in item 1. The extra propellant needed to compensate for this small velocity reduction is determined from mission requirements and TVC duty cycles. It could amount to between 0.1 and 4% of the total propellant depending on the average angle position of the thrust vector. Thrust vector control systems are described in Chapter 18.
4. In some engines with cryogenic propellants, a small portion of propellant is vaporized and then used to pressurize its own tank. As shown schematically in Fig. 1–4, a heat exchanger is used to heat liquid oxygen (LOX) from the pump discharge and pressurize the oxygen tank. This method is used in the hydrogen and oxygen tanks of several space vehicles.
5. Auxiliary rocket engines that provide for trajectory corrections, station keeping, maneuvers, or attitude control normally have a series of small restartable thrusters (see Chapter 4). Propellants for these auxiliary thrusters have to be included in the propellant budget when they are supplied from the same feed system and tanks as the larger rocket engine. Depending on the mission, the duty cycle, and the propulsion system concept, auxiliary propulsion systems may consume a significant portion of the budgeted propellants.
6. Any residual propellant that clings to tank walls or remains trapped in valves, pipes, injector passages, or cooling passages is unavailable for producing thrust. It can typically amount to between 0.5 and 2% of the total propellant load. All unused residual propellants increase the final vehicle mass at thrust termination and slightly reduce the final vehicle velocity.
7. A loading uncertainty always exists due to variations in tank volume or changes in propellant density or liquid level in the tank. This typically amounts to 0.25 to 0.75% of the total propellant. It depends, in part, on the accuracy of the method of measuring the propellant mass during loading (weighing the vehicle, flow meters, level gauges, etc.).
8. Off‐nominal rocket performance refers to manufacturing variations on the of hardware from one engine to another (such as slightly different pressure losses in cooling jackets, in injectors and valves, or somewhat different pump characteristics); these cause slight changes in combustion behavior, mixture ratio, and/or specific impulse. When there are such variations in mixture ratio, one of the two liquid propellants will be fully consumed and a residue will remain in the other propellant's tank. If a minimum total impulse requirement has to be met, extra propellant has to be tanked to allow for these mixture ratio variations. This can amount to up to 2.0% for each of the propellants.
9. Operational factors, such as filling more propellant than needed into a tank or incorrectly adjusting regulators or control valves and can also include changes in flight acceleration from the nominal value, may result in additional propellant requirements. For an engine that has been carefully calibrated and tested, this factor can remain small, usually between 0.1 and 1.0%.
10. When using cryogenic propellants, an allowance for evaporation and for engine cooling down has to be included. This represents the extra propellant mass that is allowed to evaporate (and vented overboard while the vehicle is waiting to be launched) and that is fed through the engine to lower its temperature just before start. It is common practice to replace the evaporated propellant by feeding fresh cryogenic propellant into the tank; this process is called “topping off” and it occurs just before launch. If there are significant time delays between tapping off and launch, additional cryogenic propellant will evaporate, so there is often some uncertainty about the precise amount of propellant in the tanks at launch.
11. Finally, an overall contingency or ignorance factor needs to be included to allow for unforeseen propellant needs or inadequate or uncertain estimates of any of the items above. This can also include allowances for such factors as atmospheric drag uncertainties, variations in the guidance and control systems, or propellant or gas leaks.

Only some items above provide axial thrust (items 1, 2, and sometimes also 3 and 5), but all items above need to be considered in determining the total propellant mass and tank volume.

Table 11–1 shows a propellant budget example for a spacecraft pressure‐fed engine system, where the majority of the monopropellant is consumed in a larger axial thrust chamber, and the second largest amount of propellant is fed to a set of small thrusters for extensive attitude control maneuvers. For flights where the mission may be more demanding or the engine performance may be lower, extra propellant will be needed to accomplish their missions. Conversely, when engine performance is actually better than nominal or where the mission can be accomplished with less total impulse (operate with fewer or lower orbits), then the engine will consume less than the nominal amount of propellant and the residual propellant can be larger than budgeted.

11.2 PERFORMANCE OF COMPLETE OR MULTIPLE ROCKET PROPULSION SYSTEMS

The simplified relations given here complement Eqs. 2–23 to 2–25. They represent a basic method for determining overall specific impulse, total propellant flow, and overall mixture ratio as a function of the corresponding component performance terms for complete rocket engine systems. They apply to engine systems consisting of one or more thrust chambers, exhaust nozzles, gas generators, turbines, and venting of evaporative propellant pressurization systems, all these operating at the same time.

Refer to Eqs. 2–5 and 6–1 for relations involving the specific impulse I_s, propellant flow rate or and mixture ratio r. The overall thrust F_oa is the sum of all the thrusts from thrust chambers firing in parallel together with any turbine exhausts, and the overall flow is the sum of their flows as shown in in Section 2.5. The subscripts oa, o, and f designate the overall engine system, the oxidizer, and the fuel, respectively.

11–1

11–2

11–3

These same equations represent the overall performance when more than one rocket engine is contained in a vehicle propulsion system (all operating simultaneously). They also apply to multiple solid propellant rocket motors and combinations of liquid propellant rocket engines and solid propellant rocket booster motors, as shown in Figs. 1–12 to 1–14. All nozzles and exhaust jets must be pointed in the same direction in Eqs. 2–23, 11–1, and 11–4 (since we are dealing with vectors).

Overall engine specific impulse is influenced by the propellants, the nozzle area ratio, the chamber pressure, and to a lesser extent by the engine cycle together with its mixture ratio. Table 11–2 describes 10 rocket engines, designed by different companies in different countries, that use liquid oxygen and liquid hydrogen propellants and shows the sensitivity of the specific impulse to these parameters. References 11–1 to 11–3 give additional data on several of these engines and later versions.

11.3 ENGINE DESIGN

Approaches, methods, and resources utilized for rocket engine preliminary and final design usually differ for each design organization and for each major type of engine. They also differ by the degree of novelty.

1. A totally new engine with new major components and novel design and manufacturing concepts might result in an optimum engine design for a given application, but this is by far the most expensive and longest development approach. One major development cost comes from the necessary testing of engine components and from additional testing of several engines under various environmental and performance limit conditions that must be done to establish reliability data and enough credibility and confidence to allow initial flights and initial production. Since the state of the art is relatively mature today, design and development of a truly novel engine does not happen very often.
2. Engine designs using some new major components or somewhat modified key components from proven existing engines represent the most common approach today. The design of such an engine requires working within the capability and limits of existing or slightly modified components. This approach often needs the least amount of testing for proving reliability.
3. Uprated, improved, or modified versions of an existing, proven engine. This approach is quite similar to the second. It is needed when an installed engine for a given mission requires more payload (i.e., higher thrust) and/or longer burning duration (more total impulse). Uprating often means more propellant (larger tanks), higher propellant flows and higher chamber and feed pressures, and more feed system power. Usually, an uprated engine also has an increased inert engine mass (thicker walls).

In a simplified way, we proceed to illustrate a typical process for designing an engine. Chapter 19 and Refs. 11–4 and 11–5 also describe such a process and the selection of propulsion systems but from a different point of view. The basic function together with all requirements for the new engine must be first established. These engine requirements are derived from the vehicle mission and vehicle constraints, usually determined by the customer and/or the vehicle designers, often in cooperation with one or more engine designers. Engine requirements may include key parameters such as thrust level, desired thrust–time variation, restart or pulsing, altitude flight profile, duty cycle, maximum accelerations, engine placements within the vehicle, and limitations or restraints on cost, engine envelope, test locations, or schedules. If an existing engine can be adapted to meet these requirements, any subsequent design process will be simpler and quite different than for a truly new engine.

Usually, some tentative decisions about the engine are first made, such as selection of propellants, their mixture ratio, or the cooling approach for the hot components. These must be based on mission requirements, customer preferences, past experiences, relevant analyses, and the experience of key decision makers. After some study, additional selection decisions may be made, such as having one or more thrust chambers fed from the same feed system, redundancy of auxiliary thrusters, and/or type of ignition system.

A systematic approach using systems engineering or other proper set of analyses, together with good coordination with the customers, key vendors and vehicle designers are all needed during preliminary and final design efforts. Before a meaningful proposal for an engine can be prepared, all preliminary designs have to be completed. See Refs. 11–5 to 11–7. One early design decision is the choice of feed system: pressurized gas feed or pump feed; the next two paragraphs give some guidelines.

A pressurized feed system (see Fig. 1–3) gives better vehicle performance for low values of total impulse (thrust less than about 4.5 kN or 1000 lbf with up to perhaps 2 min duration). A pump feed system gives better vehicle performance for high thrust (say above 50,000 lbf or approximately 222 kN) and a long cumulative duration—more than a few minutes. For intermediate values of total impulse the choice can go either way, and there is no simple criterion based only on total impulse. If the chamber pressure of a pressurized feed system is relatively high (say about 2.4 to 3.5 MPa or about 350 to 500 psia and occasionally more), then the inert weight of the thrust chamber will also be high, but the thrust chamber will be small and can usually fit into most available engine compartments. Because the propellant tanks and pressurizing gas tank will have to be at relatively high pressures, they will be heavy. For relatively low chamber pressures (0.689 to 1.379 MPa or 100 to 200 psia), the vehicle tank pressures will be lower and their tank walls thinner, but the thrust chamber size will be relatively large and often will exceed the limits of the engine compartment, unless it has a low nozzle exit area ratio, which implies lower performance. Pressurized feed systems and relatively low chamber pressures are preferred for reaction control systems, also known as attitude control systems with multiple small thrusters. Pressurized feed systems are relatively simple, very reliable, and they allow fast starts and fast restarts. Because of their unmatched proven reliability, NASA has at times conservatively selected pressurized feed systems for certain space applications, such as the Apollo service module engine (21,900 lbf thrust), even though there was a major weight penalty and a somewhat inferior vehicle performance compared to a pump‐fed system of equal total impulse. Also, a decision needs to be made on using either a pressurized system with a gas pressure regulator or alternatively a blow‐down system. See Table 6–3 and Section 6.4.

For a turbopump‐fed liquid propellant rocket engine (see Fig. 1–4) the overall inert weight of propellant tanks and engine will be considerably lighter and usually vehicle performance will be somewhat better for the longer total impulse applications. These engines commonly operate at high chamber pressures (3.5 to 24.1 MPa or about 500 to 3500 psia), and the thrust chamber is not normally protruding from the vehicle. Smaller and shorter thrust chambers often allow a shortening of the vehicle with a savings in vehicle structural mass. This modestly improves the vehicle's performance and the higher specific impulse will slightly reduce the amount of propellant needed for the mission. Compared to an engine with a pressurized feed system, the savings in inert mass (thin vehicle tank walls) and less propellant will allow a smaller, lighter, and probably lower cost vehicle with a somewhat superior performance. Engines with TPs are more complex with more parts and the engine itself will generally be heavier and cost more; however, the vehicles' propellant and gas tanks will be much lighter and that will often more than compensate for the heavier engine. Also, it takes more tests and more effort to prove high reliability in an engine with a pump feed system. At the higher chamber pressures, the heat transfer will be higher and cooling is more challenging, but many high heat transfer cases have been solved successfully in earlier high‐pressure rocket engines and high reliability has been achieved in many TP‐fed large rocket engines. Restartable engines will have more complexity and here one of several engine cycles will have to be selected.

At this step, trade‐off studies between several available options are appropriate. With a modified existing engine these parameters may be well established and require fewer such trade‐off studies. Initial analyses of the pressure balances, power distribution between pumps and turbines, gas generator flow, propellant flows and reserves, or the maximum cooling capacity are appropriate. Sketches and preliminary estimates of inert mass of key components need to be made, such as tanks, thrust chambers, TPs, feed and pressurization systems, thrust vector control, or support structure. Alternate arrangements of components (layouts) are usually now examined, often to get the most compact configuration and/or control of the travel of the center of gravity. Initial evaluations of combustion stability, stress analysis of critical components, water hammer, engine performance at some off‐design conditions, safety features, testing requirements, cost, and schedule are often performed here. The participation of appropriate experts from manufacturing, field service, materials, stress analysis, and/or safety, can be critical for selecting the proper engine and the key design features. A design review is usually conducted on the selected engine design and the rationale for new or key features.

Test results from subscale or full‐scale components, or from related or experimental engines, can have a strong influence on this design process. Any key engine selection decisions need to be later validated in the development process by testing all new components and new engines.

The inert mass of the engine and other mass properties (center of gravity or moment of inertia) are key parameters of interest to vehicle designers. They are needed during preliminary design and again, in more detail, in the final design. Engine mass is usually determined by summing up all component or subsystem masses, each of which is either actually weighted or estimated by calculating their volumes and knowing their densities and locations. Sometimes early estimates are based on known similar parts or subassemblies.

Preliminary engine performance estimates are often based on data from prior similar engines. If these are not available, then theoretical performance values can be used (see Chapters 2, 3, and 5) for F, I_s, or others, using appropriately established correction factors (see Chapter 3). Well‐measured static test data are, of course, better than estimates. Final performance values are obtained from flight tests, or simulated altitude tests where airflow and altitude effects can interact with the vehicle or the plume.

If the preliminary design does not meet the engine requirements, then initial engine decisions need to be changed and, if that is not sufficient, sometimes also mission requirements. Components, pressure balances, and other items will be reanalyzed, resulting in a modified version of the engine configuration, its inert mass, and performance. This process is iterated until all requirements are met and a suitable engine design has been found. The initial efforts culminate in preliminary layouts of the engine, preliminary inert mass estimates, estimated engine performance, a cost estimate, and a tentative schedule. These preliminary design data may now form the basis for a written proposal to the customer for undertaking the final or detail design, development, testing, and for delivering engines.

Optimization studies help to select the best engine parameters for meeting all requirements; some are done before a suitable engine has been identified, some afterwards. They are described further in Section 11.6. We optimize parameters such as chamber pressure, nozzle area ratio, thrust, mixture ratio, and/or number of large thrust chambers supplied by the sameTP. Results of optimization studies identify the best parameters that will give some further (usually small) improvement in vehicle performance, propellant fraction, engine volume, or cost.

Once the engine proposal has been favorably evaluated by the vehicle designers and after the customer has provided authorization and funding to proceed, then the final design can begin. Some of analyses, layouts, and estimates will be repeated in more detail, specifications and manufacturing documents will be written, vendors will be selected, and tooling will be built. Any selection of key parameters (particularly those associated with technical risk) will need to be validated. After other design review, key components and prototype engines are built and ground tested as part of a planned development effort. If proven reliable, one or two sets of engines will be installed in vehicles and operated during flight. In those programs where a fair number of vehicles are to be built, the engine will then be produced in the required quantity.

Table 11–3 shows detailed parameters for three different Russian staged‐combustion‐cycle engines designs (from Ref. 11–6). It shows primary engine parameters (chamber pressure, thrust, specific impulse, mass, propellant combination, nozzle area ratio, dimensions, etc.) that influence vehicle performance and alternate configurations. It also shows secondary parameters, those internal to the engine but important in component design and engine studies, health monitoring systems, and optimization. Figure 11–1 shows the RD‐170 engine with four thrust chambers (and their thrust vector actuators) supplied by a centrally located single large TP (257,000 hp; not visible in the photo) and one of the two oxidizer‐rich preburners. Figure 11–2 shows a flow diagram schematic for this RD‐170 rocket engine—it identifies key components of the large main TP, the two oxidizer‐rich preburners, and the two booster TPs; one is driven by a turbine using oxygen‐rich gas bled from the turbine exhaust (this gas is condensed when it mixes with the liquid oxygen flow) and the other by a liquid turbine driven by a high‐pressure liquid fuel. A version of this RD‐170 engine, identified as the RD‐180 rocket engine with two thrust chambers is used in the first stage of the U.S. Atlas V space launch vehicle. A single chamber derivative is the current RD‐191 discussed in Chapters 6, 8, and 9.

Much of today's engine preliminary design and design optimization can be performed with computers. These involve codes for calculating stress/strain and heat transfer, mass properties, water hammer, engine performance, feed system analyses (for balance of flow, pressures, and power), gas pressurization, combustion vibrations, and various exhaust plume effects (Refs. 11–4 and 11–5 are examples of such analyses and design). Some customers require certain analyses results (e.g., safety, static test performance) to be delivered to them prior to engine deliveries.

Many computer programs are specific to a certain category of applications (e.g., interplanetary flight, air‐to‐air combat, long‐range ballistic missile, or ascent to earth orbit), and many are specific to a particular engine cycle. For example, an engine balance program balances the pressure drops in the fuel, oxidizer, and pressurizing gas flow systems; similar programs balance the pump and turbine power, speeds, and torques (see Section 10.4), compare different TP configurations (see Section 10.3); some balance programs also calculate approximate masses for engine, tanks, or turbine drive fluids. Such programs allow iterations with various pressures and pressure drops, mixture ratios, thrust levels, number of thrust chambers, distribution of total velocity increment between different vehicle stages, trades between constant thrust (or propellant flow) and decreasing thrust (throttling) or pulsed (intermittent) thrust.

11.4 ENGINE CONTROLS

All liquid propellant rocket engines must have controls that accomplish some or all of these tasks (see Refs. 11–7, 11–8, and 11–9):

1. Start rocket operation.
2. Shut down rocket operation.
3. Restart, if desired. With small thrusters there may be thousands of restarts.
4. Maintain programmed operation (e.g., predetermined thrust profile, presets of propellant mixture ratio and flow). A constant flow of propellants can be achieved with sonic flow venturis in the feed lines as discussed in the last paragraph of Section 6.9.
5. Use an engine health monitoring system to prevent certain engine failures or performance losses (as explained later in this chapter).
6. Fill propellants into their vehicle tanks.
7. Drain excess propellant after operation of a reusable or test engines.
8. Cool (with cryogenic propellants) pipes, pumps, cooling jackets, injectors, and valves that must be at low temperatures prior to start, by bleeding cryogenic propellant through them. This cooling propellant is not used to produce thrust; its flow has to be periodically controlled.
9. Check out proper functioning of critical components or a group of components without actual hot operation before and/or after flight or ground tests.
10. Provide features to perform checks and recycle engines to a ready condition, as needed for recoverable or reusable rocket engines and for engines used in ground/development tests.

The complexity of these control elements together with the complexity of engine systems strongly depend on vehicle mission. In general, rockets that are used only once (single‐shot devices), that are filled with storable propellants at the factory, that operate at nearly constant propellant flow, and that operate over a narrow range of environmental conditions tend to be simpler than rocket systems intended for repeated use or for applications where satisfactory operation must be demonstrated prior to use, and for manned vehicles. Because of the nature of liquid propellants, most control actuation functions are achieved remotely by valves, regulators, pressure switches, valve position indicators, or calibrated orifices. The use of dedicated computers for automatic control in large engines is now common. Flow control devices, namely valves, are discussed in Section 6.9 and other controls are discussed in this section.

Safety controls are intended to protect personnel and equipment in case of malfunctions. This applies mostly to development engines during ground tests but can also apply to certain flight test engines and to certain operating engines. For example, any control system is usually so designed that failure of an electrical power supply to the rocket causes a nonhazardous shutdown (all electrical valves automatically returning to their normal position), and no mixing or explosion of unreacted propellant can occur. Another example is the use of an electrical interlock device which prevents the opening of the main propellant valves until the igniter has functioned properly.

Check‐out controls permit a simulation of the operation of critical control components without actual hot operation of the rocket unit. For example, many rockets have provisions for permitting actuation of the principal valves without having propellant or pressure in the system.

Control of Engine Starting and Thrust Buildup

During a rocket engine's starting and stopping processes, the mixture ratio should be expected to vary considerably from the rated design mixture ratio (because of a lead in of one of the propellants and because the hydraulic resistances to propellant flow are usually not the same for the fuel and the oxidizer passages). During this transition period, it is possible for the rocket engine to pass through regions of chamber pressure and mixture ratio which produce combustion instabilities. The starting and stopping of a rocket engine thus requires very critical timing, valve sequencing, and transient characteristics. A good control system must be designed to avoid undesirable transient effects. Close controls of propellant flow, of pressure, and of mixture ratio are necessary to obtain reliable, repeatable and safe rocket performance. The starting and ignition of thrust chambers is discussed in Section 8.6.

Fortunately, most rocket units operate with a nearly constant propellant consumption and constant mixture ratio, which simplifies the operating control problem. Stable operation of liquid propellant flows can be accomplished without automatic control devices because liquid flow systems in general tend to be inherently stable. This means that the propellant feed system reacts to any disturbance in the flow of propellant (a sudden flow increase or decrease) in such a manner as to reduce the effect of the disturbance. The system, therefore, usually has a natural tendency to control itself. However, in some cases natural resonances of the system and/or its components can exist at frequency values that tend to destabilize the system.

Start delay times for a pressure feed system are always present but usually small. Prior to start, the pressurization system has to be activated and any ullage volume pressurized. This start delay is also the time to purge the system (if needed), open valves, initiate combustion, and raise the flow and chamber pressure to rated values. Turbopump systems usually require more time to start; in addition to the above starting steps for pressurized systems, TPs have to allow a period for starting gas generators or preburners and for bringing the unit up to full speed and to a discharge pressure at which combustion can be self‐sustained. If the propellant is nonhypergolic, additional time has to be allowed for an igniter to operate and for feedback to confirm that it is working properly. All these events need to be controlled. Table 11–4 describes many of these typical steps, but not all of them belong with every engine.

1. Prior to Start

Check out functioning of certain components (without propellant flow), such as the thrust vector control or some valve actuators (optional).

Make sure that tanks and pipes are clean. Fill tanks with propellants.

Bleed liquid propellants to eliminate pockets of air or gas in all pipes up to the propellant valves.

When using propellants that can interact with air (e.g., hydrogen can freeze air, small solid air crystals can plug injection holes, and solid air crystals with liquid hydrogen can form an explosive mixture; some hypergolic start propellant will burn in air), it is necessary to purge the piping system (including injector, valves, and cooling jacket) with an inert, dry gas (e.g., helium) to remove air and moisture. In many cases, several successive purges are undertaken.

With cryogenic propellants the piping system needs to be cooled to cryogenic temperatures to prevent vapor pockets. This is done by repeated bleeding of cold propellant through the engine system (valves, pumps, pipes, injectors, etc.) just prior to start. The vented cold gas condenses moisture droplets in the air and this looks like heavy billowing clouds escaping from the engine.

Refill or “top off” tank to replace cryogenic propellant that has evaporated or been used for cooling the engine.

Pressurize vehicle's propellant tanks just before start.

2. Start: Preliminary Operation

Provide start electric signal, usually from vehicle control unit or test operator.

With nonhypergolic propellants, start the ignition systems in gas generator or preburner and main thrust chambers; for nonhypergolic propellants a signal has to be received that the igniter is burning before propellants are allowed to flow into the chambers.

Initial operation: opening of valves (in some cases only partial opening or a bypass) to admit fuel and oxidizer at low initial flows to the high‐pressure piping, cooling jacket, injector manifold, and combustion chamber(s). Valve opening rate and sequencing may be critical to achieve proper propellant lead. Propellants start to burn and turbine shaft begins to rotate.

Using an automated engine control, make checks (e.g., shaft speed, igniter function, feed pressures) to assure proper operation before initiating next step.

In systems with gearboxes the gear lubricant and coolant fluid start to flow.

For safety reasons, one of the propellants must reach the chamber first.

3. Start: Transition to Full Flow/Full Thrust

Turbopump power and shaft speed increase.

Propellant flows and thrust levels increase until they reach full‐rated values. May use controls to prevent exceeding limits of mixture ratio or rates of increase during transient.

Principal valves are fully opened. Attain full chamber pressure and thrust.

In systems where vaporized propellant is fed into the propellant tanks for tank pressurization, the flow of this heated propellant gas is initiated.

Systems for controlling thrust or mixture ratio or other parameter are activated.

4. Stop

Signal to stop deactivates the critical valve(s).

Key valves close in a predetermined sequence. For example, the valve controlling the gas generator or preburner will be closed first. Pressurization of propellant tanks is stopped.

As soon as turbine drive gas supply diminishes, the pumps will slow down. Pressure and flow of each propellant will diminish quickly until it stops. The main valves are closed, often by spring forces, as the fluid pressures diminish. In some engines the remaining propellant trapped in the lines or cooling jacket may be blown out by propellant vapor or inert gas purge.

Starting small thrusters with pressurized feed systems can be relatively fast, as short as 3 to 15 msec, enough time for a small valve to open, propellant to flow into the chamber and ignite, and for the small chamber volume to be filled with high‐pressure combustion gases. In an engine with a pressurized feed system the initial flow of each propellant is often considerably higher than the rated flow at full thrust because the pressure differential () is much higher, with the chamber pressure initially being at its lowest value. These higher flows can lead to propellant accumulation in the chamber and may lead what is called a “hard start,” with an initial surge of chamber pressure. In some cases, this surge has damaged the chamber. One solution has been to slowly open the main propellant valves or to build a throttling mechanism into them.

For TP‐fed systems and larger thrust engines, the time from start signal to full chamber pressure is about 1 to 5 sec in part because pump rotors have inertia, the igniter flame has to heat the relatively large initial mass of propellants, the propellant line volumes to be filled are large, and the number of events or steps that need to take place are more numerous.

Large TP‐fed rocket engines have been started in at least the following four ways:

1. A solid propellant start grain or start cartridge is used to pressurize the gas generator or preburner, and this starts turbine operations. This method was used on Titan III hypergolic propellant (first and second stages) and on the H‐1 (nonhypergolic) rocket engines—where the start grain flame also ignited the liquid propellants in the gas generator. This is usually the fastest starting method, but it does not provide for restarts.
2. The tank head start (used on the SSME) method is slower, does not require a start cartridge, and permits engine restarts. The “liquid head” from the vehicle tanks in vertically launched large vehicles (the term head is defined in Section 10.5), plus the tank pressure cause a small initial flow of propellants; then slowly more pressure is built up as the turbine begins to operate, and in a few seconds the engine “bootstraps”; its flows and pressures then rise to their rated values.
3. A small auxiliary pressurized propellant feed system with its own propellant tanks is used to feed an initial quantity of fuel and oxidizer (at essentially full pressure) to the thrust chamber and gas generator. This method was used on one version of the RS‐27 engine in the first stage of a Delta II space launch vehicle.
4. The spinner start method uses stored high‐pressure gas from a separate tank to spin the turbine (usually at less than full speed) until the engine provides enough hot gas to drive the turbine. High‐pressure tanks are heavy and their connections add complexity; in booster engines, the gas tank can be part of the ground equipment. This method is used on the RS‐68 engine where its high‐pressure helium tank is part of the ground equipment during launch.

Sample Start and Stop Sequences

This is an example of the transient start and stop sequence now used in the RS‐25 rocket engine and previously in the SSME (Space Shuttle Main Engine now retired). Both are complex staged combustion cycle engines designed for a “tank head start.” The flow diagram in Fig. 6–11 and the engine view of Fig. 6–1 identify the location within the engine of the key components mentioned below, and Fig. 11–3 shows the sequence and events of these transients. This section and figure are based on information provided by Aerojet‐Rocketdyne some years ago.

As stated earlier, for tank head starts, the energy to start the turbines spinning is all derived from initial propellant tank pressures (fuel and oxidizer) and from gravity (the head of a liquid column). Combining the tank head start with a staged combustion cycle consisting of four TPs, two preburners, and a main combustion chamber (MCC) results in a complicated and sophisticated start sequence, but one which proved to be robust and reliable. Prior to the start, the TPs and ducting (down to the main propellant valves) are chilled with liquid hydrogen and liquid oxygen (LOX) to cryogenic temperatures to ensure liquid propellants temperatures for proper pump operation. At engine start command, the main fuel valve (MFV) is opened first, providing chilling below the MFV and a fuel lead to the engine. Three oxidizer valves sequence the main events during the crucial first 2 sec of start—the fuel preburner oxidizer valve (FPOV) is ramped to 56% to provide LOX for ignition at the fuel preburner (FPB) in order to provide initial turbine torque for the high‐pressure fuel turbopump (HPFTP). Fuel system oscillations (FSOs), occurring due to heat transfer downstream of the initially chilled system, could result in flow rate dips that can lead to damaging temperature spikes in the FPB as well as in the oxidizer preburner (OPB) at ignition and at 2 Hz cycles thereafter, until the hydrogen is above critical pressure. The oxidizer preburner oxidizer valve (OPOV) and the main oxidizer valve (MOV) were next ramped‐open to provide LOX for OPB and MCC ignition.

The next key event was FPB prime which consists of filling the LOX system upstream of the injectors with liquid propellant. This results in increased combustion and higher power. This event occurred around 1.4 sec into start. The HPFTP speed was automatically checked at 1.24 sec into start to ensure it would be at a high enough level before the next key event, MCC prime, which was controlled by the MOV. Priming and valve timing were critical. We mention next some of the events that could go wrong: At MCC prime, an abrupt rise in backpressure on the fuel pump/turbine occurs. If flow rate through the fuel pump at this time is not high enough (as indicated by the shaft speed), then the heat imparted to the fluid as it is being pumped can vaporize it, leading to unsatisfactory flow in the engine, and subsequent high mixture ratio with high gas temperatures and possible system burnouts in hot gas system. This occurs when the MCC primes too early or HPFTP speed is abnormally low. If the MCC primes too late, the HPFTP may accelerate too fast due to low backpressures after FPB prime and exceed its safe speed. The MCC prime normally occurs at 1.5 sec. The OPB was primed last since it controls LOX flow; here a strong fuel lead and healthy fuel pump flow are desirable to prevent engine burnouts (due to high mixture ratios). The OPOV provided minimal flow rates during the early part of the start to force the oxidizer prime to last for 1.6 sec into start. Again, the FSO influences temperature spikes in the OPB and was sequenced around and prior to the MCC prime which raises the fuel pressure above critical in the fuel system. At 2 sec into start, the propellant valves were sequenced to provide 25% of rated power level (RPL). During the first 2.4 sec of start, the engine was in an open‐loop mode, but here proportional control of the OPOV was used, based on MCC pressure. At this point, additional checks were carried out to ensure engine health, and a subsequent ramp to mainstage at 2.4 sec was done using closed‐loop MCC‐chamber‐pressure/OPOV control. At 3.6 sec, closed‐loop mixture ratio/FPOV control was activated.

The chamber cooling valve (CCV) was opened at engine start and sequenced to provide optimum coolant fuel flow to the nozzle cooling jacket, the chamber and preburners during the ignition and main stage operation. It diverted flow to the cooling passages in the nozzle after MCC prime causes the heat load to increase. The description above is simplified and does not mention several other automatic checks, such as verifying ignition in the MCC or FPB or the fuel or chamber pressure buildup, which were sensed and acted upon at various times during the start sequence. Spark‐activated igniters were built into the three injectors (MCC, FPB, OPB) using the same propellants. They are not mentioned above or shown in the flow sheet.

The shutdown sequence was initiated by closing the OPOV, which powered down the engine (reducing oxygen flow, chamber pressure, and thrust); this was followed quickly by closing the FPOV, so the burning would shut down fuel rich. Shortly thereafter the MOV was closed. The MFV stayed open for a brief time and then was moved into an intermediate level to balance with the oxygen flow (from trapped oxygen downstream of the valves). The MPV and the CCV were closed after the main oxygen mass had been evaporated or expelled.

Automatic Controls

Automatically monitored controls are frequently used in liquid propellant rockets to accomplish thrust control or mixture ratio control. Automatic control of thrust vectors is discussed in Chapter 18.

Before electronic controls became common for large engines, pneumatic controls with helium gas were used. Helium is still used to actuate large valves, but no longer for logic control. A pressure ladder sequence control has been used where pressures (and a few other quantities) were sensed and, if satisfactory, the next step of the start sequence was pneumatically initiated. This arrangement was used on the U.S. H‐1 engine.

Most automatic controls utilize servomechanisms. In general, they consist of three basic elements: a sensing mechanism, which measures or senses the variable quantity to be controlled; a computing or controlling mechanism, which compares the output of the sensing mechanism with a reference value and gives a control signal to the third component, the actuating device, which manipulates the variable to be controlled. Additional discussion of computer control with automatic data recording and analysis is given in Chapter 21.

Figure 11–4 shows a typical simple thrust control system for a gas‐generator‐cycle engine aimed at regulating chamber pressure (and therefore thrust) during flight to a predetermined value. A pressure‐measuring device with an electric output is used as the sensing element, and an automatic control device compares this gauge output signal with a signal from the reference gauge or a computer referenced voltage value and thus computes an error signal. This error signal is amplified, modulated, and fed to the actuator of the throttle valve. By controlling the propellant flow to the gas generator, the generator pressure is regulated and, therefore, also the pump speed and the main propellant flow; indirectly, the chamber pressure in the thrust chamber is also regulated and, therefore, also the thrust. These quantities are varied until such time as the error signal approaches zero. Such system has been vastly simplified here, for the sake of illustration; in actual practice the system may have to be integrated with other automatic controls. In Figure 11–4, the mixture ratio in the gas generator is controlled by the pintle shapes of the fuel and oxidizer valves of the gas generator and by yoking these two valves together and having them moved in unison with a single actuator.

In the expander cycle shown schematically in Fig. 6–10, the thrust is regulated by maintaining a desired chamber pressure and controlling the amount of hydrogen gas flowing to the turbine by means of a variable bypass. The flow through this bypass is small (typically 5% of gas flow) and is controlled by the movement of a control valve.

In propellant utilization systems, the mixture ratio is varied to ensure that both fuel and oxidizer propellant tanks are simultaneously and completely emptied; no undue useable propellant residue should remain because it increases the empty mass of the vehicle, which in turn detrimentally decreases the vehicle mass ratio and the vehicle's flight performance (see Chapter 4). For example, the flow rate of oxidizer may be somewhat larger than normal due to its being slightly denser than normal or due to a lower than normal injector pressure drop; if uncontrolled, some fuel residue would remain at the time of oxidizer exhaustion; however, the control system could cause the engine to operate for a period at a propellant mixture ratio slightly more fuel‐rich than normal, to compensate and assure almost simultaneous emptying of both propellant tanks. Such control system requires accurate measurements of the amount of propellant remaining in the two propellant tanks during the flight.

Any one of the three principal components of an automatic control system may have several different forms. Typical sensing devices include those that measure chamber pressures, propellant pressures, pump rotational speeds, tank levels, and/or propellant flows. An actuating device can throttle propellant flow or control a bypass device or the gas generator discharge. There are many operating mechanisms for the controller, such as direct electrical devices, electronic analog or digital computers, hydraulic or pneumatic devices, and mechanical devices. Actuators can be driven by electrical motors or hydraulic, pneumatic, or mechanical power. Hydraulic actuators provide very high forces and quick responses. The exact type of component, the nature of the power supply, the control logic, the system type, and the operating mechanisms for the specific control will depend on details of the application and the requirements. Controls are discussed further in Refs. 11–4, 11–8, and 11–9.

In applications where the final vehicle velocity must be accurately determined, the amount of impulse that is imparted to the vehicle during any cutoff transient may be sufficiently variable to exceed any desired velocity tolerance. Therefore, for these applications close control over the thrust decay curve is necessary, and this can be accomplished by automatic control over the sequencing and closing rates of the main propellant valves and the location of the valves in relation to the injector.

11.5 ENGINE SYSTEM CALIBRATION

Although engines are designed to deliver a specific performance (F, I_s, , r), a newly manufactured engine will not usually perform precisely at their nominal parameters. The calibration process provides necessary corrections to the engine system, so it will perform at the rated/intended operating conditions. When deviations from nominal performance are more than a few percent, the vehicle will probably not complete its intended mission. There are several sources for these deviations. Because of unavoidable dimensional tolerances on the hardware, the flow–pressure time profile or injector jet impingements (related to combustion efficiency) will deviate slightly from nominal design values. Even a small change in mixture ratio can cause a significant increase of residual propellant. Also, minor changes in propellant composition or storage temperatures (which affect their density and viscosity) may cause significant deviations. Other factors involve regulator setting tolerances or changes in flight acceleration (affecting the static head). Engine calibration is the process of adjusting some of its internal parameters so that it will deliver the intended performance within the allowed tolerance bands. See Refs. 11–4 and 11–5.

Hydraulic and pneumatic components (valves, pipes, expansion joints) can readily be tested on water‐flow benches to determine their pressure drop at rated flow (corrected for the propellant density and viscosity). Components that operate at elevated temperatures (thrust chambers, turbines, preburners, etc.) have to be hot fired and cryogenic components (pumps, some valves) often have to be tested at the cryogenic propellant temperatures. Engine characteristics may be estimated by adding together the corrected values of pressure drops at the desired mass flow. Furthermore, the ratio of rated flows has to equal the desired mixture ratio r. This is shown in the example below. Adjustments include adding pressure drops with judiciously placed orifices or changing valve positions or regulator settings.

In most pressurized feed systems, the gas is supplied from its high‐pressure tank through a regulator to pressurize both the fuel and the oxidizer in their respective tanks. The two pressure drop equations for the oxidizer and the fuel (subscripts o and f) are given below for a pressurized feed system at nominal flows:

11–6

11–7

The gas pressure available in both of the propellant tanks is the regulated pressure p_gas, diminished by the pressure losses in the gas line Δp_gas, which includes the pressure drop across a pressure regulator. The static head of a liquid, Laρ (L is liquid level distance above the thrust chamber, a is flight acceleration, and ρ is propellant density), acts to augment the gas pressure. It has to equal the chamber pressure p₁ plus all other pressure drops in the liquid piping or valves, namely, Δp (Δp_f or Δp_o), the injector's Δp_inj, the cooling jacket's Δp_j, and the dynamic flow head . When the required liquid pressures (right‐hand side of Eq. 11–6 and 11–7.) do not equal the gas pressure in the propellant tank at the nominal propellant flow (left hand side of equations), then additional pressure drops (from calibration orifices) have to be inserted. A good design should provide extra pressure drop margins for this purpose.

Two methods are available for precise control of engine performance parameters. One uses an automatic system with feedback, throttling valves and a digital computer to control any deviations in real time. The other relies on the initial static calibration of the engine system. The latter approach is simpler and is preferred, and can be quite accurate.

Pressure balancing is the process of balancing the available pressure supplied to the engine (by pumps, the static head, and/or pressurized tanks) against the liquid pressure drops plus the chamber pressure. This balancing is done in order to calibrate the engine so it will operate at the desired flows and mixture ratios. Figure 11–5 shows pressure balances for one propellant branch of a bipropellant engine with a pressurized feed system. It displays the pressure drops (for injector, cooling jacket passages, pressurizing gas passages, valves, propellant feed lines, etc.) and chamber pressure against propellant flow, using actual component pressure drop measurements (or estimated values) corrected for the different flows. These curves are generally plotted in terms of a “head loss” and of the “volumetric flow” to eliminate the fluid density as an explicit variable for a particular regulated pressure. These regulated pressures are usually the same in the fuel and oxidizer pressure balance and also can be adjusted. This balance of head (the term head is defined in a footnote in Section 10.5) and flow must be made for both the fuel and oxidizer systems because the ratio of their flows establishes the actual mixture ratio and the sum of their flows establishes the thrust. The pressure balance between available and required tank pressure, both at the desired flow, is achieved by adding a calibration orifice into one of the lines, as can be seen in Fig. 11–5. Not shown in the figure is the static head provided by the elevation of the liquid level, since it is relatively small for many space launch systems. However, with high acceleration and dense propellants, it can be a significant addition to the available head.

For a pumped feed system of a bipropellant engine, Fig. 11–6 shows a balance diagram for one branch of the two propellant systems. Here, pump speed is an additional variable. Calibration procedures are usually more complex for TP systems because pump calibration curves (flow–head–power relation) cannot readily be estimated without good test data and cannot be easily approximated analytically. Propellant flows to a gas generator or preburner also need to be calibrated. In this case, the turbine shaft torque has to equal the torque required by the pumps plus the losses in bearings, seals, and/or windage. Thus, a power balance must be achieved in addition to the matching of pressures and the individual propellant flows. Since these parameters are interdependent, the determination of calibration adjustments may not always be simple. Many rocket organizations have developed computer programs to analyze some or all this required balancing.

The set of balancing equations may be programed into a computer to assist in the calibration of engines. It can also include some of the system's dynamic analogies that enable proper calibration and adjustment for transient engine performance, as during start. There is a trend to require tighter tolerances on rocket engine parameters (such as thrust, mixture ratio, or specific impulse), and therefore all measurements, calibrations, and adjustments are also being performed to much tighter tolerances than were customary 50 years ago.

11.6 SYSTEM INTEGRATION AND ENGINE OPTIMIZATION

Rocket engines as part of an overall vehicle must interact and be well integrated with other vehicle subsystems. There must exist interfaces (connections, wires, or pipelines) between the engine and the vehicle's structure, electric power system, flight control system (commands for start or thrust vector control), and ground support system (for checkout or propellant supply). The rocket engine also affects other vehicle components by its heat emissions, noise, and vibrations.

Integration means that the engine and the vehicle are compatible with each other, all interfaces are properly designed, and there is no interference or unnecessary duplication of functions with other subsystems. The engine must work properly with other subsystems to enhance the vehicle's performance and reliability, and reduce the cost. Some organizations use “system engineering” techniques to achieve this integration. See Ref. 11–7. In Chapter 19, we describe the process of selecting rocket propulsion systems and include a discussion of interfaces and of vehicle integration; the discussion in Chapter 19 is supplementary and applies to several different rocket propulsion systems. The present section only concerns liquid propellant rocket engines.

Since the propulsion system is usually the major mass component of the vehicle, its structure (which usually includes the tanks) often becomes a key structural element for the vehicle and has to withstand not only its thrust force but also various vehicle loads, such as aerodynamic forces, inertia forces, or vibration. In the design stages, several alternate tank geometries and locations (fuel, oxidizer, and pressurizing gas tanks), different tank pressures, and different structural connections need to be evaluated to determine the best arrangement.

The thermal behavior of the vehicle is strongly affected by the heat generation (hot plume, hot engine components, and/or aerodynamic heating) and the heat absorption (the liquid propellants are usually heat sinks), and by the heat rejection to its surroundings. Many vehicle components must operate within narrow temperature limits, and their thermal designs must be critically evaluated in terms of an overall heat balance before, during, and after rocket engine operation.

Optimization studies are conducted to select best values or to optimize various vehicle parameters such as vehicle performance (see below), thrust, number of restarts, or engine compartment geometry. These studies are usually performed by vehicle designers with help from propulsion system designers. Rocket engine designers conduct optimization studies (together with vehicle engineers) on engine parameters such as chamber pressure (or thrust), mixture ratio (which affects average propellant density and specific impulse), number of thrust chambers, nozzle area ratio, or engine volume. By modifying one or more of these parameters, it is usually possible to make some improvement to the vehicle performance (0.1 to 5.0%), its reliability, or to reduce costs. Depending on the mission or application, optimization studies are aimed at maximizing one or more vehicle parameter such as range, vehicle velocity increment, payload, circular orbit altitude, propellant mass fraction, or minimizing costs. For example, the mixture ratio of hydrogen–oxygen engines for maximum specific impulse is about 3.6, but most launch engines operate at mixture ratios between 5 and 6 because the total propellant volume is less, and this allows a reduced mass for the propellant tanks (resulting in a higher vehicle velocity increment) and a reduced vehicle drag (more net thrust). Selection criteria for the best nozzle area ratio were introduced in Chapter 3; they depend on things like the flight path's altitude–time history and on whether an increase in specific impulse is offset by extra nozzle weight and length. The best thrust–time profile can also usually be optimized, for a given application, by using trajectory analyses.

SYMBOLS

a	acceleration, m/sec2 (ft/sec2)
A	area, m2 (ft2)
CF	thrust coefficient (see Eq. 3–30)
Cd	orifice discharge coefficient
F	thrust, N (lbf)
g0	sea‐level or standard acceleration of gravity, 9.806 m/sec2 (32.174 ft/sec2)
H	head, m (ft)
Is	specific impulse, sec
k	specific heat ratio
L	length, m (ft)
	mass flow rate, kg/sec (lbm/sec)
p	pressure, N/m2(lbf/in.2)
Q	volume flow rate, m3/sec (ft3/sec)
r	mixture ratio (oxidizer to fuel flow)
t	time, sec
T	absolute temperature, K (°R)
	fluid or liquid velocity, m/sec3 (ft/sec)
	weight flow rate kg − m/sec3 (lbf/sec)

Greek Letters

ζd	discharge correction factor
	velocity correction factor
ρ	density, kg/m3(lb/ft3)

PROBLEMS

1. Estimate the mass and volume of nitrogen gas required to pressurize an N₂O₄ − MMH feed system for a 4500 N thrust chamber of 25 sec duration (, the ideal at 1000 psi or 6894 N/m² and expansion to 1 atm). The chamber pressure is 20 atm (absolute) and the mixture ratio is 1.65. The propellant tank pressure is 30 atm, and the initial gas tank pressure is 150 atm. Allow for 3% excess propellant and 50% excess gas to allow some nitrogen to dissolve in the propellant. The nitrogen regulator requires that the gas tank pressure does not fall below 29 atm.
2. A rocket engine operating on a gas generator engine cycle has the following test data:

   Engine thrust	100,100 N
   Engine specific impulse	250.0 sec
   Gas generator flow	3.00% of total propellant flow
   Specific impulse of turbine exhaust flowing through a low area ratio nozzle	100.2 sec

   Determine the specific impulse and thrust for the single thrust chamber.Answer: 254.6 sec and 98,899 N.
3. This problem concerns various potential propellant loss/utilization categories; the first section of this chapter identifies most of them. This engine has a TP feed system with a single TP, a single fixed‐thrust chamber (no thrust vector control) with no auxiliary small thrusters, storable propellants, good priming of the pumps prior to start, and a gas generator engine cycle.Prepare a list of propellant utilization/loss categories for which propellant have to be provided. Which of these categories will have a little more propellant or a little less propellant, if the engine is operated with either warm propellant (perhaps 30 to 35 °C) and alternatively in a cold space environment with propellants at −25 °C? Give brief reasons, such as “higher vapor pressure will be more likely to cause pump cavitation.”
4. What happens to the thrust and the total propellant flow if an engine (calibrated at 20 °C) is supplied with propellants at higher or at lower storage temperatures?

REFERENCES

1. 11–1. P. Brossel, S. Eury, P. Signol, H. Laporte, and J. B. Micewicz, “Development Status of the Vulcain Engine,” AIAA Paper 95‐2539, 1995.
2. 11–2. R. Iffly, “Performance Model of the Vulcain Ariane 5 Main Engine,” AIAA Paper 1996–2609, 1996; J.‐F. Delange et al., “VINCI®, the European Reference for Ariane 6 Upper Stage Cryogenic Propulsive System,” AIAA Paper 2015‐4063, Orlando FL, 2015.
3. 11–3. G. Mingchu and L. Guoqui, “The Oxygen/Hydrogen Engine for Long March Vehicle,” AIAA Paper 95‐2838, 1995.
4. 11–4. D. K. Huzel, and D. H. Huang, Chapter 7, “Design of Rocket Engine Controls and Condition Monitoring Systems,” and Chapter 9, “Engine System Design Integration,” of Modern Engineering Design of Liquid Propellant Rocket Engines, rev. ed., Vol. 147 of Progress in Astronautics and Aeronautics (Series), AIAA, Reston, VA, 1992.
5. 11–5. R. W. Humble, G. N. Henry, and W. J. Larson, Chapter 5, “Liquid Rocket Propulsion Systems,” in Space Propulsion Analysis and Design, McGraw‐Hill, New York, 1995.
6. 11–6. Copied from Eighth Edition of this book.
7. 11–7. P. Fortescue, J. Stark, and G. Swinerd, Spacecraft System Engineering, 3rd ed., John Wiley & Sons, Chichester, England, 2003, reprinted 2005.
8. 11–8. A. D'Souza, Design of Control Systems, Prentice Hall, New York, 1988.
9. 11–9. R. M. Mattox and J. B. White, “Space Shuttle Main Engine Controller,” NASA Technical Paper 1932, 1981.
10. 11–10. H. Zhang, J. Wu, M. Huang, H. Zhu, and Q. Chen, “Liquid Rocket Engine Health Monitoring Techniques,” Journal of Propulsion and Power, Vol. 14, No. 5, Sept.–Oct. 1988, pp. 657–663.
11. 11–11. A. Ray, X. Dai, M‐K. Wu, M. Carpino, and C. F. Lorenzo, “Damage‐Mitigating Control of a Reusable Rocket Engine,” Journal of Propulsion and Power, Vol. 10, No. 2, Mar.–Apr. 1994, pp. 225–234.