## List of figures

1.1 Konstantin 1.2 Herman 1.3 Robert 1.4 The J-2 engine used for the upper stages of Saturn 1.5 The launch of the Space Shuttle Atlantis, 3 October 1985 11 1.6 Tsiolkovsky's rocket 1.7 Spacecraft 1.8 Orbit 1.9 Injection velocity and 1.11 Launch vehicle with 2.1 A liquid-fuelled rocket 2.2 A solid-fuelled rocket 2.3 Forces in the combustion chamber and exhaust 2.4 Gas flow through the 2.5 Static force due to atmospheric 2.6 P-V diagram for a heat 2.7 Gas velocity as a function of the pressure...

## The Basic Configuration

A liquid-fuelled rocket engine (see Figure 2.1) consists of a combustion chamber into which fuel and oxidant are pumped, and an expansion nozzle which converts the high-pressure hot gas, produced by the combustion, into a high velocity exhaust stream. It is the expansion of the hot gas against the walls of the nozzle which does work and accelerates the rocket. A solid-fuelled motor (Figure 2.2) operates in the same way, except that the fuel and oxidant are pre-mixed in solid form, and are...

## Radiofrequency thrusters

Most high power and hence high thrust systems use electrodes, of one kind or another, to generate the current in the gas that provides the ions and hence the thrust. These always erode in the discharge, being worse for high power systems. Several attempts have been made to increase the power input by using microwaves to provide the internal energy source. The simplest device is analogous to the electrothermal thruster microwaves are used to heat the gas in a 'combustion' chamber connected to a...

## S V MerM V J

Note that in all cases, 'range' indicates the distance travelled during acceleration, assuming an initial velocity of zero. These equations show how the motion of the rocket is altered by gravity when the motion is vertical. This applies to the early stages of most launches, and the effect of gravity can be estimated using these equations. The general effect is that the velocity and the distance travelled are less than would have been predicted by the rocket equation, by the amount of the...

## Vehicle velocity

The above derivation of the rocket equation can easily be adapted to determine the velocity in the presence of gravity. The thrust remains the same, but the acceleration of the rocket is now governed by two forces the thrust, and the opposing force of gravity. As before, the thrust developed by the exhaust is represented by The acceleration of the rocket, under the thrust F, and the opposing force of gravity, is represented by where Mg is the current weight of the rocket. Substituting for F, dv...

## Loge [M0

This is the rocket equation as met with in Chapter 1, where the ratio of initial to current mass defines the current velocity. It is applicable to any velocity increment when the initial and final masses are correctly defined. The assumption of constant exhaust velocity is valid in the vast majority of real cases. Note that the velocity of the rocket vehicle, at any given instant during the burn, is dependent only on the exhaust velocity and the instantaneous mass ratio the thrust history does...

## More On The Rocket Equation

The rocket equation more properly called Tsiolkovsky's equation has a relatively simple derivation. It is based on calculating the acceleration of a rocket vehicle with a mass decreasing continuously due to the expenditure of propellant. The case we have to consider is that of a rocket vehicle of mass M, expelling combustion products at a rate m, with a constant exhaust velocity ve. The mass of the vehicle is decreasing at the rate m, and, due to the thrust F, developed by the exhaust, the...

## Launch vehicle dynamics

The launch of a spacecraft is fundamental to all space activity, and it is through our development of efficient launch vehicles that the present impact of space on many aspects of science, commerce, and daily life is possible. The launch lasts only a few minutes, and yet during this short period of time, many years of development and investment in the commercial use of the spacecraft can be brought to nothing if just one of the many thousands of components of the launcher fails to perform to...

## Thrust Vector Control

For orbital injection, thrust vector control is not normally needed, as the burn is too short to require the spacecraft to change its course while the motor is firing. Thrust vector control is essential for solid boosters because their thrust dominates the thrust of a launcher for the first few minutes, and so course corrections require the booster thrust to be diverted. The technique of liquid injection applicable to small solid propellant launchers cannot produce sufficient transverse thrust...

## Thrust stability

The overall thrust profile can be controlled by the shape of the charge, but other factors are important in understanding the way a solid motor performs, the most important of which is the stability of the thrust. In the liquid-fuelled engine the chamber pressure is usually constant and, with the mass flow rate, is determined by the rate at which the propellants are delivered through the injectors. On the other hand, in the solid motor the mass flow rate is not determined by external supply but...

## The Development Of Thrust And The Effect Of The Atmosphere

In Chapter 1 the discussion of the rocket equation and the application of Newton's third law to rocket propulsion ignored the effects of atmospheric pressure and the actual forces involved in producing the propulsive thrust. The concept of effective exhaust velocity enabled this simplification. The effective exhaust velocity is that velocity which, when combined with the actual mass flow in the exhaust stream, produces the measured thrust, F mve, where m is the mass flow rate, and ve is the...

## Hall thruster variants

There are two kinds of practical Hall thruster, both emerging from the Russian programmes. The first kind, as described above, has the annular cavity lined with insulator, usually boron nitride, and the cavity itself is rather deep. This is often described in the Russian literature as the Stationary Plasma Thruster, or SPT (Figure 6.17). The other type, which came from a different laboratory in Russia, has a much shallower annular cavity, lined with metal rather than insulator. This is Figure...

## Thrust profile and grain shape

The pressure in the chamber, and hence the thrust, depends on the rate at which the grain is consumed. The pressure depends on the recession rate and on the area of the burning surface, and the mass flow rate depends on the volume of propellant consumed per second. The shape of the charge can be used to preset the way the area of the burning surface evolves with time, and hence the temporal thrust profile of the motor. The pressure and the thrust are independent of the increase in chamber...

## Inclined Motion In A Gravitational Field

It is obvious that if the whole trajectory of the rocket is vertical, then unless escape velocity is reached the payload will ultimately fall back to Earth. To achieve orbit around a planet requires a high horizontal velocity. Thus the majority of the flight path of a launch vehicle is inclined to the gravitational field in order to gain velocity in the horizontal direction. Gravity now affects the direction of flight as well as the magnitude of the velocity. As we shall see, the flight path is...

## The Development Of The Rocket

Hero of Alexandria (c. 67 AD) is credited with inventing the rocket principle. He was a mathematician and inventor and devised many machines using water, air pressure, and steam, including a fire engine and a fountain. His aeolipile consisted of a metal boiler in which steam was produced, connected by a pipe through a rotating joint, to a pivoted jet system with two opposing jets. The steam issuing from the jets caused the system to rotate. It is not clear if Hero understood the cause of the...

## Hall effect thrusters

Over the years, Russia developed a plasma thruster based on the Hall effect, and implemented it on more than 100 satellites. This device has now become available worldwide, and is simple and practical. The Hall thruster belongs to the family of magnetoplasmadynamic devices, and has been shown to share the practical properties of the low-pressure arc-jet described above and it works. However, it was only in the Russian space programme that it had been brought to a practical and space-qualified...

## The Space Shuttle SRB

Table 4.1 shows that the SRB is about twice the size of the MPS. It develops a thrust of 10 MN. The casing consists of eight steel segments flow-turned with the appropriate flanges. The fore and aft sections are fitted with the igniter and nozzle respectively. The casing sections are joined in pairs by factory joints which are then thermally protected by thick rubber seals, and the inner walls of the casing are protected by insulating material to which the propellant will be bonded. The...

## The thrust coefficient and the characteristic velocity

There are two other parameters of the rocket motor which can be defined, and which are helpful in calculating the performance. These are the thrust coefficient, denoted by Cp, and the characteristic velocity, denoted by c*. The thrust coefficient represents the performance of the nozzle, and the characteristic velocity that of the propellants and combustion. The thrust coefficient is the ratio of the thrust to the notional force, Figure 2.11 shows this ratio plotted as a function of the...

## Solid propellant rocket motors

Considering the complexities of the liquid propellant rocket engine, it does not seem remarkable that so much attention has been given to the design and development of the much simpler solid propellant motor. This has a range of applications the main propulsion system for small and medium launchers as a simple and reliable third stage for orbital injection and most of all as a strap-on booster for many modern heavy launchers. The solid propellant is storable, and is relatively safe to handle no...

## Example calculations

As an example calculation we can consider a real engine design the Viking series used on Ariane 4. This is a storable propellant motor using nitrogen tetroxide and UDMH25 (unsymmetrical dimethyl hydrazine with 25 hydrazine hydrate) as propellants. This mixture is self-igniting, and both propellants are liquid at NTP. The information provided by the manufacturers is as follows The thrust coefficient can be determined from the tabulated data. The throat area can be calculated from the exit...

## Storable propellant engines

This combination is used on the Ariane Viking series and on many other launchers, and has the advantages of comprising room-temperature liquids and being self-igniting. Table 3.3 compares some typical engines. Storable propellants have many advantages. They are much easier to handle on the ground, and so found favour for use with the Ariane 1-4 series launchers. They also do not need vented tanks, and are for that reason convenient for upper stages Table 3.3. Storable propellant engines. Table...

## The RS 68 engine

From 1990 onwards the United States has been developing the Evolved Expendable Launch Vehicle, a complementary vehicle to the Shuttle. The Delta family of launchers is one manifestation of this programme, and amongst its technological innovations has been the RS 68 engine Figure 3.10 , claimed to be the first new large rocket engine to be developed in the United States since the SSME. Its main features, compared with the SSME, are its simplicity and low cost. The number of separate components...