Rocket Propulsion:Temporary

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Introduction

Rocket propulsion of an object is achieved by the combustion of fuel (propellant) and an oxidiser, both of which are carried by the object. The explosive energy of combustion is vectored in a linear fashion away from the body. This vectored energy provides an opposing thrust to the body causing it to accelerate. It is similar to jet propulsion except that here, oxygen from the atmosphere is used as the oxidant for the fuel. Because rocket propulsion can generate far greater thrust and can operate in oxygen-free environments, it is currently the only method for getting an object (a rocket) from the Earth's surface and into space. To overcome the force of gravity, a rocket must be accelerated to a speed of at least 17,000 mph in order to achieve an orbital path.

History

• Chinese
• German
• American
  • Apollo
  • Space Shuttle

See also Rocket History

Fundamental Principles

Rocket propulsion is based on Newton's three laws of motion:

1. Force equals mass times accleration, $F=ma$; or force equals the change of momentum with respect to time, $F=dp/dt$.
2. The principle of inertia: A body in motion (or at rest) tends to remain in motion (or at rest) unless acted on by a force.
3. Every action produces an equal and opposite reaction.

In general, a rocket works by taking a propellant and acclerating it to go into a particular direction. Because of Newton's third law, the rocket will go in the opposite direction of the propellant. The resulting force that is obtained in propelling the rocket is referred to as thrust.

Most rockets accelerate propellent through a thermodynamic process. For most current rockets, a chemical reaction heats the propellant in a combustion chamber. This heating of the propellant increases its pressure. The combustion chamber has an opening through which the propellant escapes.

Another option is the use of an electric ion thruster. In this case, atoms are stripped of an electron, giving them a positive electric charge. An electric field is set up to propel these ions out of the rocket, again producing thrust.

Alternately, nuclear-reactors may be used to power the rocket. The nuclear reactor may be used to heat the propellant thermodynamically or the nuclear power can be converted to electricity to power an electric ion thruster.

At the simplest level, the trade-off between thermodynamic and electric ion propulsion is thrust versus mass efficiency. Thermodynamic rockets are able to produce high levels of thrust, but are inefficient in their use of propellant. Electric ion propulsion conversely uses propellant very efficiently, but is only able to produce small amounts of thrust, much too small to overcome the Earth's gravity when launching a rocket from the Earth into orbit.

Thermodynamic Analysis

The thermodynamic cycle for a liquid rocket booster is a modified Brayton (jet) cycle. A one-dimensional analysis may be performed by asssuming the following ideal steps.

1. Fuel is injected into a combustion chamber isentropically either through used of pressurized fuel tanks or by a high-pressure pump, increasing the pressure to $p_c$ and increasing the enthalpy.
2. Heat is added to the fuel by means of combustion. In an ideal situation, it is assumed that the pressure remains constant during this step, but that the temperature rises. Both enthalpy and entropy increase during this step.
3. The combusted fuel expand isentropically to the exit pressure, $p_e$, as it goes through the nozzle into the atmosphere, which is at pressure $p_0$. Ideally $p_e$ should equal $p_0$. During this process, the enthalpy decreases from $h_c$ to $h_e$.

The thrust produced by a rocket is given by

$T=\dot{m_p}{v}_e+A_{exit}*(p_e-p_0)$,

where $\dot{m_p}$ and $v_e$ are the mass flow rate and exit velocity of the propellant, $A_{exit}$ is the exit area of the nozzle and $p_e$ and $p_0$ are the pressure at the exit point of the nozzle and the atmospheric pressure. The enthalpy represents the internal energy available for work or the potential energy. Thus, the energy change per unit time as the propellant moves from the combustion chamber to the nozzle exit is

$\dot{m_p}(h_c-h_e)=\frac{1}{2}\dot{m_p}{v}_e^2$.

Solving for the propellant velocity yields

$v_e=\sqrt{2(h_c-h_e)}$.

Let us assume that the combustion mixture of the propellants is an ideal gas. The internal energy per unit mass of an ideal gas is given by

$h={\hat{c}}_{V}T$,

producing an equation for the propellant velocity of

$v_e=\sqrt{2{\hat{c}}_V(T_c-T_e)}=\sqrt{2{\hat{c}}_V{T}_c(1-\frac{T_e}{T_c})}$.

When an ideal gas expands isentropically, a change of temperature and pressure such that the following two relations hold

$\frac{p_1}{p}={(1+\frac{\gamma -1}{2}{M}^2)}^{\gamma /(\gamma -1)}$;

$\frac{T_1}{T}=1+\frac{\gamma -1}{2}{M}^2$;

where M represents the Mach number at the location having static pressure p and temperature T. Using these two equations, we can relate the temperature and pressure ratios as

$\frac{T_1}{T}={\left(\frac{p_1}{p}\right)}^{(\gamma -1)/\gamma }$.

Thus, we can rewrite the equation for the propellant velocity as

$v_e=\sqrt{2{\hat{c}}_V(T_c-T_e)}=\sqrt{2{\hat{c}}_V{T}_c[1-{\left(\frac{p_e}{p_c}\right)}^{(\gamma -1)/\gamma }]}$.

The final analysis step in the one-dimensional analysis is the effects of the nozzle. The previous equation demonstrates that making the ratio $p_e/p_c$ as small as possible maximizes the propellant speed, which in turn maximizes the thrust. The nozzle is designed to match the exit pressure as close as possible to the pressure of the atmosphere or the vacuum of space.

A common metric describing the efficiency of fuel use of a rocket (or jet) is the specific impulse, which is defined as

$I_{sp}=\frac{T}{m_p}$.

As an example, the use of $H_2+0_2$ produces a specific impulse of 454 "seconds".

Types of Rockets

Solid Rockets

Solid rockets use a solid fuel propellant. An advantage is that the fuel is easier and safer to handle. These solid rockets have an oxidiser built into the the fuel. A disadvantage is that once the solid fuel is ignited, the combustion cannot be turned off. The two "booster" rockets on the sides of the Space Shuttle are solid fuel rockets.

Liquid Fuel Rockets

Liquid Fuel Rockets are rockets that contain a liquid fuel as well as a liquid oxidiser. In pre-launch the liquid fuel would burn slowly until the oxidiser is released creating a very rapid burn with enough force for liftoff. Liquid fuel rockets can also be controlled through limiting or regulating the fuel and oxygen supplies. The Space Shuttle's large orange tank contains liquid rocket fuel that is used by the Orbiter upon take-off.

Hybrid Rockets

Hybrid rockets use both a solid rocket fuel and a liquid oxidizer. The solid fuel generally consists of a flammable wax that normally burns slowly, but when mixed with a liquid oxidizer, it can burn very rapidy. Unlike solid fuel rockets, the oxygen supply can be controlled to dynamically vary the thrust of the rocket.

Electric Ion Rockets

Electric Ion rockets use xenon atoms charged with radio waves to create thrust. When thinking about rockets that moving them around is not all about playing with fire. Although electric ion thruster technology is currently unable to get a space craft off the Earth, it can produce a small amount of thrust that would help it navigate in space.

To understand how this works you have to think of how charged objects are attracted to or repulsed by other charged objects. Electrically charged gases are called ions. Xenon is a noble gas with a complete electronic outer shell. Its outer shell can be ionized with radio waves stripping outer layer electrons and leaving behind a positively charged ion. The ion can then be moved by introducing an electric field. This is typically done with two oppositely charged metal plates, at least one of which is perforated to allow the accelerated ions to pass through and exit the nozzle of the rocket. This does not create much thrust, but it is very efficient and can produce incredibly high speeds over great distances.

Nuclear-Powered Rockets

Nuclear powered rockets use nuclear energy to superheat hydrogen gas to a temperature at which it exits the rocket at a very high velocity. One problem with this design is that the reactor of the rockets tends to outlast the supply of hydrogen gas. The concept is possible, but debate continues as to the safety of using nuclear power in space, just as it does on the safety of terrestrial nuclear power plants.

Water Rockets

Great sport (and serious study) can be had using plastic soda bottles, water and compressed air.

External Links

NASA's Beginner's Guide to Rockets and Ideal Rocket Equation
Federation of American Scientists, Rocket Basics
Amateur Experimental Rocketry