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The necessity for propulsion systems
Effectiveness of propulsion systems When in space, the purpose of a propulsion system is to change the velocity v of a spacecraft. Since this is more difficult for more massive spacecraft, designers generally discuss momentum, mv. The amount of change in momentum is called impulse. So the goal of a propulsion method in space is to create an impulse. When launching a spacecraft from the Earth, a propulsion method must overcome a higher gravitational pull to provide a net positive acceleration. In orbit, the spacecraft tangential velocity provides a centrifugal force that counterweighs the gravity pull at a given path (which is actually the orbit path) so that any additional impulse, even very tiny, will result in a change in the orbit path. The rate of change of velocity is called acceleration, and the rate of change of momentum is called force. To reach a given velocity, one can apply a small acceleration over a long period of time, or one can apply a large acceleration over a short time. Similarly, one can achieve a given impulse with a large force over a short time or a small force over a long time. This means that for maneuvering in space, a propulsion method that produces tiny accelerations but runs for a long time can produce the same impulse as a propulsion method that produces large accelerations for a short time. When launching from a planet, tiny accelerations cannot overcome the planet's gravitational pull and so cannot be used. The law of conservation of momentum means that in order for a propulsion method to change the momentum of a space craft it must change the momentum of something else as well. A few designs take advantage of things like magnetic fields or light pressure in order to change the spacecraft's momentum, but in free space the rocket must bring along some mass to accelerate away in order to push itself forward. Such mass is called reaction mass. In order for a rocket to work, it needs two things: reaction mass and energy. The impulse provided by launching a particle of reaction mass having mass m at velocity v is mv. But this particle has kinetic energy mv2/2, which must come from somewhere. In a conventional solid, liquid, or hybrid rocket, the fuel is burned, providing the energy, and the reaction products are allowed to flow out the back, providing the reaction mass. In an ion thruster, electricity is used to accelerate ions out the back. Here some other source must provide the electrical energy (perhaps a solar panel or a nuclear reactor), while the ions provide the reaction mass. When discussing the efficiency of a propulsion system, designers often focus on effectively using the reaction mass. Reaction mass must be carried along with the rocket and is irretrievably consumed when used. One way of measuring the amount of impulse that can be obtained from a fixed amount of reaction mass is the specific impulse, the impulse per unit weight-on-Earth (typically designated by ). The unit for this value is seconds. Since the weight on Earth of the reaction mass is often unimportant when discussing vehicles in space, specific impulse can also be discussed in terms of impulse per unit mass. This alternate form of specific impulse uses the same units as velocity (e.g. m/s), and in fact it is equal to the effective exhaust velocity of the engine (typically designated ). Confusingly, both values are sometimes called specific impulse. The two values differ by a factor of g, the acceleration due to gravity on the Earth's surface (). A rocket with a high exhaust velocity can achieve the same impulse with less reaction mass. However, the energy required for that impulse is proportional to the square of the exhaust velocity, so that more mass-efficient engines require much more energy. This is a problem if the engine is to provide a large amount of thrust. To generate a large amount of impulse per second, it must use a large amount of energy per second. So highly efficient engines require enormous amounts of energy per second to produce high thrusts. As a result, most high-efficiency engine designs also provide very low thrust. Calculations Burning the entire usable propellant of a spacecraft through the engines in a straight line in free space would produce a net velocity change to the vehicle; this number is termed 'delta-v'. The total of a vehicle can be calculated using the rocket equation, where M is the mass of fuel (or rather the mass of propellant), P is the mass of the payload (including the rocket structure), and is the velocity of the rocket exhaust. This is known as the Tsiolkovsky rocket equation: ight) For historical reasons, as discussed above, is sometimes written as where is the specific impulse of the rocket, measured in seconds, and is the gravitational acceleration at sea level. For a long voyage, the majority of the spacecraft's mass may be reaction mass. Since a rocket must carry all its reaction mass with it, most of the first reaction mass goes towards accelerating reaction mass rather than payload. If we have a payload of mass P, the spacecraft needs to change its velocity by , and the rocket engine has exhaust velocity ve, then the mass M of reaction mass which is needed can be calculated using the rocket equation and the formula for ight) For much smaller than ve, this equation is roughly linear, and little reaction mass is needed. If is comparable to ve, then there needs to be about twice as much fuel as combined payload and structure (which includes engines, fuel tanks, and so on). Beyond this, the growth is exponential; speeds much higher than the exhaust velocity require very high ratios of fuel mass to payload and structural mass. In order to achieve this, some amount of energy must go into accelerating the reaction mass. Every engine will waste some energy, but even assuming 100% efficiency, the engine will need energy amounting to Comparing the rocket equation (which shows how much energy ends up in the final vehicle) and the above equation (which shows the total energy required) shows that even with 100% engine efficiency, certainly not all energy supplied ends up in the vehicle - some of it, indeed usually most of it, ends up as kinetic energy of the exhaust. For a mission, for example, when launching from or landing on a planet, the effects of gravitational attraction and any atmospheric drag must be overcome by using fuel. It is typical to combine the effects of these and other effects into an effective mission delta-v. For example a launch mission to low Earth orbit requires about 9.3-10 km/s delta-v. These mission delta-vs are typically numerically integrated on a computer. Suppose we want to send a 10,000 kg space probe to Mars. The required from LEO is approximately 3000 m/s, using a Hohmann transfer orbit. (A manned probe would need to take a faster route and use more fuel). For the sake of argument, let us say that the following thrusters may be used: Observe that the more fuel-efficient engines can use far less fuel; its mass is almost negligible (relative to the mass of the payload and the engine itself) for some of the engines. However, note also that these require a large total amount of energy. For earth launch engines require a thrust to weight ratio of much more than unity. To do this they would have to be supplied with Gigawatts of power — equivalent to a major metropolitan generating station. This would need to be carried on the vehicle, which is clearly impractical. Instead, a much smaller, less powerful generator may be included which will take much longer to generate the total energy needed. This lower power is only sufficient to accelerate a tiny amount of fuel per second, but over long periods the velocity will be finally achieved. For example. it took the Smart 1 more than a year to reach the Moon, while with a chemical rocket it takes a few days. Because the ion drive needs much less fuel, the total launched mass is usually lower, which typically results in a lower overall cost. Interestingly, for a mission delta-v, there is a fixed that minimises the overall energy used by the rocket. This comes to an exhaust velocity of about ⅔ of the mission delta-v (see the energy computed from the rocket equation). Drives with a specific impulse that is both high and fixed such as Ion thrusters have exhaust velocities that can be enormously higher than this ideal, and thus end up powersource limited and give very low thrust. Where the vehicle performance is power limited, e.g. if solar power or nuclear power is used, then in the case of a large the maximum acceleration is inversely proportional to it. Hence the time to reach a required delta-v is proportional to . Thus the latter should not be too large. On the other hand if the exhaust velocity can be made to vary so that at each instant it is equal and opposite to the vehicle velocity then the absolute minimum energy usage is achieved. When this is achieved, the exhaust stops in space and has no kinetic energy; and all the energy ends up in the vehicle (in principle such a drive would be 100% efficient, in practice there would be thermal losses from within the drive system and residual heat in the exhaust). However in most cases this uses an impractical quantity of propellant, but is a useful theoretical consideration. Some drives (such as VASIMR) actually can significantly vary their exhaust velocity. This can help reduce propellant usage and improve acceleration at different stages of the flight. However the best energetic performance and acceleration is still obtained when the exhaust velocity is close to the vehicle speed. Proposed ion and plasma drives usually have exhaust velocities enormously higher than that ideal (in the case of VASIMR the lowest quoted speed is around 15000 m/s compared to a mission delta-v from high Earth orbit to Mars of about 4000m/s). Propulsion methods Propulsion methods can be classified based on their means of accelerating the reaction mass. There are also some special methods for launches, planetary arrivals, and landings. Rocket engines
Airbreathing engines for launch Studies generally show that conventional air-breathing engines, such as ramjets or turbojets are basically too heavy (have too low a thrust/weight ratio) to give any significant performance improvement when installed on a launch vehicle. However, they can be air launched from a separate lift vehicle (e.g. X-1, Pegasus and SS1). On the other hand, very lightweight or very high speed engines have been proposed that take advantage of the air during ascent: Electromagnetic acceleration of reaction mass
Systems without reaction mass carried within the spacecraft The law of conservation of momentum states that any engine which uses no reaction mass cannot move the center of mass of a spaceship (changing orientation, on the other hand, is possible). But space is not empty, especially space inside the Solar System; there are gravitation fields, magnetic fields, solar wind and solar radiation. Various propulsion methods try to take advantage of these. However, since these phenomena are diffuse in nature, corresponding propulsion structures need to be proportionately large. Space drives that need no (or little) reaction mass: For changing the orientation of a satellite or other space vehicle, conservation of angular momentum does not pose a similar constraint. Thus many satellites use momentum wheels to control their orientations. These cannot be the only system for controlling satellite orientation, as the angular momentum built up due to torques from external forces such as solar, magnetic or tidal forces eventually needs to be "bled off" using a secondary system. Launch mechanisms
Planetary arrival and landing
Methods that may require breaking the laws of physics
Table of methods and their specific impulse Below is a summary of some of the more popular, proven technologies, followed by increasingly speculative methods. Three numbers are shown. The first is the effective exhaust velocity: the equivalent speed that the propellant leaves the vehicle. This is not necessarily the most important characteristic of the propulsion method, thrust and power consumption and other factors can be, however: The second and third are the typical amounts of thrust and the typical burn times of the method. Outside a gravitational potential small amounts of thrust applied over a long period will give the same effect as large amounts of thrust over a short period. (This result does not apply when the object is significantly influenced by gravity.) See also Notes | |||||||||||||||||||||
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