Rocket
Rocket
A rocket (from Italian: rocchetto, lit. ''bobbin/spool'', and so named for its
shape)[nb 1][1] is a vehicle that uses jet propulsion to accelerate without
using any surrounding air. A rocket engine produces thrust by reaction to
exhaust expelled at high speed.[2] Rocket engines work entirely from
propellant carried within the vehicle; therefore a rocket can fly in the
vacuum of space. Rockets work more efficiently in a vacuum and incur a
loss of thrust due to the opposing pressure of the atmosphere.
Multistage rockets are capable of attaining escape velocity from Earth and
therefore can achieve unlimited maximum altitude. Compared with
airbreathing engines, rockets are lightweight and powerful and capable of
generating large accelerations. To control their flight, rockets rely on
momentum, airfoils, auxiliary reaction engines, gimballed thrust,
momentum wheels, deflection of the exhaust stream, propellant flow, spin,        A Soyuz-FG rocket
                                                                                 launches from "Gagarin's
or gravity.
                                                                                 Start" (Site 1/5), Baikonur
                                                                                 Cosmodrome
Rockets for military and recreational uses date back to at least 13th-
century China.[3] Significant scientific, interplanetary and industrial use
did not occur until the 20th century, when rocketry was the enabling technology for the Space Age,
including setting foot on the Moon. Rockets are now used for fireworks, missiles and other weaponry,
ejection seats, launch vehicles for artificial satellites, human spaceflight, and space exploration.
Chemical rockets are the most common type of high power rocket, typically creating a high speed
exhaust by the combustion of fuel with an oxidizer. The stored propellant can be a simple pressurized gas
or a single liquid fuel that disassociates in the presence of a catalyst (monopropellant), two liquids that
spontaneously react on contact (hypergolic propellants), two liquids that must be ignited to react (like
kerosene (RP1) and liquid oxygen, used in most liquid-propellant rockets), a solid combination of fuel
with oxidizer (solid fuel), or solid fuel with liquid or gaseous oxidizer (hybrid propellant system).
Chemical rockets store a large amount of energy in an easily released form, and can be very dangerous.
However, careful design, testing, construction and use minimizes risks.
History
In China, gunpowder-powered rockets evolved in medieval China under the Song dynasty by the 13th
century. They also developed an early form of multiple rocket launcher during this time. The Mongols
adopted Chinese rocket technology and the invention spread via the Mongol invasions to the Middle East
and to Europe in the mid-13th century.[4] According to Joseph Needham, the Song navy used rockets in a
military exercise dated to 1245. Internal-combustion rocket propulsion is mentioned in a reference to
1264, recording that the "ground-rat", a type of firework, had frightened the Empress-Mother Gongsheng
at a feast held in her honor by her son the Emperor Lizong.[5] Subsequently, rockets are included in the
military treatise Huolongjing, also known as the Fire Drake Manual,
written by the Chinese artillery officer Jiao Yu in the mid-14th century.
This text mentions the first known multistage rocket, the 'fire-dragon
issuing from the water' (Huo long chu shui), thought to have been used by
the Chinese navy.[6]
The name "rocket" comes from the Italian rocchetta, meaning "bobbin" or "little spindle", given due to
the similarity in shape to the bobbin or spool used to hold the thread from a spinning wheel. Leonhard
Fronsperger and Conrad Haas adopted the Italian term into German in the mid-16th century; "rocket"
appears in English by the early 17th century.[1] Artis Magnae Artilleriae pars prima, an important early
modern work on rocket artillery, by Casimir Siemienowicz, was first printed in Amsterdam in 1650.
William Leitch first proposed the concept of using rockets to enable human spaceflight in 1861. Leitch's
rocket spaceflight description was first provided in his 1861 essay "A Journey Through Space", which
was later published in his book God's Glory in the Heavens (1862).[17] Konstantin Tsiolkovsky later (in
1903) also conceived this idea, and extensively developed a body of theory that has provided the
foundation for subsequent spaceflight development.
The British Royal Flying Corps designed a guided rocket during World War I. Archibald Low stated "...in
1917 the Experimental Works designed an electrically steered rocket… Rocket experiments were
conducted under my own patents with the help of Cdr. Brock."[18] The patent "Improvements in Rockets"
was raised in July 1918 but not published until February 1923 for security reasons. Firing and guidance
controls could be either wire or wireless. The propulsion and guidance rocket eflux emerged from the
deflecting cowl at the nose.
The Americans captured a large number of German rocket scientists, including Wernher von Braun, in
1945, and brought them to the United States as part of Operation Paperclip. After World War II scientists
used rockets to study high-altitude conditions, by radio telemetry of temperature and pressure of the
atmosphere, detection of cosmic rays, and further techniques; note too the Bell X-1, the first crewed
vehicle to break the sound barrier (1947). Independently, in the Soviet Union's space program research
continued under the leadership of the chief designer Sergei Korolev (1907–1966).
During the Cold War rockets became extremely important militarily with the development of modern
intercontinental ballistic missiles (ICBMs). The 1960s saw rapid development of rocket technology,
particularly in the Soviet Union (Vostok, Soyuz, Proton) and in the United States (e.g. the X-15). Rockets
came into use for space exploration. American crewed programs (Project Mercury, Project Gemini and
later the Apollo programme) culminated in 1969 with the first crewed landing on the Moon – using
equipment launched by the Saturn V rocket.
Types
Vehicle configurations
Rocket vehicles are often constructed in the archetypal tall thin "rocket" shape that takes off vertically,
but there are actually many different types of rockets including:[30]
    tiny models such as balloon rockets, water rockets, skyrockets or small solid rockets that
    can be purchased at a hobby store
    missiles
    space rockets such as the enormous Saturn V used for the Apollo program
    rocket cars
    rocket bike[31]
    rocket-powered aircraft (including rocket-assisted takeoff
    of conventional aircraft – RATO)
    rocket sleds
    rocket trains
    rocket torpedoes[32][33]
    rocket-powered jet packs[34]
    rapid escape systems such as ejection seats and launch
    escape systems
    space probes                                                         Launch of Apollo 15 Saturn V
                                                                         rocket: T − 30 s through T + 40 s
Design
A rocket design can be as simple as a cardboard tube filled with black powder, but to make an efficient,
accurate rocket or missile involves overcoming a number of difficult problems. The main difficulties
include cooling the combustion chamber, pumping the fuel (in the case of a liquid fuel), and controlling
and correcting the direction of motion.[35]
Components
Rockets consist of a propellant, a place to put propellant (such as a propellant tank), and a nozzle. They
may also have one or more rocket engines, directional stabilization device(s) (such as fins, vernier
engines or engine gimbals for thrust vectoring, gyroscopes) and a structure (typically monocoque) to hold
these components together. Rockets intended for high speed atmospheric use also have an aerodynamic
fairing such as a nose cone, which usually holds the payload.[36]
As well as these components, rockets can have any number of other components, such as wings
(rocketplanes), parachutes, wheels (rocket cars), even, in a sense, a person (rocket belt). Vehicles
frequently possess navigation systems and guidance systems that typically use satellite navigation and
inertial navigation systems.
Engines
Rocket engines employ the principle of jet propulsion.[2] The rocket engines powering rockets come in a
great variety of different types; a comprehensive list can be found in the main article, Rocket engine.
Most current rockets are chemically powered rockets (usually internal combustion engines,[37] but some
employ a decomposing monopropellant) that emit a hot exhaust gas. A rocket engine can use gas
propellants, solid propellant, liquid propellant, or a hybrid mixture of both solid and liquid. Some rockets
use heat or pressure that is supplied from a source other than the chemical reaction of propellant(s), such
as steam rockets, solar thermal rockets, nuclear thermal rocket engines or simple pressurized rockets such
as water rocket or cold gas thrusters. With combustive propellants a chemical reaction is initiated between
the fuel and the oxidizer in the combustion chamber, and the resultant hot gases accelerate out of a rocket
engine nozzle (or nozzles) at the rearward-facing end of the rocket. The acceleration of these gases
through the engine exerts force ("thrust") on the combustion chamber and nozzle, propelling the vehicle
(according to Newton's Third Law). This actually happens because the
force (pressure times area) on the combustion chamber wall is unbalanced
by the nozzle opening; this is not the case in any other direction. The
shape of the nozzle also generates force by directing the exhaust gas along
the axis of the rocket.[2]
Propellant
                                       Rocket propellant is mass that is
                                       stored, usually in some form of
                                       propellant tank or casing, prior to
                                       being used as the propulsive mass
                                       that is ejected from a rocket engine
                                                                             Viking 5C rocket engine
                                       in the form of a fluid jet to produce
                                       thrust.[2] For chemical rockets
 Gas Core light bulb
                                       often the propellants are a fuel such as liquid hydrogen or
                                       kerosene burned with an oxidizer such as liquid oxygen or nitric
                                       acid to produce large volumes of very hot gas. The oxidiser is
either kept separate and mixed in the combustion chamber, or comes premixed, as with solid rockets.
Sometimes the propellant is not burned but still undergoes a chemical reaction, and can be a
'monopropellant' such as hydrazine, nitrous oxide or hydrogen peroxide that can be catalytically
decomposed to hot gas.
Alternatively, an inert propellant can be used that can be externally heated, such as in steam rocket, solar
thermal rocket or nuclear thermal rockets.[2]
For smaller, low performance rockets such as attitude control thrusters where high performance is less
necessary, a pressurised fluid is used as propellant that simply escapes the spacecraft through a propelling
nozzle.[2]
Uses
Rockets or other similar reaction devices carrying their own propellant must be used when there is no
other substance (land, water, or air) or force (gravity, magnetism, light) that a vehicle may usefully
employ for propulsion, such as in space. In these circumstances, it is necessary to carry all the propellant
to be used.
Rocket engines are also used to propel rocket sleds along a rail at
extremely high speed. The world record for this is Mach 8.5.[44]
Spaceflight
Larger rockets are normally launched from a launch pad that provides
stable support until a few seconds after ignition. Due to their high exhaust
velocity—2,500 to 4,500 m/s (9,000 to 16,200 km/h; 5,600 to
10,100 mph)—rockets are particularly useful when very high speeds are
required, such as orbital speed at approximately 7,800 m/s (28,000 km/h;
17,000 mph). Spacecraft delivered into orbital trajectories become           A Trident II missile launched
artificial satellites, which are used for many commercial purposes. Indeed,  from sea
rockets remain the only way to launch spacecraft into orbit and
beyond.[45] They are also used to rapidly accelerate spacecraft when they change orbits or de-orbit for
landing. Also, a rocket may be used to soften a hard parachute landing immediately before touchdown
(see retrorocket).
Rescue
Rockets were used to propel a line to a stricken ship so that a Breeches buoy can be used to rescue those
on board. Rockets are also used to launch emergency flares.
Some crewed rockets, notably the Saturn V[46] and Soyuz,[47] have launch escape systems. This is a
small, usually solid rocket that is capable of pulling the crewed capsule away from the main vehicle
towards safety at a moments notice. These types of systems have been operated several times, both in
                               testing and in flight, and operated correctly
                               each time.
A successful escape of a crewed capsule occurred when Soyuz T-10, on a mission to the Salyut 7 space
station, exploded on the pad.[52]
Solid rocket propelled ejection seats are used in many military aircraft to propel crew away to safety from
a vehicle when flight control is lost.[53]
According to the United States National Association of Rocketry (nar) Safety Code,[54] model rockets are
constructed of paper, wood, plastic and other lightweight materials. The code also provides guidelines for
motor use, launch site selection, launch methods, launcher placement, recovery system design and
deployment and more. Since the early 1960s, a copy of the Model Rocket Safety Code has been provided
with most model rocket kits and motors. Despite its inherent association with extremely flammable
substances and objects with a pointed tip traveling at high speeds, model rocketry historically has
proven[55][56] to be a very safe hobby and has been credited as a significant source of inspiration for
children who eventually become scientists and engineers.[57]
Hobbyists build and fly a wide variety of model rockets. Many companies produce model rocket kits and
parts but due to their inherent simplicity some hobbyists have been known to make rockets out of almost
anything. Rockets are also used in some types of consumer and professional fireworks. A water rocket is
a type of model rocket using water as its reaction mass. The pressure vessel (the engine of the rocket) is
usually a used plastic soft drink bottle. The water is forced out by a pressurized gas, typically compressed
air. It is an example of Newton's third law of motion.
The scale of amateur rocketry can range from a small rocket launched in one's own backyard to a rocket
that reached space.[58] Amateur rocketry is split into three categories according to total engine impulse:
low-power, mid-power, and high-power.
Hydrogen peroxide rockets are used to power jet packs,[59] and have been used to power cars and a rocket
car holds the all time (albeit unofficial) drag racing record.[60]
Corpulent Stump is the most powerful non-commercial rocket ever launched on an Aerotech engine in the
United Kingdom.[61][62][63]
Flight
Launches for orbital spaceflights, or into interplanetary space, are
usually from a fixed location on the ground, but would also be
possible from an aircraft or ship.
Orbital launch vehicles commonly take off vertically, and then begin to progressively lean over, usually
following a gravity turn trajectory.
Once above the majority of the atmosphere, the vehicle then angles the rocket jet, pointing it largely
horizontally but somewhat downwards, which permits the vehicle to gain and then maintain altitude
while increasing horizontal speed. As the speed grows, the vehicle will become more and more horizontal
until at orbital speed, the engine will cut off.
All current vehicles stage, that is, jettison hardware on the way to orbit. Although vehicles have been
proposed which would be able to reach orbit without staging, none have ever been constructed, and, if
powered only by rockets, the exponentially increasing fuel requirements of such a vehicle would make its
useful payload tiny or nonexistent. Most current and historical launch vehicles "expend" their jettisoned
hardware, typically by allowing it to crash into the ocean, but some have recovered and reused jettisoned
hardware, either by parachute or by propulsive landing.
When launching a spacecraft to orbit, a "dogleg" is a guided, powered turn during ascent phase that
causes a rocket's flight path to deviate from a "straight" path. A dogleg is necessary if the desired launch
azimuth, to reach a desired orbital inclination, would take the ground track over land (or over a populated
area, e.g. Russia usually does launch over land, but over unpopulated areas), or if the rocket is trying to
reach an orbital plane that does not reach the latitude of the launch site. Doglegs are undesirable due to
extra onboard fuel required, causing heavier load, and a reduction of vehicle performance.[64][65]
Noise
Rocket exhaust generates a significant amount of acoustic energy. As the supersonic exhaust collides with
the ambient air, shock waves are formed. The sound intensity from these shock waves depends on the size
of the rocket as well as the exhaust velocity. The sound intensity of large, high performance rockets could
potentially kill at close range.[66]
For crewed rockets various methods are used to reduce the sound
intensity for the passengers, and typically the placement of the
astronauts far away from the rocket engines helps significantly.
For the passengers and crew, when a vehicle goes supersonic the
sound cuts off as the sound waves are no longer able to keep up
with the vehicle.[66]                                                    Workers and media witness the
                                                                         Sound Suppression Water System
                                                                         test at Launch Pad 39A
Physics
Operation
The effect of the combustion of propellant in the rocket engine is to increase the internal energy of the
resulting gases, utilizing the stored chemical energy in the fuel. As the internal energy increases, pressure
increases, and a nozzle is used to convert this energy into a directed kinetic energy. This produces thrust
against the ambient environment to which these gases are released. The ideal direction of motion of the
exhaust is in the direction so as to cause thrust. At the top end of the combustion chamber the hot,
energetic gas fluid cannot move forward, and so, it pushes upward against the top of the rocket engine's
combustion chamber. As the combustion gases approach the exit of the combustion chamber, they
increase in speed. The effect of the convergent part of the rocket engine nozzle on the high pressure fluid
of combustion gases, is to cause the gases to accelerate to high speed. The higher the speed of the gases,
the lower the pressure of the gas (Bernoulli's principle or conservation of energy) acting on that part of
the combustion chamber. In a properly designed engine, the flow will reach Mach 1 at the throat of the
nozzle. At which point the speed of the flow increases. Beyond the throat of the nozzle, a bell shaped
expansion part of the engine allows the gases that are expanding to push against that part of the rocket
engine. Thus, the bell part of the nozzle gives additional thrust. Simply expressed, for every action there
is an equal and opposite reaction, according to Newton's third law with the result that the exiting gases
produce the reaction of a force on the rocket causing it to accelerate the rocket.[69][nb 2]
In a closed chamber, the pressures are equal in each direction and no
acceleration occurs. If an opening is provided in the bottom of the
chamber then the pressure is no longer acting on the missing section. This
opening permits the exhaust to escape. The remaining pressures give a
resultant thrust on the side opposite the opening, and these pressures are
what push the rocket along.
Drag
Drag is a force opposite to the direction of the rocket's motion relative to any air it is moving through.
This slows the speed of the vehicle and produces structural loads. The deceleration forces for fast-moving
rockets are calculated using the drag equation.
Drag can be minimised by an aerodynamic nose cone and by using a shape with a high ballistic
coefficient (the "classic" rocket shape—long and thin), and by keeping the rocket's angle of attack as low
as possible.
During a launch, as the vehicle speed increases, and the atmosphere thins, there is a point of maximum
aerodynamic drag called max Q. This determines the minimum aerodynamic strength of the vehicle, as
the rocket must avoid buckling under these forces.[75]
Net thrust
A typical rocket engine can handle a significant fraction of its own mass in propellant each second, with
the propellant leaving the nozzle at several kilometres per second. This means that the thrust-to-weight
ratio of a rocket engine, and often the entire vehicle can be very high, in extreme cases over 100. This
compares with other jet propulsion engines that can exceed 5 for some of the better[76] engines.[77]
where
Total impulse
Impulse is defined as a force acting on an object over time, which in the
absence of opposing forces (gravity and aerodynamic drag), changes the
momentum (integral of mass and velocity) of the object. As such, it is the
best performance class (payload mass and terminal velocity capability)
indicator of a rocket, rather than takeoff thrust, mass, or "power". The
total impulse of a rocket (stage) burning its propellant is:[2]: 27
                                                                                 A rocket jet shape varies
                                                                                 based on external air
                                                                                 pressure. From top to
                                                                                 bottom:
When there is fixed thrust, this is simply:
                                                                                 Underexpanded
                                                                                 Ideally expanded
The total impulse of a multi-stage rocket is the sum of the impulses of the      Overexpanded
individual stages.                                                               Grossly overexpanded
Specific impulse
As can be seen from the thrust equation, the effective
                                                                     Isp in vacuum of various rockets
speed of the exhaust controls the amount of thrust
produced from a particular quantity of fuel burnt per           Rocket        Propellants    Isp, vacuum (s)
second.                                                      Space Shuttle
                                                             liquid engines
                                                                                LOX/LH2           453[78]
An equivalent measure, the net impulse per weight unit       Space Shuttle
of propellant expelled, is called specific Impulse,     ,    solid motors
                                                                                 APCP             268[78]
and this is one of the most important figures that           Space Shuttle
                                                                               NTO/MMH            313[78]
describes a rocket's performance. It is defined such that        OMS
it is related to the effective exhaust velocity by:            Saturn V
                                                               stage 1
                                                                               LOX/RP-1           304[78]
                      [2]: 29
where:
When      is constant, the delta-v that a rocket vehicle can provide can be
calculated from the Tsiolkovsky rocket equation:[81]
where:
The required delta-v can also be calculated for a particular manoeuvre; for example the delta-v to launch
from the surface of the Earth to low Earth orbit is about 9.7 km/s, which leaves the vehicle with a
sideways speed of about 7.8 km/s at an altitude of around 200 km. In this manoeuvre about 1.9 km/s is
lost in air drag, gravity drag and gaining altitude.
Mass ratios
Almost all of a launch vehicle's mass consists of propellant.[82]
Mass ratio is, for any 'burn', the ratio between the rocket's initial
mass and its final mass.[83] Everything else being equal, a high
mass ratio is desirable for good performance, since it indicates that
the rocket is lightweight and hence performs better, for essentially
the same reasons that low weight is desirable in sports cars.
The highest mass ratios are generally achieved with liquid rockets, and these types are usually used for
orbital launch vehicles, a situation which calls for a high delta-v. Liquid propellants generally have
densities similar to water (with the notable exceptions of liquid hydrogen and liquid methane), and these
types are able to use lightweight, low pressure tanks and typically run high-performance turbopumps to
force the propellant into the combustion chamber.
Some notable mass fractions are found in the following table (some aircraft are included for comparison
purposes):
                                                                                             Mass       Mass
         Vehicle               Takeoff mass                    Final mass
                                                                                             ratio    fraction
Titan 23G first stage 117,020 kg (258,000 lb) 4,760 kg (10,500 lb) 24.6 0.959
                          448,648 kg[86]
 Saturn 1B (stage only)                             41,594 kg[86] (91,700 lb)            10.7        0.907
                          (989,100 lb)
Staging
Thus far, the required velocity (delta-v) to achieve orbit has been
unattained by any single rocket because the propellant, tankage,
structure, guidance, valves and engines and so on, take a particular
minimum percentage of take-off mass that is too great for the
propellant it carries to achieve that delta-v carrying reasonable
payloads. Since Single-stage-to-orbit has so far not been
achievable, orbital rockets always have more than one stage.
For example, the first stage of the Saturn V, carrying the weight of        Spacecraft staging involves
the upper stages, was able to achieve a mass ratio of about 10, and         dropping off unnecessary parts of
                                                                            the rocket to reduce mass
achieved a specific impulse of 263 seconds. This gives a delta-v of
around 5.9 km/s whereas around 9.4 km/s delta-v is needed to
achieve orbit with all losses allowed for.
where m is the instantaneous mass of the vehicle and          is the net force acting on the rocket (mostly
thrust, but air drag and other forces can play a part).
As the remaining propellant decreases, rocket vehicles become lighter and their acceleration tends to
increase until the propellant is exhausted. This means that much of the speed change occurs towards the
end of the burn when the vehicle is much lighter.[2] However, the thrust can be throttled to offset or vary
this if needed. Discontinuities in acceleration also occur when stages burn out, often starting at a lower
acceleration with each new stage firing.
Peak accelerations can be increased by designing the vehicle with a reduced mass, usually achieved by a
reduction in the fuel load and tankage and associated structures, but obviously this reduces range, delta-v
and burn time. Still, for some applications that rockets are used for, a high peak acceleration applied for
just a short time is highly desirable.
The minimal mass of vehicle consists of a rocket engine with minimal fuel and structure to carry it. In
that case the thrust-to-weight ratio[nb 3] of the rocket engine limits the maximum acceleration that can be
designed. It turns out that rocket engines generally have truly excellent thrust to weight ratios (137 for the
NK-33 engine;[90] some solid rockets are over 1000[2]: 442 ), and nearly all really high-g vehicles employ
or have employed rockets.
The high accelerations that rockets naturally possess means that rocket vehicles are often capable of
vertical takeoff, and in some cases, with suitable guidance and control of the engines, also vertical
landing. For these operations to be done it is necessary for a vehicle's engines to provide more than the
local gravitational acceleration.
Energy
Energy efficiency
The energy density of a typical rocket propellant is often around
one-third that of conventional hydrocarbon fuels; the bulk of the
mass is (often relatively inexpensive) oxidizer. Nevertheless, at
take-off the rocket has a great deal of energy in the fuel and
oxidizer stored within the vehicle. It is of course desirable that as
much of the energy of the propellant end up as kinetic or potential
energy of the body of the rocket as possible.
                                                                         Space Shuttle Atlantis during launch
Energy from the fuel is lost in air drag and gravity drag and is         phase
used for the rocket to gain altitude and speed. However, much of
the lost energy ends up in the exhaust.[2]: 37–38
In a chemical propulsion device, the engine efficiency is simply the ratio of the kinetic power of the
exhaust gases and the power available from the chemical reaction:[2]: 37–38
100% efficiency within the engine (engine efficiency                ) would mean that all the heat energy of
the combustion products is converted into kinetic energy of the jet. This is not possible, but the near-
adiabatic high expansion ratio nozzles that can be used with rockets come surprisingly close: when the
nozzle expands the gas, the gas is cooled and accelerated, and an energy efficiency of up to 70% can be
achieved. Most of the rest is heat energy in the exhaust that is not recovered.[2]: 37–38 The high efficiency
is a consequence of the fact that rocket combustion can be performed at very high temperatures and the
gas is finally released at much lower temperatures, and so giving good Carnot efficiency.
However, engine efficiency is not the whole story. In common with the other jet-based engines, but
particularly in rockets due to their high and typically fixed exhaust speeds, rocket vehicles are extremely
inefficient at low speeds irrespective of the engine efficiency. The problem is that at low speeds, the
exhaust carries away a huge amount of kinetic energy rearward. This phenomenon is termed propulsive
efficiency ( ).[2]: 37–38
However, as speeds rise, the resultant exhaust speed goes down, and the overall vehicle energetic
efficiency rises, reaching a peak of around 100% of the engine efficiency when the vehicle is travelling
exactly at the same speed that the exhaust is emitted. In this case the exhaust would ideally stop dead in
space behind the moving vehicle, taking away zero energy, and from conservation of energy, all the
energy would end up in the vehicle. The efficiency then drops off again at even higher speeds as the
exhaust ends up traveling forwards – trailing behind the vehicle.
From these principles it can be shown that the propulsive efficiency        for a rocket moving at speed
with an exhaust velocity is:
                         [2]: 37–38
And the overall (instantaneous) energy efficiency   is:
Since the energy ultimately comes from fuel, these considerations mean that rockets are mainly useful
when a very high speed is required, such as ICBMs or orbital launch. For example, NASA's Space
Shuttle fired its engines for around 8.5 minutes, consuming 1,000 tonnes of solid propellant (containing
16% aluminium) and an additional 2,000,000 litres of liquid propellant (106,261 kg of liquid hydrogen
fuel) to lift the 100,000 kg vehicle (including the 25,000 kg payload) to an altitude of 111 km and an
orbital velocity of 30,000 km/h. At this altitude and velocity, the vehicle had a kinetic energy of about
3 TJ and a potential energy of roughly 200 GJ. Given the initial energy of 20 TJ,[nb 4] the Space Shuttle
was about 16% energy efficient at launching the orbiter.
Thus jet engines, with a better match between speed and jet exhaust speed (such as turbofans—in spite of
their worse )—dominate for subsonic and supersonic atmospheric use, while rockets work best at
hypersonic speeds. On the other hand, rockets serve in many short-range relatively low speed military
applications where their low-speed inefficiency is outweighed by their extremely high thrust and hence
high accelerations.
Oberth effect
One subtle feature of rockets relates to energy. A rocket stage, while carrying a given load, is capable of
giving a particular delta-v. This delta-v means that the speed increases (or decreases) by a particular
amount, independent of the initial speed. However, because kinetic energy is a square law on speed, this
means that the faster the rocket is travelling before the burn the more orbital energy it gains or loses.
This fact is used in interplanetary travel. It means that the amount of delta-v to reach other planets, over
and above that to reach escape velocity can be much less if the delta-v is applied when the rocket is
travelling at high speeds, close to the Earth or other planetary surface; whereas waiting until the rocket
has slowed at altitude multiplies up the effort required to achieve the desired trajectory.
Most of the takeoff mass of a rocket is normally propellant. However propellant is seldom more than a
few times more expensive than gasoline per kilogram (as of 2009 gasoline was about $1/kg [$0.45/lb] or
less), and although substantial amounts are needed, for all but the very cheapest rockets, it turns out that
the propellant costs are usually comparatively small, although not completely negligible.[96] With liquid
oxygen costing $0.15 per kilogram ($0.068/lb) and liquid hydrogen $2.20/kg ($1.00/lb), the Space Shuttle
in 2009 had a liquid propellant expense of approximately $1.4 million for each launch that cost $450
million from other expenses (with 40% of the mass of propellants used by it being liquids in the external
fuel tank, 60% solids in the SRBs).[97][98][99]
Even though a rocket's non-propellant, dry mass is often only between 5–20% of total mass,[100]
nevertheless this cost dominates. For hardware with the performance used in orbital launch vehicles,
expenses of $2000–$10,000+ per kilogram of dry weight are common, primarily from engineering,
fabrication, and testing; raw materials amount to typically around 2% of total expense.[101][102] For most
rockets except reusable ones (shuttle engines) the engines need not function more than a few minutes,
which simplifies design.
Extreme performance requirements for rockets reaching orbit correlate with high cost, including intensive
quality control to ensure reliability despite the limited safety factors allowable for weight reasons.[102]
Components produced in small numbers if not individually machined can prevent amortization of R&D
and facility costs over mass production to the degree seen in more pedestrian manufacturing.[102]
Amongst liquid-fueled rockets, complexity can be influenced by how much hardware must be
lightweight, like pressure-fed engines can have two orders of magnitude lesser part count than pump-fed
engines but lead to more weight by needing greater tank pressure, most often used in just small
maneuvering thrusters as a consequence.[102]
To change the preceding factors for orbital launch vehicles, proposed methods have included mass-
producing simple rockets in large quantities or on large scale,[96] or developing reusable rockets meant to
fly very frequently to amortize their up-front expense over many payloads, or reducing rocket
performance requirements by constructing a non-rocket spacelaunch system for part of the velocity to
orbit (or all of it but with most methods involving some rocket use).
The costs of support equipment, range costs and launch pads generally scale up with the size of the
rocket, but vary less with launch rate, and so may be considered to be approximately a fixed cost.[96]
Rockets in applications other than launch to orbit (such as military rockets and rocket-assisted take off),
commonly not needing comparable performance and sometimes mass-produced, are often relatively
inexpensive.
See also
Aviation portal
Rocketry portal
Spaceflight portal
Lists
    Lists of rockets
    Timeline of rocket and missile technology
General rocketry
   Aircraft – Vehicle or machine that is able to fly by gaining support from the air
   Equivalence principle – Hypothesis that inertial and gravitational masses are equivalent
   Launch Pad (card game) – strategy card game
   Rocket Festival – Traditional festival of Laos and Thailand
   Rocket mail – Mail delivery by rockets or missiles
Notes
 1. English rocket, first attested in 1566 (OED), adopted from the Italian term, given due to the
    similarity in shape to the bobbin or spool used to hold the thread from a spinning wheel. The
    modern Italian term is razzo.
 2. "If you have ever seen a big fire hose spraying water, you may have noticed that it takes a
    lot of strength to hold the hose (sometimes you will see two or three firefighters holding the
    hose). The hose is acting like a rocket engine. The hose is throwing water in one direction,
    and the firefighters are using their strength and weight to counteract the reaction. If they
    were to let go of the hose, it would thrash around with tremendous force. If the firefighters
    were all standing on skateboards, the hose would propel them backward at great speed!"[70]
 3. "thrust-to-weight ratio F/W g is a dimensionless parameter that is identical to the
    acceleration of the rocket propulsion system (expressed in multiples of g 0) ... in a gravity-
    free vacuum"[2]: 442
 4. The energy density is 31MJ per kg for aluminum and 143 MJ/kg for liquid hydrogen, this
    means that the vehicle consumed around 5 TJ of solid propellant and 15 TJ of hydrogen
    fuel.
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