Definitions

# Rocket

[rok-it]

A rocket or rocket vehicle is a missile, aircraft or other vehicle which obtains thrust by the reaction of the rocket to the ejection of fast moving fluid from a rocket engine. Chemical rockets work by the action of hot gas produced by the combustion of the propellant against the inside of combustion chambers and expansion nozzles. This generates forces that accelerate the gas to extremely high speed and exert a large thrust on the rocket (since every action has an equal and opposite reaction).

The history of rockets goes back to at least the 13th century. By the 20th century, they have enabled human spaceflight to the Moon. In the 21st century, they have made commercial space tourism possible.

Rockets are used for fireworks and weaponry, as launch vehicles for artificial satellites, human spaceflight and exploration of other planets. While inefficient for low speed use, they are, compared to other propulsion systems, very lightweight and powerful, capable of attaining extremely high speeds with reasonable efficiency.

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 minimize the risks.

Larger rockets are normally launched from a launch pad which serves as stable support until a few seconds after ignition.

## History of rockets

### In antiquity

The availability of black powder (gunpowder) to propel projectiles was a precursor to the development of the first solid rocket. Ninth Century Chinese Taoist alchemists discovered black powder while searching for the Elixir of life; this accidental discovery led to experiments in the form of weapons such as bombs, cannon, incendiary fire arrows and rocket-propelled fire arrows.

Exactly when the first flights of rockets occurred is contested. Some say that the first recorded use of a rocket in battle was by the Chinese in 1232 against the Mongol hordes. There were reports of fire arrows and 'iron pots' that could be heard for 5 leagues (15 miles) when they exploded upon impact, causing devastation for a radius of 2,000 feet, apparently due to shrapnel. The lowering of the iron pots may have been a way for a besieged army to blow up invaders. The fire arrows were either arrows with explosives attached, or arrows propelled by gunpowder, such as the Korean Hwacha.

Less controversially, one of the earliest devices recorded that used internal-combustion rocket propulsion was the 'ground-rat,' a type of firework, recorded in 1264 as having frightened the Empress-Mother Kung Sheng at a feast held in her honor by her son the Emperor Lizong.

Subsequently, one of the earliest texts to mention the use of rockets was the Huolongjing, written by the Chinese artillery officer Jiao Yu in the mid-14th century. This text also mentioned the use of the first known multistage rocket, the 'fire-dragon issuing from the water' (huo long chu shui), used mostly by the Chinese navy. Frank H. Winter proposed in The Proceedings of the Twentieth and Twenty-First History Symposia of the International Academy of Astronautics that southern China and the Laotian community rocket festivals might have been key in the subsequent spread of rocketry in the Orient.

Rocket technology first became known to Europeans following their use by the Mongols Genghis Khan and Ögedei Khan when they conquered parts of Russia, Eastern, and Central Europe. The Mongolians had acquired the Chinese technology by conquest of the northern part of China and also by the subsequent employment of Chinese rocketry experts as mercenaries for the Mongol military. Reports of the Battle of Sejo in the year 1241 describe the use of rocket-like weapons by the Mongols against the Magyars. Rocket technology also spread to Korea, with the 15th century wheeled hwacha that would launch singijeon rockets. These first Korean rockets had an amazingly long range at the time, and were designed and built by Byun Eee-Joong. They were just like arrows but had small explosives attached to the back, and were fired in swarms.

Additionally, the spread of rockets into Europe was also influenced by the Ottomans at the siege of Constantinople in 1453, although it is very likely that the Ottomans themselves were influenced by the Mongol invasions of the previous few centuries. In their history of rockets published on the Internet, NASA says "Rockets appear in Arab literature in 1258 A.D., describing Mongol invaders' use of them on February 15 to capture the city of Baghdad. Quick to learn, the Arabs adopted the rocket into their own arms inventory and, during the Seventh Crusade, used them against the French Army of King Louis IX in 1268."

Between 1270 and 1280, Hasan al-Rammah wrote al-furusiyyah wa al-manasib al-harbiyya (The Book of Military Horsemanship and Ingenious War Devices), which included 107 gunpowder recipes, 22 of which are for rockets; if one takes the median of 17 of these 22 compositions for rockets (75% nitrates, 9.06% sulphur and 15.94% carbon), it is almost identical with the reported ideal recipe (75% potassium nitrate, 10% sulphur, and 15% carbon). According to Ahmad Y Hassan, al-Rammah's recipes were more explosive than rockets used in China at the time. He also invented a torpedo running on water with a rocket system filled with explosive materials.

The name Rocket comes from the Italian Rocchetta (i.e. little fuse), a name of a small firecracker created by the Italian artificer Muratori in 1379.

Between 1529 and 1556 Conrad Haas wrote a book that described the concept of multi-stage rockets.

"Artis Magnae Artilleriae pars prima" ("Great Art of Artillery, the First Part", also known as "The Complete Art of Artillery"), first printed in Amsterdam in 1650, was translated to French in 1651, German in 1676, English and Dutch in 1729 and Polish in 1963. For over two centuries, this work of Polish-Lithuanian Commonwealth nobleman Kazimierz Siemienowicz was used in Europe as a basic artillery manual. The book provided the standard designs for creating rockets, fireballs, and other pyrotechnic devices. It contained a large chapter on caliber, construction, production and properties of rockets (for both military and civil purposes), including multi-stage rockets, batteries of rockets, and rockets with delta wing stabilizers (instead of the common guiding rods).

In 1792, iron-cased rockets were successfully used militarily by Tipu Sultan, Ruler of the Kingdom of Mysore in India against the larger British East India Company forces during the Anglo-Mysore Wars. The British then took an active interest in the technology and developed it further during the 19th century. The major figure in the field at this time was William Congreve. From there, the use of military rockets spread throughout Europe. At the Battle of Baltimore in 1814, the rockets fired on Fort McHenry by the rocket vessel HMS Erebus were the source of the rockets' red glare described by Francis Scott Key in The Star-Spangled Banner. Rockets were also used in the Battle of Waterloo.

### Accuracy of early rockets

Early rockets were very inaccurate. Without the use of spinning or any gimballing of the thrust, they had a strong tendency to veer sharply off course. The early British Congreve rockets reduced this somewhat by attaching a long stick to the end of a rocket (similar to modern bottle rockets) to make it harder for the rocket to change course. The largest of the Congreve rockets was the 32-pound (14.5 kg) Carcass, which had a 15-foot (4.6 m) stick. Originally, sticks were mounted on the side, but this was later changed to mounting in the center of the rocket, reducing drag and enabling the rocket to be more accurately fired from a segment of pipe.

The British were greatly impressed by the Mysorean Rocket artillery made from iron tubes used by the armies of Tipu Sultan and his father, Haidar Ali. Tipu Sultan championed the use of mass attacks with rocket brigades in the army. The effect of these weapons on the British during the Second, Third and Fourth Mysore Wars was sufficiently impressive to inspire William Congreve to develop his own rocket designs. Several Mysore rockets were sent to England, and after thoroughly examining the Indian specimens, from 1801, William Congreve, son of the Comptroller of the Royal Arsenal, Woolwich, London, set on a vigorous research and development programme at the Arsenal's laboratory. Congreve prepared a new propellant mixture, and developed a rocket motor with a strong iron tube with conical nose, weighing about 32 pounds (14.5 kilograms). The Royal Arsenal's first demonstration of solid fuel rockets was in 1805. The rockets were effectively used during the Napoleonic Wars and the War of 1812. Congreve published three books on rocketry.

In 1815, Alexander Dmitrievich Zasyadko began his work on creating military gunpowder rockets. He constructed rocket-launching platforms, which allowed to fire in salvos (6 rockets at a time), and gun-laying devices. Zasyadko elaborated a tactic for military use of rocket weaponry. In 1820, Zasyadko was appointed head of the Petersburg Armory, Okhtensky Powder Factory, pyrotechnic laboratory and the first Highest Artillery School in Russia. He organized rocket production in a special rocket workshop and created the first rocket sub-unit in the Russian army.

The accuracy problem was mostly solved in 1844 when William Hale modified the rocket design so that thrust was slightly vectored, causing the rocket to spin along its axis of travel like a bullet. The Hale rocket removed the need for a rocket stick, travelled further due to reduced air resistance, and was far more accurate.

### Early manned rocketry

According to legend, a manned rocket sled with 47 gunpowder-filled rockets was attempted in China by Wan Hu in the 16th Century. The alleged flight is said to have been interrupted by an explosion at the start, and the pilot did not seem to have survived (he was never found). There are no known Chinese sources for this event, and the earliest known account is an unsourced reference in a book by an American, Herbert S. Zim in 1945.

In Ottoman Turkey in 1633, Lagari Hasan Çelebi took off with what was described as a cone-shaped rocket, glided with wings through Bosporus from Topkap Palace, and made a successful landing, winning him a position in the Ottoman army. The flight was accomplished as a part of celebrations performed for the birth of Ottoman Emperor Murat IV's daughter and was rewarded by the sultan. The device was composed of a large winged cage with a conical top with 7 rockets filled with 70 kg of gunpowder. The flight was estimated to have lasted about 200 seconds and the maximum height reached around 300 metres.

### Theories of interplanetary rocketry

In 1903, high school mathematics teacher Konstantin Tsiolkovsky (1857–1935) published Исследование мировых пространств реактивными приборами (The Exploration of Cosmic Space by Means of Reaction Devices), the first serious scientific work on space travel. The Tsiolkovsky rocket equation—the principle that governs rocket propulsion—is named in his honor (although it had been discovered previously). He also advocated the use of liquid hydrogen and oxygen as fuel, calculating their maximum exhaust velocity. His work was essentially unknown outside the Soviet Union, but inside the country it inspired further research, experimentation and the formation of the Society for Studies of Interplanetary Travel in 1924.

In 1912, Robert Esnault-Pelterie published a lecture on rocket theory and interplanetary travel. He independently derived Tsiolkovsky's rocket equation, did basic calculations about the energy required to make round trips to the Moon and planets, and he proposed the use of atomic power (i.e. Radium) to power a jet drive.

Robert Goddard began a serious analysis of rockets in 1912, concluding that conventional solid-fuel rockets needed to be improved in three ways. First, fuel should be burned in a small combustion chamber, instead of building the entire propellant container to withstand the high pressures. Second, rockets could be arranged in stages. And third, the exhaust speed could be greatly increased to beyond the speed of sound by using a De Laval nozzle. He patented these concepts in 1914.

In 1920, Goddard published these ideas and experimental results in A Method of Reaching Extreme Altitudes. The work included remarks about sending a rocket to the Moon, which attracted worldwide attention and was both praised and ridiculed. A New York Times editorial suggested that Professor Goddard: "does not know of the relation of action to reaction, and the need to have something better than a vacuum against which to react--to say that would be absurd" but that "there are such things as intentional mistakes or oversights."

Goddard's historical impact was diminished by the fact that he worked in secret. This was prompted in part by his bad experience with the press and in part by his belief that his ideas were being plagiarized by foreign scientists.

In 1923, Hermann Oberth (1894–1989) published Die Rakete zu den Planetenräumen ("The Rocket into Planetary Space"), a version of his doctoral thesis, after the University of Munich rejected it.

In 1924, Tsiolkovsky also wrote about multi-stage rockets, in 'Cosmic Rocket Trains'

### Modern rocketry

#### Pre-World War II

Modern rockets were born when Goddard attached a supersonic (de Laval) nozzle to a liquid fuelled rocket engine's combustion chamber. These nozzles turn the hot gas from the combustion chamber into a cooler, hypersonic, highly directed jet of gas, more than doubling the thrust and raising the engine efficiency from 2% to 64%. Early rockets had been grossly inefficient because of the thermal energy that was wasted in the exhaust gases. In 1926, Robert Goddard launched the world's first liquid-fueled rocket in Auburn, Massachusetts.

During the 1920s, a number of rocket research organizations appeared in the United States, Austria, Britain, Czechoslovakia, France, Italy, Germany, and Russia. In the mid-1920s, German scientists had begun experimenting with rockets which used liquid propellants capable of reaching relatively high altitudes and distances. 1927 the German car manufacturer Opel began to research with rockets together with Mark Valier and the rocket builder Friedrich Wilhelm Sander. In 1928, Fritz von Opel drove with a rocket car, the Opel RAK1 on the Opel raceway in Rüsselsheim, Germany. In 1929 von Opel started at the Frankfurt-Rebstock airport with the Opel-Sander RAK 1-airplane. This was maybe the first flight with a manned rocket-aircraft. In 1927 and also in Germany, a team of amateur rocket engineers had formed the Verein für Raumschiffahrt (German Rocket Society, or VfR), and in 1931 launched a liquid propellant rocket (using oxygen and gasoline).

From 1931 to 1937, the most extensive scientific work on rocket engine design occurred in Leningrad, at the Gas Dynamics Laboratory. Well-funded and staffed, over 100 experimental engines were built under the direction of Valentin Glushko. The work included regenerative cooling, hypergolic propellant ignition, and fuel injector designs that included swirling and bi-propellant mixing injectors. However, the work was curtailed by Glushko's arrest during Stalinist purges in 1938. Similar work was also done by the Austrian professor Eugen Sänger who worked on rocket powered spaceplanes such as Silbervogel (sometimes called the 'antipodal' bomber.)

On November 12, 1932 at a farm in Stockton NJ, the American Interplanetary Society's attempt to static fire their first rocket (based on German Rocket Society designs) fails in a fire.

In 1932, the Reichswehr (which in 1935 became the Wehrmacht) began to take an interest in rocketry. Artillery restrictions imposed by the Treaty of Versailles limited Germany's access to long distance weaponry. Seeing the possibility of using rockets as long-range artillery fire, the Wehrmacht initially funded the VfR team, but seeing that their focus was strictly scientific, created its own research team. At the behest of military leaders, Wernher von Braun, at the time a young aspiring rocket scientist, joined the military (followed by two former VfR members) and developed long-range weapons for use in World War II by Nazi Germany, notably the A-series of rockets, which led to the infamous V-2 rocket (initially called A4).

#### World War II

In 1943, production of the V-2 rocket began. The V-2 had an operational range of 300 km (185 miles) and carried a 1000 kg (2204 lb) warhead, with an amatol explosive charge. Highest point of altitude of its flight trajectory is 90 km. The vehicle was only different in details from most modern rockets, with turbopumps, inertial guidance and many other features. Thousands were fired at various Allied nations, mainly England, as well as Belgium and France. While they could not be intercepted, their guidance system design and single conventional warhead meant that the V-2 was insufficiently accurate against military targets. The later versions however, were more accurate, sometimes within metres, and could be devastating. 2,754 people in England were killed, and 6,523 were wounded before the launch campaign was terminated. While the V-2 did not significantly affect the course of the war, it provided a lethal demonstration of the potential for guided rockets as weapons.

Under Projekt Amerika Nazi Germany also tried to develop and use the first submarine-launched ballistic missile (SLBMs) and the first intercontinental ballistic missiles (ICBMs) A9/A10 Amerika-Raketen to bomb New York and other American cities. The tests of SLBM-variants of the A4 rocket was achieved with U-boat submarines towing launch platforms. The second stage of the A9/A10 rocket was tested a few times in January, February and March 1945.

In parallel with the guided missile programme in Nazi Germany, rockets were also being used for aircraft, either for rapid horizontal take-off (JATO) or for powering the aircraft (Me 163,etc) and for vertical take-off (Bachem Ba 349 "Natter").

#### Post World War II

At the end of World War II, competing Russian, British, and U.S. military and scientific crews raced to capture technology and trained personnel from the German rocket program at Peenemünde. Russia and Britain had some success, but the United States benefited the most. The US captured a large number of German rocket scientists (many of whom were members of the Nazi Party, including von Braun) and brought them to the United States as part of Operation Paperclip. In America, the same rockets that were designed to rain down on Britain were used instead by scientists as research vehicles for developing the new technology further. The V-2 evolved into the American Redstone rocket, used in the early space program.

After the war, rockets were used to study high-altitude conditions, by radio telemetry of temperature and pressure of the atmosphere, detection of cosmic rays, and further research; notably for the Bell X-1 to break the sound barrier. This continued in the U.S. under von Braun and the others, who were destined to become part of the U.S. scientific complex.

Independently, research continued in the Soviet Union under the leadership of the chief designer Sergei Korolev. With the help of German technicians, the V-2 was duplicated and improved as the R-1, R-2 and R-5 missiles. German designs were abandoned in the late 1940s, and the foreign workers were sent home. A new series of engines built by Glushko and based on inventions of Aleksei Mihailovich Isaev formed the basis of the first ICBM, the R-7. The R-7 launched the first satellite, and Yuri Gagarin, the first man into space and the first lunar and planetary probes, and is still in use today. These events attracted the attention of top politicians, along with more money for further research.

Rockets became extremely important militarily in the form of modern intercontinental ballistic missiles (ICBMs) when it was realised that nuclear weapons carried on a rocket vehicle were essentially not defensible against once launched, and ICBM/Launch vehicles such as the R-7, Atlas and Titan became the delivery platform of choice for these weapons.

Fueled partly by the Cold War, the 1960s became the decade of rapid development of rocket technology particularly in the Soviet Union (Vostok, Soyuz, Proton) and in the United States (e.g. the X-15 and X-20 Dyna-Soar aircraft). There was also significant research in other countries, such as Britain, Japan, Australia, etc. and their growing use for Space exploration, with pictures returned from the far side of the Moon and unmanned flights for Mars exploration.

In America the manned programmes, Project Mercury, Project Gemini and later the Apollo programme culminated in 1969 with the first manned landing on the moon via the Saturn V, causing the New York Times to retract their earlier editorial implying that spaceflight couldn't work:

"Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th century and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere. The Times regrets the error."

In the 1970s America made further lunar landings, before abandoning the Apollo launch vehicle. The replacement vehicle, the partially reusable 'Space Shuttle' was intended to be cheaper, but this large reduction in costs was largely not achieved. Meanwhile in 1973, the expendable Ariane programme was begun, a launcher that by the year 2000 would capture much of the geosat market.

#### Current day

Rockets remain a popular military weapon. The use of large battlefield rockets of the V-2 type has given way to guided missiles. However rockets are often used by helicopters and light aircraft for ground attack, being more powerful than machine guns, but without the recoil of a heavy cannon. In the 1950s there was a brief vogue for air-to-air rockets, ending with the AIR-2 'Genie' nuclear rocket, but by the early 1960s these had largely been abandoned in favor of air-to-air missiles.

Economically, rocketry is the enabler of all space technologies particularly satellites, many of which impact people's everyday lives in almost countless ways, satellite navigation, communications satellites and even things as simple as weather satellites.

Scientifically, rocketry has opened a window on our universe, allowing the launch of space probes to explore our solar system, satellites to view the Earth itself, and space-based telescopes to obtain a clearer view of the rest of the universe.

However, in the minds of much of the public, the most important use of rockets is perhaps manned spaceflight. Vehicles such as the Space Shuttle for scientific research, the Soyuz for orbital tourism and SpaceShipOne for suborbital tourism may show a trend towards greater commercialisation of manned rocketry, away from government funding, and towards more widespread access to space.

## Types

There are many different types of rockets, and a comprehensive list of the basic engine types can be found in rocket engine — the vehicles themselves range in size from tiny models such as water rockets or small solid rockets that can be purchased at a hobby store, to the enormous Saturn V used for the Apollo program, and in many different vehicle types such as rocket cars and rocket planes.

Most current rockets are chemically powered rockets (usually internal combustion engines, but some employ a decomposing monopropellant) that emit a hot exhaust gas. A chemical rocket engine can use gas propellant, solid propellant, liquid propellant, or a hybrid mixture of both solid and liquid. 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 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 (in accordance with Newton's Third Law). See rocket engine for details.

Rockets in which the heat is supplied from a source other than a propellant, such as solar thermal rockets, can be classed as external combustion engines. Other examples of external combustion rocket engines include most designs for nuclear powered rocket engines. Use of hydrogen as the propellant for such engines gives very high exhaust velocities (around 6-10 km/s).

Steam rockets, are another example of non chemical rockets. These rockets release very hot water through a nozzle where, due to the lower pressure there, it instantly flashes to high velocity steam, propelling the rocket. The efficiency of steam as a rocket propellant is relatively low, but it is simple and reasonably safe, and the propellant is cheap and widely available. Most steam rockets have been used for propelling land-based vehicles but it formed the basis of Evel Knievel's skycycle, and a small steam rocket was tested in 2004 on board the UK-DMC satellite, as an alternative, with higher performance, to cold gas thrusters for attitude jets. There are even proposals to use steam rockets for interplanetary transport using either nuclear or solar heating as the power source to vaporize water collected from around the solar system, at system costs that are claimed to be orders of magnitude lower than electrolysis-based hydrogen systems.

## 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.

However, they are also useful in other situations:

### Weaponry

In many military weapons, rockets are used to propel payloads to their targets. A rocket and its payload together are generally referred to as a missile, especially when the weapon has a guidance system.

### Science

Sounding rockets are commonly used to carry instruments that take readings from to above the surface of the Earth, the altitudes between those reachable by weather balloons and satellites.

### Spaceflight

Due to their high exhaust velocity (Mach ~10+), rockets are particularly useful when very high speeds are required, such as orbital speed (Mach 25+). Spacecraft delivered into orbital trajectories become artificial satellites which are used for many commercial purposes. Indeed, rockets remain the only way to launch spacecraft into orbit and beyond. 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 Soyuz spacecraft).

### Hobby, sport and entertainment

Hobbyists build and fly Model rockets of various types and rockets are used to launch both commercially available fireworks and professional fireworks displays.

Hydrogen peroxide rockets are used to power jet packs, and have been used to power cars and a rocket car holds the all time drag racing record.

## Components of a rocket

Rockets at minimum have a place to put propellant (such as a propellant tank), one or more rocket engines and nozzle, directional stabilization device(s) (such as fins, attitude jets or engine gimbals) 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.

As well as these components, rockets can have any number of other components, such as wings (rocketplanes), wheels (rocket cars), even, in a sense, a person (rocket belt).

## Noise

For all but the very smallest sizes, rocket exhaust compared to other engines is generally very noisy. As the hypersonic exhaust mixes with the ambient air, shock waves are formed. The sound intensity from these shock waves depends on the size of the rocket. The sound intensity of large rockets could potentially kill at close range.

The Space Shuttle generates over 200 dB(A) of noise around its base. A Saturn V launch was detectable on seismometers a considerable distance from the launch site.

Generally speaking, noise is most intense when a rocket is close to the ground, since the noise from the engines radiates up away from the plume, as well as reflecting off the ground. This noise can be reduced somewhat by flame trenches with roofs, by water injection around the plume and by deflecting the plume at an angle.

For manned rockets various methods are used to reduce the sound intensity for the passengers as much as possible, 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.

## Physics

### Operation

In all rockets, the exhaust is formed from propellants carried within the rocket prior to use. Rocket thrust is due to the rocket engine, which propels the rocket forwards by exhausting the propellant rearwards at extreme high speed.

In a closed chamber, the pressures are equal in each direction and no acceleration occurs. If an opening is provided at the bottom of the chamber then the pressure is no longer acting on that side. The remaining pressures give a resultant thrust on the side opposite the opening; as well as permitting exhaust to escape. Using a nozzle increases the forces further, in fact multiplies the thrust as a function of the area ratio of the nozzle, since the pressures also act on the nozzle. As a side effect the pressures act on the exhaust in the opposite direction and accelerate this to very high speeds (in accordance with Newton's Third Law).

If propellant gas is continuously added to the chamber then this disequilibrium of pressures can be maintained for as long as propellant remains.

It turns out (from conservation of momentum) that the speed of the exhaust of a rocket determines how much momentum increase is created for a given amount of propellant, and this is termed a rocket's specific impulse. Because a rocket, propellant and exhaust in flight, away from any external perturbations, may be usefully considered as a closed system, then the total momentum is constant at all times. Therefore the faster the net speed of the exhaust is in one direction the greater the speed of the rocket itself in the opposite direction can become, and even more so because the rocket mass is typically far lower than the final total exhaust mass.

As the remaining propellant decreases, the vehicle's becomes lighter and acceleration tends to increase until eventually it runs out of propellant, and this means that much of the speed change occurs towards the end of the burn when the vehicle is much lighter.

### Forces on a rocket in flight

The general study of the forces on a rocket or other spacecraft is called astrodynamics.

Flying rockets are primarily affected by the following:

In addition, the inertia/centrifugal pseudo-force can be significant due to the path of the rocket around the center of a celestial body; when high enough speeds in the right direction and altitude are achieved a stable orbit or escape velocity is obtained.

During a rocket launch, there is a point of maximum aerodynamic drag called Max Q. This determines the minimum aerodynamic strength of the vehicle.

These forces, with a stabilizing tail present will, unless deliberate control efforts are made, to naturally cause the vehicle to follow a trajectory termed a gravity turn, and this trajectory is often used at least during the initial part of a launch. (This is true even if the rocket engine is mounted at the nose). This means that the vehicle can maintain low or even zero angle of attack. This minimizes transverse stress on the launch vehicle; allowing for a weaker, and thus lighter, launch vehicle.

### Net thrust

The thrust of a rocket is often deliberately varied over a flight, to provide a way to control the airspeed of the vehicle so as to minimize aerodynamic losses but also so as to limit g-forces that would otherwise occur during the flight as the propellant mass decreases, which could damage the vehicle, crew or payload.

Below is an approximate equation for calculating the gross thrust of a rocket:

$F_n = dot\left\{m\right\};V_\left\{e\right\} + A_\left\{e\right\}\left(P_\left\{e\right\} - P_\left\{amb\right\}\right)$

where:

$dot\left\{m\right\} =,$propellant flow (kg/s or lb/s)

$V_\left\{e\right\} =,$jet velocity at nozzle exit plane (m/s or s)

$A_\left\{e\right\} =,$flow area at nozzle exit plane (m2 or ft2)

$P_\left\{e\right\} =,$static pressure at nozzle exit plane (Pa or lb/ft2)

$P_\left\{amb\right\} =,$ambient (or atmospheric) pressure (Pa or lb/ft2)

Since, unlike a jet engine, a conventional rocket motor lacks an air intake, there is no 'ram drag' to deduct from the gross thrust. Consequently the net thrust of a rocket motor is equal to the gross thrust.

The $dot\left\{m\right\}V_\left\{e\right\},$ term represents the momentum thrust, which remains constant at a given throttle setting, whereas the $A_\left\{e\right\}\left(P_\left\{e\right\} - P_\left\{amb\right\}\right),$ term represents the pressure thrust term. At full throttle, the net thrust of a rocket motor improves slightly with increasing altitude, because the reducing atmospheric pressure increases the pressure thrust term.

### Specific impulse

As can be seen from the thrust equation the effective speed of the exhaust, Ve, has a large impact on the amount of thrust produced from a particular quantity of fuel burnt per second. The net thrust-seconds (impulse) per unit of propellant is called Specific Impulse (Isp) or effective exhaust velocity and this is one of the most important figures that describes a rocket's performance.

Vacuum Isp

Due to the specific impulse varying with pressure, a quantity that is easy to compare and calculate with is useful. Because rockets choke at the throat, and because the supersonic exhaust prevents external pressure influences travelling upstream, it turns out that the pressure at the exit is ideally exactly proportional to the propellant flow $dot\left\{m\right\}$, provided the mixture ratios and combustion efficiencies are maintained. It is thus quite usual to rearrange the above equation slightly:

$Fvac = C_f dot\left\{m\right\} c^*$

and so define the vacuum Isp (Pamb = 0) to be:

$V_\left\{evac\right\} = C_f c^*$

Where:

$c^* =,$ the speed of sound constant at the throat
$C_f =,$ the thrust coefficient constant of the nozzle (typically between 0.8 and 1.9)

And hence (from the 'net thrust' equation above):

$F_n = dot\left\{m\right\} V_\left\{evac\right\} - A_\left\{e\right\} P_\left\{amb\right\}$

By definition, the effective exhaust velocity is:

$F_n = dot\left\{m\right\} V_\left\{eff\right\}$

So within the atmosphere:

$V_\left\{eff\right\} = V_\left\{evac\right\} \left(1 - frac\left\{A_\left\{e\right\} P_\left\{amb\right\}\right\} \left\{dot\left\{m\right\}\right\}\right)$

### Delta-v (rocket equation)

The delta-v capacity of a rocket is the theoretical total change in velocity that a rocket can achieve without any external interference (without air drag or gravity or other forces).

The delta-v that a rocket vehicle can provide can be calculated from the Tsiolkovsky rocket equation:

$Delta v = v_e ln frac \left\{m_0\right\} \left\{m_1\right\}$

where:

$m_0$ is the initial total mass, including propellant, in kg (or lb)
$m_1$ is the final total mass in kg (or lb)
$v_e$ is the effective exhaust velocity in m/s or (ft/s) or $V_e = I_\left\{sp\right\} cdot g_0$
$Delta v$ is the delta-v in m/s (or ft/s)

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

Persons not familiar with spaceflight rarely realize that almost all of a rocket's launch mass consists of propellant. Mass ratio is the ratio between the initial fuelled mass and the mass after the 'burn'. 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.

Rockets as a group have the highest thrust-to-weight ratio of any type of engine; and this helps vehicles achieve high mass ratios, which improves the performance of flights. The higher this ratio, the less engine mass is needed to be carried and permits the carrying of even more propellant, this enormously improves performance.

Achievable mass ratios are highly dependent on many factors such as propellant type, the design of engine the vehicle uses, structural safety margins and construction techniques.

The best mass ratios are generally achieved with liquid rockets. 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 low pressure tanks and commonly run turbopumps to force the propellant into the combustion chamber. Low pressure tanks permit much thinner, lighter walls to be used.

Some notable mass fractions are found in the following table (some aircraft are included for comparison purposes):

### Staging

Often, the required velocity (delta-v) for a mission is unattainable 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.

The mass ratios that can be achieved with a single set of fixed rocket engines and tankage varies depends on acceleration required, construction materials, tank layout, engine type and propellants used, but for example the first stage of the Saturn V, carrying the weight of the upper stages, was able to achieve a mass ratio of about 10, and 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.

This problem is frequently solved by staging — the rocket sheds excess weight (usually empty tankage and associated engines) during launch to reduce its weight and effectively increase its mass ratio. Staging is either serial where the rockets light after the previous stage has fallen away, or parallel, where rockets are burning together and then detach when they burn out.

Typically, the acceleration of a rocket increases with time (if the thrust stays the same) as the weight of the rocket decreases as propellant is burned. Discontinuities in acceleration will occur when stages burn out, often starting at a lower acceleration with each new stage firing.

### Energy efficiency

Rocket launch vehicles take-off with a great deal of flames, noise and drama, and it might seem obvious that they are grievously inefficient. However while they are far from perfect, their energy efficiency is not as bad as might be supposed.

The energy density of rocket propellant is around 1/3 that of conventional hydrocarbon fuels; the bulk of the mass is in the form of (often relatively inexpensive) oxidiser. Nevertheless, at take-off the rocket has a great deal of energy in the form of fuel and oxidiser stored within the vehicle, and it is of course desirable that as much of the energy stored in the propellant ends up as kinetic or potential energy of the body of the rocket as possible.

Energy from the fuel is lost in air drag and gravity drag and is used to gain altitude. However, much of the lost energy ends up in the exhaust.

100% efficiency within the engine ($eta_c$) would mean that all of the heat energy of the combustion products is converted into kinetic energy of the jet. This is not possible, but the 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. This compares very well with other engine designs. 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 many 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 ($eta_p$).

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 travelling forwards behind the vehicle.

From these principles it can be shown that the propulsive efficiency $eta_p$ for a rocket moving at speed $u$ with an exhaust velocity $c$ is:

$eta_p= frac \left\{2 frac \left\{u\right\} \left\{c\right\}\right\} \left\{1 + \left(frac \left\{u\right\} \left\{c\right\} \right)^2 \right\}$

And the overall energy efficiency $eta$ is:

$eta= eta_p eta_c$

Since the energy ultimately comes from fuel, these joint considerations mean that rockets are mainly useful when a very high speed is required, such as ICBMs or orbital launch, and they are rarely if ever used for general aviation. For example, from the equation, with an $eta_c$ of 0.7, a rocket flying at Mach 0.85 (which most aircraft cruise at) with an exhaust velocity of Mach 10, would have a predicted overall energy efficiency of 5.9%, whereas a conventional, modern, air breathing jet engine achieves closer to 30% or more efficiency. Thus a rocket would need about 5x more energy; and allowing for the ~3x lower specific energy of rocket propellant than conventional air fuel, roughly 15x more mass of propellant would need to be carried for the same journey.

Thus jet engines which have a better match between speed and jet exhaust speed such as turbofans (in spite of their worse $eta_c$) dominate for subsonic and supersonic atmospheric use while rockets work best at hypersonic speeds. On the other hand rockets do also see many short-range relatively low speed military applications where their low-speed inefficiency is outweighed by their extremely high thrust and hence high accelerations.

## Safety, reliability and accidents

Rockets are not inherently highly dangerous. In military usage quite adequate reliability is obtained.

Because of the enormous chemical energy in all useful rocket propellants (greater energy per weight than explosives, but lower than gasoline), accidents can and have happened. The number of people injured or killed is usually small because of the great care typically taken, but this record is not perfect.

Lists

General rocketry

Recreational rocketry

Recreational pyrotechnic rocketry

• Bottle rocket - small firework type rocket often launched from bottles
• Skyrocket - fireworks that typically explode at apogee

Weaponry

Rockets for Research

Misc

• Rocket mail - an ill-fated attempt to commercialise rocketry