Multistage rocket

thumb|Each stage of the [[Black Brant (rocket)|Black Brant 12 sounding rocket has its own set of tail fins.]]

thumb|The second stage of a [[Minuteman III rocket]]

A multistage rocket or step rocket is a launch vehicle that uses two or more rocket stages, each of which contains its own engines and propellant. A tandem or serial stage is mounted on top of another stage; a parallel stage is attached alongside another stage. The result is effectively two or more rockets stacked on top of or attached next to each other. Two-stage rockets are quite common, but rockets with as many as five separate stages have been successfully launched.

By jettisoning stages when they run out of propellant, the mass of the remaining rocket is decreased. Each successive stage can also be optimized for its specific operating conditions, such as decreased atmospheric pressure at higher altitudes. This staging allows the thrust of the remaining stages to more easily accelerate the rocket to its final velocity and height.

In serial or tandem staging schemes, the first stage is at the bottom and is usually the largest, the second stage and subsequent upper stages are above it, usually decreasing in size. In parallel staging schemes solid or liquid rocket boosters are used to assist with launch. These are sometimes referred to as "stage 0". In the typical case, the first-stage and booster engines fire to propel the entire rocket upwards. When the boosters run out of fuel, they are detached from the rest of the rocket (usually with some kind of small explosive charge or explosive bolts) and fall away. The first stage then burns to completion and falls off. This leaves a smaller rocket, with the second stage on the bottom, which then fires. Known in rocketry circles as staging, this process is repeated until the desired final velocity is achieved. In some cases with serial staging, the upper stage ignites before the separation—the interstage ring is designed with this in mind, and the thrust is used to help positively separate the two vehicles.

Only multistage rockets have reached orbital speed. Single-stage-to-orbit designs are sought, but have not yet been demonstrated on Earth.

Performance

thumb|right|Cutaway drawings showing three multi-stage rockets

thumb|right|Apollo 11 Saturn V first-stage separation

thumb|upright|right|The second stage being lowered onto the first stage of a [[Saturn V rocket]]

thumb|right|A diagram of the second stage and how it fits into the complete rocket

Multi-stage rockets overcome a limitation imposed by the laws of physics on the velocity change achievable by a rocket stage. The limit depends on the fueled-to-dry mass ratio and on the effective exhaust velocity of the engine. This relation is given by the classical rocket equation:

:<math>\Delta v = v_\text{e} \ln \left(\frac {m_0} {m_f}\right)</math>

where:

:<math>\Delta v\ </math> is delta-v of the vehicle (change of velocity plus losses due to gravity and atmospheric drag);

:<math>m_0</math> is the initial total (wet) mass, equal to final (dry) mass plus propellant;

:<math>m_f</math> is the final (dry) mass, after the propellant is expended;

:<math>v_\text{e}</math> is the effective exhaust velocity (determined by propellant, engine design and throttle condition);

:<math>\ln</math> is the natural logarithm function.

The delta v required to reach low Earth orbit (or the required velocity of a sufficiently heavy suborbital payload) requires a wet to dry mass ratio larger than has been achieved in a single rocket stage. The multistage rocket overcomes this limit by splitting the delta-v into fractions. As each lower stage drops off and the succeeding stage fires, the rest of the rocket is still traveling near the burnout speed. Each lower stage's dry mass includes the propellant in the upper stages, and each succeeding upper stage has reduced its dry mass by discarding the useless dry mass of the spent lower stages.

A further advantage is that each stage can use a different type of rocket engine, each tuned for its particular operating conditions. Thus the lower-stage engines are designed for use at atmospheric pressure, while the upper stages can use engines suited to near vacuum conditions. Lower stages tend to require more structure than upper as they need to bear their own weight plus that of the stages above them. Optimizing the structure of each stage decreases the weight of the total vehicle and provides further advantage.

The advantage of staging comes at the cost of the lower stages lifting engines which are not yet being used, as well as making the entire rocket more complex and harder to build than a single stage. In addition, each staging event is a possible point of launch failure, due to separation failure, ignition failure, or stage collision. Nevertheless, the savings are so great that every rocket ever used to deliver a payload into orbit has had staging of some sort.

One of the most common measures of rocket efficiency is its specific impulse, which is defined as the thrust per flow rate (per second) of propellant consumption:

: <math>I_\mathrm{sp} </math> = <math>\ \frac{T}{\frac{dm}{dt} g_\mathrm{0 </math>

When rearranging the equation such that thrust is calculated as a result of the other factors, we have:

: <math> T = I_\mathrm{sp}g_\mathrm{0} \frac{dm}{dt}</math>

These equations show that a higher specific impulse means a more efficient rocket engine, capable of burning for longer periods of time. In terms of staging, the initial rocket stages usually have a lower specific impulse rating, trading efficiency for superior thrust in order to quickly push the rocket into higher altitudes. Later stages of the rocket usually have a higher specific impulse rating because the vehicle is further outside the atmosphere and the exhaust gas does not need to expand against as much atmospheric pressure.

When selecting the ideal rocket engine to use as an initial stage for a launch vehicle, a useful performance metric to examine is the thrust-to-weight ratio, and is calculated by the equation:

: <math> TWR = \frac{T}{mg_\mathrm{0</math>

The common thrust-to-weight ratio of a launch vehicle is within the range of 1.3 to 2.0.

The second dimensionless performance quantity is the structural ratio, which is the ratio between the empty mass of the stage, and the combined empty mass and propellant mass as shown in this equation: During hot-staging, the earlier stage throttles down its engines. and Proton-M. The N1 rocket was designed to use hot staging, but none of the test flights lasted long enough for this to occur. Starting with the Titan II, the Titan family of rockets used hot staging. SpaceX retrofitted their Starship rocket to use hot staging after its first flight, making it the largest rocket ever to do so, as well as the first reusable vehicle to utilize hot staging.

Tandem vs parallel staging design

A rocket system that implements tandem staging means that each individual stage runs in order one after the other. The rocket breaks free from the previous stage, then begins burning through the next stage in straight succession. On the other hand, a rocket that implements parallel staging has two or more different stages that are active at the same time. For example, the Space Shuttle has two Solid Rocket Boosters that burn simultaneously. Upon launch, the boosters ignite, and at the end of the stage, the two boosters are discarded while the external fuel tank is kept for another stage.

Assembly

Each individual stage is generally assembled at its manufacturing site and shipped to the launch site; the term vehicle assembly refers to the mating of all rocket stage(s) and the spacecraft payload into a single assembly known as a space vehicle. Single-stage vehicles (suborbital), and multistage vehicles on the smaller end of the size range, can usually be assembled directly on the launch pad by lifting the stage(s) and spacecraft vertically in place by means of a crane.

This is generally not practical for larger space vehicles, which are assembled off the pad and moved into place on the launch site by various methods. NASA's Apollo/Saturn V crewed Moon landing vehicle, and Space Shuttle, were assembled vertically onto mobile launcher platforms with attached launch umbilical towers, in a Vehicle Assembly Building, and then a special crawler-transporter moved the entire vehicle stack to the launch pad in an upright position. In contrast, vehicles such as the Russian Soyuz rocket and the SpaceX Falcon 9 are assembled horizontally in a processing hangar, transported horizontally, and then brought upright at the pad.

Passivation and space debris

alt=Bluish-white streaks, like the tail of a comet, glow in the night sky over a dark site over silhouetted trees and red lights from astronomers.|thumb|Propellant dumps from upper stage passivation can be seen from the ground if sunlight can reach it while it is visible in the night sky.

Spent upper stages of launch vehicles are a significant source of space debris remaining in orbit in a non-operational state for many years after use, and occasionally, large debris fields created from the breakup of a single upper stage while in orbit. Passivation means removing any sources of stored energy remaining on the vehicle, as by dumping fuel or discharging batteries.

Many early upper stages, in both the Soviet and U.S. space programs, were not passivated after mission completion. During the initial attempts to characterize the space debris problem, it became evident that a good proportion of all debris was due to the breaking up of rocket upper stages, particularly unpassivated upper-stage propulsion units.

History and development

An illustration and description in the 14th century Chinese Huolongjing by Jiao Yu and Liu Bowen shows the oldest known multistage rocket; this was the "fire-dragon issuing from the water" (火龙出水, huǒ lóng chū shuǐ), which was used mostly by the Chinese navy. It was a two-stage rocket that had booster rockets that would eventually burn out, yet, before they did so, automatically ignited a number of smaller rocket arrows that were shot out of the front end of the missile, which was shaped like a dragon's head with an open mouth. The rocket had the length of 15 cm and 13 cm; the diameter was 2.2 cm. It was attached to an arrow 110 cm long; experimental records show that the first results were around 200m in range. There are records that show Korea kept developing this technology until it came to produce the Singijeon, or 'magical machine arrows' in the 16th century.

The earliest experiments with multistage rockets in Europe were made in 1551 by Austrian Conrad Haas (1509–1576), the arsenal master of the town of Hermannstadt, Transylvania (now Sibiu/Hermannstadt, Romania). This concept was developed independently by at least five individuals:

Polish–Lithuanian Kazimierz Siemienowicz (1600–1651)
Russian Konstantin Tsiolkovsky (1857–1935)
American Robert Goddard (1882–1945)
German Hermann Oberth (1894–1989)
French (1889–1969)

In 1944, German military tested the Rheinbote, a four-stage, solid-fuel, unguided ballistic artillery rocket developed by Rheinmetall-Borsig. It reached speeds of about at an altitude of .

The first high-speed multistage rockets were the RTV-G-4 Bumper rockets tested at the White Sands Proving Ground and later at Cape Canaveral from 1948 to 1950. These consisted of a V-2 rocket and a WAC Corporal sounding rocket. The greatest altitude ever reached was 393 km, attained on February 24, 1949, at White Sands.

In 1947, the Soviet rocket engineer and scientist Mikhail Tikhonravov developed a theory of parallel stages, which he called "packet rockets". In his scheme, three parallel stages were fired from liftoff, but all three engines were fueled from the outer two stages, until they are empty and could be ejected. This is more efficient than sequential staging, because the second-stage engine is never just dead weight. In 1951, Soviet engineer and scientist Dmitry Okhotsimsky carried out a pioneering engineering study of general sequential and parallel staging, with and without the pumping of fuel between stages. The design of the R-7 Semyorka emerged from that study. The trio of rocket engines used in the first stage of the American Atlas I and Atlas II launch vehicles, arranged in a row, used parallel staging in a similar way: the outer pair of booster engines existed as a jettisonable pair which would, after they shut down, drop away with the lowermost outer skirt structure, leaving the central sustainer engine to complete the first stage's engine burn towards apogee or orbit.

Separation events

Separation of each portion of a multistage rocket introduces additional risk into the success of the launch mission. Reducing the number of separation events results in a reduction in complexity.

Separation events occur when stages or strap-on boosters separate after use, when the payload fairing separates prior to orbital insertion, or when used, a launch escape system which separates after the early phase of a launch. Pyrotechnic fasteners, or in some cases pneumatic systems like on the Falcon 9 Full Thrust, are typically used to separate rocket stages.

Two-stage-to-orbit

A two-stage-to-orbit (TSTO) or two-stage rocket launch vehicle is a spacecraft in which two distinct stages provide propulsion consecutively in order to achieve orbital velocity. It is intermediate between a three-stage-to-orbit launcher and a hypothetical single-stage-to-orbit (SSTO) launcher.

Three-stage-to-orbit

The three-stage-to-orbit launch system is a commonly used rocket system to attain Earth orbit. The spacecraft uses three distinct stages to provide propulsion consecutively in order to achieve orbital velocity. It is intermediate between a four-stage-to-orbit launcher and a two-stage-to-orbit launcher.

Examples of three-stage-to-orbit systems

Saturn V
Vanguard
Ariane 4 (optional boosters)
Ariane 2
Ariane 1 (four stages)
GSLV (three stages and boosters)
Proton (optional fourth stage)
Long March 5 (optional boosters and optional third stage)
Long March 1, Long March 1D
Zenit-3SL
Unha-3
KSLV-2 "Nuri"

Examples of two stages with boosters

Other designs (in fact, most modern medium- to heavy-lift designs) do not have all three stages inline on the main stack, instead having strap-on boosters for the "stage-0" with two core stages. In these designs, the boosters and first stage fire simultaneously instead of consecutively, providing extra initial thrust to lift the full launcher weight and overcome gravity losses and atmospheric drag. The boosters are jettisoned a few minutes into flight to reduce weight.

US Space Shuttle — SRB first stage; External Tank + SSME second stage; OMS on internal tanks third stage;
Angara A5
Ariane 5
Atlas V 551
Delta II third stage)
Delta III
Delta IV-Medium+ and -Heavy
Falcon Heavy
Geosynchronous Satellite Launch Vehicle Mk III (However, like the Titan IIIC, the GSLV MkIII is launched solely by the side boosters. The main core only ignites a few minutes into flight, shortly before the boosters are jettisoned.)
H-IIA, H-IIB
Soyuz
Space Launch System
Titan IV
Long March 2E, Long March 2F, Long March 3B

Four-stage-to-orbit

The four-stage-to-orbit launch system is a rocket system used to attain Earth orbit. The spacecraft uses four distinct stages to provide propulsion consecutively in order to achieve orbital velocity. It is intermediate between a five-stage-to-orbit launcher and a three-stage-to-orbit launcher, most often used with solid-propellant launch systems.

Examples of four-stage-to-orbit systems

Ariane 1
PSLV
Minotaur IV
Proton (optional fourth stage)
Vega
Minotaur V (five stages)
ASLV (five stages)
Juno I
Juno II

The concept is found in some rockets of the Atlas rocket family where all three engines are ignited on the ground and during flight two of the three engines are jettisoned. This was done because of reliability issues with engine ignition in the 1950s. Ignition of all three engines on the ground allowed for confirmation of the functionality of the engines before lift-off.

Examples of stage-and-a-half rockets

SM-65 Atlas
Atlas LV-3B

References

ja:ロケット#多段式ロケット