Misplaced Pages

#71928

106-470: Tsyklon-4 was a three-stage-to-orbit expendable launch system , built on the successful Tsyklon-3 rocket and using improved versions of that rocket's first two stages. The new features were mostly in the newly developed third stage: Tsyklon-4 would have improved the fuelling system, allowing safe capture of toxic vapours from the vehicle's hypergolic propellant system. The launch system would have been able to deliver up to 5,250 kg (11,570 lb) to

212-400: A Δ v {\displaystyle \Delta v} of 9,700 meters per second (32,000 ft/s) (Earth to LEO , including Δ v {\displaystyle \Delta v} to overcome gravity and aerodynamic drag). In the case of sequentially thrusting rocket stages , the equation applies for each stage, where for each stage the initial mass in the equation is

318-416: A 185 km (115 mi) orbit, 4,900 kg (10,800 lb) to a 400 km (250 mi) orbit, or 500 kg (1,100 lb) to a geosynchronous orbit . Development began in 2002, with the maiden flight aimed for 2006. Following a series of production delays, this launch date slipped, and was estimated to occur some time after 2015. Tsyklon-4 had been planned to launch from a proposed launch pad at

424-533: A Canadian launch service provider. The new rocket was originally scheduled to be in service by 2020, though this date has been repeatedly pushed due to construction delays at the Canso launch site . Construction is currently estimated to be complete by 2024 or 2025. According to a 2021 press release, the first flight of Cyclone-4M was planned to take place at Canso in 2023; however, it failed to eventuate. Three-stage-to-orbit A multistage rocket or step rocket

530-417: 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

636-510: A dragon's head with an open mouth. The British scientist and historian Joseph Needham points out that the written material and depicted illustration of this rocket come from the oldest stratum of the Huolongjing , which can be dated roughly 1300–1350 AD (from the book's part 1, chapter 3, page 23). Another example of an early multistaged rocket is the Juhwa (走火) of Korean development. It

742-408: A higher cost for deployment. Hot-staging is a type of rocket staging in which the next stage fires its engines before separation instead of after. During hot-staging, the earlier stage throttles down its engines. Hot-staging may reduce the complexity of stage separation, and gives a small extra payload capacity to the booster. It also eliminates the need for ullage motors , as the acceleration from

848-518: A launch vehicle, a useful performance metric to examine is the thrust-to-weight ratio, and is calculated by the equation: The common thrust-to-weight ratio of a launch vehicle is within the range of 1.3 to 2.0. Another performance metric to keep in mind when designing each rocket stage in a mission is the burn time, which is the amount of time the rocket engine will last before it has exhausted all of its propellant. For most non-final stages, thrust and specific impulse can be assumed constant, which allows

954-472: 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

1060-629: A planet with an atmosphere, the effects of these forces must be included in the delta-V requirement (see Examples below). In what has been called "the tyranny of the rocket equation", there is a limit to the amount of payload that the rocket can carry, as higher amounts of propellant increment the overall weight, and thus also increase the fuel consumption. The equation does not apply to non-rocket systems such as aerobraking , gun launches , space elevators , launch loops , tether propulsion or light sails . The rocket equation can be applied to orbital maneuvers in order to determine how much propellant

1166-835: A positive Δ m {\displaystyle \Delta m} results in a decrease in rocket mass in time), ∑ i F i = m d V d t + v e d m d t {\displaystyle \sum _{i}F_{i}=m{\frac {dV}{dt}}+v_{\text{e}}{\frac {dm}{dt}}} If there are no external forces then ∑ i F i = 0 {\textstyle \sum _{i}F_{i}=0} ( conservation of linear momentum ) and − m d V d t = v e d m d t {\displaystyle -m{\frac {dV}{dt}}=v_{\text{e}}{\frac {dm}{dt}}} Assuming that v e {\displaystyle v_{\text{e}}}

SECTION 10

#1732800796072

1272-1272: A rest mass of m 1 {\displaystyle m_{1}} ) in the inertial frame of reference where the rocket started at rest (with the rest mass including fuel being m 0 {\displaystyle m_{0}} initially), and c {\displaystyle c} standing for the speed of light in vacuum: m 0 m 1 = [ 1 + Δ v c 1 − Δ v c ] c 2 v e {\displaystyle {\frac {m_{0}}{m_{1}}}=\left[{\frac {1+{\frac {\Delta v}{c}}}{1-{\frac {\Delta v}{c}}}}\right]^{\frac {c}{2v_{\text{e}}}}} Writing m 0 m 1 {\textstyle {\frac {m_{0}}{m_{1}}}} as R {\displaystyle R} allows this equation to be rearranged as Δ v c = R 2 v e c − 1 R 2 v e c + 1 {\displaystyle {\frac {\Delta v}{c}}={\frac {R^{\frac {2v_{\text{e}}}{c}}-1}{R^{\frac {2v_{\text{e}}}{c}}+1}}} Then, using

1378-466: A rocket system will be when performing optimizations and comparing varying configurations for a mission. For initial sizing, the rocket equations can be used to derive the amount of propellant needed for the rocket based on the specific impulse of the engine and the total impulse required in N·s. The equation is: where g is the gravity constant of Earth. This also enables the volume of storage required for

1484-399: A technical algorithm that generates an analytical solution that can be implemented by a program, or simple trial and error. For the trial and error approach, it is best to begin with the final stage, calculating the initial mass which becomes the payload for the previous stage. From there it is easy to progress all the way down to the initial stage in the same manner, sizing all the stages of

1590-549: Is NOT constant, we might not have rocket equations that are as simple as the above forms. Many rocket dynamics researches were based on the Tsiolkovsky's constant v e {\displaystyle v_{\text{e}}} hypothesis. The value m 0 − m f {\displaystyle m_{0}-m_{f}} is the total working mass of propellant expended. Δ V {\displaystyle \Delta V} ( delta-v )

1696-513: 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,

1802-483: 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. 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

1908-440: Is a measure of the impulse that is needed to perform a maneuver such as launching from, or landing on a planet or moon, or an in-space orbital maneuver . It is a scalar that has the units of speed . As used in this context, it is not the same as the physical change in velocity of the vehicle. Delta- v is produced by reaction engines, such as rocket engines , is proportional to the thrust per unit mass and burn time, and

2014-415: Is a safe and reasonable assumption to say that 91 to 94 percent of the total mass is fuel. It is also important to note there is a small percentage of "residual" propellant that will be left stuck and unusable inside the tank, and should also be taken into consideration when determining amount of fuel for the rocket. A common initial estimate for this residual propellant is five percent. With this ratio and

2120-1378: Is constant (known as Tsiolkovsky's hypothesis ), so it is not subject to integration, then the above equation may be integrated as follows: − ∫ V V + Δ V d V = v e ∫ m 0 m f d m m {\displaystyle -\int _{V}^{V+\Delta V}\,dV={v_{e}}\int _{m_{0}}^{m_{f}}{\frac {dm}{m}}} This then yields Δ V = v e ln ⁡ m 0 m f {\displaystyle \Delta V=v_{\text{e}}\ln {\frac {m_{0}}{m_{f}}}} or equivalently m f = m 0 e − Δ V   / v e {\displaystyle m_{f}=m_{0}e^{-\Delta V\ /v_{\text{e}}}} or m 0 = m f e Δ V / v e {\displaystyle m_{0}=m_{f}e^{\Delta V/v_{\text{e}}}} or m 0 − m f = m f ( e Δ V / v e − 1 ) {\displaystyle m_{0}-m_{f}=m_{f}\left(e^{\Delta V/v_{\text{e}}}-1\right)} where m 0 {\displaystyle m_{0}}

2226-847: Is equal to m 0 – m f . For the constant mass flow rate R it will therefore take a time T = ( m 0 – m f )/ R to burn all this fuel. Integrating both sides of the equation with respect to time from 0 to T (and noting that R = dm/dt allows a substitution on the right) obtains:   Δ v = v f − v 0 = − v e [ ln ⁡ m f − ln ⁡ m 0 ] =   v e ln ⁡ ( m 0 m f ) . {\displaystyle ~\Delta v=v_{f}-v_{0}=-v_{\text{e}}\left[\ln m_{f}-\ln m_{0}\right]=~v_{\text{e}}\ln \left({\frac {m_{0}}{m_{f}}}\right).} The rocket equation can also be derived as

SECTION 20

#1732800796072

2332-586: Is found to be: J   ln ⁡ ( m 0 ) − ln ⁡ ( m f ) Δ m {\displaystyle J~{\frac {\ln({m_{0}})-\ln({m_{f}})}{\Delta m}}} Realising that impulse over the change in mass is equivalent to force over propellant mass flow rate (p), which is itself equivalent to exhaust velocity, J Δ m = F p = V exh {\displaystyle {\frac {J}{\Delta m}}={\frac {F}{p}}=V_{\text{exh}}}

2438-453: 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

2544-409: Is given by 1 2 v eff 2 {\textstyle {\tfrac {1}{2}}v_{\text{eff}}^{2}} . In the rocket's center-of-mass frame, if a pellet of mass m p {\displaystyle m_{p}} is ejected at speed u {\displaystyle u} and the remaining mass of the rocket is m {\displaystyle m} ,

2650-428: Is intermediate between a five-stage-to-orbit launcher and a three-stage-to-orbit launcher, most often used with solid-propellant launch systems. Other designs do not have all four stages inline on the main stack, instead having strap-on boosters for the "stage-0" with three core stages. In these designs, the boosters and first stage fire simultaneously instead of consecutively, providing extra initial thrust to lift

2756-414: Is its propelling force F divided by its current mass m :   a = d v d t = − F m ( t ) = − R v e m ( t ) {\displaystyle ~a={\frac {dv}{dt}}=-{\frac {F}{m(t)}}=-{\frac {Rv_{\text{e}}}{m(t)}}} Now, the mass of fuel the rocket initially has on board

2862-401: Is needed to change to a particular new orbit, or to find the new orbit as the result of a particular propellant burn. When applying to orbital maneuvers, one assumes an impulsive maneuver , in which the propellant is discharged and delta-v applied instantaneously. This assumption is relatively accurate for short-duration burns such as for mid-course corrections and orbital insertion maneuvers. As

2968-468: Is the fraction of initial weight that is payload. The effective exhaust velocity is often specified as a specific impulse and they are related to each other by: v e = g 0 I sp , {\displaystyle v_{\text{e}}=g_{0}I_{\text{sp}},} where The rocket equation captures the essentials of rocket flight physics in a single short equation. It also holds true for rocket-like reaction vehicles whenever

3074-393: Is the initial to final mass ratio, which is the ratio between the rocket stage's full initial mass and the rocket stage's final mass once all of its fuel has been consumed. The equation for this ratio is: Where m E {\displaystyle m_{\mathrm {E} }} is the empty mass of the stage, m p {\displaystyle m_{\mathrm {p} }}

3180-431: Is the initial total mass including propellant, m f {\displaystyle m_{f}} the final mass, and v e {\displaystyle v_{\text{e}}} the velocity of the rocket exhaust with respect to the rocket (the specific impulse , or, if measured in time, that multiplied by gravity -on-Earth acceleration). If v e {\displaystyle v_{\text{e}}}

3286-430: Is the integration over time of the magnitude of the acceleration produced by using the rocket engine (what would be the actual acceleration if external forces were absent). In free space, for the case of acceleration in the direction of the velocity, this is the increase of the speed. In the case of an acceleration in opposite direction (deceleration) it is the decrease of the speed. Of course gravity and drag also accelerate

Tsyklon-4 - Misplaced Pages Continue

3392-402: Is the mass of the oxidizer and m f u e l {\displaystyle m_{\mathrm {fuel} }} is the mass of the fuel. This mixture ratio not only governs the size of each tank, but also the specific impulse of the rocket. Determining the ideal mixture ratio is a balance of compromises between various aspects of the rocket being designed, and can vary depending on

3498-404: Is the mass of the propellant, and m P L {\displaystyle m_{\mathrm {PL} }} is the mass of the payload. 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: The last major dimensionless performance quantity

3604-960: Is the momentum of the rocket at time t = 0 {\displaystyle t=0} : P → 0 = m V → {\displaystyle {\vec {P}}_{0}=m{\vec {V}}} and P → Δ t {\displaystyle {\vec {P}}_{\Delta t}} is the momentum of the rocket and exhausted mass at time t = Δ t {\displaystyle t=\Delta t} : P → Δ t = ( m − Δ m ) ( V → + Δ V → ) + Δ m V → e {\displaystyle {\vec {P}}_{\Delta t}=\left(m-\Delta m\right)\left({\vec {V}}+\Delta {\vec {V}}\right)+\Delta m{\vec {V}}_{\text{e}}} and where, with respect to

3710-455: Is the payload ratio, which is the ratio between the payload mass and the combined mass of the empty rocket stage and the propellant: After comparing the three equations for the dimensionless quantities, it is easy to see that they are not independent of each other, and in fact, the initial to final mass ratio can be rewritten in terms of structural ratio and payload ratio: These performance ratios can also be used as references for how efficient

3816-521: Is thrust, m 0 {\displaystyle m_{0}} is the initial (wet) mass and Δ m {\displaystyle \Delta m} is the initial mass minus the final (dry) mass, and realising that the integral of a resultant force over time is total impulse, assuming thrust is the only force involved, ∫ t 0 t f F   d t = J {\displaystyle \int _{t_{0}}^{t_{f}}F~dt=J} The integral

3922-429: Is used to determine the mass of propellant required for the given manoeuvre through the rocket equation. For multiple manoeuvres, delta- v sums linearly. For interplanetary missions delta- v is often plotted on a porkchop plot which displays the required mission delta- v as a function of launch date. In aerospace engineering , the propellant mass fraction is the portion of a vehicle's mass which does not reach

4028-612: The Alcântara Launch Center in Brazil, which would have given the rocket access to all orbital regimes. However, Brazil backed out of the partnership with Ukraine in 2015, citing concerns over the project budget, the ongoing financial situation in both countries, and the future of the commercial launch market. Yuzhnoye began developing a two-stage derivative of Tsyklon-4, the Cyclone-4M , for Maritime Launch Services ,

4134-480: The Falcon 9 Full Thrust , are typically used to separate rocket stages. 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. The three-stage-to-orbit launch system

4240-734: 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

4346-509: 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: The first high-speed multistage rockets were

Tsyklon-4 - Misplaced Pages Continue

4452-490: 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. An illustration and description in the 14th century Chinese Huolongjing by Jiao Yu and Liu Bowen shows

4558-421: The conservation of momentum . It is credited to Konstantin Tsiolkovsky , who independently derived it and published it in 1903, although it had been independently derived and published by William Moore in 1810, and later published in a separate book in 1813. Robert Goddard also developed it independently in 1912, and Hermann Oberth derived it independently about 1920. The maximum change of velocity of

4664-429: The identity R 2 v e c = exp ⁡ [ 2 v e c ln ⁡ R ] {\textstyle R^{\frac {2v_{\text{e}}}{c}}=\exp \left[{\frac {2v_{\text{e}}}{c}}\ln R\right]} (here "exp" denotes the exponential function ; see also Natural logarithm as well as the "power" identity at logarithmic identities ) and

4770-523: 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. 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

4876-464: The amount of energy converted to increase the rocket's and pellet's kinetic energy is 1 2 m p v eff 2 = 1 2 m p u 2 + 1 2 m ( Δ v ) 2 . {\displaystyle {\tfrac {1}{2}}m_{p}v_{\text{eff}}^{2}={\tfrac {1}{2}}m_{p}u^{2}+{\tfrac {1}{2}}m(\Delta v)^{2}.} Using momentum conservation in

4982-963: The boat in the other direction (ignoring friction / drag). Consider the following system: In the following derivation, "the rocket" is taken to mean "the rocket and all of its unexpended propellant". Newton's second law of motion relates external forces ( F → i {\displaystyle {\vec {F}}_{i}} ) to the change in linear momentum of the whole system (including rocket and exhaust) as follows: ∑ i F → i = lim Δ t → 0 P → Δ t − P → 0 Δ t {\displaystyle \sum _{i}{\vec {F}}_{i}=\lim _{\Delta t\to 0}{\frac {{\vec {P}}_{\Delta t}-{\vec {P}}_{0}}{\Delta t}}} where P → 0 {\displaystyle {\vec {P}}_{0}}

5088-401: The breakup of a single upper stage while in orbit. After the 1990s, spent upper stages are generally passivated after their use as a launch vehicle is complete in order to minimize risks while the stage remains derelict 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

5194-437: The burn duration increases, the result is less accurate due to the effect of gravity on the vehicle over the duration of the maneuver. For low-thrust, long duration propulsion, such as electric propulsion , more complicated analysis based on the propagation of the spacecraft's state vector and the integration of thrust are used to predict orbital motion. Assume an exhaust velocity of 4,500 meters per second (15,000 ft/s) and

5300-440: 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

5406-590: The definite integral lim N → ∞ Δ v = v eff ∫ 0 ϕ d x 1 − x = v eff ln ⁡ 1 1 − ϕ = v eff ln ⁡ m 0 m f , {\displaystyle \lim _{N\to \infty }\Delta v=v_{\text{eff}}\int _{0}^{\phi }{\frac {dx}{1-x}}=v_{\text{eff}}\ln {\frac {1}{1-\phi }}=v_{\text{eff}}\ln {\frac {m_{0}}{m_{f}}},} since

SECTION 50

#1732800796072

5512-489: 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

5618-566: The desired delta-v. The equation is named after Russian scientist Konstantin Tsiolkovsky who independently derived it and published it in his 1903 work. The equation had been derived earlier by the British mathematician William Moore in 1810, and later published in a separate book in 1813. American Robert Goddard independently developed the equation in 1912 when he began his research to improve rocket engines for possible space flight. German engineer Hermann Oberth independently derived

5724-415: The destination, usually used as a measure of the vehicle's performance. In other words, the propellant mass fraction is the ratio between the propellant mass and the initial mass of the vehicle. In a spacecraft, the destination is usually an orbit, while for aircraft it is their landing location. A higher mass fraction represents less weight in a design. Another related measure is the payload fraction , which

5830-419: The different stages of the rocket should be clearly defined. Continuing with the previous example, the end of the first stage which is sometimes referred to as 'stage 0', can be defined as when the side boosters separate from the main rocket. From there, the final mass of stage one can be considered the sum of the empty mass of stage one, the mass of stage two (the main rocket and the remaining unburned fuel) and

5936-404: The drawbacks of a less efficient specific impulse rating. But suppose the defining constraint for the launch system is volume, and a low density fuel is required such as hydrogen. This example would be solved by using an oxidizer-rich mixture ratio, reducing efficiency and specific impulse rating, but will meet a smaller tank volume requirement. The ultimate goal of optimal staging is to maximize

6042-613: The effective exhaust velocity determined by the rocket motor's design, the desired delta-v (e.g., orbital speed or escape velocity ), and a given dry mass m f {\displaystyle m_{f}} , the equation can be solved for the required propellant mass m 0 − m f {\displaystyle m_{0}-m_{f}} : m 0 = m f e Δ v / v e . {\displaystyle m_{0}=m_{f}e^{\Delta v/v_{\text{e}}}.} The necessary wet mass grows exponentially with

6148-411: The effective exhaust velocity is constant, and can be summed or integrated when the effective exhaust velocity varies. The rocket equation only accounts for the reaction force from the rocket engine; it does not include other forces that may act on a rocket, such as aerodynamic or gravitational forces. As such, when using it to calculate the propellant requirement for launch from (or powered descent to)

6254-598: 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. 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

6360-410: The equation about 1920 as he studied the feasibility of space travel. While the derivation of the rocket equation is a straightforward calculus exercise, Tsiolkovsky is honored as being the first to apply it to the question of whether rockets could achieve speeds necessary for space travel . [REDACTED] In order to understand the principle of rocket propulsion, Konstantin Tsiolkovsky proposed

6466-444: The equation for burn time to be written as: Where m 0 {\displaystyle m_{\mathrm {0} }} and m f {\displaystyle m_{\mathrm {f} }} are the initial and final masses of the rocket stage respectively. In conjunction with the burnout time, the burnout height and velocity are obtained using the same values, and are found by these two equations: When dealing with

SECTION 60

#1732800796072

6572-411: The equations for determining the burnout velocities, burnout times, burnout altitudes, and mass of each stage. This would make for a better approach to a conceptual design in a situation where a basic understanding of the system behavior is preferential to a detailed, accurate design. One important concept to understand when undergoing restricted rocket staging, is how the burnout velocity is affected by

6678-423: The famous experiment of "the boat". A person is in a boat away from the shore without oars. They want to reach this shore. They notice that the boat is loaded with a certain quantity of stones and have the idea of quickly and repeatedly throwing the stones in succession in the opposite direction. Effectively, the quantity of movement of the stones thrown in one direction corresponds to an equal quantity of movement for

6784-479: The final remaining mass of the rocket is m f = m 0 ( 1 − ϕ ) {\displaystyle m_{f}=m_{0}(1-\phi )} . If special relativity is taken into account, the following equation can be derived for a relativistic rocket , with Δ v {\displaystyle \Delta v} again standing for the rocket's final velocity (after expelling all its reaction mass and being reduced to

6890-486: 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 of each portion of

6996-467: The fuel to be calculated if the density of the fuel is known, which is almost always the case when designing the rocket stage. The volume is yielded when dividing the mass of the propellant by its density. Asides from the fuel required, the mass of the rocket structure itself must also be determined, which requires taking into account the mass of the required thrusters, electronics, instruments, power equipment, etc. These are known quantities for typical off

7102-414: The fueled-to-dry mass ratio and on the effective exhaust velocity of the engine. This relation is given by the classical rocket equation : where: 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

7208-496: The full launcher weight and overcome gravity losses and atmospheric drag. The boosters are jettisoned a few minutes into flight to reduce weight. Classical rocket equation The classical rocket equation , or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket : a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to

7314-679: The identity tanh ⁡ x = e 2 x − 1 e 2 x + 1 {\textstyle \tanh x={\frac {e^{2x}-1}{e^{2x}+1}}} ( see Hyperbolic function ), this is equivalent to Δ v = c tanh ⁡ ( v e c ln ⁡ m 0 m 1 ) {\displaystyle \Delta v=c\tanh \left({\frac {v_{\text{e}}}{c}}\ln {\frac {m_{0}}{m_{1}}}\right)} Delta- v (literally " change in velocity "), symbolised as Δ v and pronounced delta-vee , as used in spacecraft flight dynamics ,

7420-489: The initial fuel mass fraction on board and m 0 {\displaystyle m_{0}} the initial fueled-up mass of the rocket. Divide the total mass of fuel ϕ m 0 {\displaystyle \phi m_{0}} into N {\displaystyle N} discrete pellets each of mass m p = ϕ m 0 / N {\displaystyle m_{p}=\phi m_{0}/N} . The remaining mass of

7526-451: 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

7632-416: The integral can be equated to Δ v = V exh   ln ⁡ ( m 0 m f ) {\displaystyle \Delta v=V_{\text{exh}}~\ln \left({\frac {m_{0}}{m_{f}}}\right)} Imagine a rocket at rest in space with no forces exerted on it ( Newton's First Law of Motion ). From the moment its engine is started (clock set to 0)

7738-443: The largest rocket ever to do so, as well as the first reusable vehicle to utilize hot staging. 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

7844-402: 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

7950-1048: The last term in the denominator ϕ / N ≪ 1 {\displaystyle \phi /N\ll 1} and can be neglected to give Δ v ≈ v eff ∑ j = 1 j = N ϕ / N 1 − j ϕ / N = v eff ∑ j = 1 j = N Δ x 1 − x j {\displaystyle \Delta v\approx v_{\text{eff}}\sum _{j=1}^{j=N}{\frac {\phi /N}{1-j\phi /N}}=v_{\text{eff}}\sum _{j=1}^{j=N}{\frac {\Delta x}{1-x_{j}}}} where Δ x = ϕ N {\textstyle \Delta x={\frac {\phi }{N}}} and x j = j ϕ N {\textstyle x_{j}={\frac {j\phi }{N}}} . As N → ∞ {\displaystyle N\rightarrow \infty } this Riemann sum becomes

8056-406: The limiting case of the speed change for a rocket that expels its fuel in the form of N {\displaystyle N} pellets consecutively, as N → ∞ {\displaystyle N\to \infty } , with an effective exhaust speed v eff {\displaystyle v_{\text{eff}}} such that the mechanical energy gained per unit fuel mass

8162-420: 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

8268-403: The mass of the payload. High-altitude and space-bound upper stages are designed to operate with little or no atmospheric pressure. This allows the use of lower pressure combustion chambers and engine nozzles with optimal vacuum expansion ratios . Some upper stages, especially those using hypergolic propellants like Delta-K or Ariane 5 ES second stage, are pressure fed , which eliminates

8374-464: The mass of the propellant calculated, the mass of the empty rocket weight can be determined. Sizing rockets using a liquid bipropellant requires a slightly more involved approach because there are two separate tanks that are required: one for the fuel, and one for the oxidizer. The ratio of these two quantities is known as the mixture ratio, and is defined by the equation: Where m o x {\displaystyle m_{\mathrm {ox} }}

8480-408: 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

8586-423: 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: When rearranging the equation such that thrust is calculated as a result of the other factors, we have: 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,

8692-566: The nearly spent stage keeps the propellants settled at the bottom of the tanks. Hot-staging is used on Soviet-era Russian rockets such as Soyuz and Proton-M . The N1 rocket was designed to use hot staging, however 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

8798-708: The need for complex turbopumps . Other upper stages, such as the Centaur or DCSS , use liquid hydrogen expander cycle engines, or gas generator cycle engines like the Ariane 5 ECA's HM7B or the S-IVB 's J-2 . These stages are usually tasked with completing orbital injection and accelerating payloads into higher energy orbits such as GTO or to escape velocity . Upper stages, such as Fregat , used primarily to bring payloads from low Earth orbit to GTO or beyond are sometimes referred to as space tugs . Each individual stage

8904-419: The number of stages that split up the rocket system. Increasing the number of stages for a rocket while keeping the specific impulse, payload ratios and structural ratios constant will always yield a higher burnout velocity than the same systems that use fewer stages. However, the law of diminishing returns is evident in that each increment in number of stages gives less of an improvement in burnout velocity than

9010-1547: The observer: The velocity of the exhaust V → e {\displaystyle {\vec {V}}_{\text{e}}} in the observer frame is related to the velocity of the exhaust in the rocket frame v e {\displaystyle v_{\text{e}}} by: v → e = V → e − V → {\displaystyle {\vec {v}}_{\text{e}}={\vec {V}}_{\text{e}}-{\vec {V}}} thus, V → e = V → + v → e {\displaystyle {\vec {V}}_{\text{e}}={\vec {V}}+{\vec {v}}_{\text{e}}} Solving this yields: P → Δ t − P → 0 = m Δ V → + v → e Δ m − Δ m Δ V → {\displaystyle {\vec {P}}_{\Delta t}-{\vec {P}}_{0}=m\Delta {\vec {V}}+{\vec {v}}_{\text{e}}\Delta m-\Delta m\Delta {\vec {V}}} If V → {\displaystyle {\vec {V}}} and v → e {\displaystyle {\vec {v}}_{\text{e}}} are opposite, F → i {\displaystyle {\vec {F}}_{\text{i}}} have

9116-454: 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

9222-525: 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

9328-632: The overall payload ratio of the entire system. It is important to note that when computing payload ratio for individual stages, the payload includes the mass of all the stages after the current one. The overall payload ratio is: Where n is the number of stages the rocket system comprises. Similar stages yielding the same payload ratio simplify this equation, however that is seldom the ideal solution for maximizing payload ratio, and ΔV requirements may have to be partitioned unevenly as suggested in guideline tips 1 and 2 from above. Two common methods of determining this perfect ΔV partition between stages are either

9434-573: The payload ratio (see ratios under performance), meaning the largest amount of payload is carried up to the required burnout velocity using the least amount of non-payload mass, which comprises everything else. This goal assumes that the cost of a rocket launch is proportional to the total liftoff mass of the rocket, which is a rule of thumb in rocket engineering. Here are a few quick rules and guidelines to follow in order to reach optimal staging: The payload ratio can be calculated for each individual stage, and when multiplied together in sequence, will yield

9540-402: The previous increment. The burnout velocity gradually converges towards an asymptotic value as the number of stages increases towards a very high number. In addition to diminishing returns in burnout velocity improvement, the main reason why real world rockets seldom use more than three stages is because of increase of weight and complexity in the system for each added stage, ultimately yielding

9646-441: The problem of calculating the total burnout velocity or time for the entire rocket system, the general procedure for doing so is as follows: The burnout time does not define the end of the rocket stage's motion, as the vehicle will still have a velocity that will allow it to coast upward for a brief amount of time until the acceleration of the planet's gravity gradually changes it to a downward direction. The velocity and altitude of

9752-430: 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

9858-430: The rocket after burnout can be easily modeled using the basic physics equations of motion. When comparing one rocket with another, it is impractical to directly compare the rocket's certain trait with the same trait of another because their individual attributes are often not independent of one another. For this reason, dimensionless ratios have been designed to enable a more meaningful comparison between rockets. The first

9964-833: The rocket after ejecting j {\displaystyle j} pellets is then m = m 0 ( 1 − j ϕ / N ) {\displaystyle m=m_{0}(1-j\phi /N)} . The overall speed change after ejecting j {\displaystyle j} pellets is the sum Δ v = v eff ∑ j = 1 j = N ϕ / N ( 1 − j ϕ / N ) ( 1 − j ϕ / N + ϕ / N ) {\displaystyle \Delta v=v_{\text{eff}}\sum _{j=1}^{j=N}{\frac {\phi /N}{\sqrt {(1-j\phi /N)(1-j\phi /N+\phi /N)}}}} Notice that for large N {\displaystyle N}

10070-410: The rocket expels gas mass at a constant mass flow rate R (kg/s) and at exhaust velocity relative to the rocket v e (m/s). This creates a constant force F propelling the rocket that is equal to R × v e . The rocket is subject to a constant force, but its total mass is decreasing steadily because it is expelling gas. According to Newton's Second Law of Motion , its acceleration at any time t

10176-427: The rocket system. Restricted rocket staging is based on the simplified assumption that each of the stages of the rocket system have the same specific impulse, structural ratio, and payload ratio, the only difference being the total mass of each increasing stage is less than that of the previous stage. Although this assumption may not be the ideal approach to yielding an efficient or optimal system, it greatly simplifies

10282-478: The rocket's frame just prior to ejection, u = Δ v m m p {\textstyle u=\Delta v{\tfrac {m}{m_{p}}}} , from which we find Δ v = v eff m p m ( m + m p ) . {\displaystyle \Delta v=v_{\text{eff}}{\frac {m_{p}}{\sqrt {m(m+m_{p})}}}.} Let ϕ {\displaystyle \phi } be

10388-501: The same direction as V → {\displaystyle {\vec {V}}} , Δ m Δ V → {\displaystyle \Delta m\Delta {\vec {V}}} are negligible (since d m d v → → 0 {\displaystyle dm\,d{\vec {v}}\to 0} ), and using d m = − Δ m {\displaystyle dm=-\Delta m} (since ejecting

10494-518: 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. Most quantitative approaches to the design of the rocket system's performance are focused on tandem staging, but the approach can be easily modified to include parallel staging. To begin with,

10600-419: 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. 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

10706-518: The shelf hardware that should be considered in the mid to late stages of the design, but for preliminary and conceptual design, a simpler approach can be taken. Assuming one engine for a rocket stage provides all of the total impulse for that particular segment, a mass fraction can be used to determine the mass of the system. The mass of the stage transfer hardware such as initiators and safe-and-arm devices are very small by comparison and can be considered negligible. For modern day solid rocket motors, it

10812-869: The total mass of the rocket after discarding the previous stage, and the final mass in the equation is the total mass of the rocket just before discarding the stage concerned. For each stage the specific impulse may be different. For example, if 80% of the mass of a rocket is the fuel of the first stage, and 10% is the dry mass of the first stage, and 10% is the remaining rocket, then Δ v   = v e ln ⁡ 100 100 − 80 = v e ln ⁡ 5 = 1.61 v e . {\displaystyle {\begin{aligned}\Delta v\ &=v_{\text{e}}\ln {100 \over 100-80}\\&=v_{\text{e}}\ln 5\\&=1.61v_{\text{e}}.\\\end{aligned}}} With three similar, subsequently smaller stages with

10918-406: The type of fuel and oxidizer combination being used. For example, a mixture ratio of a bipropellant could be adjusted such that it may not have the optimal specific impulse, but will result in fuel tanks of equal size. This would yield simpler and cheaper manufacturing, packing, configuring, and integrating of the fuel systems with the rest of the rocket, and can become a benefit that could outweigh

11024-479: The vehicle, Δ v {\displaystyle \Delta v} (with no external forces acting) is: Δ v = v e ln ⁡ m 0 m f = I sp g 0 ln ⁡ m 0 m f , {\displaystyle \Delta v=v_{\text{e}}\ln {\frac {m_{0}}{m_{f}}}=I_{\text{sp}}g_{0}\ln {\frac {m_{0}}{m_{f}}},} where: Given

11130-680: The vehicle, and they can add or subtract to the change in velocity experienced by the vehicle. Hence delta-v may not always be the actual change in speed or velocity of the vehicle. The equation can also be derived from the basic integral of acceleration in the form of force (thrust) over mass. By representing the delta-v equation as the following: Δ v = ∫ t 0 t f | T | m 0 − t Δ m   d t {\displaystyle \Delta v=\int _{t_{0}}^{t_{f}}{\frac {|T|}{{m_{0}}-{t}\Delta {m}}}~dt} where T

11236-515: Was proposed by medieval Korean engineer, scientist and inventor Ch'oe Mu-sŏn and developed by the Firearms Bureau (火㷁道監) during the 14th century. 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

#71928