Misplaced Pages

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78-483: The use of less dense fuel components at maximum efficiency conditions allows minimizing the volume of fuel tanks and subsequently their mass down to 30%. The RD-701 was developed into the RD-704 with one combustion chamber. Until 2020, the engine held the record for the highest pressure successfully recorded in a combustion chamber with a pressure of 30 MPa (300 bar; 4,400 psi). In August 2020, this record

156-402: A n t . {\displaystyle m_{A}v_{A}+m_{B}v_{B}+m_{C}v_{C}+...=constant.} This conservation law applies to all interactions, including collisions (both elastic and inelastic ) and separations caused by explosive forces. It can also be generalized to situations where Newton's laws do not hold, for example in the theory of relativity and in electrodynamics . Momentum

234-418: A Galilean transformation . If a particle is moving at speed ⁠ d x / d t ⁠ = v in the first frame of reference, in the second, it is moving at speed v ′ = d x ′ d t = v − u . {\displaystyle v'={\frac {{\text{d}}x'}{{\text{d}}t}}=v-u\,.} Since u does not change,

312-402: A collision. For example, suppose there are two bodies of equal mass m , one stationary and one approaching the other at a speed v (as in the figure). The center of mass is moving at speed ⁠ v / 2 ⁠ and both bodies are moving towards it at speed ⁠ v / 2 ⁠ . Because of the symmetry, after the collision both must be moving away from the center of mass at

390-417: A direct measure of the engine's effectiveness in converting propellant mass into forward momentum. The specific impulse in terms of propellant mass spent has units of distance per time, which is a notional velocity called the effective exhaust velocity . This is higher than the actual exhaust velocity because the mass of the combustion air is not being accounted for. Actual and effective exhaust velocity are

468-434: A given propellant, when paired with a given engine, can accelerate its own initial mass at 1 g. The longer it can accelerate its own mass, the more delta-V it delivers to the whole system. In other words, given a particular engine and a mass of a particular propellant, specific impulse measures for how long a time that engine can exert a continuous force (thrust) until fully burning that mass of propellant. A given mass of

546-526: A heavier engine with a higher specific impulse may not be as effective in gaining altitude, distance, or velocity as a lighter engine with a lower specific impulse, especially if the latter engine possesses a higher thrust-to-weight ratio . This is a significant reason for most rocket designs having multiple stages. The first stage is optimised for high thrust to boost the later stages with higher specific impulse into higher altitudes where they can perform more efficiently. The most common unit for specific impulse

624-421: A maximum thrust of 5.7 N (1.3 lbf). Momentum In Newtonian mechanics , momentum ( pl. : momenta or momentums ; more specifically linear momentum or translational momentum ) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then

702-656: A momentum of 1 kg⋅m/s due north measured with reference to the ground. The momentum of a system of particles is the vector sum of their momenta. If two particles have respective masses m 1 and m 2 , and velocities v 1 and v 2 , the total momentum is p = p 1 + p 2 = m 1 v 1 + m 2 v 2 . {\displaystyle {\begin{aligned}p&=p_{1}+p_{2}\\&=m_{1}v_{1}+m_{2}v_{2}\,.\end{aligned}}} The momenta of more than two particles can be added more generally with

780-417: A more energy-dense propellant can burn for a longer duration than some less energy-dense propellant made to exert the same force while burning in an engine. Different engine designs burning the same propellant may not be equally efficient at directing their propellant's energy into effective thrust. For all vehicles, specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by

858-417: A much higher specific impulse than rocket engines. For air-breathing engines, only the fuel mass is counted, not the mass of air passing through the engine. Air resistance and the engine's inability to keep a high specific impulse at a fast burn rate are limiting factors to the propellant consumption rate. If it were not for air resistance and the reduction of propellant during flight, specific impulse would be

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936-421: A much larger specific impulse than a rocket; for example a turbofan jet engine may have a specific impulse of 6,000 seconds or more at sea level whereas a rocket would be between 200 and 400 seconds. An air-breathing engine is thus much more propellant efficient than a rocket engine, because the air serves as reaction mass and oxidizer for combustion which does not have to be carried as propellant, and

1014-400: A rocket can be defined in terms of thrust per unit mass flow of propellant. This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, v e . "In actual rocket nozzles, the exhaust velocity is not really uniform over

1092-413: Is a good example of an almost totally elastic collision, due to their high rigidity , but when bodies come in contact there is always some dissipation . A head-on elastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are v A1 and v B1 before the collision and v A2 and v B2 after,

1170-599: Is a measurable quantity, and the measurement depends on the frame of reference . For example: if an aircraft of mass 1000 kg is flying through the air at a speed of 50 m/s its momentum can be calculated to be 50,000 kg.m/s. If the aircraft is flying into a headwind of 5 m/s its speed relative to the surface of the Earth is only 45 m/s and its momentum can be calculated to be 45,000 kg.m/s. Both calculations are equally correct. In both frames of reference, any change in momentum will be found to be consistent with

1248-484: Is a measure of how efficiently a reaction mass engine, such as a rocket using propellant or a jet engine using fuel, generates thrust . A propulsion system with a higher specific impulse uses the mass of the propellant more efficiently. In the case of a rocket, this means less propellant needed for a given delta- v , so that the vehicle attached to the engine can more efficiently gain altitude and velocity. For engines like cold gas thrusters whose reaction mass

1326-490: Is also ionized, which would interfere with radio communication with the rocket. Nuclear thermal rocket engines differ from conventional rocket engines in that energy is supplied to the propellants by an external nuclear heat source instead of the heat of combustion . The nuclear rocket typically operates by passing liquid hydrogen gas through an operating nuclear reactor. Testing in the 1960s yielded specific impulses of about 850 seconds (8,340 m/s), about twice that of

1404-450: Is also valid for air-breathing jet engines, but is rarely used in practice. (Note that different symbols are sometimes used; for example, c is also sometimes seen for exhaust velocity. While the symbol I sp {\displaystyle I_{\text{sp}}} might logically be used for specific impulse in units of (N·s )/(m·kg); to avoid confusion, it is desirable to reserve this for specific impulse measured in seconds.) It

1482-466: Is an inelastic collision . An elastic collision is one in which no kinetic energy is transformed into heat or some other form of energy. Perfectly elastic collisions can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps the objects apart. A slingshot maneuver of a satellite around a planet can also be viewed as a perfectly elastic collision. A collision between two pool balls

1560-452: Is an expression of one of the fundamental symmetries of space and time: translational symmetry . Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics , allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems the conserved quantity is generalized momentum , and in general this is different from the kinetic momentum defined above. The concept of generalized momentum

1638-505: Is carried over into quantum mechanics, where it becomes an operator on a wave function . The momentum and position operators are related by the Heisenberg uncertainty principle . In continuous systems such as electromagnetic fields , fluid dynamics and deformable bodies , a momentum density can be defined as momentum per volume (a volume-specific quantity ). A continuum version of the conservation of momentum leads to equations such as

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1716-605: Is equal to the instantaneous force F acting on it, F = d p d t . {\displaystyle F={\frac {{\text{d}}p}{{\text{d}}t}}.} If the net force experienced by a particle changes as a function of time, F ( t ) , the change in momentum (or impulse J ) between times t 1 and t 2 is Δ p = J = ∫ t 1 t 2 F ( t ) d t . {\displaystyle \Delta p=J=\int _{t_{1}}^{t_{2}}F(t)\,{\text{d}}t\,.} Impulse

1794-434: Is impractical. Lithium and fluorine are both extremely corrosive, lithium ignites on contact with air, fluorine ignites on contact with most fuels, and hydrogen, while not hypergolic, is an explosive hazard. Fluorine and the hydrogen fluoride (HF) in the exhaust are very toxic, which damages the environment, makes work around the launch pad difficult, and makes getting a launch license that much more difficult. The rocket exhaust

1872-493: Is inversely proportional to specific fuel consumption (SFC) by the relationship I sp = 1/( g o ·SFC) for SFC in kg/(N·s) and I sp = 3600/SFC for SFC in lb/(lbf·hr). An example of a specific impulse measured in time is 453 seconds, which is equivalent to an effective exhaust velocity of 4.440 km/s (14,570 ft/s), for the RS-25 engines when operating in a vacuum. An air-breathing jet engine typically has

1950-407: Is known as Euler's first law . If the net force F applied to a particle is constant, and is applied for a time interval Δ t , the momentum of the particle changes by an amount Δ p = F Δ t . {\displaystyle \Delta p=F\Delta t\,.} In differential form, this is Newton's second law ; the rate of change of the momentum of a particle

2028-468: Is measured in the derived units of the newton second (1 N⋅s = 1 kg⋅m/s) or dyne second (1 dyne⋅s = 1 g⋅cm/s) Under the assumption of constant mass m , it is equivalent to write F = d ( m v ) d t = m d v d t = m a , {\displaystyle F={\frac {{\text{d}}(mv)}{{\text{d}}t}}=m{\frac {{\text{d}}v}{{\text{d}}t}}=ma,} hence

2106-423: Is needed to produce a given thrust for a given time and the more efficient the propellant is. This should not be confused with the physics concept of energy efficiency , which can decrease as specific impulse increases, since propulsion systems that give high specific impulse require high energy to do so. Thrust and specific impulse should not be confused. Thrust is the force supplied by the engine and depends on

2184-466: Is numerically equivalent to 3 newtons. In a closed system (one that does not exchange any matter with its surroundings and is not acted on by external forces) the total momentum remains constant. This fact, known as the law of conservation of momentum , is implied by Newton's laws of motion . Suppose, for example, that two particles interact. As explained by the third law, the forces between them are equal in magnitude but opposite in direction. If

2262-421: Is only the fuel they carry, specific impulse is exactly proportional to the effective exhaust gas velocity. In an atmospheric context, specific impulse can include the contribution to impulse provided by the mass of external air that is accelerated by the engine, such as by fuel combustion or by external propeller. Jet engines and turbofans breathe external air for both combustion and bypass, and therefore have

2340-408: Is proportional to the effective exhaust velocity. A spacecraft without propulsion follows an orbit determined by its trajectory and any gravitational field. Deviations from the corresponding velocity pattern (these are called Δ v ) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change. When an engine is run within the atmosphere, the exhaust velocity

2418-410: Is reduced by atmospheric pressure, in turn reducing specific impulse. This is a reduction in the effective exhaust velocity, versus the actual exhaust velocity achieved in vacuum conditions. In the case of gas-generator cycle rocket engines, more than one exhaust gas stream is present as turbopump exhaust gas exits through a separate nozzle. Calculating the effective exhaust velocity requires averaging

RD-701 - Misplaced Pages Continue

2496-409: Is related to the thrust , or forward force on the rocket by the equation: F thrust = v e ⋅ m ˙ , {\displaystyle F_{\text{thrust}}=v_{\text{e}}\cdot {\dot {m}},} where m ˙ {\displaystyle {\dot {m}}} is the propellant mass flow rate, which is the rate of decrease of

2574-452: Is that it may be used for rockets, where all the reaction mass is carried on board, as well as airplanes, where most of the reaction mass is taken from the atmosphere. In addition, giving the result as a unit of time makes the result easily comparable between calculations in SI units, imperial units, US customary units or other unit framework. The English unit pound mass is more commonly used than

2652-422: Is the center of mass frame – one that is moving with the center of mass. In this frame, the total momentum is zero. If two particles, each of known momentum, collide and coalesce, the law of conservation of momentum can be used to determine the momentum of the coalesced body. If the outcome of the collision is that the two particles separate, the law is not sufficient to determine the momentum of each particle. If

2730-401: Is the product of the average specific gravity of a given propellant mixture and the specific impulse. While less important than the specific impulse, it is an important measure in launch vehicle design, as a low specific impulse implies that bigger tanks will be required to store the propellant, which in turn will have a detrimental effect on the launch vehicle's mass ratio . Specific impulse

2808-478: Is the second, as values are identical regardless of whether the calculations are done in SI , imperial , or US customary units. Nearly all manufacturers quote their engine performance in seconds, and the unit is also useful for specifying aircraft engine performance. The use of metres per second to specify effective exhaust velocity is also reasonably common. The unit is intuitive when describing rocket engines, although

2886-455: Is unchanged. Forces such as Newtonian gravity, which depend only on the scalar distance between objects, satisfy this criterion. This independence of reference frame is called Newtonian relativity or Galilean invariance . A change of reference frame, can, often, simplify calculations of motion. For example, in a collision of two particles, a reference frame can be chosen, where, one particle begins at rest. Another, commonly used reference frame,

2964-475: Is used to pump kerosene and oxygen, the other is used to pump hydrogen and oxygen. In mode one, both burn kerosene. Liquid hydrogen is combined with kerosene and oxygen rich preburner exhaust in the combustion chamber. In this mode, it produces 4 MN of thrust, with a vacuum specific impulse of 415s, using 73.7 kg/s (12.6% of propellant mass) of kerosene, 29.5 kg/s (6% of propellant mass) of hydrogen, and 388.4 kg/s (81.4% of propellant mass) of oxygen. In mode two,

3042-414: Is used, impulse is divided by propellant weight (weight is a measure of force), resulting in units of time (seconds). These two formulations differ from each other by the standard gravitational acceleration ( g 0 ) at the surface of the earth. The rate of change of momentum of a rocket (including its propellant) per unit time is equal to the thrust. The higher the specific impulse, the less propellant

3120-459: The Franck–Hertz experiment ); and particle accelerators in which the kinetic energy is converted into mass in the form of new particles. In a perfectly inelastic collision (such as a bug hitting a windshield), both bodies have the same motion afterwards. A head-on inelastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If

3198-532: The Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids. Momentum is a vector quantity : it has both magnitude and direction. Since momentum has a direction, it can be used to predict the resulting direction and speed of motion of objects after they collide. Below, the basic properties of momentum are described in one dimension. The vector equations are almost identical to

RD-701 - Misplaced Pages Continue

3276-404: The effective exhaust velocity while reducing the actual exhaust velocity. Again, this is because the mass of the air is not counted in the specific impulse calculation, thus attributing all of the thrust momentum to the mass of the fuel component of the exhaust, and omitting the reaction mass, inert gas, and effect of driven fans on overall engine efficiency from consideration. Essentially,

3354-675: The Space Shuttle engines. A variety of other rocket propulsion methods, such as ion thrusters , give much higher specific impulse but with much lower thrust; for example the Hall-effect thruster on the SMART-1 satellite has a specific impulse of 1,640 s (16.1 km/s) but a maximum thrust of only 68 mN (0.015 lbf). The variable specific impulse magnetoplasma rocket (VASIMR) engine currently in development will theoretically yield 20 to 300 km/s (66,000 to 984,000 ft/s), and

3432-408: The actual exhaust speed is much lower, so the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust. While the actual exhaust velocity is lower for air-breathing engines, the effective exhaust velocity is very high for jet engines. This is because the effective exhaust velocity calculation assumes that the carried propellant is providing all

3510-419: The amount of reaction mass flowing through the engine. Specific impulse measures the impulse produced per unit of propellant and is proportional to the exhaust velocity. Thrust and specific impulse are related by the design and propellants of the engine in question, but this relationship is tenuous. For example, LH 2 /LO 2 bipropellant produces higher I sp but lower thrust than RP-1 / LO 2 due to

3588-427: The burned fuel. Next, inert gases in the atmosphere absorb heat from combustion, and through the resulting expansion provide additional thrust. Lastly, for turbofans and other designs there is even more thrust created by pushing against intake air which never sees combustion directly. These all combine to allow a better match between the airspeed and the exhaust speed, which saves energy/propellant and enormously increases

3666-474: The definition of specific impulse as impulse per unit mass of propellant. Specific fuel consumption is inversely proportional to specific impulse and has units of g/(kN·s) or lb/(lbf·h). Specific fuel consumption is used extensively for describing the performance of air-breathing jet engines. Specific impulse, measured in seconds, can be thought of as how many seconds one kilogram of fuel can produce one kilogram of thrust. Or, more precisely, how many seconds

3744-492: The effective exhaust speed of the engines may be significantly different from the actual exhaust speed, especially in gas-generator cycle engines. For airbreathing jet engines , the effective exhaust velocity is not physically meaningful, although it can be used for comparison purposes. Metres per second are numerically equivalent to newton-seconds per kg (N·s/kg), and SI measurements of specific impulse can be written in terms of either units interchangeably. This unit highlights

3822-638: The entire exit cross section and such velocity profiles are difficult to measure accurately. A uniform axial velocity, v e , is assumed for all calculations which employ one-dimensional problem descriptions. This effective exhaust velocity represents an average or mass equivalent velocity at which propellant is being ejected from the rocket vehicle." The two definitions of specific impulse are proportional to one another, and related to each other by: v e = g 0 ⋅ I sp , {\displaystyle v_{\text{e}}=g_{0}\cdot I_{\text{sp}},} where This equation

3900-914: The equations expressing conservation of momentum and kinetic energy are: m A v A 1 + m B v B 1 = m A v A 2 + m B v B 2 1 2 m A v A 1 2 + 1 2 m B v B 1 2 = 1 2 m A v A 2 2 + 1 2 m B v B 2 2 . {\displaystyle {\begin{aligned}m_{A}v_{A1}+m_{B}v_{B1}&=m_{A}v_{A2}+m_{B}v_{B2}\\{\tfrac {1}{2}}m_{A}v_{A1}^{2}+{\tfrac {1}{2}}m_{B}v_{B1}^{2}&={\tfrac {1}{2}}m_{A}v_{A2}^{2}+{\tfrac {1}{2}}m_{B}v_{B2}^{2}\,.\end{aligned}}} A change of reference frame can simplify analysis of

3978-435: The exhaust gases having a lower density and higher velocity ( H 2 O vs CO 2 and H 2 O). In many cases, propulsion systems with very high specific impulse—some ion thrusters reach 10,000 seconds—produce low thrust. When calculating specific impulse, only propellant carried with the vehicle before use is counted. For a chemical rocket, the propellant mass therefore would include both fuel and oxidizer . In rocketry,

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4056-455: The following equation: F thrust = g 0 ⋅ I sp ⋅ m ˙ , {\displaystyle F_{\text{thrust}}=g_{0}\cdot I_{\text{sp}}\cdot {\dot {m}},} where: I sp in seconds is the amount of time a rocket engine can generate thrust, given a quantity of propellant whose weight is equal to the engine's thrust. The advantage of this formulation

4134-765: The following: p = ∑ i m i v i . {\displaystyle p=\sum _{i}m_{i}v_{i}.} A system of particles has a center of mass , a point determined by the weighted sum of their positions: r cm = m 1 r 1 + m 2 r 2 + ⋯ m 1 + m 2 + ⋯ = ∑ i m i r i ∑ i m i . {\displaystyle r_{\text{cm}}={\frac {m_{1}r_{1}+m_{2}r_{2}+\cdots }{m_{1}+m_{2}+\cdots }}={\frac {\sum _{i}m_{i}r_{i}}{\sum _{i}m_{i}}}.} If one or more of

4212-456: The force is between particles. Similarly, if there are several particles, the momentum exchanged between each pair of particles adds to zero, so the total change in momentum is zero. The conservation of the total momentum of a number of interacting particles can be expressed as m A v A + m B v B + m C v C + . . . = c o n s t

4290-1047: The initial velocities are known, the final velocities are given by v A 2 = ( m A − m B m A + m B ) v A 1 + ( 2 m B m A + m B ) v B 1 v B 2 = ( m B − m A m A + m B ) v B 1 + ( 2 m A m A + m B ) v A 1 . {\displaystyle {\begin{aligned}v_{A2}&=\left({\frac {m_{A}-m_{B}}{m_{A}+m_{B}}}\right)v_{A1}+\left({\frac {2m_{B}}{m_{A}+m_{B}}}\right)v_{B1}\\v_{B2}&=\left({\frac {m_{B}-m_{A}}{m_{A}+m_{B}}}\right)v_{B1}+\left({\frac {2m_{A}}{m_{A}+m_{B}}}\right)v_{A1}\,.\end{aligned}}} If one body has much greater mass than

4368-437: The mass is in kilograms and the velocity is in meters per second then the momentum is in kilogram meters per second (kg⋅m/s). In cgs units , if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters per second (g⋅cm/s). Being a vector, momentum has magnitude and direction. For example, a 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has

4446-490: The momentum of engine exhaust includes a lot more than just fuel, but specific impulse calculation ignores everything but the fuel. Even though the effective exhaust velocity for an air-breathing engine seems nonsensical in the context of actual exhaust velocity, this is still useful for comparing absolute fuel efficiency of different engines. A related measure, the density specific impulse , sometimes also referred to as Density Impulse and usually abbreviated as I s d

4524-411: The momentum of one particle after the collision is known, the law can be used to determine the momentum of the other particle. Alternatively if the combined kinetic energy after the collision is known, the law can be used to determine the momentum of each particle after the collision. Kinetic energy is usually not conserved. If it is conserved, the collision is called an elastic collision ; if not, it

4602-742: The negative sign indicating that the forces oppose. Equivalently, d d t ( p 1 + p 2 ) = 0. {\displaystyle {\frac {\text{d}}{{\text{d}}t}}\left(p_{1}+p_{2}\right)=0.} If the velocities of the particles are v A1 and v B1 before the interaction, and afterwards they are v A2 and v B2 , then m A v A 1 + m B v B 1 = m A v A 2 + m B v B 2 . {\displaystyle m_{A}v_{A1}+m_{B}v_{B1}=m_{A}v_{A2}+m_{B}v_{B2}.} This law holds no matter how complicated

4680-400: The net force is equal to the mass of the particle times its acceleration . Example : A model airplane of mass 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s. The net force required to produce this acceleration is 3  newtons due north. The change in momentum is 6 kg⋅m/s due north. The rate of change of momentum is 3 (kg⋅m/s)/s due north which

4758-468: The object's momentum p (from Latin pellere "push, drive") is: p = m v . {\displaystyle \mathbf {p} =m\mathbf {v} .} In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second . Newton's second law of motion states that

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4836-465: The only reaction mass is the propellant, so the specific impulse is calculated using an alternative method, giving results with units of seconds. Specific impulse is defined as the thrust integrated over time per unit weight -on-Earth of the propellant: I sp = v e g 0 , {\displaystyle I_{\text{sp}}={\frac {v_{\text{e}}}{g_{0}}},} where In rockets, due to atmospheric effects,

4914-447: The other, its velocity will be little affected by a collision while the other body will experience a large change. In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy (such as heat or sound ). Examples include traffic collisions , in which the effect of loss of kinetic energy can be seen in the damage to the vehicles; electrons losing some of their energy to atoms (as in

4992-456: The particles are numbered 1 and 2, the second law states that F 1 = ⁠ d p 1 / d t ⁠ and F 2 = ⁠ d p 2 / d t ⁠ . Therefore, d p 1 d t = − d p 2 d t , {\displaystyle {\frac {{\text{d}}p_{1}}{{\text{d}}t}}=-{\frac {{\text{d}}p_{2}}{{\text{d}}t}},} with

5070-421: The particles is moving, the center of mass of the system will generally be moving as well (unless the system is in pure rotation around it). If the total mass of the particles is m {\displaystyle m} , and the center of mass is moving at velocity v cm , the momentum of the system is: p = m v cm . {\displaystyle p=mv_{\text{cm}}.} This

5148-475: The preburner used to pump kerosene is shut down, and the other is switched to burning hydrogen. A small amount of kerosene is still used to ensure oxygen is effectively atomised. Gases from the preburner combined with hydrogen in the combustion chamber. In this mode it burns 27.4 kg/s of hydrogen, and 148 kg/s of oxygen. Thrust reduces to 1.6 MN, and specific impulse increases to 460s. Specific impulse Specific impulse (usually abbreviated I sp )

5226-486: The rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference , but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics , quantum mechanics , quantum field theory , and general relativity . It

5304-414: The reaction mass and all the thrust. Hence effective exhaust velocity is not physically meaningful for air-breathing engines; nevertheless, it is useful for comparison with other types of engines. The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was 542 seconds (5.32 km/s) with a tripropellant of lithium , fluorine , and hydrogen . However, this combination

5382-402: The relevant laws of physics. Suppose x is a position in an inertial frame of reference. From the point of view of another frame of reference, moving at a constant speed u relative to the other, the position (represented by a primed coordinate) changes with time as x ′ = x − u t . {\displaystyle x'=x-ut\,.} This is called

5460-422: The same in rocket engines operating in a vacuum. The amount of propellant can be measured either in units of mass or weight. If mass is used, specific impulse is an impulse per unit of mass, which dimensional analysis shows to have units of speed, specifically the effective exhaust velocity . As the SI system is mass-based, this type of analysis is usually done in meters per second. If a force-based unit system

5538-644: The same speed. Adding the speed of the center of mass to both, we find that the body that was moving is now stopped and the other is moving away at speed v . The bodies have exchanged their velocities. Regardless of the velocities of the bodies, a switch to the center of mass frame leads us to the same conclusion. Therefore, the final velocities are given by v A 2 = v B 1 v B 2 = v A 1 . {\displaystyle {\begin{aligned}v_{A2}&=v_{B1}\\v_{B2}&=v_{A1}\,.\end{aligned}}} In general, when

5616-414: The scalar equations (see multiple dimensions ). The momentum of a particle is conventionally represented by the letter p . It is the product of two quantities, the particle's mass (represented by the letter m ) and its velocity ( v ): p = m v . {\displaystyle p=mv.} The unit of momentum is the product of the units of mass and velocity. In SI units , if

5694-418: The second reference frame is also an inertial frame and the accelerations are the same: a ′ = d v ′ d t = a . {\displaystyle a'={\frac {{\text{d}}v'}{{\text{d}}t}}=a\,.} Thus, momentum is conserved in both reference frames. Moreover, as long as the force has the same form, in both frames, Newton's second law

5772-574: The slug, and when using pounds per second for mass flow rate, it is more convenient to express standard gravity as 1 pound-force per pound-mass. Note that this is equivalent to 32.17405 ft/s2, but expressed in more convenient units. This gives: F thrust = I sp ⋅ m ˙ ⋅ ( 1 l b f l b m ) . {\displaystyle F_{\text{thrust}}=I_{\text{sp}}\cdot {\dot {m}}\cdot \left(1\mathrm {\frac {lbf}{lbm}} \right).} In rocketry,

5850-490: The specific impulse varies with altitude, reaching a maximum in a vacuum. This is because the exhaust velocity isn't simply a function of the chamber pressure, but is a function of the difference between the interior and exterior of the combustion chamber . Values are usually given for operation at sea level ("sl") or in a vacuum ("vac"). Because of the geocentric factor of g 0 in the equation for specific impulse, many prefer an alternative definition. The specific impulse of

5928-415: The two mass flows as well as accounting for any atmospheric pressure. For air-breathing jet engines, particularly turbofans , the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This happens for several reasons. First, a good deal of additional momentum is obtained by using air as reaction mass, such that combustion products in the exhaust have more mass than

6006-446: The vehicle's mass. A rocket must carry all its propellant with it, so the mass of the unburned propellant must be accelerated along with the rocket itself. Minimizing the mass of propellant required to achieve a given change in velocity is crucial to building effective rockets. The Tsiolkovsky rocket equation shows that for a rocket with a given empty mass and a given amount of propellant, the total change in velocity it can accomplish

6084-531: Was surpassed by the SpaceX Raptor engine, which reached 33 MPa (330 bar) during a static fire test. The 'RD-701' is a two chamber engine. It can operate in two modes. In the first, it burns both kerosene and hydrogen, granting it greater thrust and impulse density, allowing for smaller, lighter tanks. In the second, it burns only hydrogen, allowing for greater specific impulse. The RD-701 has two preburners per combustion chamber, both of which run oxygen rich. One

#198801