2340:
discharge into a bell nozzle. At higher altitudes, where the ambient pressure is lower, the central nozzle would be shut off, reducing the throat area and thereby increasing the nozzle area ratio. These designs require additional complexity, but an advantage of having two thrust chambers is that they can be configured to burn different propellants or different fuel mixture ratios. Similarly, Aerojet has also designed a nozzle called the "Thrust
Augmented Nozzle", which injects propellant and oxidiser directly into the nozzle section for combustion, allowing larger area ratio nozzles to be used deeper in an atmosphere than they would without augmentation due to effects of flow separation. They would again allow multiple propellants to be used (such as RP-1), further increasing thrust.
130:
pressure, it decreases the net thrust produced by the rocket, which can be seen through a force-balance analysis. If ambient pressure is lower, while the force balance indicates that the thrust will increase, the isentropic Mach relations show that the area ratio of the nozzle could have been greater, which would result in a higher exit velocity of the propellant, increasing thrust. For rockets traveling from the Earth to orbit, a simple nozzle design is only optimal at one altitude, losing efficiency and wasting fuel at other altitudes.
2175:
212:
39:
31:
2718:
1876:
1369:
171:
provided the majority of the initial liftoff thrust. In the vacuum of space virtually all nozzles are underexpanded because to fully expand the gas's the nozzle would have to be infinitely long, as a result engineers have to choose a design which will take advantage of the extra expansion (thrust and
145:
Slight overexpansion causes a slight reduction in efficiency, but otherwise does little harm. However, if the exit pressure is less than approximately 40% that of ambient, then "flow separation" occurs. This can cause exhaust instabilities that can cause damage to the nozzle, control difficulties of
2256:
Other design aspects affect the efficiency of a rocket nozzle. The nozzle's throat should have a smooth radius. The internal angle that narrows to the throat also has an effect on the overall efficiency, but this is small. The exit angle of the nozzle needs to be as small as possible (about 12°) in
158:
design, the second stage rocket engine is primarily designed for use at high altitudes, only providing additional thrust after the first-stage engine performs the initial liftoff. In this case, designers will usually opt for an overexpanded nozzle (at sea level) design for the second stage, making
914:
system of the rocket through the application of Newton's third law of motion: "For every action there is an equal and opposite reaction". A gas or working fluid is accelerated out the rear of the rocket engine nozzle, and the rocket is accelerated in the opposite direction. The thrust of a rocket
2339:
These have either two throats or two thrust chambers (with corresponding throats). The central throat is of a standard design and is surrounded by an annular throat, which exhausts gases from the same (dual-throat) or a separate (dual-expander) thrust chamber. Both throats would, in either case,
2195:
If a nozzle is under- or overexpanded, then loss of efficiency occurs relative to an ideal nozzle. Grossly overexpanded nozzles have improved efficiency relative to an underexpanded nozzle (though are still less efficient than a nozzle with the ideal expansion ratio), however the exhaust jet is
2301:
Each of these allows the supersonic flow to adapt to the ambient pressure by expanding or contracting, thereby changing the exit ratio so that it is at (or near) optimal exit pressure for the corresponding altitude. The plug and aerospike nozzles are very similar in that they are radial in-flow
2208:
The supersonic nature of the exhaust jet means that the pressure of the exhaust can be significantly different from ambient pressure—the outside air is unable to equalize the pressure upstream due to the very high jet velocity. Therefore, for supersonic nozzles, it is actually possible for the
129:
The optimal size of a rocket engine nozzle is achieved when the exit pressure equals ambient (atmospheric) pressure, which decreases with increasing altitude. The reason for this is as follows: using a quasi-one-dimensional approximation of the flow, if ambient pressure is higher than the exit
1124:
2240:
The shape of the nozzle also modestly affects how efficiently the expansion of the exhaust gases is converted into linear motion. The simplest nozzle shape has a ~15° cone half-angle, which is about 98% efficient. Smaller angles give very slightly higher efficiency, larger angles give lower
180:
For nozzles that are used in vacuum or at very high altitude, it is impossible to match ambient pressure; rather, nozzles with larger area ratio are usually more efficient. However, a very long nozzle has significant mass, a drawback in and of itself. A length that optimises overall vehicle
2252:
There is also a theoretically optimal nozzle shape for maximal exhaust speed. However, a shorter bell shape is typically used, which gives better overall performance due to its much lower weight, shorter length, lower drag losses, and only very marginally lower exhaust speed.
181:
performance typically has to be found. Additionally, as the temperature of the gas in the nozzle decreases, some components of the exhaust gases (such as water vapour from the combustion process) may condense or even freeze. This is highly undesirable and needs to be avoided.
2248:
or parabolic shapes. These give perhaps 1% higher efficiency than the cone nozzle and can be shorter and lighter. They are widely used on launch vehicles and other rockets where weight is at a premium. They are, of course, harder to fabricate, so are typically more costly.
2074:
133:
Just past the throat, the pressure of the gas is higher than ambient pressure and needs to be lowered between the throat and the nozzle exit by expansion. If the pressure of the exhaust leaving the nozzle exit is still above ambient pressure, then a nozzle is said to be
2302:
designs but plug nozzles feature a solid centerbody (sometimes truncated) and aerospike nozzles have a "base-bleed" of gases to simulate a solid center-body. ED nozzles are radial out-flow nozzles with the flow deflected by a center pintle.
153:
performance, the pressure of the gases exiting nozzle should be at sea-level pressure when the rocket is near sea level (at takeoff). However, a nozzle designed for sea-level operation will quickly lose efficiency at higher altitudes. In a
1735:
2232:
The ratio of the area of the narrowest part of the nozzle to the exit plane area is mainly what determines how efficiently the expansion of the exhaust gases is converted into linear velocity, the exhaust velocity, and therefore the
2215:
This separation generally occurs if the exit pressure drops below roughly 30-45% of ambient, but separation may be delayed to far lower pressures if the nozzle is designed to increase the pressure at the rim, as is achieved with the
420:
1228:
2223:
In addition, as the rocket engine starts up or throttles, the chamber pressure varies, and this generates different levels of efficiency. At low chamber pressures the engine is almost inevitably going to be grossly over-expanded.
2162:
921:
215:
Diagram of a de Laval nozzle, showing flow velocity (v) increasing in the direction of flow, with decreases in temperature (t) and pressure (p). The Mach number (M) increases from subsonic, to sonic at the throat, to
2347:
calls its design "Secondary
Injection Thrust Vector Control System"; strontium perchlorate is injected through various fluid paths in the nozzle to achieve the desired control. Some ICBMs and boosters, such as the
2170:
Essentially then, for rocket nozzles, the ambient pressure acting on the engine cancels except over the exit plane of the rocket engine in a rearward direction, while the exhaust jet generates forward thrust.
926:
1970:
2212:
If the exit pressure is too low, then the jet can separate from the nozzle. This is often unstable, and the jet will generally cause large off-axis thrusts and may mechanically damage the nozzle.
1178:
590:
1727:
1962:
203:. However, there are often thermal design challenges presented by the coils themselves, particularly if superconducting coils are used to form the throat and expansion fields.
1639:
1605:
1208:
1906:
1673:
1571:
1537:
1503:
1469:
729:
695:
661:
624:
274:
velocities. As the throat constricts, the gas is forced to accelerate until at the nozzle throat, where the cross-sectional area is the least, the linear velocity becomes
1935:
1435:
544:
1871:{\displaystyle I_{\text{sp}}={\frac {F}{{\dot {m}}\,g_{\text{o}}}}={\frac {{\dot {m}}\,v_{\text{e}}}{{\dot {m}}\,g_{\text{o}}}}={\frac {v_{\text{e}}}{g_{\text{o}}}}}
2325:
These are generally very similar to bell nozzles but include an insert or mechanism by which the exit area ratio can be increased as ambient pressure is reduced.
1364:{\displaystyle I_{\text{sp}}={\frac {F}{{\dot {m}}g_{\text{o}}}}={\frac {{\dot {m}}v_{\text{eq}}}{{\dot {m}}g_{\text{o}}}}={\frac {v_{\text{eq}}}{g_{\text{o}}}},}
199:
instead of walls made of solid materials. These can be advantageous, since a magnetic field itself cannot melt, and the plasma temperatures can reach millions of
188:
1399:
763:
514:
481:
450:
291:
2703:
2495:
149:
In some cases, it is desirable for reliability and safety reasons to ignite a rocket engine on the ground that will be used all the way to orbit. For optimal
2085:
2297:(SERN), a linear expansion nozzle, where the gas pressure transfers work only on one side and which could be described as a single-sided aerospike nozzle.
1119:{\displaystyle {\begin{aligned}F&={\dot {m}}v_{\text{e}}+\left(p_{\text{e}}-p_{\text{o}}\right)A_{\text{e}}\\&={\dot {m}}\left,\end{aligned}}}
2615:
820:
As an example calculation using the above equation, assume that the propellant combustion gases are: at an absolute pressure entering the nozzle of
2801:
2671:
2566:
2592:
2603:
2643:
2581:
861:
The technical literature can be very confusing because many authors fail to explain whether they are using the universal gas law constant
2343:
Liquid injection thrust vectoring nozzles are another advanced design that allow pitch and yaw control from un-gimbaled nozzles. India's
2701:
Journal of
Propulsion and Power Vol.18 No.1, "Experimental and Analytical Design Verification of the Dual-Bell Concept", Hagemann et al.
2205:
As the gas travels down the expansion part of the nozzle, the pressure and temperature decrease, while the speed of the gas increases.
2939:
85:
are injected into a combustion chamber to burn, and the combustion chamber leads into a nozzle which converts the energy contained in
2749:
2069:{\displaystyle I_{\text{sp,vac}}={\frac {1}{g_{\text{o}}}}\left(v_{\text{e}}+{\frac {p_{\text{e}}A_{\text{e}}}{\dot {m}}}\right),}
2465:
278:. From the throat the cross-sectional area then increases, the gas expands and the linear velocity becomes progressively more
259:
The gas flow is non-turbulent and axisymmetric from gas inlet to exhaust gas exit (i.e., along the nozzle's axis of symmetry).
2294:
2266:
2276:
34:
Figure 1: A de Laval nozzle, showing approximate flow velocity increasing from green to red in the direction of flow
2974:
2903:
2794:
2700:
2504:
159:
it more efficient at higher altitudes, where the ambient pressure is lower. This was the technique employed on the
110:
2167:
which is simply the vacuum thrust minus the force of the ambient atmospheric pressure acting over the exit plane.
167:(SSMEs), which spent most of their powered trajectory in near-vacuum, while the shuttle's two sea-level efficient
2383:
2217:
1135:
550:
2861:
1692:
226:
The analysis of gas flow through de Laval nozzles involves a number of concepts and simplifying assumptions:
2415:
89:
combustion products into kinetic energy by accelerating the gas to high velocity and near-ambient pressure.
2619:
2419:
629:
2678:
2209:
pressure of the gas exiting the nozzle to be significantly below or very greatly above ambient pressure.
2979:
2787:
2454:
911:
113:, one of the fathers of modern rocketry. It has since been used in almost all rocket engines, including
1940:
2856:
168:
2950:
2876:
2851:
2410:
1617:
1583:
1186:
1884:
1651:
1549:
1515:
1481:
1447:
707:
673:
639:
602:
2821:
101:
were developed in the 1500s. The de Laval nozzle was originally developed in the 19th century by
2744:
1911:
1411:
285:
The linear velocity of the exiting exhaust gases can be calculated using the following equation
172:
efficiency) whilst also not adding excessive weight and compromising the vehicle's performance.
2640:
876:
which only applies to a specific individual gas. The relationship between the two constants is
2667:
2562:
2449:
2394:
263:
246:
82:
51:
2418:– a single-stage-to-orbit spaceplane powered by hybrid air-breathing/internal-oxygen engine (
2368:– when a gas velocity reaches the speed of sound in the gas as it flows through a restriction
851: = 22 kg/kmol. Using those values in the above equation yields an exhaust velocity
529:
2969:
2459:
2405:
2309:
2288:
1678:
1219:
192:
98:
67:
2898:
2826:
2759:
2707:
2647:
2371:
2318:
1215:
593:
415:{\displaystyle v_{\text{e}}={\sqrt {{\frac {TR}{M}}\,{\frac {2\gamma }{\gamma -1}}\left}}}
221:
184:
102:
55:
2689:
2174:
211:
2836:
2690:
Journal of
Propulsion and Power Vol.14 No.5, "Advanced Rocket Nozzles", Hagemann et al.
2471:
2431:
1384:
788:
748:
519:
499:
466:
435:
271:
196:
910:
is the force that moves a rocket through the air or space. Thrust is generated by the
38:
2963:
2908:
2886:
2871:
2443:
2157:{\displaystyle F=I_{\text{sp,vac}}\,g_{\text{o}}{\dot {m}}-A_{\text{e}}p_{\text{o}},}
738:
160:
106:
59:
17:
2921:
2881:
2353:
800:
794:
490:
114:
2769:
2545:
858:= 2802 m/s or 2.80 km/s which is consistent with above typical values.
817:
because it based on the assumption that the exhaust gas behaves as an ideal gas.
146:
the vehicle or the engine, and in more extreme cases, destruction of the engine.
2926:
2846:
2831:
2810:
2377:
2365:
2282:
2245:
456:
275:
155:
2729:
2866:
2841:
2388:
2349:
1211:
279:
253:
238:
63:
30:
2531:
2891:
2754:
2257:
order to minimize the chances of separation problems at low exit pressures.
866:
231:
2664:
Rocket
Propulsion Elements: An Introduction to the Engineering of Rockets
2559:
Rocket
Propulsion Elements: An Introduction to the Engineering of Rockets
734:
86:
847:
K; with an isentropic expansion factor of γ = 1.22 and a molar mass of
242:
150:
252:
The gas flow rate is constant (i.e., steady) during the period of the
2425:
2374:– a convergent-divergent nozzle designed to produce supersonic speeds
2234:
907:
200:
78:
270:
As the combustion gas enters the rocket nozzle, it is traveling at
2730:
THRUST AUGMENTED NOZZLE (TAN) the New
Paradigm for Booster Rockets
2399:
2173:
1937:, it is possible to define a constant quantity that is the vacuum
1610:
equivalent (or effective) velocity of gas at nozzle exhaust (m/s)
210:
37:
29:
2764:
2237:
of the rocket engine. The gas properties have an effect as well.
2775:
2750:
NASA Space
Vehicle Design Criteria, Liquid Rocket Engine Nozzles
2437:
2344:
164:
74:
2783:
2779:
2244:
More complex shapes of revolution are frequently used, such as
2265:
A number of more sophisticated designs have been proposed for
1210:
is the ratio of the thrust produced to the weight flow of the
187:
have been proposed for some types of propulsion (for example,
118:
1881:
In cases where this may not be so, since for a rocket nozzle
245:, as the result of the assumption of non-viscous fluid, and
2446:– the visible bands formed in the exhaust of rocket engines
828:
MPa and exit the rocket exhaust at an absolute pressure of
109:. It was first used in an early rocket engine developed by
2774:
793:
2.9 to 4.5 km/s (6500 to 10100 mi/h) for liquid
787:
1.7 to 2.9 km/s (3800 to 6500 mi/h) for liquid
2497:
NASA SP-125, Design of Liquid
Propellant Rocket Engines
138:; if the exhaust is below ambient pressure, then it is
1681:(at sea level on Earth); approximately 9.807 m/s
1129:
the term in brackets is known as equivalent velocity,
666:
specific heat capacity, under constant volume, of gas
2088:
1973:
1943:
1914:
1887:
1738:
1695:
1654:
1620:
1586:
1552:
1518:
1484:
1450:
1414:
1387:
1231:
1189:
1138:
924:
751:
710:
676:
642:
605:
553:
532:
502:
469:
438:
294:
783:
for rocket engines burning various propellants are:
2770:"Rocket Propulsion" on Robert Braeuning's Web Site
2156:
2068:
1956:
1929:
1900:
1870:
1721:
1667:
1633:
1599:
1565:
1531:
1497:
1463:
1429:
1393:
1363:
1202:
1172:
1118:
799:2.1 to 3.2 km/s (4700 to 7200 mi/h) for
757:
723:
689:
655:
618:
584:
538:
508:
475:
444:
414:
2561:(6th ed.). Wiley-Interscience. p. 636.
117:'s implementation, which made possible Germany's
1542:external ambient, or free stream, pressure (Pa)
776:Some typical values of the exhaust gas velocity
2391:– engines propelled by jets (including rockets)
869:or whether they are using the gas law constant
700:velocity of gas at the nozzle exit plane (m/s)
2765:Richard Nakka's Experimental Rocketry Web Site
2272:Nozzles with an atmospheric boundary include:
2201:Aerostatic back-pressure and optimal expansion
189:Variable Specific Impulse Magnetoplasma Rocket
2795:
8:
2305:Controlled flow-separation nozzles include:
1689:For a perfectly expanded nozzle case, where
81:to anywhere between two and several hundred
2541:
2539:
1576:cross-sectional area of nozzle exhaust (m)
1378:
429:
2802:
2788:
2780:
1173:{\displaystyle F={\dot {m}}v_{\text{eq}}.}
585:{\displaystyle =c_{\text{p}}/c_{\text{v}}}
73:Simply: propellants pressurized by either
2657:
2655:
2145:
2135:
2117:
2116:
2110:
2105:
2099:
2087:
2046:
2039:
2029:
2022:
2013:
1996:
1987:
1978:
1972:
1948:
1942:
1916:
1915:
1913:
1892:
1886:
1860:
1850:
1844:
1832:
1827:
1816:
1815:
1807:
1802:
1791:
1790:
1787:
1775:
1770:
1759:
1758:
1752:
1743:
1737:
1722:{\displaystyle p_{\text{e}}=p_{\text{o}}}
1713:
1700:
1694:
1659:
1653:
1625:
1619:
1591:
1585:
1557:
1551:
1523:
1517:
1489:
1483:
1455:
1449:
1416:
1415:
1413:
1386:
1350:
1340:
1334:
1322:
1307:
1306:
1298:
1283:
1282:
1279:
1267:
1252:
1251:
1245:
1236:
1230:
1194:
1188:
1161:
1146:
1145:
1137:
1098:
1078:
1071:
1058:
1051:
1038:
1018:
1017:
1001:
986:
973:
955:
940:
939:
925:
923:
750:
715:
709:
681:
675:
647:
641:
610:
604:
576:
567:
561:
552:
531:
501:
468:
437:
386:
371:
365:
326:
325:
310:
308:
299:
293:
2494:Huzel, D. K. & Huang, D. H. (1971).
1474:velocity of gas at nozzle exhaust (m/s)
2527:
2525:
2483:
1508:pressure of gas at nozzle exhaust (Pa)
768:absolute pressure of gas at inlet (Pa)
230:The combustion gas is assumed to be an
2489:
2487:
2315:bell nozzles with a removable insert,
7:
2755:NASA's "Beginners' Guide to Rockets"
2666:(7th ed.). Wiley-Interscience.
2503:(2nd ed.). NASA. Archived from
2220:(SSME) (1-2 psi at 15 psi ambient).
895:is the universal gas constant, and
839:MPa; at an absolute temperature of
2940:Timeline of heat engine technology
2438:SERN, Single-expansion ramp nozzle
1404:gross thrust of rocket engine (N)
632:, under constant pressure, of gas
25:
1957:{\displaystyle I_{\text{sp,vac}}}
915:engine nozzle can be defined as:
737:of gas at the nozzle exit plane (
2618:. March 16, 2009. Archived from
2546:Robert Braeuning's Equation 2.22
2466:Staged combustion cycle (rocket)
2434:– used to propel rocket vehicles
813:is sometimes referred to as the
191:, VASIMR), in which the flow of
2745:Exhaust gas velocity calculator
2178:Nozzles can be (top to bottom):
163:'s overexpanded (at sea level)
87:high pressure, high temperature
2641:PWR Engineering: Nozzle Design
2440:– a non-axisymmetric aerospike
899:is the molar mass of the gas.
207:de Laval nozzle in 1 dimension
1:
1634:{\displaystyle I_{\text{sp}}}
1600:{\displaystyle v_{\text{eq}}}
1440:mass flow rate of gas (kg/s)
1203:{\displaystyle I_{\text{sp}}}
2604:NASA:Rocket specific impulse
2462:– a measure of exhaust speed
2295:single-expansion ramp nozzle
1901:{\displaystyle p_{\text{e}}}
1668:{\displaystyle g_{\text{o}}}
1566:{\displaystyle A_{\text{e}}}
1532:{\displaystyle p_{\text{o}}}
1498:{\displaystyle p_{\text{e}}}
1464:{\displaystyle v_{\text{e}}}
724:{\displaystyle p_{\text{e}}}
690:{\displaystyle v_{\text{e}}}
656:{\displaystyle c_{\text{v}}}
619:{\displaystyle c_{\text{p}}}
2593:NASA: Rocket thrust summary
2532:Richard Nakka's Equation 12
2328:Dual-mode nozzles include:
2277:expansion-deflection nozzle
1964:for any given engine thus:
1648:
1614:
1580:
1546:
1512:
1478:
1444:
1408:
1381:
594:isentropic expansion factor
522:or weight of gas (kg/kmol)
2996:
2662:Sutton, George P. (2001).
2557:Sutton, George P. (1992).
1930:{\displaystyle {\dot {m}}}
1677:
1643:
1609:
1575:
1541:
1507:
1473:
1439:
1430:{\displaystyle {\dot {m}}}
1403:
815:ideal exhaust gas velocity
491:universal gas law constant
219:
2948:
2935:
2917:
2817:
2468:– a type of rocket engine
2384:Giovanni Battista Venturi
2218:Space Shuttle Main Engine
1220:English Engineering units
1214:. It is a measure of the
62:to expand and accelerate
27:Type of propelling nozzle
195:or ions are directed by
42:Density flow in a nozzle
2719:Thrust Augmented Nozzle
2416:Reaction Engines Skylon
2402:– Russian rocket engine
2356:, use similar designs.
2321:, or dual-bell nozzles.
1218:of a rocket engine. In
806:As a note of interest,
539:{\displaystyle \gamma }
2420:Reaction Engines SABRE
2197:
2158:
2070:
1958:
1931:
1902:
1872:
1729:, the formula becomes
1723:
1669:
1635:
1601:
1567:
1533:
1499:
1465:
1431:
1395:
1365:
1222:it can be obtained as
1204:
1174:
1120:
759:
725:
691:
657:
630:specific heat capacity
620:
586:
540:
510:
477:
446:
416:
266:as the fluid is a gas.
217:
43:
35:
2882:Steam (reciprocating)
2455:Spacecraft propulsion
2332:dual-expander nozzle,
2267:altitude compensation
2191:grossly overexpanded.
2177:
2159:
2071:
1959:
1932:
1903:
1873:
1724:
1670:
1644:specific impulse (s)
1636:
1602:
1568:
1534:
1500:
1466:
1432:
1396:
1366:
1205:
1183:The specific impulse
1175:
1121:
865:which applies to any
760:
726:
692:
658:
621:
587:
541:
511:
478:
447:
417:
214:
169:solid rocket boosters
41:
33:
18:Rocket engine nozzles
2760:The Aerospike Engine
2510:on 20 September 2022
2086:
1971:
1941:
1912:
1885:
1736:
1693:
1652:
1618:
1584:
1550:
1516:
1482:
1448:
1412:
1385:
1229:
1187:
1136:
922:
749:
708:
674:
640:
603:
551:
530:
500:
467:
459:of gas at inlet (K)
436:
292:
241:; i.e., at constant
48:rocket engine nozzle
2951:Thermodynamic cycle
2862:Pistonless (Rotary)
2852:Photo-Carnot engine
2582:NASA: Rocket thrust
2411:Pulsed rocket motor
2335:dual-throat nozzle.
1908:is proportional to
99:bell-shaped nozzles
2706:2011-06-16 at the
2646:2008-03-16 at the
2622:on October 2, 2011
2198:
2154:
2066:
1954:
1927:
1898:
1868:
1719:
1665:
1631:
1597:
1563:
1529:
1495:
1461:
1427:
1391:
1361:
1200:
1170:
1116:
1114:
755:
721:
687:
653:
616:
582:
536:
506:
473:
442:
412:
218:
44:
36:
2975:Rocket propulsion
2957:
2956:
2673:978-0-471-32642-7
2568:978-0-471-52938-5
2450:Solid-fuel rocket
2428:– rocket vehicles
2395:Multistage rocket
2148:
2138:
2125:
2113:
2102:
2056:
2054:
2042:
2032:
2016:
2002:
1999:
1981:
1951:
1924:
1895:
1866:
1863:
1853:
1839:
1835:
1824:
1810:
1799:
1782:
1778:
1767:
1746:
1716:
1703:
1685:
1684:
1662:
1628:
1594:
1560:
1526:
1492:
1458:
1424:
1394:{\displaystyle F}
1356:
1353:
1343:
1329:
1325:
1315:
1301:
1291:
1274:
1270:
1260:
1239:
1197:
1164:
1154:
1101:
1088:
1086:
1074:
1061:
1041:
1026:
1004:
989:
976:
958:
948:
801:solid propellants
772:
771:
758:{\displaystyle p}
735:absolute pressure
718:
684:
650:
613:
579:
564:
509:{\displaystyle M}
476:{\displaystyle R}
445:{\displaystyle T}
410:
402:
380:
374:
347:
323:
302:
77:or high pressure
66:products to high
52:propelling nozzle
16:(Redirected from
2987:
2804:
2797:
2790:
2781:
2732:
2727:
2721:
2716:
2710:
2698:
2692:
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2677:
2659:
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2595:
2590:
2584:
2579:
2573:
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2554:
2548:
2543:
2534:
2529:
2520:
2519:
2517:
2515:
2509:
2502:
2491:
2460:Specific impulse
2406:Pulse jet engine
2310:expanding nozzle
2269:and other uses.
2261:Advanced designs
2163:
2161:
2160:
2155:
2150:
2149:
2146:
2140:
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2136:
2127:
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2118:
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2100:
2075:
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2067:
2062:
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2047:
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2044:
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2034:
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2030:
2023:
2018:
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1988:
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1728:
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1714:
1705:
1704:
1701:
1679:standard gravity
1674:
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1398:
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1379:
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1362:
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1351:
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1199:
1198:
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1179:
1177:
1176:
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1165:
1162:
1156:
1155:
1147:
1125:
1123:
1122:
1117:
1115:
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1103:
1102:
1099:
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1087:
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1072:
1063:
1062:
1059:
1052:
1043:
1042:
1039:
1028:
1027:
1019:
1010:
1006:
1005:
1002:
996:
992:
991:
990:
987:
978:
977:
974:
960:
959:
956:
950:
949:
941:
903:Specific impulse
846:
838:
827:
764:
762:
761:
756:
730:
728:
727:
722:
720:
719:
716:
696:
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625:
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398:
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372:
366:
348:
346:
335:
327:
324:
319:
311:
309:
304:
303:
300:
237:The gas flow is
185:Magnetic nozzles
58:type) used in a
54:(usually of the
21:
2995:
2994:
2990:
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2708:Wayback Machine
2699:
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2648:Wayback Machine
2639:
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2625:
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2616:"Nozzle Design"
2614:
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2598:
2591:
2587:
2580:
2576:
2569:
2556:
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2537:
2530:
2523:
2513:
2511:
2507:
2500:
2493:
2492:
2485:
2480:
2372:De Laval nozzle
2362:
2319:stepped nozzles
2263:
2230:
2203:
2194:
2141:
2131:
2106:
2095:
2084:
2083:
2035:
2025:
2024:
2009:
2008:
2004:
1992:
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1944:
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1479:
1451:
1446:
1445:
1410:
1409:
1383:
1382:
1346:
1336:
1318:
1305:
1294:
1281:
1263:
1250:
1232:
1227:
1226:
1216:fuel efficiency
1190:
1185:
1184:
1157:
1134:
1133:
1113:
1112:
1094:
1067:
1054:
1053:
1047:
1034:
1033:
1029:
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1007:
997:
982:
969:
968:
964:
951:
932:
920:
919:
905:
882:
875:
857:
844:
836:
834:
825:
812:
789:monopropellants
782:
747:
746:
711:
706:
705:
677:
672:
671:
643:
638:
637:
606:
601:
600:
572:
557:
549:
548:
528:
527:
498:
497:
486:
465:
464:
434:
433:
388:
367:
361:
360:
353:
349:
336:
328:
312:
295:
290:
289:
224:
222:De Laval nozzle
209:
197:magnetic fields
178:
127:
125:Atmospheric use
103:Gustaf de Laval
95:
28:
23:
22:
15:
12:
11:
5:
2993:
2991:
2983:
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2977:
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2933:
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2930:
2929:
2924:
2918:
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2912:
2911:
2906:
2904:Thermoacoustic
2901:
2896:
2895:
2894:
2884:
2879:
2874:
2869:
2864:
2859:
2854:
2849:
2844:
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2739:External links
2737:
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2474:
2472:Venturi effect
2469:
2463:
2457:
2452:
2447:
2444:Shock diamonds
2441:
2435:
2432:Rocket engines
2429:
2423:
2413:
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2028:
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2012:
2007:
1995:
1991:
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1947:
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520:molecular mass
517:
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260:
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250:
235:
220:Main article:
208:
205:
177:
174:
126:
123:
111:Robert Goddard
107:steam turbines
94:
91:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2992:
2981:
2978:
2976:
2973:
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2968:
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2952:
2947:
2941:
2938:
2937:
2934:
2928:
2925:
2923:
2920:
2919:
2916:
2910:
2909:Manson engine
2907:
2905:
2902:
2900:
2897:
2893:
2890:
2889:
2888:
2887:Steam turbine
2885:
2883:
2880:
2878:
2875:
2873:
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2868:
2865:
2863:
2860:
2858:
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2848:
2845:
2843:
2840:
2838:
2835:
2833:
2830:
2828:
2825:
2823:
2822:Carnot engine
2820:
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2816:
2812:
2805:
2800:
2798:
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2380:rocket motors
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2250:
2247:
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2238:
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2228:Optimal shape
2227:
2225:
2221:
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2213:
2210:
2206:
2200:
2190:
2187:
2184:
2182:underexpanded
2181:
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2151:
2142:
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2107:
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2019:
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795:bipropellants
792:
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161:Space Shuttle
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136:underexpanded
131:
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60:rocket engine
57:
53:
49:
40:
32:
19:
2980:Pyrotechnics
2922:Beale number
2877:Split-single
2811:Heat engines
2725:
2714:
2696:
2685:
2663:
2636:
2626:November 23,
2624:. Retrieved
2620:the original
2610:
2599:
2588:
2577:
2558:
2552:
2514:17 September
2512:. Retrieved
2505:the original
2496:
2354:Minuteman II
2342:
2338:
2327:
2324:
2304:
2300:
2271:
2264:
2255:
2251:
2246:bell nozzles
2243:
2241:efficiency.
2239:
2231:
2222:
2214:
2211:
2207:
2204:
2188:overexpanded
2169:
2166:
2078:
1880:
1688:
1373:
1182:
1128:
906:
896:
892:
888:
884:
877:
870:
862:
860:
852:
848:
840:
829:
821:
819:
814:
807:
805:
777:
775:
424:
284:
269:
264:compressible
262:The flow is
225:
183:
179:
165:main engines
148:
144:
140:overexpanded
139:
135:
132:
128:
115:Walter Thiel
96:
72:
70:velocities.
47:
45:
2927:West number
2847:Minto wheel
2832:Gas turbine
2378:Dual-thrust
2366:Choked flow
2283:plug nozzle
2079:and hence:
1212:propellants
824: = 7.0
457:temperature
216:supersonic.
156:multi-stage
105:for use in
83:atmospheres
2964:Categories
2867:Rijke tube
2478:References
2389:Jet engine
2350:Titan IIIC
2196:unstable.
912:propulsion
489:J/kmol·K,
280:supersonic
254:propellant
239:isentropic
176:Vacuum use
79:ullage gas
68:supersonic
64:combustion
2892:Aeolipile
2289:aerospike
2129:−
2123:˙
2052:˙
1922:˙
1822:˙
1797:˙
1765:˙
1422:˙
1313:˙
1289:˙
1258:˙
1152:˙
1084:˙
1065:−
1024:˙
980:−
946:˙
867:ideal gas
534:γ
455:absolute
400:γ
393:−
390:γ
358:−
341:−
338:γ
333:γ
247:adiabatic
232:ideal gas
2899:Stirling
2827:Fluidyne
2704:Archived
2644:Archived
2360:See also
891:, where
485:≈ 8314.5
272:subsonic
249:process.
121:rocket.
56:de Laval
2970:Nozzles
2837:Hot air
2185:ambient
1374:where:
425:where:
243:entropy
201:kelvins
151:liftoff
97:Simple
93:History
2872:Rocket
2857:Piston
2670:
2565:
2426:Rocket
2235:thrust
2101:sp,vac
1980:sp,vac
1950:sp,vac
908:Thrust
845:
843:= 3500
837:
826:
487:
193:plasma
2679:p. 84
2508:(PDF)
2501:(PDF)
2400:NK-33
835:= 0.1
276:sonic
256:burn.
75:pumps
50:is a
2668:ISBN
2628:2011
2563:ISBN
2516:2022
2352:and
2345:PSLV
2842:Jet
119:V-2
2966::
2654:^
2538:^
2524:^
2486:^
1745:sp
1675:,
1641:,
1627:sp
1607:,
1593:eq
1573:,
1539:,
1505:,
1471:,
1437:,
1401:,
1342:eq
1300:eq
1238:sp
1196:sp
1163:eq
883:=
765:,
741:)
739:Pa
731:,
697:,
663:,
626:,
592:,
516:,
452:,
282:.
142:.
46:A
2803:e
2796:t
2789:v
2676:.
2630:.
2571:.
2518:.
2422:)
2312:,
2291:,
2285:,
2279:,
2152:,
2147:o
2143:p
2137:e
2133:A
2120:m
2112:o
2108:g
2097:I
2093:=
2090:F
2064:,
2060:)
2049:m
2041:e
2037:A
2031:e
2027:p
2020:+
2015:e
2011:v
2006:(
1998:o
1994:g
1990:1
1985:=
1976:I
1946:I
1919:m
1894:e
1890:p
1862:o
1858:g
1852:e
1848:v
1842:=
1834:o
1830:g
1819:m
1809:e
1805:v
1794:m
1785:=
1777:o
1773:g
1762:m
1755:F
1750:=
1741:I
1715:o
1711:p
1707:=
1702:e
1698:p
1661:o
1657:g
1623:I
1589:v
1559:e
1555:A
1525:o
1521:p
1491:e
1487:p
1457:e
1453:v
1419:m
1389:F
1359:,
1352:o
1348:g
1338:v
1332:=
1324:o
1320:g
1310:m
1296:v
1286:m
1277:=
1269:o
1265:g
1255:m
1248:F
1243:=
1234:I
1192:I
1168:.
1159:v
1149:m
1143:=
1140:F
1110:,
1106:]
1100:e
1096:A
1091:)
1081:m
1073:o
1069:p
1060:e
1056:p
1049:(
1045:+
1040:e
1036:v
1031:[
1021:m
1015:=
1003:e
999:A
994:)
988:o
984:p
975:e
971:p
966:(
962:+
957:e
953:v
943:m
937:=
930:F
897:M
893:R
889:M
887:/
885:R
881:s
878:R
874:s
871:R
863:R
856:e
853:v
849:M
841:T
833:e
830:p
822:p
811:e
808:v
781:e
778:v
753:p
717:e
713:p
683:e
679:v
649:v
645:c
612:p
608:c
578:v
574:c
569:/
563:p
559:c
555:=
504:M
471:R
440:T
407:]
396:1
383:)
378:p
373:e
369:p
363:(
355:1
351:[
344:1
330:2
321:M
317:R
314:T
306:=
301:e
297:v
234:.
20:)
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