Jet engine

is tested at Robins Air Force Base, Georgia, USA. The tunnel behind the engine muffles noise and allows exhaust to escape. The mesh cover at the front of the engine (left of photo) prevents debris—or people—from being pulled into the engine by the huge volume of air rushing into the inlet.]] A jet engine is any engine that accelerates and discharges a fast moving jet of fluid to generate thrust in accordance with Newton's third law of motion. This broad definition of jet engines includes turbojets, turbofans, turboprops, rockets and ramjets, but in common usage, the term generally refers to a gas turbine used to produce a jet of high speed exhaust gases for propulsive purposes.

Turbojet engines

A turbojet engine is a type of internal combustion engine often used to propel aircraft. Air is drawn into the rotating compressor via the intake and is compressed to a higher pressure before entering the combustion chamber. Fuel is mixed with the compressed air and ignited by flame in the eddy of a flame holder. This combustion process significantly raises the temperature of the gas. Hot combustion products leaving the combustor expand through the turbine, where power is extracted to drive the compressor. Although this expansion process reduces both the gas temperature and pressure at exit from the turbine, both parameters are usually still well above ambient conditions. The gas stream exiting the turbine expands to ambient pressure via the propelling nozzle, producing a high velocity jet in the exhaust plume. If the jet velocity exceeds the aircraft flight velocity, there is a net forward thrust upon the airframe. Under normal circumstances, the pumping action of the compressor prevents any backflow, thus facilitating the continuous flow process of the engine. Indeed, the entire process is similar to a four-stroke cycle, but with induction, compression, ignition, expansion and exhaust taking place simultaneously. The efficiency of a jet engine is strongly dependent upon the Overall Pressure Ratio (Combustor Entry Pressure/Intake Delivery Pressure) and the Turbine Inlet Temperature of the cycle. It is also perhaps instructive to compare turbojet engines with propeller engines. Turbojet engines take a relatively small mass of air and accelerate it by a large amount, whereas a propeller takes a large mass of air and accelerates it by a small amount. The high-speed exhaust of a jet engine makes it efficient at high speeds (especially supersonic speeds) and high altitudes. On slower aircraft and those required to fly short stages, a gas turbine-powered propeller engine, commonly known as a turboprop, is more common and much more efficient. Very small aircraft generally use conventional piston engines to drive a propeller but small turboprops are getting smaller as engineering technology improves. The turbojet described above is a single spool design, where a single shaft connects the turbine to the compressor. Higher Overall Pressure Ratio designs often have two concentric shafts, to improve compressor stability during engine throttle movements. The outer (HP) shaft connects the High Pressure (HP) Compressor to the HP turbine. This HP Spool, with the combustor, forms the core or gas generator of the engine. The inner shaft connects the Low Pressure (LP) Compressor to the LP Turbine to create the LP Spool. Both spools are free to operate at their optimum shaft speed.

Turbofan engines

Most modern jet engines are actually turbofans, where the LP Compressor acts as a fan, supplying supercharged air to not only the engine core, but to a bypass duct. The bypass airflow either passes to a separate Cold Nozzle or mixes with LP Turbine exhaust gases, before expanding through a Mixed Flow Nozzle. Forty years ago there was little difference between civil and military jet engines, apart from the use of afterburning in some (supersonic) applications. Turbofans, today, have a low specific thrust (net thrust/airflow) to keep jet noise to a minimum and to improve fuel efficiency. Consequently the bypass ratio (bypass flow/core flow) is relatively high (usually much greater than 3.0). Only a single fan stage is required, because a low specific thrust implies a low fan pressure ratio. Today's military turbofans, however, have a relatively high specific thrust, to maximize the thrust for a given frontal area, jet noise being of little consequence. Multi-stage fans are normally required to achieve the relatively high fan pressure ratio needed for a high specific thrust. Although high Turbine Inlet Temperatures are frequently employed, the bypass ratio tends to be low (usually significantly less than 2.0). An approximate equation for calculating the net thrust of a jet engine is: :F_net = m(v_jfe - v_a ) where: :m = intake mass flow :v_jfe = fully expanded jet velocity (in the exhaust plume) :v_a = aircraft flight velocity While the m·v_jfe term represents the gross thrust of the nozzle, the m·v_a term represents the ram drag of the intake. Most types of jet engine have an air intake, which provides the bulk of the gas exiting the exhaust. There is, however, a penalty for picking this air up and this is known as the ram drag. Conventional rocket motors, however, do not have an air intake, the oxidizer being carried within the airframe. Consequently, rocket motors do not have ram drag; the gross thrust of the nozzle is the net thrust of the engine. Consequently, the thrust characteristics of a rocket motor are completely different from that of an air breathing jet engine; at full throttle, the thrust of a rocket motor improves slightly with increasing altitude (because the back pressure from the atmosphere falls), whereas with a turbojet (or turbofan) the falling density of the air entering the intake causes the net thrust to decrease with increasing altitude.

History

Before the advent of the jet engine, the reciprocating piston engine in its different forms (rotary and static radial, aircooled and liquid-cooled inline) had been the only type of powerplant available to aircraft designers. This was understandable so long as low aircraft performance parameters were considered acceptable, and indeed inevitable. However, by approximately the late 1930s, engineers were beginning to realize that conceptually the piston engine was self-limiting in terms of the maximum performance which could be obtained from it; the limit was essentially one of propeller efficiency, which seemed to peak as blade tips approached supersonic tangential velocity. If engine, and thus aircraft, performance were ever to increase beyond such a barrier, a way would have to be found to radically improve the design of the piston engine, or a wholly new type of powerplant would have to be conceived. The latter would prove to be the case. The gas turbine (turbojet, or simply jet) engine, as subsequently developed, would become almost as revolutionary to aviation as the Wright brothers' first flight. The gas turbine was not an idea developed in the 1930s: the patent for a stationary turbine was granted to John Barber in England in 1791, although Colin Sullivan of Cowplain, England was said to have drawn up identical blueprints 2 years beforehand. The earliest attempts at jet engines were hybrid designs in which an external power source supplied the compression. In this system (called a thermojet by Secondo Campini) the air is first compressed by a fan driven by a conventional piston engine, then it is mixed with fuel and burned for jet thrust. The examples of this type of design were the Henri Coanda's Coanda-1910 aircraft, and the much later Campini Caproni CC.2, and the Japanese Tsu-11 engine intended to power Ohka kamikaze planes towards the end of World War II. None were entirely successful and the CC.2 ended up being slower than the same design with a traditional engine and propeller combination. World War II The key to the useful jet engine was the gas turbine, used to extract energy to drive the compressor from the engine itself. The first gas turbine to successfully run self-sustaining was built in 1903 by Norwegian engineer Aegidius Elling. The first patents for jet propulsion were issued in 1917. Limitations in design and practical engineering and metallurgy prevented such engines reaching manufacture. The main problems were safety, reliability, weight and, especially, sustained operation. On January 16, 1930, in England Frank Whittle submitted patents for his own design for a full-scale aircraft engine (granted in 1932). In 1935 Hans von Ohain started work on a similar design in Germany, seemingly unaware of Whittle's work. Ohain approached Ernst Heinkel, one of the larger aircraft industrialists of the day, who immediately saw the promise of the design. Heinkel had recently purchased the Hirth engine company, and Ohain and his master machinist Max Hahn were set up there as a new division of the Hirth company. They had their first HeS 1 engine running by September 1937. Unlike Whittle's design, Ohain used hydrogen as fuel, which he credits for the early success. Their subsequent designs culminated in the gasoline-fuelled HeS 3 of 1,100 lbf (5 kN), which was fitted to Heinkel's simple and compact He 178 airframe and flown by Erich Warsitz in the early morning of August 27, 1939, from Marienehe aerodrome, an impressively short time for development. The He 178 was the world's first jetplane. The engine was starting to look useful, and Whittle's Power Jets Ltd. started receiving Air Ministry money. In 1941 a flyable version of the engine called the W.1, capable of 1000 lbf (4 kN) of thrust, was fitted to the Gloster E28/39 airframe, and first flew on May 15, 1941 at RAF Cranwell. RAF Cranwell One problem with both of these early designs, which are called centrifugal-flow engines, was that the compressor works by "throwing" (accelerating) air outward from the central intake to the outer periphery of the engine where the air is then compressed by a divergent duct setup—converting velocity into pressure. The advantage was that such compressor designs were well understood in centrifugal superchargers but this leads to a very large cross section for the engine at rotational speeds that were usable at the time. A disadvantage was that the air flow had to be "bent" to flow rearwards through the combustion section and to the turbine and tailpipe. With improvements to bearings, the shaft speed of the engine would increase and the diameter of the centrifugal compressor would reduce greatly. The shortness of this engine is an advantage. The strength of this type of compressor is an advantage over the later axial-flow compressors that are still liable to foreign object damage (FOD in aviation parlance). Austrian Anselm Franz of Junkers' engine division (Junkers Motoren or Jumo) addressed this problem with the introduction of the axial-flow compressor. Essentially, this is a turbine in reverse. Air coming in the front of the engine is blown to the rear of the engine by a fan stage (convergent ducts), where it is crushed against a set of non-rotating blades called stators (divergent ducts). The process is nowhere near as powerful as the centrifugal compressor, so a number of these pairs of fans and stators are placed in series to get the needed compression. Even with all the added complexity, the resulting engine is much smaller in diameter. Jumo was assigned the next engine number, 4, and the result was the Jumo 004 engine. After many lesser technical difficulties were solved, mass production of this engine started in 1944 as a powerplant for the world's first jet-fighter aircraft, the Messerschmitt Me 262. Because Hitler wanted a new bomber the Me 262 came too late to decisively impact Germany's position in World War II, but it will be remembered as the first use of jet engines in service. After the end of the war the German Me 262 aircraft were extensively studied by the victorious allies and contributed to work on early Soviet and US jet fighters. British engines also were licensed widely in the US (see Tizard Mission). Their most famous design, the Nene would also power the USSR's jet aircraft also after a technology exchange. American designs would not come fully into their own until the 1960s.

Types

There are a large number of types of jet engines, which get propulsion from a high speed exhaust jet. Some examples are as follows:

Type	Description	Advantages	Disadvantages
Water jet	Squirts water out the back of a boat	Can run in shallow water, powerful, less harmful to wildlife	Can be less efficient than a propeller, more vulnerable to debris
Thermojet	Most primitive airbreathing jet engine		Very inefficient and underpowered
Turbojet	Generic term for simple turbine engine	Simplicity of design	Basic design, misses many improvements in efficiency and power
Turbofan	Power tapped off exhaust used to drive bypass fan	Quieter due to greater mass flow and lower total exhaust speed, more efficient for a useful range of subsonic airspeeds for same reason	Greater complexity (additional ducting, usually multiple shafts), large diameter engine, need to contain heavy blades. More subject to FOD and ice damage. Different degrees of bypass are possible - this is the design most commonly used on commercial airliners
Rocket	Carries own propellant onboard, emits jet for propulsion	Very few moving parts, Mach 0 to Mach 25+, efficient at very high speed (> Mach 10.0 or so), thrust/weight ratio over 100, relatively simple, no air inlet, doesn't require atmosphere, high compression ratio, very high speed exhaust	very low specific impulse- typically 100-450 seconds. Typically requires carrying oxidiser onboard which increases risks.
Ramjet	Intake air is compressed entirely by speed of oncoming air and duct shape (divergent)	Very few moving parts, Mach 0.8 to Mach 5+, efficient at high speed (> Mach 2.0 or so), lightest of all airbreathing jets (thrust/weight ratio up to 30 at optimum speed)	Must have a high initial speed to function, inherently inefficient at slow speeds due to poor compression ratio, difficult to arrange shaft power for accessories, difficult to engineer to be efficient over a wide range of airspeeds.
Turboprop (Turboshaft similar)	Strictly not a jet at all- a gas turbine engine is used as powerplant to drive (propeller) shaft	High efficiency at lower subsonic airspeeds(300 knots plus), high shaft power to weight	Limited top speed (aeroplanes), somewhat noisy, complexity of propeller drive, very large yaw (aeroplane) if engine fails
Propfan	Turboprop engine drives one or more propellers. much like a turbofan but without ductwork	Higher fuel efficiency, some designs are less noisy than turbofans, could lead to higher-speed commercial aircraft, popular in the 1980s during fuel shortages,	Development of propfan engines has been very limited, typically more noisy than turbofans, complexity
Pulsejet	Air enters a divergent-duct inlet, the front of the combustion area is shut, fuel injected into the air ignites, exhaust vents from other end of engine	Very simple design, commonly used on model aircraft	Noisy, inefficient (low compression ratio), works best at small scale, valves need to be replaced very often
Pulse detonation engine	Similar to a pulsejet, but combustion occurs as a detonation instead of a deflagration, may or may not need valves	Maximum theoretical engine efficiency	Extremely noisy, parts subject to extreme mechanical fatigue, hard to start detonation, not practical for current use
Integral rocket ramjet	Essentially a ramjet where intake air is compressed and burnt with the exhaust from a rocket	Mach 0 to Mach 4.5+ (can also run exoatmospheric), good efficiency at Mach 2 to 4	Similar efficiency to rockets at low speed or exoatmospheric, inlet difficulties, a relatively undeveloped and unexplored type, cooling difficulties
Scramjet	Intake air is compressed but not slowed to below supersonic, intake, combustion and exhaust occur in a single constricted tube	can operate at very high Mach numbers (Mach 8 to 15)[http://www.dod.mil/ddre/downloads/ddre_briefings/Merging_Air_and_Space071603.pdf]	still in development stages, must have a very high initial speed to function (Mach >6), cooling difficulties, inlet difficulties, very poor thrust/weight ratio (~2), airframe difficulties, testing difficulties
Turborocket	An additional oxidizer such as oxygen is added to the airstream to increase max altitude	Very close to existing designs, operates in very high altitude, wide range of altitude and airspeed	Airspeed limited to same range as turbojet engine, carrying oxidizer like LOX can be dangerous
Precooled jets / LACE	Intake air is chilled to very low temperatures at inlet	Very high thrust/weight ratios are possible (~14) together with good fuel efficiency over a wide range of airspeeds, mach 0-5+	Exists only at the lab protoyping stage. Examples include RB545, SABRE, ATREX

Components

The components of a jet engine are standard across the different types of engines, although not all engine types have all components. The parts include:

Air Induction
The standard reference frame for a jet engine is the aircraft itself. For subsonic aircraft, the air intake to a jet engine presents no special difficulties, and consists essentially of an opening which is designed to minimise drag, as with any other aircraft component. However, the air reaching the compressor of a normal jet engine must be travelling below the speed of sound, even for supersonic aircraft, to sustain the flow mechanics of the compressor and turbine blades. At supersonic flight speeds, shockwaves form in the intake system and reduce the recovered pressure at inlet to the compressor. So some supersonic intakes use devices, such as a cone or ramp, to increase pressure recovery, by more making more efficient use of the shock wave system.
Compressor or Fan
In many cases, the compressor is a series of fans that are spaced very closely together. Each fan compresses the air a little more. Energy is derived from the turbine (see below), passed along the shaft.
Shaft
This carries power from the turbine to the compressor, and runs most of the length of the engine. There may be as many as three concentric shafts, rotating at independent speeds, with as many sets of turbines and compressors. Other services, like a bleed of cool air, may also run down the shaft.
Combustor or Can or Flameholders or Combustion Chamber
This is a chamber where fuel is continuously burned in the compressed air.
Turbine
The turbine acts like a windmill, extracting energy from the hot gases leaving the combustor. This energy is used to drive the compressor through the shaft, or bypass fans, or props, or even (for a gas turbine-powered helicopter) converted entirely to rotational energy for use elsewhere.
Afterburner or reheat (chiefly UK)
(mainly military) Produces extra thrust by burning extra fuel, usually inefficiently, to significantly raise Nozzle Entry Temperature at the exhaust. Owing to a larger volume flow (i.e. lower density) at exit from the afterburner, an increased nozzle flow area is required, to maintain satisfactory engine matching, when the afterburner is alight.
Exhaust or Nozzle
Hot gases leaving the engine exhaust to atmospheric pressure via a nozzle, the objective being to produce a high velocity jet. In most cases, the nozzle is convergent and of fixed flow area.
Supersonic Nozzle
If the Nozzle Pressure Ratio (Nozzle Entry Pressure/Ambient Pressure) is very high, to maximize thrust it may be worthwhile, despite the additional weight, to fit a convergent-divergent (de Laval) nozzle. As the name suggests, initially this type of nozzle is convergent, but beyond the throat (smallest flow area), the flow area starts to increase to form the divergent portion. The expansion to atmospheric pressure and supersonic gas velocity continues downstream of the throat, whereas in a convergent nozzle the expansion beyond sonic velocity occurs externally, in the exhaust plume. The former process is more efficient.

Design considerations

The various components named above have constraints on how they are put together to generate the most efficiency or performance. Important here is air intake design, overall size, number of compressor stages (sets of blades), fuel type, number of exhaust stages, metallurgy of components, amount of bypass air used, where the bypass air is introduced, and many other factors. For instance, let us consider design of the air intake.

Air intakes

See also: Inlet cone
Subsonic inlets
At low speeds a subsonic inlet is little more than a hole, with an aerodynamic fairing around it. However, from around mach 0.85, the air entering the inlet can start to experience shock waves, and then careful radiusing is required for optimum performance at all speeds.
Supersonic inlets
Inlet cone For aircraft travelling at supersonic speeds, a design complexity arises, since the air ingested by the engine must be below supersonic speed, otherwise the engine will "choke" and cease working. This subsonic air speed is achieved by passing the approaching air through a deliberately generated shock wave (since one characteristic of a shock wave is that the air flowing through it is slowed). Therefore, some means is needed to create a shockwave ahead of the intake. The earliest types of supersonic aircraft featured a central shock cone, called an inlet cone, which was used to form the shock wave. This type of shock cone is clearly seen on the English Electric Lightning and MiG-21 aircraft, for example. The same approach can be used for air intakes mounted at the side of the fuselage, where a half cone serves the same purpose with a semicircular air intake, as seen on the F-104 Starfighter and BAC TSR-2. A more sophisticated approach is to angle the intake so that one of its edges forms a leading blade. A shockwave will form at this blade, and the air ingested by the engine will be behind the shockwave and hence subsonic. The Century series of US jets featured a number of variations on this approach, usually with the leading blade at the outer vertical edge of the intake which was then angled back inwards towards the fuselage. Typical examples include the Republic F-105 Thunderchief and F-4 Phantom. Later this evolved so that the leading edge was at the top horizontal edge rather than the outer vertical edge, with a pronounced angle downwards and rearwards. This approach simplified the construction of the intakes and permitted the use of variable ramps to control the airflow into the engine. Most designs since the early 1960s now feature this style of intake, for example the F-14 Tomcat, Panavia Tornado and the Concorde.
SR 71
The SR-71's engines were rather unusual in that a variable air intake design was used to convert the engine from a turbojet to a ramjet, in flight. To get good efficiency over a wide range of speeds the Pratt & Whitney J58 could move a conical spike fore and aft within the engine nacelle, to keep the supersonic shock wave just in front of the inlet. In this manner, the airflow behind the shock wave, and more importantly, through the engine, was kept subsonic at all times. At high mach, the compressor for the J58 was unable to carry the high air flow entering the inlet without stalling its blades, and so the engine directed the excess air through 6 bypass pipes straight to the afterburner. At high speeds the engine actually obtained 80% of its thrust, versus 20% through the turbines itself, in this way. Essentially, this allowed the engine to operate as a ramjet, actually improving specific impulse (fuel efficiency) by 10%–15%.
Heat exchangers
For engines that may need to operate at almost hypersonic speeds (mach 0 to 6), there is strong theoretical and experimental support for using a heat-exchanger to cool the air at the intake. This can increase the density of the air and thus reduce the necessary compression. The lower temperatures also permit lighter alloys to be used hence reducing the engine's weight by several times. This leads to plausible designs like SABRE and ATREX that might permit jet engined vehicles to be used to launch to space. ATREX
Compressors
Each design of compressor has an operating map or characteristic peculiar to that unit. At a given throttle condition, the compressor operates somewhere along the steady state running line. Unfortunately, this operating line is displaced during transients and under extreme conditions can cross the surge or stall line (see compressor map), causing, in some cases, the compressor flow to reverse direction violently. Many compressors are fitted with variable geometry to decrease the likelihood of surge. Another ploy is to split the compressor into two or more units, operating on separate concentric shafts. Another design consideration is the average stage loading. This can be kept at a sensible level either by increasing the number of compression stages (more weight/cost) or the mean blade speed (more blade/disc stress). Although large flow compressors are usually all-axial, the rear stages on smaller units are too small to be robust. Consequently, these stages are often replaced by a single centrifugal unit. Very small flow compressors often employ two centrifugal compressors, connected in series. Although in isolation centrifugal compessors are capable of running at quite high pressure ratios (e.g. 10:1), impeller stress considerations (i.e. T3, NH implications) limit the CF pressure ratio that can be employed in high overall pressure ratio engine cycles. Increasing overall pressure ratio implies a higher (HP) compressor exit temperature (i.e. T3. This implies a higher HP shaft speed, to maintain the datum blade tip Mach number on the rear compressor stages. Stress considerations, however, may limit shaft speed increases, leading to a reduction in the pressure ratio of the rear stages. compressor map
Combustors
Care must be taken to keep the flame burning in a moderately fast moving airstream, at all throttle conditions, as efficiently as possible. Since the turbine cannot withstand stoichiometric temperatures, resulting from the optimum combustion process, some of the compressor air is used to quench the exit temperature of the combustor to an acceptable level.
Turbines
stoichiometric Because a turbine expands from high to low pressure, there is no such thing as turbine surge or stall. Designers must, however, prevent the turbine blades and vanes from melting in a very high temperature and stress environment. Consequently bleed air extracted from the compression system is often used to cool the turbine blades/vanes internally. Other solutions are improved materials and/or special insulating coatings. The discs must be specially shaped to withstand the huge stresses imposed by the rotating blades. Improved materials help to keep disc weight down.
Nozzles
stresses Most jet engines use a simple convergent nozzle, which is relatively easy to design. However, afterburning engines require a variable area nozzle, to maintain sensible engine matching when the afterburner is alight. This is usually accommodated by using a series of interlocking petals (driven by pneumatic or hydraulic rams) to adjust the throat area. Even more complexity is introduced if a convergent-divergent nozzle is fitted, especially if the throat and exit areas are adjusted independently. convergent-divergent nozzle Rocket motors also employ convergent-divergent nozzles, but these are usually of fixed geometry, to minimize weight. Because of the much higher nozzle pressure ratios experienced, rocket motor con-di nozzles have a much greater area ratio (exit/throat) than those fitted to jet engines. At the other extreme, some high bypass ratio civil turbofans use an extremely low area ratio (less than 1.01 area ratio), convergent-divergent, nozzle on the bypass (or mixed exhaust) stream, to control the fan working line. The nozzle acts as if it has variable geometry. At low flight speeds the nozzle is unchoked (less than a Mach number of unity), so the exhaust gas speeds up as it approaches the throat and then slows down slightly as it reaches the divergent section. Consequently, the nozzle exit area controls the fan match and, being larger than the throat, pulls the fan working line slightly away from surge. At higher flight speeds, the ram rise in the intake increases nozzle pressure ratio to the point where the throat becomes choked (M=1.0). Under these circumstances, the throat area dictates the fan match and being smaller than the exit pushes the fan working line slightly towards surge. This is not a problem, since fan surge margin is much better at high flight speeds.
Engine Performance

TS Diagram
Mach number °R) = 1 Btu/(lb °F) = 1 kcal/(kg °C) = 4.184 kJ/(kg·K).]] Temperature vs. entropy diagrams (see example, above) are usually used to illustrate the cycle of gas turbine engines. All the reader really needs to know about entropy is that it represents the degree of disorder of the molecules in the fluid and that it tends to increase! Apart from stations 0 and 8s, stagnation pressure and stagnation temperature are used. Station 0 is ambient. The processes depicted are: ;Freestream (stations 0 to 1) :In the example, the aircraft is stationary, so stations 0 and 1 are coincident. Station 1 is not depicted on the diagram. ;Intake (stations 1 to 2) :In the example, a 100% intake pressure recovery is assumed, so stations 1 and 2 are coincident. ;Compression (stations 2 to 3) :The ideal process would appear vertical on a TS diagram. In the real process there is friction, turbulence and, possibly, shock losses, making the exit temperature, for a given pressure ratio, higher than ideal. The shallower the positive slope on the TS diagram, the less efficient the compression process. ;Combustion (stations 3 to 4) :Heat (usually by burning fuel) is added, raising the temperature of the fluid. There is an associated pressure loss, some of which is unavoidable ;Turbine (stations 4 to 5) :The temperature rise in the compressor dictates that there will be an associated temperature drop across the turbine. Ideally the process would be vertical on a TS diagram. However, in the real process, friction and turbulence cause the pressure drop to be greater than ideal. The shallower the negative slope on the TS diagram, the less efficient the expansion process. ;Jetpipe (stations 5 to 8) :In the example the jetpipe is very short, so there is no pressure loss. Consequently, stations 5 and 8 are coincident on the TS diagram. ;Nozzle (stations 8 to 8s) :These two stations are both at the throat of the (convergent) nozzle. Station 8s represents static conditions. Not shown on the TS diagram is the expansion process, external to the nozzle, down to ambient pressure.
Design Point Performance Equations
In theory, any combination of flight condition/throttle setting can be nominated as the engine performance Design Point. Usually, however, the Design Point corresponds to the highest corrected flow at inlet to the compression system (e.g. Take-off Rating, Sea Level Static, ISA) The design point net thrust of any jet engine can be estimated by working through the engine cycle, step by step. Below are the equations for a single spool turbojet. Freestream
$T_1 = t_0 \cdot (1 + (_c-1)\cdot M^2/2)$ $P_1 = p_0 \cdot (T_1/t_0)^$ Intake
$T_2=T_1 \,$ $P_2=P_1 \cdot \mathrm$ Compressor
$T_3 = T_2 \cdot ((P_3/P_2) ^$ $P_3 = P_2 \cdot (P_3/P_2)$ Combustor
$T_4 = \mathrm \,$ $P_4 = P_3 \cdot (P_4/P_3)$ Turbine
Equating the turbine and compressor powers, we have:
$w_4 \cdot C_(T_4-T_5) = w_2 \cdot C_(T_3-T_2)$ A simplyfying assumption sometimes made is for the addition of fuel flow to be exactly offset by an overboard compressor bleed, so mass flow remains constant throughout the cycle. $P4/P5 = (T4/T5)^$ Jetpipe
$T_8 = T_5 \,$ $P_8 = P_5 (P_8/P_5) \,$ Nozzle
$t_ = T_8/((_t+1)/2) \,$ $p_ = P_8/((T_8/t_)^)$ $V_8^2 = 2gJC_(T_8 - t_)$ $_ = p_/(R \cdot t_)$ $A_8 = w_8/(_ \cdot V_8)$ Gross Thrust
$F_g = C_\mathrm((w_8 \cdot V_8/g) + A_8(p_ - p_0))$ Ram Drag
$F_r = w_0 \cdot V_0/g$ Net Thrust
$F_n = F_g - F_r \,$ Note that mass flow is the sizing parameter: doubling the airflow, doubles the thrust. Note:
- A flow area
- C_pc specific heat at constant pressure for air
- C_pt specific heat at constant pressure for combustion products
- C_x thrust coefficient
- g acceleration of gravity
- J mechanical equivalent of heat
- M flight Mach number
- p static pressure
- P total pressure
- prf intake pressure recovery factor
- R gas constant
- RIT (turbine) rotor inlet temperature
- t static temperature
- T total temperature
- V velocity
- w mass flow
- ρ density
- γ_c ratio of specific heats for air
- γ_t ratio of specific heats for combustion products
- η_pc compressor polytropic efficiency
- η_pt turbine polytropic efficiency
Off-design
An engine is said to be running off-design if any of the following apply: :a) change of throttle setting :b) change of altitude :c) change of flight speed :d) change of climate :e) change of installation (e.g. customer bleed or power off-take) Although each off-design point is effectively a design point calculation, the resulting cycle (normally) has the same turbine and nozzle geometry as that at the engine design point. Obviously the final nozzle cannot be over or underfilled with flow. This rule also applies to the turbine nozzle guide vanes, which act like small nozzles. Design point calculations are normally done by a computer program. By the addition of an iterative loop, such a program can also be used to create a crude off-design model. The variables for the single spool turbojet iteration would typically be: RIT (or some other function of fuel flow), w₂,P₃/P₂ Typically, the constraints imposed would be: Engine match (e.g. F_n , fuel flow, etc), A_{8 geometric},w4cor The latter two are the physical constraints that must be met. Corrected flow is the flow that would pass through a device, if the entry pressure and temperature corresponded to ambient conditions at sea level on a Standard Day. A more refined off-design model can be created using compressor maps and turbine maps to predict off-design efficiencies, relative shaft speeds, etc. The nominal net thrust quoted for a jet engine usually refers to the Sea Level Static (SLS) condition, either for the International Standard Atmosphere (ISA) or a hot day condition (e.g. ISA+10 °C). As an example, the GE90-76B has a take-off static thrust of 76,000 lbf (360 kN) at SLS, ISA+15 °C. Naturally, net thrust will decrease with altitude, because of the lower density. There is also, however, a flight speed effect. Initially as the aircraft gains speed down the runway, there will be little increase in nozzle pressure and temperature, because the ram rise in the intake is very small. There will also be little change in mass flow. Consequently, nozzle gross thrust initially only increases marginally with flight speed. However, being an air breathing engine (unlike a conventional rocket) there is a penalty for taking on-board air from the atmosphere. This is known as ram drag. Although the penalty is zero at static conditions, it rapidly increases with flight speed causing the net thrust to be eroded. As flight speed builds up after take-off, the ram rise in the intake starts to have a significant effect upon nozzle pressure/temperature and intake airflow, causing nozzle gross thrust to climb more rapidly. This term now starts to offset the still increasing ram drag, eventually causing net thrust to start to increase. In some engines, the net thrust at say Mach 1.0, sea level can even be slightly greater than the static thrust. Above Mach 1.0, with a subsonic inlet design, shock losses tend to decrease net thrust, however a suitably designed supersonic inlet can give a subsonic airspeed entering the compressor, while giving a useful compression, and thus net thrust and efficiency can continue to climb. The thrust lapse described above depends on the design specific thrust and, to a certain extent, on how the engine is rated with intake temperature.
Rated Performance

Civil
turbine map Nowadays, civil engines are usually flat-rated on net thrust up to a 'break-point' climate. So at a given flight condition, net thrust is held approximately constant over a very wide range of ambient temperature, by increasing (HP) turbine rotor inlet temperature (RIT or SOT). However, beyond the break-point, SOT is held constant and net thrust starts to fall for further increases in ambient temperature. Consequently, aircraft fuel load and/or payload must be decreased. Usually, for a given rating, the kink-point SOT is held constant, regardless of altitude or flight speed. Some engines have a special rating, known as the 'Denver Bump'. This invokes a higher RIT than normal, to enable fully laden aircraft to Take-off safely from Denver, CO in the summer months. Denver Airport is extremely hot in the summer and the runways are over a mile above sea level. Both of these factors affect engine thrust.
Military
turbine map The rating systems used on military engines vary from engine to engine. A typical military rating structure is shown on the left. At low intake temperatures, the engine tends to operate at maximum corrected speed or corrected flow. As intake temperature rises, a limit on (HP) turbine rotor inlet temperature (SOT) takes effect, progressively reducing corrected flow. At even higher intake temperatures, a limit on compressor delivery temperature (T₃) is invoked, which decreases both SOT and corrected flow. corrected flow The impact of design intake temperature is shown on the right hand side. An engine with a low design T₁ combines high corrected flow with high rotor turbine temperature (SOT), maximizing net thrust at low T₁ conditions (e.g. Mach 0.9, 30000 ft, ISA). However, although turbine rotor inlet temperature stays constant as T₁ increases, there is a steady decrease in corrected flow, resulting in poor net thrust at high T₁ conditions (e.g. Mach 0.9, sea level, ISA). Although an engine with a high design T₁ has a high corrected flow at low T₁ conditions, the SOT is low, resulting in a poor net thrust. Only at high T₁ conditions is there the combination of a high corrected flow and a high SOT, to give good thrust characteristics. A compromise between these two extremes would be to design for a medium intake temperature (say 290 K).
See also

- Jet aircraft
- Jetboat
- Spacecraft propulsion
- Supercharger
- Turbocharger
- Gas turbine
- Kurt Schreckling who built practical jet engines for model aircraft
- Wikibooks: Jet propulsion
External link

- [http://www.rmcybernetics.com/projects/DIY_Devices/homemade_jet_engine.htm RMCybernetics - A simple Homemade Jet Engine]
- [http://www.rolls-royce.com/education/schools/journey02/flash.html Journey through a jet engine(flash)]
- [http://travel.howstuffworks.com/turbine.htm How Stuff Works article on how a Gas Turbine Engine works]
- [http://www.generalatomic.com/jetmakers/chapter15.html Influence of the Jet Engine on the Aerospace Industry]
- [http://www.rand.org/publications/MR/MR1596/MR1596.appb.pdf An Overview of Military Jet Engine History] (Rand Corp., 24 pgs, PDF)
- [http://bikerodnkustom3.homestead.com/danger.html A jet propulsion bicycle] Category:Energy conversion Category:Gas turbines Category:Jet engines ja:ジェットエンジン

Isaac Newton
Sir Isaac Newton, PRS ( – ) was an English physicist, mathematician, astronomer, alchemist and philosopher associated with the scientific revolution and the advancement of heliocentrism. He was one of the most influential scientists in history. Among his scientific accomplishments, Newton wrote the Philosophiae Naturalis Principia Mathematica, wherein he described universal gravitation and, via his laws of motion, laid the groundwork for classical mechanics. With Gottfried Leibniz he shares credit for the development of calculus. Newton was the first to promulgate a set of natural laws that could govern both terrestrial motion and celestial motion, and is credited with providing mathematical substantiation for Kepler's laws of planetary motion, which he expanded by arguing that orbits (such as those of comets) could include all conic sections (such as the ellipse, hyperbola, and parabola). Newton realised that the spectrum of colours observed when white light passed through a prism is inherent in the white light and not added by the prism (as Roger Bacon had claimed in the 13th century), and also notably argued that light is composed of particles. Newton additionally developed a law of cooling, proved the binomial theorem, and discovered the principles of conservation of momentum and angular momentum. Newton is regarded by many as having "unrivalled mathematical genius" [see Dampier & Dampier]. The mathematician Joseph Louis Lagrange (1736-1813), Director of the Berlin Academy of Sciences, said this about Newton: ::"Newton was the greatest genius that ever existed and the most fortunate, for we cannot find more than once a system of the world to establish." [See Shapley.]
Biography

Early years
Newton was born in Woolsthorpe-by-Colsterworth (at Woolsthorpe Manor), a hamlet in the county of Lincolnshire. Newton was prematurely born and no one expected him to live; indeed, his mother, Hannah Ayscough Newton, is reported to have said that his body at that time could have fit inside a quart mug (Bell, 1937). His father, Isaac, had died three months before Newton's birth. When Newton was two years old, his mother went to live with her new husband, leaving her son in the care of his grandmother. According to E.T. Bell (1937, Simon and Schuster) and H. Eves: :Newton began his schooling in the village schools and was later sent to Grantham Grammar School where he became the top boy in the school. At Grantham he lodged with the local apothecary, William Clarke and eventually became engaged to the apothecary's stepdaughter, Anne Storer, before he went off to Cambridge University at the age of 19. As Newton became engrossed in his studies, the romance cooled and Miss Storer married someone else. It is said he kept a warm memory of this love, but Newton had no other recorded 'sweethearts' and never married. Cambridge University From the age of twelve until he was seventeen, Newton was educated at Grantham Grammar School. His family then removed him from school and attempted to make a farmer of him. However he was thoroughly unhappy with the work and eventually with the help of his uncle and of his schoolteacher, he managed to persuade his mother to send him back to school so that he might complete his schooling. This he did at the age of eighteen, achieving an admirable final report. His teacher said: :His genius now begins to mount upwards apace and shine out with more strength. He excels particularly in making verses. In everything he undertakes, he discovers an application equal to the pregnancy of his parts and exceeds even the most sanguine expectations I have conceived of him. In 1661 he joined Trinity College, Cambridge, where his uncle William Ayscough had studied. At that time, the college's teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers such as Descartes, Galileo, Copernicus and Kepler. In 1665 he discovered the binomial theorem and began to develop a mathematical theory that would later become calculus. Soon after Newton had obtained his degree in 1665, the University closed down as a precaution against the Great Plague. For the next two years Newton worked at home on calculus, optics and gravitation. He later continued his studies at Woolsthorpe Manor. The popular tradition has it that Newton was sitting under an apple tree when an apple fell on his head, and that this made him understand that earthly and celestial gravitation are the same. A contemporary writer, William Stukeley, recorded in his Memoirs of Sir Isaac Newton's Life a conversation with Newton in Kensington on 15 April 1726, in which Newton recalled "when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth's centre." In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), "Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree." These accounts are exaggerations of Newton's own tale about sitting by a window in his home (Woolsthorpe Manor) and watching an apple fall from a tree. It is now generally considered probable that even this story was invented by Newton in later life, to illustrate how he drew inspiration from everyday events.
Middle years

Mathematical research
Woolsthorpe Manor.]] Newton became a fellow of Trinity College in 1669. In the same year he circulated his findings in De Analysi per Aequationes Numeri Terminorum Infinitas (On Analysis by Infinite Series), and later in De methodis serierum et fluxionum (On the Methods of Series and Fluxions), whose title gave the name to his "method of fluxions". Newton is generally credited as the discoverer of the binomial theorem, an essential step toward the development of modern analysis. Newton and Gottfried Leibniz developed the theory of calculus independently, using different notations. Although Newton had worked out his own method before Leibniz, the latter's notation and "Differential Method" were superior, and were generally adopted throughout the world. Though Newton belongs among the brightest scientists of his era, the last twenty-five years of his life were marred by a bitter dispute with Leibniz, whom he accused of plagiarism. The dispute created a divide between British and Continental mathematicians that persisted even after Newton's death. He was elected Lucasian professor of mathematics in 1669. Any fellow of Cambridge or Oxford had to be ordained at the time. However the terms of the Lucasian professorship required that the holder not be active in the church (presumably so as to have more time for science). Newton argued that this should exempt him from the normal ordination requirement, and Charles II, whose permission was needed, accepted this argument. This prevented the conflict that would have occurred between his religious views and the orthodoxy of the church.
Optics
From 1670 to 1672 he lectured on optics. During this period he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light. He also showed that the coloured light does not change its properties, by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus the colours we observe are the result of how objects interact with the incident already-coloured light, not the result of objects generating the colour. For more details, see Newton's theory of colour. Many of his findings in this field were critized by later theorists, the most well-known being Johann Wolfgang von Goethe, who postulated his own colour theories. Johann Wolfgang von Goethe From this work he concluded that any refracting telescope would suffer from the dispersion of light into colours, and invented a reflecting telescope (today, known as a Newtonian telescope) to bypass that problem. By grinding his own mirrors, using Newton's rings to judge the quality of the optics for his telescopes, he was able to produce a superior instrument to the refracting telescope, due primarily to the wider diameter of the mirror. (Only later, as glasses with a variety of refractive properties became available, did achromatic lenses for refractors become feasible.) In 1671 the Royal Society asked for a demonstration of his reflecting telescope. Their interest encouraged him to publish his notes On Colour, which he later expanded into his Opticks. When Robert Hooke criticised some of Newton's ideas, Newton was so offended that he withdrew from public debate. The two men remained enemies until Hooke's death. In one experiment, to prove that colour perception is caused by pressure on the eye, Newton slid a darning needle around the side of his eye until he could poke at its rear side, dispassionately noting "white, darke & coloured circles" so long as he kept stirring with "y^e bodkin." Newton argued that light is composed of particles; thus he could not explain the diffraction of light. Later physicists instead favoured a wave explanation of light to account for diffraction. Today's quantum mechanics recognises a "wave-particle duality"; however photons bear very little semblance to Newton's corpuscles (e.g., corpuscles refracted by accelerating toward the denser medium). Newton is believed to have been the first to explain precisely the formation of the rainbow from water droplets dispersed in the atmosphere in a rain shower. Figure 15 of Part II of Book One of the Opticks shows a perfect illustration of how this occurs. In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. Newton was in contact with Henry More, the Cambridge Platonist who was born in Grantham, on alchemy, and now his interest in the subject revived. He replaced the ether with occult forces based on Hermetic ideas of attraction and repulsion between particles. John Maynard Keynes, who acquired many of Newton's writings on alchemy, stated that "Newton was not the first of the age of reason: he was the last of the magicians." Newton's interest in alchemy cannot be isolated from his contributions to science.² (This was at a time when there was no clear distinction between alchemy and science.) Had he not relied on the occult idea of action at a distance, across a vacuum, he might not have developed his theory of gravity. (See also Isaac Newton's occult studies.) In 1704 Newton wrote Opticks, in which he expounded his corpuscular theory of light. The book is also known for the first exposure of the idea of the interchangeability of mass and energy: "Gross bodies and light are convertible into one another...". Newton also constructed a primitive form of a frictional electrostatic generator, using a glass globe (Optics, 8th Query).
Gravity and motion
glass In 1679, Newton returned to his work on mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler's laws of motion, and consulting with Hooke and Flamsteed on the subject. He published his results in De Motu Corporum (1684). This contained the beginnings of the laws of motion that would inform the Principia. The Philosophiae Naturalis Principia Mathematica (now known as the Principia) was published on 5 July 1687¹) with encouragement and financial help from Edmond Halley. In this work Newton stated the three universal laws of motion that were not to be improved upon for more than two hundred years. He used the Latin word gravitas (weight) for the force that would become known as gravity, and defined the law of universal gravitation. In the same work he presented the first analytical determination, based on Boyle's law, of the speed of sound in air. With the Principia, Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship that lasted until 1693. The end of this friendship led Newton to a nervous breakdown.
Later life
nervous breakdown In the 1690s Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry More's belief in the infinity of the universe and rejection of Cartesian dualism may have influenced Newton's religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works — The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733) — were published after his death. He also devoted a great deal of time to alchemy (see above)². Newton was also a member of the Parliament of England from 1689 to 1690 and in 1701, but his only recorded comments were to complain about a cold draft in the chamber and request that the window be closed. Newton moved to London to take up the post of warden of the Royal Mint in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England's great recoining, somewhat treading on the toes of Master Lucas (and finagling Edmond Halley into deputy comptroller of the temporary Chester branch). Newton became Master of the Mint upon Lucas' death in 1699. These appointments were intended as sinecures, but Newton took them seriously, exercising his power to reform the currency and punish clippers and counterfeiters. He retired from his Cambridge duties in 1701. Ironically, it was his work at the Mint, rather than his contributions to science, which earned him a knighthood. Newton was knighted by Queen Anne in 1705. Newton was made President of the Royal Society in 1703 and an associate of the French Académie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by attempting to steal his catalogue of observations. Newton died in London and was buried in Westminster Abbey. It is believed Newton never had a romantic relationship, and he is said to have died a virgin. There is some speculation that Newton had Asperger syndrome, a form of autism. See People speculated to have been autistic. His niece, Catherine Barton Conduitt³, served as his hostess in social affairs at his house on Jermyn Street in London; he was her "very loving Uncle"⁴, according to his letter to her when she was recovering from smallpox.
Religious views
4 The law of gravity became Newton's best-known discovery. He warned against using it to view the universe as a mere machine, like a great clock. He said, "Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done." His scientific fame notwithstanding, the Bible was Newton's greatest passion. He devoted more time to the study of Scripture and Alchemy than to science, and said, "I have a fundamental belief in the Bible as the Word of God, written by those who were inspired. I study the Bible daily." Newton himself wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture. He also attempted, unsuccessfully, to find hidden messages within the Bible (See Bible code). Despite his focus in theology and alchemy, Newton tested and investigated these myths with the scientific method, observing, hypothesizing, and testing his theories. To Newton, his scientific and mythical experiments were one in the same, observing and understanding how the world functioned. Newton is often accused of being a Unitarian and Arian, and not believing in the church's doctrine of divine trinity. However, T.C. Pfizenmaier argued that he more likely held the Eastern Orthodox view of the Trinity rather than the Western one held by Roman Catholics, Anglicans, and most Protestants.⁷ In his own day, he was also accused of being a Rosicrucian (as were many in the Royal Society and in the court of Charles II). In his own lifetime, Newton wrote more on religion than he did on natural science. He believed in a rationally emanent world, but he rejected the hylozoism implicit in Leibniz and Baruch Spinoza. Thus, the ordered and dynamically informed universe could be understood, and must be understood, by an active reason, but this universe, to be perfect and ordained, had to be regular.
Newton's effect on religious thought
Newton and Robert Boyle’s mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians. Thus, the clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheism, and, at the same time, the second wave of English deists used Newton's discoveries to demonstrate the possibility of a "Natural Religion." The attacks made against pre-Enlightenment "magical thinking," and the mystical elements of Christianity, were given their foundation with Boyle’s mechanical conception of the universe. Newton gave Boyle’s ideas their completion through mathematical proofs, and more importantly was very successful in popularizing them. Newton refashioned the world governed by an interventionist God into a world crafted by a God that designs along rational and universal principles. These principles were available for all people to discover, allowed man to pursue his own aims fruitfully in this life, not the next, and to perfect himself with his own rational powers. The perceived ability of Newtonians to explain the world, both physical and social, through logical calculations alone is the crucial idea in the disenchantment of Christianity. Newton saw God as the masterful creator whose existence could not be denied in the face of the grandeur of all creation.⁵'^6' But the unforeseen theological consequence of his conception of God, as Leibniz pointed out, was that God was now entirely removed from the world’s affairs, since the need for intervention would only evidence some imperfection in God’s creation, something impossible for a perfect and omnipotent creator. Leibniz's theodicy cleared God from the responsibility for "l'origine du mal" by making God removed from participation in his creation. The understanding of the world was now brought down to the level of simple human reason, and humans, as Odo Marquard argued, became responsible for the correction and elimination of evil. On the other hand, latitudinarian and Newtonian ideas taken too far resulted in the millenarians, a religious faction dedicated to the concept of a mechanical universe, but finding in it the same enthusiasm and mysticism that the Enlightenment had fought so hard to extinguish.
Newton versus the counterfeiters
Newton estimated that 20% of the coins taken in during The Great Recoinage were counterfeit. Counterfeiting was treason, punishable by death by drawing and quartering. As gruesome as the penalties were, the courts were not arbitrary or capricious. The rights of free men had a long tradition in England and the crown had to prove its case to a jury. The law also allowed for plea bargaining. Convictions of the most flagrant criminals could be maddeningly impossible to achieve; however, Newton proved to be equal to the task. He assembled facts and proved his theories with the same brilliance in law that he had shown in science. He gathered much of that evidence himself, disguised, while he hung out at bars and taverns. For all the barriers placed to prosecution, and separating the branches of government, English law still had ancient and formidable customs of authority. Newton was made a justice of the peace and between June 1698 and Christmas 1699 conducted some 200 cross-examinations of witnesses, informers and suspects. During this time he obtained the confessions he needed and while he could not resort to open torture, whatever means he did use must have been fearsome because Newton himself later ordered all records of these interrogations to be destroyed. However he did it, Newton won his convictions and in February 1699, he had ten prisoners waiting to be executed. Newton's greatest triumph as the king's attorney was against William Chaloner. Chaloner was a rogue with a devious intelligence. He set up phony conspiracies of Catholics and then turned in the hapless conspirators whom he entrapped. Chaloner made himself rich enough to posture as a gentleman. Petitioning Parliament, Chaloner accused the Mint of providing tools to counterfeiters. (This charge was made also by others.) He proposed that he be allowed to inspect the Mint's processes in order to improve them. He petitioned Parliament to adopt his plans for a coinage that could not be counterfeited. All the time, he struck false coins, or so Newton eventually proved to a court of competent jurisdiction. On March 23, 1699, Chaloner was hanged, drawn and quartered.
Enlightenment philosophers
Enlightenment philosophers chose a short history of scientific predecessors—Galileo, Boyle, and Newton principally—as the guides and guarantors of their applications of the singular concept of Nature and Natural Law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded. It was Newton’s conception of the universe based upon Natural and rationally understandable laws that became the seed for Enlightenment ideology. Locke and Voltaire applied concepts of Natural Law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied Natural conceptions of psychology and self-interest to economic systems, and sociologists critiquing the current social order fit history into Natural models of progress.
Newton's legacy
progress]] Newton's laws of motion and gravity provided a basis for predicting a wide variety of different scientific or engineering situations, especially the motion of celestial bodies. His calculus proved vitally important to the development of further scientific theories. Finally, he unified many of the isolated physics facts that had been discovered earlier into a satisfying system of laws. Newton's conceptions of gravity and mechanics, though not entirely correct in light of Einstein's Theory of Relativity, still represent an enormous step in the evolution of human understanding of the universe. For this reason, he is generally considered one of history's greatest scientists, ranking alongside such figures as Einstein and Carl Friedrich Gauss. In 1717, the Kingdom of Great Britain went on to an unofficial gold standard when Newton, then Master of the Mint, established a fixed price of £3.17.10 ½d per standard (22 carat) troy ounce, equal to £4.4.11 ½d per fine ounce. Under the gold standard the value of the pound (measured in gold weight) remained largely constant until the beginning of the 20th century. Newton is reputed to have invented the cat flap. This was said to be done so that he would not have to disrupt his optical experiments, conducted in a darkened room, to let his cat in or out. Newtonmas is a holiday celebrated by some scientists as an alternative to Christmas, taking advantage of the fact that Newton's birthday falls on December 25. In July 1992, the Isaac Newton Institute for Mathematical Sciences was opened at Cambridge University - it is regarded as the United Kingdom's national institute for mathematical research.
Fictional appearances
Isaac Newton appears in many works of fiction. He is a recurring figure in Rubrique-à-brac, a French comic strip by Marcel Gotlieb. An ongoing gag involves various depictions of the legend that he discovered the law of gravity due to an apple falling on his head. Newton also figures as a major character in Neal Stephenson's Baroque Cycle and in Philip Kerr's novel, Dark Matter. Newton has a cameo role, along with Stephen Hawking and Albert Einstein, in a poker game in an episode of Star Trek: The Next Generation during season 6. Newton is notable in that scene for being the only scientist without a sense of humour. He also takes offence at the notion that the story of the apple would be fictitious. He also appears in an episode of Star Trek: Voyager where it is claimed that a member of the Q Continuum shook the tree he was sitting under, causing the apple to fall. "Isaac Newton's College" is one of the "Wonders of the World" bonus achievements in the classic computer strategy game by Sid Meier, Civilization. One of the more bizarre fictional apperances have been made in a Japanese animated show Vision of Escaflowne, where the main antagonist, Dornkirk, is revealed to be a 200+ year-old Isaac Newton.
Writings by Newton

- Method of Fluxions (1671)
- De Motu Corporum in Gyrum (1684)
- Philosophiae Naturalis Principia Mathematica (1687)
- Opticks (1704)
- [http://www.pierre-marteau.com/currency/ed/newton-intro.html Reports as Master of the Mint] (1701-1725)
- Arithmetica Universalis (1707)
- An Historical Account of Two Notable Corruptions of Scripture (1754) Short Chronicle, The System of the World, Optical Lectures, Universal Arithmetic, The Chronology of Ancient Kingdoms, Amended and De mundi systemate were published posthumously in 1728.
Notes

- Note 1: The remainder of the dates in this article follow the Gregorian calendar.
- Note 2: Westfall (pp. 530–531) notes that Newton apparently abandoned his alchemical researches.
- Note 3: Westfall, p. 44.
- Note 4: Westfall, p. 595.
- Note 5: Principia, Book III; cited in; Newton’s Philosophy of Nature: Selections from his writings, p. 42, ed. H.S. Thayer, Hafner Library of Classics, NY, 1953.
- Note 6: A Short Scheme of the True Religion, manuscript quoted in Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton by Sir David Brewster, Edinburgh, 1850; cited in; ibid, p. 65.
- Note 7: Pfizenmaier, T.C., "Was Isaac Newton an Arian?" Journal of the History of Ideas 68(1):57–80, 1997.
- Yates, Frances A. The Rosicrucian Enlightenment. London: Routledge and Kegan Paul, 1972.
- Jacob, Margaret C. The Newtonians and the English Revolution: 1689-1720. p28.
- Jacob, Margaret C. The Newtonians and the English Revolution: 1689-1720. p37 and p44.
- Westfall, Richard S. Science and Religion in Seventeenth-Century England. Yale University Press, New Haven: 1958. p200.
- Fitzpatrick, Martin. ed. Knud Haakonssen. “The Enlightenment, politics and providence: some Scottish and English comparisons.” Enlightenment and Religion: Rational Dissent in eighteenth-century Britain. Cambridge University Press, Cambridge: 1996. p64.
- Frankel, Charles. The Faith of Reason: The Idea of Progress in the French Enlightenment. King’s Crown Press, New York: 1948. p1.
- Germain, Gilbert G. A Discourse on Disenchantment: Reflections on Politics and Technology. p28.
- Webb, R.K. ed. Knud Haakonssen. “The emergence of Rational Dissent.” Enlightenment and Religion: Rational Dissent in eighteenth-century Britain. Cambridge University Press, Cambridge: 1996. p19.
- Westfall, Richard S. Science and Religion in Seventeenth-Century England. p201.
- Marquard, Odo. "Burdened and Disemburdened Man and the Flight into Unindictability," in Farewell to Matters of Principle. Robert M. Wallace trans. London: Oxford UP, 1989.
- Jacob, Margaret C. The Newtonians and the English Revolution: 1689-1720. p100-101.
- Jacob, Margaret C. The Newtonians and the English Revolution: 1689-1720. p61.
- Cassels, Alan. Ideology and International Relations in the Modern World. p2.

See also

- World Almanac's Ten Most Influential People of the Second Millennium
- History of calculus
- "Standing on the shoulders of giants"
Resources

References

- [http://scidiv.bcc.ctc.edu/Math/Newton.html Excerpt]
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Further reading

- John Maynard Keynes, Essays in Biography, W W Norton & Co, 1963, paperback, ISBN 039300189X. Keynes had taken a close interest in Newton and owned many of Newton's private papers.
- Isaac Newton, Papers and Letters in Natural Philosophy, edited by I. Bernard Cohen ISBN 0-674-46853-8 Harvard 1958,1978
- Michael H. Hart, The 100, Carol Publishing Group, July 1992, paperback, 576 pages, ISBN 0806513500
- Simmons, J, The giant book of scientists -- The 100 greatest minds of all time, Sydney: The Book Company, (1996)
- Isaac Newton (1642-1727), The Principia: a new Translation, Guide by I. Bernard Cohen ISBN 0-520-08817-4 University of California 1999 Warning: common mistranslations exposed!
- Berlinski, David, Newton's Gift:How Sir Isaac Newton Unlocked the System of our World, ISBN 0684843927 (hardback), also in paperback, Simon & Schuster, 2000
- Stephen Hawking, ed. On the Shoulders of Giants, ISBN 0-7624-1348-5 Places selections from Newton's Principia in the context of selected writings by Copernicus, Kepler, Galileo and Einstein.
- James Gleick, Isaac Newton, Knopf, 2003, hardcover, 288 pages, ISBN 0375422331
- Gale E. Christianson, In the Presence of the Creator: Isaac Newton and His Times Collier MacMillan, 1984, 608 pages
- Harlow Shapley, S. Rapport, H. Wright, A Treasury of Science; "Newtonia" pp. 147-9; "Discoveries" pp. 150-4. Harper & Bros., New York, 1946.
- William C. Dampier & M. Dampier, Readings in the Literature of Science, Harper & Row, New York, 1959.
External links

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- [http://www.lucidcafe.com/library/95dec/newton.html Sir Isaac Newton Scientist and Mathematician by Lucidcafé]
- [http://www.dmoz.org/Science/Physics/History/People/Newton,_Isaac/ Isaac Newton Directory]
- [http://www.newtonproject.ic.ac.uk/ Newton Research Project]
- [http://www.skepticreport.com/astrology/newton.htm Rebuttal of Newton as an astrologer]
- [http://www.galilean-library.org/snobelen.html Newton Reconsidered], an interview with Newton scholar Stephen D. Snobelen at the Galilean Library
- [http://www.huntington.org/LibraryDiv/Newton/Newtonexhibit.htm March 5-June 12, 2005 Isaac Newton's personal copy of Principia on display at] Huntington Library
- [http://www.pierre-marteau.com/currency/ed/newton-intro.html Newton's Reports as Master of the Royal Mint]
- [http://www.pbs.org/wgbh/nova/newton/ Newton's Dark Secrets] NOVA television program.
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- [http://plato.stanford.edu/entries/newton-stm/ Stanford Encyclopedia of Philosophy entry on Newton's views on space, time, and motion]
- [http://fermatslasttheorem.blogspot.com/2005/09/sir-isaac-newton.html Sir Isaac Newton] an article that traces his life and achievements.
- [http://www.tqnyc.org/NYC051308/index.htm Newton's Castle] Educational material about Newton
- [http://www.dlib.indiana.edu/collections/newton The Chymistry of Isaac Newton] Research about Isaac Newton's Alchemical writings
- [http://www.newton.cam.ac.uk/ The Isaac Newton Institute for Mathematical Sciences] Newton, Issac Newton, Issac Newton, Issac Newton, Isaac Newton, Isaac Newton, Isaac Newton, Isaac Newton, Isaac Newton, Isaac Newton, Isaac Newton, Isaac Newton, Isaac Newton,Isaac Newton,Isaac Newton, Isaac Newton, Isaac ko:아이작 뉴턴 ms:Isaac Newton ja:アイザック・ニュートン simple:Isaac Newton th:ไอแซก นิวตัน

Turbojet

:For the transportation company, see TurboJET. TurboJET Turbojets are the simplest and oldest kind of general purpose jet engine. Two different engineers, Frank Whittle in Britain and Hans von Ohain in Germany, developed the concept during the late '30's. Fighter aircraft, fitted with turbojet engines, first entered service in 1944, towards the end of WW2. A turbojet engine is used primarily to propel aircraft. Air is drawn into the rotating compressor via the intake and is compressed to a higher pressure before entering the combustion chamber. Fuel is mixed with the compressed air and ignited by flame in the eddy of a flame holder. This combustion process significantly raises the temperature of the gas. Hot combustion products leaving the combustor expand through the turbine, where power is extracted to drive the compressor. Although this expansion process reduces the turbine exit gas temperature and pressure, both parameters are usually still well above ambient conditions. The gas stream exiting the turbine expands to ambient pressure via the propelling nozzle, producing a high velocity jet in the exhaust plume. If the jet velocity exceeds the aircraft flight velocity, there is a net forward thrust upon the airframe. Modern jet engines are mainly turbofans, where some (if not most) of the air entering the intake bypasses the combustor. Although ramjet engines are simpler in design (virtually no moving parts), they are incapable of operating at low flight speeds.

Air intake

Preceding the compressor is the air intake (or inlet), which is designed to recover, as efficiently as possible, the ram pressure of the streamtube approaching the intake. Downstream of the intake, air enters the compression system.

Compressor

The compressor, which rotates at very high speed, adds energy to the airflow, at the same time squeezing it into a smaller space, thereby increasing its pressure and temperature (try rapidly pumping on a bicycle pump - it will quickly become very warm!). Several types of compressor are used in turbojets and gas turbines in general: axial, centrifugal, axial-centrifugal, double-centrifugal, etc. Early turbojet compressors had overall pressure ratios as low as 5:1 (as do a lot of simple auxiliary power units and small propulsion turbojets today). Aerodynamic improvements, plus splitting the compression system into two separate units and/or fitting variable stators, enabled later turbojets to have overall pressure ratios of 15:1 or more. In comparison, modern civil turbofan engines have overall pressure ratios as high as 44:1 or more. After leaving the compression system, the compressed air enters the combustor.

Combustor

The burning process in the combustor is significantly different from that in a piston engine. In a piston engine the burning gases are confined to a small volume and, as the fuel burns, the pressure increases dramatically. In a turbojet the air and fuel mixture passes, unconfined, through the combustion chamber. As the mixture burns its temperature increases dramatically, the pressure actually decreasing a few percent. In detail, the fuel-air mixture must be brought almost to a stop so that a stable flame can be maintained, this occurs just after the beginning of the combustion chamber. The aft part of this flame front is allowed to progress rearward in the engine. This ensures that the rest of the fuel is burned as the flame becomes hotter when it leans out, and because of the shape of the combustion chamber the flow is accelerated rearwards. Some pressure drop is unavoidable, as it is the reason why the expanding gases travel out the rear of the engine rather than out the front. Less than 25% of the air is involved in combustion, in some engines as little as 12%, the rest acting as a reservoir to soak up the heating effect of the fuel burning. Another difference between piston engines and jet engines is that the peak flame temperature in a piston engine is experienced only momentarily, and for a small portion of the entire cycle. The combustor in a jet engine is exposed to the peak flame temperature continuously and operates at a pressure high enough that a stoichiometric fuel-air ratio would melt the can and everything downstream. Instead, jet engines run a very lean mixture, so lean that it would not normally support combustion. A central core of the flow is mixed with enough fuel to burn readily. The cans are carefully shaped to maintain a layer of fresh unburned air between the metal surfaces and the central core. This unburned air mixes into the burned gases to bring the temperature down to something the turbine can tolerate.

Turbine

Hot gases leaving the combustor are allowed to expand through the turbine. In the first stage the turbine is largely a reaction turbine (similar to a pelton wheel) and rotates because of the impact of the hot gas stream. Later stages are convergent ducts that accelerate the gas rearward and gain energy from that process. Pressure drops, and energy is transferred into the shaft. The turbine's rotational energy is used primarily to drive the compressor. Some shaft power is extracted to drive accessories, like fuel, oil, and hydraulic pumps. Because of its significantly higher entry temperature, the turbine pressure ratio is much lower than that of the compressor. In a turbojet almost two thirds of all the power generated by burning fuel is used by the compressor to compress the air for the engine.

Nozzle

After the turbine, the gases are allowed to expand through the exhaust nozzle to atmospheric pressure, producing a high velocity jet in the exhaust plume. In a convergent nozzle, the ducting narrows progressively to a throat. The nozzle pressure ratio on a turbojet is usually high enough for the expanding gases to reach Mach 1.0 and choke the throat. Normally the flow will go supersonic in the exhaust plume, external to the engine. If, however, a convergent-divergent nozzle is fitted, the divergent (increasing flow area) section allows the gases to reach supersonic velocity within the nozzle itself. This is slightly more efficient on thrust, than using a convergent nozzle. There is, however, the added weight and complexity, since the con-di nozzle must be fully variable, to cope basically with engine throttling.

Net thrust

Below is an approximate equation for calculating the net thrust of a turbojet:

F_n = m \cdot (V_ - V_a)

where:

m =

intake mass flow

V_ =

fully expanded jet velocity (in the exhaust plume)

V_a =

= aircraft flight velocity Whilst the m
- V_jfe term represents the nozzle gross thrust, the m
- V_a term represents the ram drag of the intake. Obviously, the jet velocity must exceed that of the flight velocity if there is to be a net forward thrust on the airframe.

Cycle improvements

Increasing the overall pressure ratio of the compression system raises the combustor entry temperature. Therefore, at a fixed fuel flow and airflow, there is an increase in turbine inlet temperature. Although the higher temperature rise across the compression system, implies a larger temperature drop over the turbine system, the nozzle temperature is unaffected, because the same amount of heat is being added to the system. There is, however, a rise in nozzle pressure, because overall pressure ratio increases faster than the turbine expansion ratio. Consequently, net thrust increases, whilst specific fuel consumption (fuel flow/net thrust) decreases. So turbojets can be made more fuel efficient by raising overall pressure ratio and turbine inlet temperature in unison. However, better turbine materials and/or improved vane/blade cooling are required to cope with increases in both turbine inlet temperature and compressor delivery temperature. Increasing the latter requires better compressor materials.

Early designs

Early German engines had serious problems controlling the turbine inlet temperature. Their early engines averaged only ten hours of operation before failing—often with chunks of metal flying out the back of the engine when the turbine overheated. British engines tended to fare better due to better metals. The Americans had the best materials because of their reliance on turbosupercharging in high altitude bombers of World War II. For a time some US jet engines included the ability to inject water into the engine to cool the compressed flow before combustion, usually during takeoff. The water would tend to prevent complete combustion and as a result the engine ran cooler again, but the planes would takeoff leaving a huge plume of smoke. Today these problems are much better handled, but temperature still limits airspeeds in supersonic flight. At the very highest speeds, the compression of the intake air raises the temperature to the point that the compressor blades will melt. At lower speeds, better materials have increased the critical temperature, and automatic fuel management controls have made it nearly impossible to overheat the engine.

Turboprop

A Turboprop (Turbo-propeller) or turboshaft engine is a type of gas turbine. It differs from a Turbojet in that the design is optimized to produce rotating shaft power to drive a propeller, instead of thrust from the exhaust gas. Basically, a turbojet consists of an intake, compressor, combustor, turbine and a propelling nozzle. Air drawn into the intake is compressed by the compressor. Fuel is burnt with the compressed air in the combustor. The hot combustion gases expand through the turbine, to provide power to the compressor. Further expansion of the gases occurs in the propelling nozzle; the high velocity jet produced providing forward thrust. In a turboprop much of the jet thrust is sacrificed in favor of shaftpower, which is obtained by extracting additional power (to that necessary to drive the compressor) from the turbine expansion process. Whilst the power turbine may be integral with the compressor turbine, most turboprops today feature a Free Power Turbine, on a separate coaxial shaft. This enables the propeller to rotate freely, independent of compressor speed. Owing to the additional expansion in the turbine system, the residual energy in the jet is fairly low (<10% of total thrust, including that of the propeller). Because the propeller is very much larger in diameter than the power turbine, the tip speed of the propeller can become supersonic. Consequently, to prevent this, a speed reduction gearbox is inserted between the power turbine and propeller shafts. The gearbox is part of the engine, whereas in a turboshaft the (helicopter) rotor reduction gearbox is remote from the engine. Turboprops are very efficient at modest flight speeds (below 450mph), because the jet velocity of the propeller (and exhaust) is relatively low. Consequently, small commuter aircraft and military transports tend to feature turboprop engines. Although turboprops are used in some General Aviation applications, their high price deters more widespread acceptance. While most modern turbojet and turbofan engines use axial-flow compressors, turboprop engines usually contain at least one stage of centrifugal compression, because of the small size of the engines. centrifugal compression Propellers lose efficiency as aircraft speed increases, which is why turboprops are not used on higher-speed aircraft. However, turboprops are far more efficient than piston-driven propeller engines. The worlds first Turboprop was the 'Jendrassik CS-1' designed by Gyorgy Jendrassik. It was produced and flown briefly in Czecho-Slovakia between 1939 and 1942. The aircraft it was fitted to was the Varga XG/XH twin-engined Recconaisance bomber. Not surprisingly the engines proved very unreliable. For more info. visit "Podklady", a Czech Aircraft drawing site (Czech text). Jendrassik had also produced a small scale turboprop of 75 kW in 1937. (Added By Peter Butt 03/12/05) The first British turboprop engine was the Rolls-Royce RB.50 Trent, a converted Derwent II fitted with reduction gear and a Rotol 7' 11" five-bladed propeller. Two Trents were fitted to Gloster Meteor EE227 - the sole "Trent-Meteor" - which became the first relataively reliable turboprop powered aircraft. From their experience with the Trent, Rolls-Royce developed the Dart, which became one of the most reliable turbprop engines ever built. Dart production continued for more than fifty years. For info on Trent go to Rolls-Royce Heritage Trust) The first American Turboprop was the General-Electric T-31. A European consortium is currently developing the 11000shp TP400-D6 turboprop for the A400M military transport. The engine is all-axial and has a two shaft core, with a free power turbine mounted on a third coaxial shaft. Residual thrust on a turboshaft is avoided by: a) further expansion in the turbine system and/or b) truncating and turning the exhaust through 90degrees, to produce two opposing jets. Apart from the above and the remote location of the gearbox, there is very little difference between a turboprop and a turboshaft.

External links

- [http://Innodyn.com Innodyn]
- [http://tanks45.tripod.com/Jets45/Histories/Trent/Trent.htm Gloster Trent-Meteor] Category:Gas turbines Category:Aircraft engines Category:Jet engines

Rocket

A rocket is a vehicle, missile or aircraft which obtains thrust by the reaction to the ejection of fast moving exhaust gas from within a rocket engine. Often the term rocket is also used to mean a rocket engine. In military terminology, a rocket generally uses solid propellant and is unguided. These rockets can be fired by ground-attack aircraft at fixed targets such as buildings, or can be launched by ground forces at other ground targets. During the Vietnam era, there were also air launched unguided rockets that carried a nuclear payload designed to attack aircraft formations in flight. A missile, by contrast, can use either solid or liquid propellant, and has a guidance system. This distinction generally applies only in the case of weapons, though, and not to civilian or orbital launch vehicles. In all rockets the exhaust is formed from propellant which is carried within the rocket prior to its release. Rocket thrust is due to accelerating the exhaust gases (see Newton's 3rd Law of Motion). There are many different types of rockets, and a comprehensive list can be found in spacecraft propulsion- they range in size from tiny models that can be purchased at a hobby store, to the enormous Saturn V used for the Apollo program. Rockets are used to accelerate, change orbits, de-orbit for landing, for the whole landing if there is no atmosphere (e.g. for landing on the Moon), and sometimes to soften a parachute landing immediately before touchdown (see Soyuz spacecraft). Most current rockets are chemically powered rockets (internal combustion engines). A chemical rocket engine can use solid propellant (see Space Shuttle's SRBs), liquid propellant (see Space shuttle main engine), or a hybrid mixture of both. A chemical reaction is initiated between the fuel and the oxidizer in the combustion chamber, and the resultant hot gases accelerate out of a nozzle (or nozzles) at the rearward facing end of the rocket. The acceleration of these gases through the engine exerts force ('thrust') on the combustion chamber and nozzle, propelling the vehicle (in accordance with Newton's Third Law). See rocket engine for details. Not all rockets use chemical reactions. Steam rockets, for example, release superheated water through a nozzle where it instantly flashes to high velocity steam, propelling the rocket. The efficiency of steam as a rocket propellant is relatively low, but it is simple and reasonably safe, and the propellant is cheap and widely available. Most steam rockets have been used for propelling land-based vehicles but a small steam rocket was tested in 2004 on board the UK-DMC satellite. There are proposals to use steam rockets for interplanetary transport using either nuclear or solar heating as the power source to vaporize water collected from around the solar system. Rockets where the heat is supplied from other than the propellant, such as steam rockets, are classed as external combustion engines. Other examples of external combustion rocket engines include most designs for nuclear powered rocket engines. Use of hydrogen as the propellant for external combustion engines gives very high velocities. Due to their high exhaust velocity (mach ~10+), rockets are particularly useful when very high speeds are required, such as orbital speed (mach 25). The speeds that a rocket vehicle can reach can be calculated by the rocket equation; which gives the speed difference ('delta-v') in terms of the exhaust speed and ratio of initial mass to final mass ('mass ratio'). Rockets must be used when there is no other substance (land, water, or air) or force (gravity, magnetism, light) that a vehicle may employ for propulsion, such as in space. In these circumstances, it is necessary to carry all the propellant to be used. Common mass ratios for vehicles are 20/1 for dense propellants such as liquid oxygen and kerosene, 25/1 for dense monopropellants such as hydrogen peroxide, and 10/1 for liquid oxygen and liquid hydrogen. However, mass ratio is highly dependent on many factors such as the type of engine the vehicle uses and structural safety margins. Often, the required velocity (delta-v) for a mission is unattainable by any single rocket because the propellant, structure, guidance and engines weigh so much as to prevent the mass ratio from being high enough. This problem is frequently solved by staging - the rocket sheds excess weight (usually tankage and engines) during launch to reduce its weight and effectively increase its mass ratio. Typically, the acc