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Thrust is a reaction force described quantitatively by Newton's second and third laws. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction on that system.

In mechanical engineering, force orthogonal to the main load (such as in parallel helical gears) is referred to as thrust.

Examples[link]

Forces on an aerofoil cross section

A fixed-wing aircraft generates forward thrust when air is pushed in the direction opposite to flight. This can be done in several ways including by the spinning blades of a propeller, or a rotating fan pushing air out from the back of a jet engine, or by ejecting hot gases from a rocket engine. The forward thrust is proportional to the mass of the airstream multiplied by the change in velocity of the airstream. Reverse thrust can be generated to aid braking after landing by reversing the pitch of variable pitch propeller blades, or using a thrust reverser on a jet engine. Rotary wing aircraft and thrust vectoring V/STOL aircraft use engine thrust to support the weight of the aircraft, and vector sum of this thrust fore and aft to control forward speed.

Birds normally achieve thrust during flight by flapping their wings.

A motorboat generates thrust (or reverse thrust) when the propellers are turned to accelerate water backwards (or forwards). The resulting thrust pushes the boat in the opposite direction to the sum of the momentum change in the water flowing through the propeller.

A rocket is propelled forward by a thrust force equal in magnitude, but opposite in direction, to the time-rate of momentum change of the exhaust gas accelerated from the combustion chamber through the rocket engine nozzle. This is the exhaust velocity with respect to the rocket, times the time-rate at which the mass is expelled, or in mathematical terms:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{T}=\frac{dm}{dt}\mathbf{v}

where:

• T is the thrust generated (force)
• Failed to parse (Missing texvc executable; please see math/README to configure.): \frac {dm} {dt}

is the rate of change of mass with respect to time (mass flow rate of exhaust);

• v is the speed of the exhaust gases measured relative to the rocket.

For vertical launch of a rocket the initial thrust must be more than the weight.

Each of the three Space Shuttle Main Engines can produce a thrust of 1.8 MN, and each of the Space Shuttle's two Solid Rocket Boosters 14.7 MN, together 29.4 MN. Compare with the mass at lift-off of 2,040,000 kg, hence a weight of 20 MN.

By contrast, the simplified Aid for EVA Rescue (SAFER) has 24 thrusters of 3.56 N each.

In the air-breathing category, the AMT-USA AT-180 jet engine developed for radio-controlled aircraft produce 90 N (20 lbf) of thrust.^[1] The GE90-115B engine fitted on the Boeing 777-300ER, recognized by the Guinness Book of World Records as the "World's Most Powerful Commercial Jet Engine," has a thrust of 569 kN (127,900 lbf).

Thrust to power[link]

The power needed to generate thrust and the force of the thrust can be related in a non-linear way. In general, Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{P}^2 \propto \mathbf{T}^3 . The proportionality constant varies, and can be solved for a uniform flow:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{dm}{dt} = \rho A {v}

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{T} = \frac{dm}{dt} {v}, \mathbf{P} = \frac{1}{2} \frac{dm}{dt} {v}^2

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{T} = \rho A {v}^2, \mathbf{P} = \frac{1}{2} \rho A {v}^3

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{P}^2 = \frac{\mathbf{T}^3}{4 \rho A}

Note that these calculations are only valid for when the incoming air is accelerated from a standstill - for example when hovering.

The inverse of the proportionality constant, the "efficiency" of an otherwise-perfect thruster, is proportional to the area of the cross section of the propelled volume of fluid (Failed to parse (Missing texvc executable; please see math/README to configure.): A ) and the density of the fluid (Failed to parse (Missing texvc executable; please see math/README to configure.): \rho ). This helps to explain why moving through water is easier and why aircraft have much larger propellers than watercraft do.

Thrust to propulsive power[link]

A very common question is how to compare the thrust rating of a jet engine with the power rating of a piston engine. Such comparison is difficult, as these quantities are not equivalent. A piston engine does not move the aircraft by itself (the propeller does that), so piston engines are usually rated by how much power they deliver to the propeller. Except for changes in temperature and air pressure, this quantity depends basically on the throttle setting.

Now, a jet engine has no propeller. So let's find out the propulsive power of a jet engine from its thrust. Power is the force (F) it takes to move something over some distance (d) divided by the time (t) it takes to move that distance ^[2]:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{P}=\mathbf{F}\frac{d}{t}

In case of a rocket or a jet aircraft, the force is exactly the thrust produced by the engine. If the rocket or aircraft is moving at about a constant speed, then distance divided by time is just speed, so power is thrust times speed:^[3]

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{P}=\mathbf{T}{v}

This formula looks very surprising, but it is correct: the propulsive power (or power available ^[4]) of a jet engine increases with its speed. If the speed is zero, then the propulsive power is zero. If a jet aircraft is at full throttle but is tied to a very strong tree with a very strong chain, then the jet engine produces no propulsive power. It certainly transfers a lot of power around, but all that is wasted. Compare that to a piston engine. The combination piston engine–propeller also has a propulsive power with exactly the same formula, and it will also be zero at zero speed –- but that is for the engine–propeller set. The engine alone will continue to produce its rated power at a constant rate, whether the aircraft is moving or not.

Two aircraft tied to a tree

Now, imagine the strong chain is broken, and the jet and the piston aircraft start to move. At low speeds:

The piston engine will have constant 100% power, and the propeller's thrust will vary with speed
The jet engine will have constant 100% thrust, and the engine's power will vary with speed

This shows why one cannot compare the rated power of a piston engine with the propulsive power of a jet engine – these are different quantities (even if the name "power" is the same). There isn't any useful power measurement in a jet engine that compares directly to a piston engine rated power. However, instead of comparing engine performance, the gross aircraft performance as complete systems can be compared using first principle definitions of power, force and work with the requisite considerations of constantly changing effects like drag and the mass (of the fuel) in both systems. There is of course an implicit relationship between thrust and their engines. Thrust specific fuel consumption is a useful measure for comparing engines.

See also[link]

• Aerodynamic force
• Astern propulsion
• Gimballed thrust, the most common thrust system in modern rockets
• Stream thrust averaging
• Thrust-to-weight ratio
• Thrust vectoring
• Tractive effort

References[link]

U.S. Navy F/A-18 breaking the sound barrier. The white halo formed by condensed water droplets is thought to result from a drop in air pressure around the aircraft at transonic speeds (see Prandtl-Glauert Singularity).^[1][2]

1. Subsonic
2. Mach 1
3. Supersonic
4. Shock wave

The sound barrier, in aerodynamics, is the point at which an aircraft moves from transonic to supersonic speed. The term, which occasionally has other meanings, came into use during World War II, when a number of aircraft started to encounter the effects of compressibility, a collection of several unrelated aerodynamic effects that "struck" their planes like an impediment to further acceleration. By the 1950s, new aircraft designs routinely "broke" the sound barrier.^{[N 1]}

History[link]

Some common whips such as the bullwhip or sparewhip are able to move faster than sound: the tip of the whip breaks the sound barrier and causes a sharp crack—literally a sonic boom.^[3] Firearms since the 19th century have generally had a supersonic muzzle velocity.

The sound barrier may have been first breached in nature some 150 million years ago. Some paleobiologists report that, based on computer models of their biomechanical capabilities, certain long-tailed dinosaurs such as Apatosaurus and Diplodocus may have possessed the ability to flick their tails at supersonic velocities, possibly used to generate an intimidating booming sound. This finding is theoretical and disputed by others in the field.^[4] Meteorites entering the Earth's atmosphere usually, if not always, descend faster than sound.

Early problems[link]

The tip of the propeller on many early aircraft may reach supersonic speeds, producing a noticeable buzz that differentiates such aircraft. This is particularly noticeable on the Stearman, and noticeable on the T-6 Texan when it enters a sharp-breaking turn. This is undesirable, as the transonic air movement creates disruptive shock waves and turbulence. It is due to these effects that propellers are known to suffer from dramatically decreased performance as they approach the speed of sound. It is easy to demonstrate that the power needed to improve performance is so great that the weight of the required engine grows faster than the power output of the propeller. This problem was one of the issues that led to early research into jet engines, notably by Frank Whittle in England and Hans von Ohain in Germany, who were led to their research specifically in order to avoid these problems in high-speed flight.

Nevertheless, propeller aircraft were able to approach the speed of sound in a dive. Unfortunately, doing so led to numerous crashes for a variety of reasons. For instance, pilots flew full power into terrain because the rapidly increasing forces acting on the control surfaces of their aircraft- most infamously, the Mitsubishi Zero^{[citation needed]}- overpowered them. In its case, several attempts to fix it only made the problem worse. Likewise, the flexing caused by the low torsional stiffness of the Supermarine Spitfire's wings caused them, in turn, to counteract aileron control inputs, leading to a condition known as control reversal. This was solved in later models with changes to the wing. Worse still, a particularly dangerous interaction of the airflow between the wings and tail surfaces of diving P-38 Lightning's made "pulling out" of dives difficult; however, the problem was later solved by the addition of a "dive flap" that upset the airflow under these circumstances. Flutter due to the formation of shock waves on curved surfaces was another major problem, which led most famously to the breakup of de Havilland Swallow and death of its pilot, Geoffrey de Havilland, Jr.

All of these effects, although unrelated in most ways, led to the concept of a "barrier" that makes it difficult for an aircraft to break the speed of sound. ^{[N 2]}

Early claims[link]

There are, however, several claims that the sound barrier was broken during World War II. Hans Guido Mutke claimed to have broken the sound barrier on 9 April 1945 in a Messerschmitt Me 262. Mutke reported not just transonic buffeting but the resumption of normal control once a certain speed was exceeded, then a resumption of severe buffeting once the Me 262 slowed again. He also reported engine flame out. However, this claim is widely disputed by various experts believing the Me 262's structure could not support high transonic, let alone supersonic flight.^[6] The lack of area ruled fuselage and 10 percent thick wings did not prevent other aircraft from exceeding Mach 1 in dives. Chuck Yeager's Bell X-1, the North American F-86 Sabre (with Me-262 profile ^[7][8]) and the Convair Sea Dart seaplane exceeded Mach 1 without area rule fuselages. Computational tests carried out by Professor Otto Wagner of the Munich Technical University in 1999 suggest the Me 262 was capable of supersonic flight during steep dives. Recovering from the dive and the resumption of severe buffeting once subsonic flight was resumed would have been very likely to damage the craft terminally.

On page 13 of the "Me 262 A-1 Pilot's Handbook" issued by Headquarters Air Materiel Command, Wright Field, Dayton, Ohio as Report No. F-SU-1111-ND on January 10, 1946:

Speeds of 950 km/h (590 mph) are reported to have been attained in a shallow dive 20° to 30° from the horizontal. No vertical dives were made. At speeds of 950 to 1,000 km/h (590 to 620 mph) the air flow around the aircraft reaches the speed of sound, and it is reported that the control surfaces no longer affect the direction of flight. The results vary with different airplanes: some wing over and dive while others dive gradually. It is also reported that once the speed of sound is exceeded, this condition disappears and normal control is restored.

The comments about restoration of flight control and cessation of buffeting above Mach 1 are very significant in a 1946 document.

In his book Me-163, former Messerschmitt Me 163 "Komet" pilot Mano Ziegler claims that his friend, test pilot Heini Dittmar, broke the sound barrier when steep diving the rocket plane and that several people on the ground heard the sonic booms. Heini Dittmar had been accurately and officially recorded at 1,004.5 km/h (623.8 mph) in level flight on 2 October 1941 in the prototype Me 163 V4. He reached this speed at less than full throttle, as he was concerned by the transonic buffeting. The craft's Walter RII-203 cold rocket engine produced 7.34 kN (750 kgp / 1,650 lbf) thrust. The flight was made after a drop launch from a carrier plane to conserve fuel, a record that was kept secret until the war's end. The craft's potential performance in a powered dive is unknown, but the Me 163B test version of the series rocket plane had an even more powerful engine (HWK 109-509 A-2) and a greater wing sweep than the Me 163A. Ziegler claims that on 6 July 1944, Heini Dittmar, flying a test Me 163 B V18 VA + SP, was measured traveling at a speed of 1,130 km/h.^[9]

Similar claims for the Spitfire and other propeller aircraft are more suspect. It is now known that traditional airspeed gauges using a pitot tube give inaccurately high readings in the transonic regime, apparently due to shock waves interacting with the tube or the static source. This led to problems then known as "Mach jump^[10]

Attempts to break the sound barrier[link]

The first powered flight faster than sound may have been the Soviet ramjet experiments of Yuri Pobedonostsev in 1933. Phosphorus-powered ramjets achieved speeds of 600–680 meters/second (Mach 2).^[11] Another early vehicle to break the sound barrier was probably the first successful test launch of the German V-2 ballistic missile on 3 October 1942, at Peenemünde in Germany. By September 1944, the V-2s routinely achieved Mach 4 (1,200 m/s) during terminal descent.

In 1942 the United Kingdom's Ministry of Aviation began a top secret project with Miles Aircraft to develop the world's first aircraft capable of breaking the sound barrier. The project resulted in the development of the prototype Miles M.52 jet aircraft, which was designed to reach 1,000 mph (417 m/s; 1,600 km/h) at 36,000 ft (11 km) in 1 minute 30 sec.

The aircraft's design introduced many innovations which are still used on today's supersonic aircraft. The single most important development was the all-moving tailplane, giving extra control to counteract the Mach tuck which allowed control to be maintained to and beyond supersonic speeds. This was wind-tunnel tested at Mach 0.86 in 1944 in the UK.^[12] In the immediate postwar era new data from captured German records suggested that major savings in drag could be had through a variety of means such as swept wings, and Director of Scientific Research, Sir Ben Lockspeiser, decided to cancel the project in light of this new information. Later experimentation with the Miles M.52 design proved that the aircraft would indeed have broken the sound barrier, with an unpiloted 3/10 scale replica of the M.52 achieving Mach 1.5 in October 1948.^[13] By that time, the sound barrier had been broken by the Americans, and also by the British De Havilland DH 108.

Sound barrier officially broken[link]

U.S. efforts progressed apace soon after Britain had disclosed all its research and designs to the U.S. government on the promise that U.S. information would be shared the other way - a promise that the Americans did not keep.^[14] They utilized the information to initiate work on the Bell XS-1. The final version of the Bell XS-1 has many design similarities to the original Miles M.52 version. Also featuring the all-moving tail, the XS-1 was later known as the X-1. It was in the X-1 that Chuck Yeager was credited with being the first man to break the sound barrier in level flight on 14 October 1947, flying at an altitude of 45,000 ft (13.7 km). George Welch made a plausible but officially unverified claim to have broken the sound barrier on 1 October 1947, while flying an XP-86 Sabre. He also claimed to have repeated his supersonic flight on 14 October 1947, 30 minutes before Yeager broke the sound barrier in the Bell X-1. Although evidence from witnesses and instruments strongly imply that Welch achieved supersonic speed, the flights were not properly monitored and are not officially recognized. The XP-86 officially achieved supersonic speed on 26 April 1948.^[15]

On 14 October 1947, just under a month after the United States Air Force had been created as a separate service, the tests culminated in the first manned supersonic flight, piloted by Air Force Captain Charles "Chuck" Yeager in aircraft #46-062, which he had christened Glamorous Glennis. The rocket-powered aircraft was launched from the bomb bay of a specially modified B-29 and glided to a landing on a runway. XS-1 flight number 50 is the first one where the X-1 recorded supersonic flight, at Mach 1.06 (361 m/s, 1,299 km/h, 807.2 mph) peak speed; however, Yeager and many other personnel believe Flight #49 (also with Yeager piloting), which reached a top recorded speed of Mach 0.997 (339 m/s, 1,221 km/h), may have, in fact, exceeded Mach 1.^{[citation needed]} (The measurements were not accurate to three significant figures and no sonic boom was recorded for that flight.)

As a result of the X-1's initial supersonic flight, the National Aeronautics Association voted its 1948 Collier Trophy to be shared by the three main participants in the program. Honored at the White House by President Harry S. Truman were Larry Bell for Bell Aircraft, Captain Yeager for piloting the flights, and John Stack for the NACA contributions.

Jackie Cochran was the first woman to break the sound barrier on May 18, 1953, in a Canadair Sabre, with Yeager as her wingman.

The sound barrier fades[link]

Chuck Yeager broke the sound barrier on October 14, 1947 in the Bell X-1, as shown in this newsreel.

As the science of high-speed flight became more widely understood, a number of changes led to the eventual disappearance of the "sound barrier". Among these were the introduction of swept wings, the area rule, and engines of ever-increasing performance. By the 1950s many combat aircraft could routinely break the sound barrier in level flight, although they often suffered from control problems when doing so, such as Mach tuck. Modern aircraft can transit the "barrier" without it even being noticeable.^{[citation needed]}

By the late 1950s the issue was so well understood that many companies started investing in the development of supersonic airliners, or SSTs, believing that to be the next "natural" step in airliner evolution. History has proven this not to be the case, at least yet, but Concorde and the Tupolev Tu-144 both entered service in the 1970s regardless.

Although Concorde and the Tu-144 were the first aircraft to carry commercial passengers at supersonic speeds, they were not the first or only commercial airliners to break the sound barrier. On 21 August 1961, a Douglas DC-8 broke the sound barrier at Mach 1.012 or 1,240 km/h (776.2 mph) while in a controlled dive through 41,088 feet (12,510 m). The purpose of the flight was to collect data on a new leading-edge design for the wing.^[16] A China Airlines 747 may have broken the sound barrier in an unplanned descent from 41,000 ft (12,500 m) to 9,500 ft (2,900 m) after an in-flight upset on 19 February 1985. It also reached over 5g.^[17]

Breaking the sound barrier in a land vehicle[link]

On 12 January 1948, a Northrop unmanned rocket sled became the first land vehicle to break the sound barrier. At a military test facility at Muroc Air Force Base (now Edwards AFB), California, it reached a peak speed of 1,019 mph (1,640 km/h) before jumping the rails. ^[18][19]

On 15 October 1997, in a vehicle designed and built by a team led by Richard Noble, British driver (and Royal Air Force pilot) Andy Green became the first person to break the sound barrier in a land vehicle in compliance with Fédération Internationale de l'Automobile rules. The vehicle, called the ThrustSSC ("Super Sonic Car"), captured the record exactly 50 years and one day after Yeager's flight.

References[link]

Notes

Citations

Bibliography

External links[link]

Wikimedia Commons has media related to: Sound barrier

• Fluid Mechanics, a collection of tutorials by Dr. Mark S. Cramer, Ph.D
• Breaking the Sound Barrier with an Aircraft by Carl Rod Nave, Ph.D
• a video of a Concorde reaching Mach 1 at intersection TESGO taken from below
• An interactive Java applet, illustrating the sound barrier.
• F-18 breaks the sound barrier