The theory of supersonic flight,
There exists four different types of speeds in a flights. Knowing these speeds would go a long way into understanding the supertonic speed. These flight regime speeds includes that subtonic speed, the transonic speed, the supertonic speed as well as the hypertonic speed. A plane is said to be flying at a Subsonic speed when all the air flowing around it is at a velocity of less than Mach one or below the speed of the sound (Stengel, 2015). It should be noted that the air accelerates when it flows in certain aircrafts part like top of the wing and therefore, a plane flying at 500Mph might have the air at its top wing accelerating at a speed of 600mph. The fastness of a plane in subsonic aircrafts is determined by the design of the wing but for the Mach number, it is usually over 0.8. a plane is said to be flying at transonic speed if some parts of the aircraft is experiencing subsonic airflows while others parts are experiencing supersonic airflows (Cole & Cook, 2012). Over the top of the plane, Mach 1 will be reached and a shock wave will develop. It forms 90 degrees towards the airflow and is regarded as a normal flow. Under this type of flight, stability issues could be encountered because the shock waves may cause the air to separate from the plane’s wing. The shock wave may also cause the center of the lift to shaft-aft thereby leading to the nose pitching down. The speed that leads to the formation of a shockwave is called the critical Mach number and ranges from 0.8 to 1.2. A plane is said to be flying at supersonic speed if its entirety is flowing at supersonic airflow. The air that was moving at the transonic state moves to the plans trailing edge (see below diagram).
The Mach of supersonic speed is tabulated to range from 1.2-5.0. Any speed higher than 5.0 is said to be a hypersonic flight.
An example of a supersonic speed is a bullet fired from a gun, military fighter crafts as well as space shuttle orbiters use this speed during their missions. The supersonic aircrafts were manufactured in the half of the 20th century and have been mostly used for research and military activities. In fact there are only two known supersonic aircrafts that were designed to be used for civil use and they include the concord and the tupolevTu-144 and though they do not always fly supersonically, fighter jets can be the best and most common example of a supersonic flight.
When an airplane is travelling at a speed lower than that of the sound, the air ahead begins to flow sideways (out of the way) before the plane could reach it. The pressure waves that are created by the passing plane creates smooth and gradual air. As the plane reaches the sound speed, and beyond, thereby catching its own pressure waves, the air speed ahead do not receive the plane approaching warning and therefore works through the air creating shock waves. As the air flows through these waves, the pressure, density as well as the temperatures increases sharply and aggressively.
Supersonic aircrafts are therefore the planes that are able to fly at a speed faster than the speed of sound. The aerodynamics of the supersonic flights is known as the compressible flow because of the compression that is associated with the shock waves or the sonic booms that are created as a result of an object travelling faster than the sound (Hitchen, 2015). The American Bell X-1 was the first plane to be flown supersonically and was an experimental plane that was powered by some 6000-Lb thrust rocket consisting of liquid oxygen and ethyl alcohol. Due to the political, environmental as well as the economic factors, these types of planes were never utilized to achieve their full commercial success and are therefore no longer used for commercial purposes especially after the crash of one concord.
The supersonic flights have substantial technical challenges since they are different from the subsonic makes and this is attributed to their speed. Specifically, the aerodynamic drag rises sharply when the aircraft passes the transonic regime that require more engine power and additional streamlined airframes.
Shock waves
A shock wave is a pressure wave that transmits faster than the sound speed of the medium in which it propagates (Cole & cook, 2012). It exhibits the nonlinear phenomena’s characteristics that occurs when energy is deposited and then suddenly released in in very restrained regions of the states of matter (solid, liquid and gases). The pressures occurring in shock waves usually occur in any medium, provided it is elastic like air, water or solid that is produced by a supersonic aircraft (or near a supersonic flight), explosions, lighting or any other occurrences that creates violent pressure changes. The difference between a shock wave and a sound wave is that the wave front where the where the compression takes place is characterized by sudden and violent variations in stress, density and temperatures. As a result of this, the shock waves spreads in a manner/form different from what an ordinary acoustic wave undergoes. In general, the shockwaves travels faster than the speed of the sound and the speed increases as the amplitude is raised (Babinsky & Harvey, 2011). However, the intensity of a shock wave is said to decrease at a faster rate than that of a sound because some energies in the shock waves decreases faster than the speed of sound waves because of the effect of energy of the shockwave heating the medium in which it travels in. when the aircrafts wing is tilted upward, formation of shock waves occur below its leading edge and above the leading edge of the plane, expansion waves occurs (Emmons, 2012). The higher pressure that is behind the shockwaves as well as the lower pressure forming behind the expansion wave leads to a situation of single force pushing the wing up and back. In this case, the lift (the upward part of the force) and the drag (the backward part of the force) principle occurs causing the place to move forward.
For aircrafts travelling at subsonic speed, the sounds or the pressure disturbances that it generates usually extends in all directions as shown in the below figure
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And because the disturbances is propagated earthward continuously because of the movement and speed, there are no sharp sounds/disturbances or changes of pressure. However, at supersonic speed, the pressure is restrained to a region mostly that extends towards the rear and extends from the craft in a Mach cone (this is a restricted widening cone) ( see below).
As the aircraft moves on, the parabolic edge of the cone that is trailing intercepts the earth thereby producing a sharp bang or boom sound on earth with silence before and after. When such a supersonic aircraft flies at low altitude, there could arise glass breakages and other damages since the shock wave have had sufficient intensity. The intensity of the sound/bang or the sonic boom is determined by various factors including the distance between the aircraft and the ground as well as the size and the shape of the aircraft, the type of maneuvers that the aircraft makes, the atmospheric pressure, the temperature and the wind (Hitchen, 2015). For long aircrafts, there could be detected double sonic booms usually one coming from the leading edge of the aircraft and the other from the end of the aircraft (trailing edge).
Research indicates that if the speed of the source is greater than that of the sound, apart from the supersonic boom, another type of a wave phenomenon is bound to occur known as the supersonic boom. A sonic boom is a wave shock type that occurs when the waves that are generated by a source and after some times add together coherently, thereby creating an abnormal/unusual sum wave. Relative/resembling the sonic boom is the V-shaped bow wave that is usually created in water by motorboats when the speed of the motorboat is faster/greater than that of the waves. In the case of planes flying at a speed higher/faster than that of the sound usually about 764 miles per hour, the shock waves are said to take the shape of a diamond shaped cone in Mach cone (three dimensional space). The ratio as to which the speed of the aircraft measures to the speed of the sound is usually referred top as the mac number. It is therefore logical to indicate that the higher the Mach number, the faster the aircraft and the smaller the angle of the Mach cone (Rom, 2012).
In fluid mechanics, Mach is defined as the velocity of a given fluid to the velocity of the sound in the fluid (Dole & lewis, 2000). This theory was named after an Australian physicist and a philosopher Ernst Mach who lived between 1838 and 1916. For an object moving through a fluid like a plane for example, the principle indicates that the Mach number of the plane is equal to the velocity of the object relative the fluid and dividend by the sounds velocity in that fluid. For Mach number that are less than one (<1), the indication is that the flow is subsonic, while those that are greater than one (1) represents a supersonic flow as explained in the figure below.
Another classification of fluid flow is the compressible and the incompressible based on the Mach number for example, for gas flowing with Mach number (<3/10) three tenths, they are considered to be incompressible or generally of constant density (this approximation greatly simplifies the behavior analysis of the matter in question). For those matter that have Mach numbers (>1) more than one, their shock wave pattern develop on the moving body form because of the compression of the surrounding fluid. To address the issue associated with shock waves, streamlining is necessary as it alleviates the effects of the shock waves.
Transonic in aerodynamics is defined as the condition of flight where a range of velocities of airflows occurs and flows past an aircraft or airfoil concurrently below at a speed faster than that of a sound with Mach ranging from 0.8-1.2. This conditions is dependent on the sped of the aircraft, the temperature of the airflow in the environment that the aircraft is flowing in (Fos & Farokhio, 2015). It is defined as the range of critical speed between critical Mach numbers when parts of the airflow over the aircraft or airfoil are supersonic and of higher speed near Mach 1.2 when most of the airflow is supersonic (cook, 2012).
Supersonic wing designs
For aircrafts flying faster than the speed of the sound, the best type of wings to fly in are the delta wings. These includes the fighter jets and the space shuttle ships. Two commercial passenger jets also used the supersonic wing design and included the Russian tu (1mg.6) and the BOACS Concorde (1mg.7). These types of wings are the advanced technology of the swept wing concept and pulls the wing further back thereby creating les drag. To be effective, the aircraft have to fly extremely fast, and maneuverable and are difficult to control at lower speed, compared to the swept wing type that has additional components to assist is when flying at low speeds. A delta wing looks like a large triangle when looked from above.
The aircrafts wing span must be limited to lower the drag and to reduce the aerodynamic efficiencies when the plane is flying slowly (Hicks & Henne, 1978). And since the plane requires relatively slow speed during takeoff and landing, the planes aerodynamics designs of the plane must be compromised so as to attain the differential speed ranges. To enable this, the use of variable geometry wing called the swing wing which spreads wide for low speed flights and sharply mostly backwards for supersonic flight is added to the plane. Despite this fact, the swinging affects the longitudinal trim of the plane and this mechanism adds weight and cost to the plane thereby making it less often used. Delta wing has the advantage of attaining high angle of attach with low speeds that produces a vortex on the top of the plane thereby increasing the lift and lowers the landing speed. Other wing types are the short thin wing, the sweep back as well as the swept forward type of wing.
References
Babinsky, H., & Harvey, J. K. (Eds.). (2011). Shock wave-boundary-layer interactions (Vol. 32). Cambridge University Press.
Cole, J. D., & Cook, L. P. (2012). Transonic aerodynamics. Elsevier.
Cook, M. V. (2012). Flight dynamics principles: a linear systems approach to aircraft stability and control. Butterworth-Heinemann.
Dole, C. E., & Lewis, J. E. (2000). Flight theory and aerodynamics: a practical guide for operational safety. John Wiley & Sons.
Emmons, H. W. (2012). Shock waves in aerodynamics. Journal of the Aeronautical Sciences.Aircraft, 15(7), 407-412.
Hicks, R. M., & Henne, P. A. (1978). Wing design by numerical optimization. Journal of
Hitchens, F. E. (2015). The encyclopedia of aerodynamics.
Rom, J. (2012). High angle of attack aerodynamics: subsonic, transonic, and supersonic flows. Springer Science & Business Media.
Stengel, R. F. (2015). Flight dynamics. Princeton University Press.
Vos, R., & Farokhi, S. (2015). Introduction to Transonic Aerodynamics (Vol. 110). Springer.