# Sample Aviation Paper on Aerodynamics of supersonic aircraft

Aerodynamics of supersonic aircraft

The theory of supersonic flight

The theory of flight can be traced back from the subsonic flight speed whereby at normal speed, that is speed below the sound speed, a plane flies with a speed of Mach>1. At this speed, the air gives way for the plane too pass but upon reaching the supersonic speed, there is no time to warn the air in front of an incoming plane and therefore the plane compresses over the air forming shock waves (Johnson, 2014) . Above these pressures

What is shock wave? How do they form?

A shock wave is defined as the pressure wave that has the capability of propagating faster that the speed of a sound in the medium that is transmitting (Dole & Lewis, 2000). A shock is a transmitting/propagating disturbance. It carries with it energy and can transmit through any medium but it is characterized by a sudden/drastic, nearly discontinuous pressure, temperature as well as density change of the medium in which it is being transmitted. In aerodynamics and specifically in supersonic flows, the expansion is achieved through a prandtl-Meyer expansion fan or generally expansion fan. Different from other nonlinear waves like the solutions, the shock wave energy dispels faster with distance. At the same time, the accompanying expansion wave comes near and merge with the shock wave thereby cancelling it. When shock waves are subjected to mater, energy is preserved though entropy is increase. The change in matter properties is seen as a decrease of the energy which could be extracted as work and is usually an irreversible process. As indicated, shock wave is a nonlinear phenomenon occurring when energy is deposited and abruptly released in confines zones of either gas, liquids of solids. They occur in elastic mediums that are produces by supersonic aircrafts, mining explosions or general explosions, lighting as well as other scenarios that are capable of creating violent changes in pressure (Kudu & Cohen, 2010). The difference between as shock wave and a sound wave is the fact that in shock waves, the wave front where the compression occurs is characterized by sudden or violent change in stress, temperatures and density and this being the case, these waves (shock waves) transmits in similar manner to that of acoustic waves. Of particular importance is that fact that the shock waves travel faster than the speed of sound and their speed presents increases when the amplitude is raised. The wave intensity of shock wave though decreases faster than that of the sound wave as explained by the fact that some energy of the shock waves are consumed to heat the matter/medium that the shock wave is travelling.

How shock wave behave with increasing speed

An airplane flying at normal speed (in this case slower than that of the sound), the air ahead of the plane is warned of the coming lane by pressure change that is transmitted ahead of the aircraft at the speed of the sound. Because of the warning, the air begins to move sideways before the arrival of the plane and the air is prepared to let the plan pass smoothly. When the planes speed reaches the sounds speed, the pressure change can no longer be able to warn the airplane ahead. Because at this time the plane is keeping up with its own pressure waves rather than relying on the air in front and this causes a sharp decrease in velocity in the rear of the pane with the corresponding increase in the air pressure and density (Wegener, 1991).

As the speed increases beyond the speed of the sound, the pressure and the density that is compressed ahead usually increases extending beyond the airplane. At some given point in the air steam, air may be undisturbed after receiving no waning from the air pressure from the approaching plane and in an instant, they are forced to experience/undergo sudden changes in temperature, pressure, density as well as velocity. The boundary thus formed as the result of the sudden actions is termed as the compression wave or the shock wave. This type of a wave is formed always when the supersonic airstream slows to subsonic without any change in direction.  For example when the airstream accelerates to sonic speed, over one part of the wing and drastically decelerates to the subsonic speed, a shock wave forms and this forms to border the supersonic and subsonic ranges/waves. Waves that are perpendicular to the airflow are referred to as the normal waves and the wave flow that is left behind the plane is subtonic. Some of the characteristics of a supersonic airstream that has passed through the normal shock areas include

1. The airstream is usually slowed to subsonic
2. There is no change in direction for the airflow that is behind the wave shock
3. There is increased static pressure as well as density of airstream that is behind the wave
4. There is reduced static pressure and density (this is given by the total pressure less dynamics add static)

How shock wave affect the flight in transonic region,

The formation of shock wave increases drag. A key effect of the shock wave leads to the formation of dense high pressure zones behind the wave. The fact that the regions with high pressure experiences instability and the reality that some velocity energy is converted back to heat may be a better explanation as to why drag increases.  However, it should be noted that the drag emanating from airflow separation is greater but if the wave is strong, there might not be enough kinetic energy to withstand the airflow separation.  The drag that occurs at the transonic zones as a result of shock wave formation and the separation of airflow is referred to as the wave drag, and when speed exceeds beyond 10% of the critical Mach number, the wave drag increases sharply. Beyond this point, more thrust is needed to enhance/increase flight speed to supersonic speed range. To attain this, the shape of the airfoil and the attack angle is key to reattach the boundary layer.

The normal shock waves form on the upper surface of the wing and on the lower surface, a layer/an area of supersonic flow together with the normal flow forms. As higher speed is achieved (approaching that of a sound), the supersonic flow area enlarges moving the shock waves nearer to the planes trail edge. See figure below

Lift loss as a result of airflow separation lead to downwash loss and position change of the center pressure on the plane’s wing. The airflow separation produces a raging wake at the back of the wing causing the tail surface to vibrate (buffet). The nose up and nose down pitch control that is provided by the tail located horizontally depends on the downwash occurring behind the wing. Therefore downwash increase decreases the effectiveness of the horizontal’s tail pitch control as it increases the attack angle that the tail surface is seeing.

What is sonic boom?

A sonic boom  is an impulsive noise that resembles that of a thunder and is caused by moving objects that have the capability of flying faster than the speed of sound at sea lever usually approximately 750 miles per hour. An airplane that is travelling at the atmosphere on a continuous basis is said to produce air pressure waves that are similar to those of the water waves that are caused by motorboats. Exceeding the speed of the sound, these pressure waves join together to form shock waves, which generally travel forward from the release point. Aircrafts or jet fighters flying at supersonic speed therefore continually generate shock waves and releases sonic booms along the flight path similar to the dropping of object from moving vehicles. From the perspective of the aircraft, the booms are swept backwards away from the plane and if the plane make sharp U-turn, or even pulls up, the sonic boom would hit the ground while in front of the plane. See figure below:

The sound heard while on the ground is as a result of the sudden onset and release of the pressure that builds up following the shock wave/overpressures. It should always be known that these sounds are heard only from aeroplanes flying faster than the speed of the sound. Otherwise, for normal airplanes having smooth flight, this sound is radiated in all directions. The supersonic aircraft produces a wave in the form of a Machcone similar to a vapor cone whose vertex is near the nose of an aircraft and whose end/base lies at the end/behind the plane, (see the diagram below)

The half angle that lies between the flight angle and the shock wave is given by the equation;

sin (α)=Vsound/vobject

WhereVsound/vobject is the inverse of 1/Ma (planes Mach number) and Ma=Vobject/Vsound.

This therefore means that as the plane travels faster, the finer and more cone shaped it will be. The diagram below illustrates the effect of Mach variation

The sonic booms are caused by planes flying at Mach 1 and usually take the form of a double boom. Here the first boom is caused by the changes of air pressure as the front end of the plane reaches Mach 1 and the other boom is caused by the changes in pressure occurring when the tail end of the aircraft passes and the air pressure returns normal condition (Anderson, Graham & Williams, 2015).

Mach number

Named after Ernst Mach who was a philosopher and a physicist and who survived between 1838 and 1916, Mach number is defined in fluid mechanics as the ratio of the velocity of a given fluid to that of sound (Hitchen, 2015). For an object that is moving through fluid like an airplane in flight, the Mach number is equated to the velocity of the plane relative to the fluid and dividend by the sounds velocity in the fluid. Generally, Mach numbers that are less than one are indicative of a subsonic flows and those which have Mach numbers more than one are said to be supersonic. Fluid flow is also classified based on the Mach number where compressible occurs in matters having shock waves of greater than one.

Lifts and drags during supersonic

There is a big difference in the way the air act during speeding and at subsonic speeding. Upon reaching the sounds speed, the airflow over the wings reaches the supersonic speed faster that the aircraft itself and shock wave forms on the wing. The airflow left behind by the shock wave break up into vibrations thereby increasing drag. When the speed of the sound is exceeded shock waves forms ahead of the aircrafts wings leading edge and the shock wave that previously formed moves to the trailing edge. Tilting the wing upward, shockwave forms below the leading edge while the expansion wave form above. The pressure behind the shock wave that is high and the low pressure at the expansion wave lead to a single force pushing the wing up and back (Zobieczky, 2014). The upward part of the force is termed as the lift while the backward is the drag.

The supersonic wings are used in-flight as a means of control and stability as well as to maintain stability. The designation of the supersonic crafts should be of limited drag so that the aerodynamic efficiency of the plane is increased (Jones, 2012). Research indicates that two aircraft operated under the supersonic technology and these were the Concorde and the Tupolev Tu-144.  However, various challenges facing the supersonic passenger planes included the aerodynamics, engine, structural issues, high costs, and sonic boom.

References

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Anderson, D., Graham, I., & Williams, B. (2015). Flight and Motion: The History and Science of Flying. Routledge.

Dole, C. E., & Lewis, J. E. (2000). Flight theory and aerodynamics: a practical guide for operational safety. John Wiley & Sons

Hitchens, F. E. (2015). The encyclopedia of aerodynamics.

Johnson, R. S. (2014). Fluid Mechanics and the Theory of Flight. Bookboon.

Jones, R. T. (2012). The minimum drag of thin wings in frictionless flow.Journal of the Aeronautical Sciences.

Kundu, P. K., & Cohen, I. M. (2010). Fluid Mechanics. Burlington: Elsevier.

Sobieczky, H. (Ed.). (2014). New design concepts for high speed air transport (Vol. 366). Springer.

Wegener, P. P. (1991). What Makes Airplanes Fly?: History, Science, and Applications of Aerodynamics. New York, NY: Springer US.