Photo: T-38, supersonic, from NASA.

### Eddie Sez:

The U.S. Air Force used to think every pilot needs to experience supersonic flight so we all got trained in it. They no longer do that so the training was either too expensive or unnecessary. In any case, most of us are constrained with a VMO that begins with a zero so this section of Basic Aerodynamics has been pared down a bit, but it hasn't gone away.

You might be thinking "High Speed Flight" doesn't apply to you and that might be true. But chances are it does apply to your wings. Critical Mach affects most jet aircraft that fly in the transonic range and that impacts your Stability and Control, so please read on...

Oh yes, most of this comes from my notes from Air Force pilot training with a little help from a number of the references listed at the bottom of the page.

### Critical Mach

Figure: Critical Mach, from Eddie's notebook.

• If the flight Mach number increases, so does the local velocity on top of the wing. At some flight Mach number the local maximum velocity reaches sonic speed, M = 1.0. This flight Mach number is called the critical Mach number.

• Once MCRIT is exceeded, the aircraft is flying in the transonic speed range. Supersoninc airflow exists in the area of maximum thickness on top of the wing, subsonic flow exists elsewhere.

• As the air flows through the normal shock wave it undergoes a rapid compression. The compression decreases the kinetic energy of the airstream and converts it into a pressure and temperature increase behind the shock wave. The heat rise behind the shock wave is either radiated to the atmosphere or absorbed by the wing surface, but in either case it is lost, and this lost energy must be continuously supplied by the engines. This energy loss represents a type of drag known as wave drag.

#### Below Critical Mach

If the speed of the air foil is such that all of the local air flow is subsonic, the air foil is said to be below its critical Mach number. The lift and drag characteristics of the airfoil are, for the most part, conventional.

#### At Critical Mach

At the point where the first hint of supersonic air flow occurs above the wing, the air foil is said to be at its critical Mach number. This is the last point at which air can be considered incompressible and there is no shock wave to disturb the local air flow.

#### Above Critical Mach

As critical Mach number is exceeded a normal shockwave forms between the boundary of supersonic and subsonic airflow. The area in front of this shockwave tends to be smooth, as the airflow has a gradual transition over the leading edge of the airfoil.

Behind the shockwave is a greatly increased static pressure, fighting to pull up the boundary layer. There is a tug of war between the kinetic energy of the air holding it to the airfoil, and the static pressure pulling it away. As the speed of the airfoil is further increased, the static pressure begins to win out and airflow separation occurs.

As a result, induced drag increases, lift decreases, and the wing may experience stability and control issues.

### Obtaining a Higher Critical Mach Number

Figure: Wing sweepback effects, from Hurt, figure 3.14.

[Hurt, pg. 223]

• In order to obtain a high critical Mach number from an airfoil at some low lift coefficient the section must have:
1. Low thickness ratio. The point of maximum thickness should be aft to smooth the pressure distribution.

2. Low camber. The mean camber line should be shaped to help minimize the local velocity peaks.
• If supersonic flight is a possibility the thickness ratio and leading edge radius must be small to decrease wave drag.

• Sweepback produces an unusual effect on the high speed characteristics of a surface and has basis in a very fundamental concept of aerodynamics. The swept wing shown has the streamwise velocity broken down to a component of velocity perpendicular to the leading edge and a component parallel to the leading edge. The component of speed perpendicular to the leading edge is less than the free stream speed (by the cosine of the sweep angle) and it is this velocity component which determines the magnitude of the pressure distribution.

• The component of speed parallel to the leading edge could be visualized as moving across constant sections and, in doing so, does not contribute to the pressure distribution on the swept wing. Hence, sweep of a surface produces a beneficial effect in high speed flight since higher flight speeds may be obtained before components of speed perpendicular to the leading edge produce critical conditions on the wing. This is one of the most important advantage of sweep since there is an increase in critical Mach number, force divergence Mach number, and the Mach number at which the drag rise will peak. In other words, sweep with delay the onset of compressibility effects.

• ### Adjusting Critical Mach With Wing Sweep

Figure: Effect of Wing Sweep on Airflow Normal to the Leading Edge, from [Davies, pg. 97]

• A wing produces lift by accelerating the air which passes over the top surface to a higher speed than that which passes under the bottom surface. The greater the difference between these two speeds the higher to difference in pressure, hence the larger the lift vector.

• Because the local speed of the upper surface air is higher than the free stream speed — a good bit higher where the camber is marked — it is clear that this airstream will become sonic before the effect first become apparent free stream reaches the sonic value. At this speed local shock waves are formed on the wing and compressibility effects become apparent; the drag increases, buffeting is felt and changes in lift and the position of the centre of pressure occur which, at a fixed tail angle, are reflected as changes in pitch. The Mach number at which these compressibility effects first become apparent is the critical Mach number; all other parameters aside, this can be quite low for a straight wing, around 0.7 Mach number.

• By sweeping a wing significantly, it will be remembered, the velocity vector normal to the leading edge is made less than the chord wise resultant. In [the figure] AC is shorter than AB. As the wing is responsive only to the velocity vector normal to the leading edge, for a given Mach number the effective chord wise velocity is reduced (in effect the wing is persuaded to believe that it is flying slower than it really is). This means that the airspeed can be increased before the effective chord wise component become sonic and thus the critical Mach number is raised.

See Basic Aerodynamics / Stability for more about wing sweep.

### Mach Number Effect

[Davies, pg. 24] With the advent of the big jet three things occurred to make life even more difficult. The size of the aeroplane increased enormously and, with increase altitude capability, the speed increase difficulty was compounded by Mach number effects which caused pitch changes on the aeroplane, upset the pressure distribution over the control surfaces and brought about unwanted changes in hinge moments. It was about this time that the design of the pure aerodynamic control was seen to be, perhaps not impossible, but certainly very difficult, costly and time consuming. Something was needed to remove the problems — and the answer lay in operating the control surface by pure power.

As we've seen, the aerodynamic forces on a wing change at critical Mach. Using powered flight controls and increasing the wing sweep help, but these fixes may not be enough for some wings.

### Book Notes

Portions of this page can be found in the book Flight Lessons 1: Basic Flight, Chapter 18.

### References

14 CFR 25, Title 14: Aeronautics and Space, Federal Aviation Administration, Department of Transportation

Air Training Command Manual 51-3, Aerodynamics for Pilots, 15 November 1963

Connolly, Thomas F., Dommasch, Daniel 0., and Sheryby, Sydney S., Airplane Aerodynamics, Pitman Publishing Corporation, New York, NY, 1951.

Davies, D. P., Handling the Big Jets, Civil Aviation Authority, Kingsway, London, 1985.

Dole, Charles E., Flight Theory and Aerodynamics, 1981, John Wiley & Sons, Inc, New York, NY, 1981.

FAA-H-8083-15, Instrument Flying Handbook, U.S. Department of Transportation, Flight Standards Service, 2001.

Gulfstream G450 Airplane Flight Manual, Revision 35, April 18, 2013.

Gulfstream G450 Aircraft Operating Manual, Revision 35, April 30, 2013.

Hage, Robert E. and Perkins, Courtland D., Airplane Performance Stability and Control, John Wiley & Sons, Inc., 1949.

Hurt, H. H., Jr., Aerodynamics for Naval Aviators, Skyhorse Publishing, Inc., New York NY, 2012.

Technical Order 1T-38A-1, T-38A/B Flight Manual, USAF Series, 1 July 1978.