Figure 5-64.  Wing airflow.  Figure 5-65.  Critical Mach.  5-45  speed flight and/or high-altitude flight, the measurement of  speed is expressed in terms of a “Mach number”—the ratio  of the true airspeed of the aircraft to the speed of sound in  the same atmospheric conditions. An aircraft traveling at  the speed of sound is traveling at Mach 1.0. Aircraft speed  regimes are defined approximately as follows:  While flights in the transonic and supersonic ranges are  common occurrences for military aircraft, civilian jet aircraft  normally operate in a cruise speed range of Mach 0.7 to  Mach 0.90.  The speed of an aircraft in which airflow over any part of  the aircraft or structure under consideration first reaches  (but does not exceed) Mach 1.0 is termed “critical Mach  number” or “Mach Crit.” Thus, critical Mach number is  the boundary between subsonic and transonic flight and is  largely dependent on the wing and airfoil design. Critical  Mach number is an important point in transonic flight. When  shock waves form on the aircraft, airflow separation followed  by buffet and aircraft control difficulties can occur. Shock  waves, buffet, and airflow separation take place above critical  Mach number. A jet aircraft typically is most efficient when  cruising at or near its critical Mach number. At speeds 5–10  percent above the critical Mach number, compressibility  effects begin. Drag begins to rise sharply. Associated with  the “drag rise” are buffet, trim, and stability changes and a  decrease in control surface effectiveness. This is the point  of “drag divergence.”  [Figure 5-65]  V$_{MO}$/M$_{MO}$ is defined as the maximum operating limit speed.  V$_{MO}$ is expressed in knots calibrated airspeed (KCAS), while  It is important to understand how airspeed varies with Mach  number. As an example, consider how the stall speed of a  jet transport aircraft varies with an increase in altitude. The  increase in altitude results in a corresponding drop in air  density and outside temperature. Suppose this jet transport  is in the clean configuration (gear and flaps up) and weighs  550,000 pounds. The aircraft might stall at approximately 152  KCAS at sea level. This is equal to (on a standard day) a true  velocity of 152 KTAS and a Mach number of 0.23. At FL 380,  the aircraft will still stall at approximately 152 KCAS, but the  true velocity is about 287 KTAS with a Mach number of 0.50.  For example, an early civilian jet aircraft had a V$_{MO}$ limit of  306 KCAS up to approximately FL 310 (on a standard day).  At this altitude (FL 310), an M$_{MO}$ of 0.82 was approximately  equal to 306 KCAS. Above this altitude, an M$_{MO }$ of 0.82  always equaled a KCAS less than 306 KCAS and, thus,  became the operating limit as you could not reach the V$_{MO }$ limit without first reaching the M$_{MO}$ limit. For example, at  FL 380, an M$_{MO}$ of 0.82 is equal to 261 KCAS.  Adherence to these speeds prevents structural problems due  to dynamic pressure or flutter, degradation in aircraft control  response due to compressibility effects (e.g., Mach Tuck,  aileron reversal, or buzz), and separated airflow due to shock  waves resulting in loss of lift or vibration and buffet. Any of  these phenomena could prevent the pilot from being able to  adequately control the aircraft.  M$_{MO}$ is expressed in Mach number. The V$_{MO}$ limit is usually  associated with operations at lower altitudes and deals with  structural loads and flutter. The M$_{MO}$ limit is associated with  operations at higher altitudes and is usually more concerned  with compressibility effects and flutter. At lower altitudes,  structural loads and flutter are of concern; at higher altitudes,  compressibility effects and flutter are of concern.  Mach Number Versus Airspeed  Subsonic—Mach numbers below 0.75  Transonic—Mach numbers from 0.75 to 1.20  Supersonic—Mach numbers from 1.20 to 5.00  Hypersonic—Mach numbers above 5.00  C  D  (Drag coefficient)  M (Mach number)  0.5  1.0  C$_{L}$ 0.3 Force divergence Mach number Critical Mach number P o s i b l e s e p a ra tio n  M = 0.50  M = 0.72  M = 0.77  Maximum local velocity is less than sonic  Critical mach number  Maximum local velocity equal to sonic  Normal shock wave S u p e r s o n i c  f $_{l}$o w  Subsonic 