Professional Pilot, October 2016

W 2 W 1 Fig 1 Flight envelope s for a typical civilian jet airplane Not to scale suffices to say that with increasing M number the critical AOA and the C Lmax of the airfoil are reduced working hand in hand with decreasing Re numbers Both Re and M effects result in increasingly higher stalling IAS CAS EAS at higher altitudes On the other hand for constant M number flight EAS decreases steeply with altitude and the spread between the slowest and the fastest flying speed decreases Climbing at constant CAS results in decreasing EAS and the margin above the stalling speed High speed flight is limited by the maximum dynamic pressure or max Q at lower altitudes and the constant maximum operating Mach M MO number at higher altitudes M MO is typically in the neighborhood of the drag divergence M number M DD Steep increase in drag follows exceeding the M DD During flight testing airplanes are flown up to V DF M DF or maximum dive speeds defined by still acceptable handling characteristics and the onset of dangerous aero elastic vibrations or flutter Typically M MO will be about 007 lower than M DF Freestream critical Mach M CR signifies the first appearance of local shock waves and pockets of transonic flow on wings airfoils The drag divergence or the drag rise M DD M numbers indicate the onset of stronger shocks and the start of steep rise in transonic wave drag Wing sweep moves the critical M 108 PROFESSIONAL PILOT October 2016 number upwards while the supercritical wing design increases the spread between the critical and the drag rise M numbers Details of transonic aerodynamics are immense and only transonic wind tunnel measurements provide more or less reliable picture However it must be noted that computational fluid dynamics CFD is making steady progress and is becoming an integral part of jet aircraft designs Climb speeds Traditionally the climb schedules have been designed to maximize ROC Widely used constant CAS M climb schedule closely resembles minimum time to climb profile Such climb schedules are also simple for pilots and ATC to implement The altitude at which climb changes from constant EAS CAS to constant Mach is called change over altitude A change over altitude increases for slower climbing EAS or for higher M climbs Although climb may be constant in IAS CAS or EAS the airplane will be accelerating in TAS In troposphere with constant negative temperature lapse rate constant EAS climb results in accelerating CAS TAS and M as illustrated in Fig 2 Conversely TAS will be decreasing during constant Mach climb in troposphere If the airplane is climbing in tropopause TAS and M will change at the same rate as the local speed of sound LSS or a remains constant for steady temperature θ const For airplane climbing through temperature inversion a constant M climb will result in increasing TAS because LSS is rising with altitude During constant EAS climb in the troposphere a pilot or A P is gradually decreasing pitch angle at fixed throttles to maintain constant EAS or Altitude ISA T C M 36000 ft Change over altitude SL 250 300 078 250 M 10000 ft Speed knots EAS CAS TAS Climb schedule Fig 2 Typical constant EAS Mach climb schedule 250 300 078 and relationships between airspeeds at constant weight in ISA troposphere and tropopause Not to scale Altitude EAS Safe flight envelope EAS SR V SR @ W 1 EAS SR V SR @ W 2 V MO const M MO const M const M DF const V DF const