Mach Transition
Fleet Manager
Joined: Apr 2001
Aviation Qualifications: ATPL
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From: various places .....
(a) Mach can be expressed as an equation involving only pressures etc ... with no temperature term. Crossover height not related to OAT.
The idealised flow equations (see just about any old garden variety aerodynamics text) give -
Pt/P = (1 + (g-1)/2 * M^2)^(g/g-1)
where g = 1.4, typically.
(b) From jtr's post and (a), the climb IAS/climb IMN combination determines the pressure height at which the two coincide - ie the "crossover height".
The idealised flow equations (see just about any old garden variety aerodynamics text) give -
Pt/P = (1 + (g-1)/2 * M^2)^(g/g-1)
where g = 1.4, typically.
(b) From jtr's post and (a), the climb IAS/climb IMN combination determines the pressure height at which the two coincide - ie the "crossover height".
Joined: Aug 2001
Posts: 775
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From: Dorset
If you want to produce an indication of how changes in CAS or Mach number tend to affect the crossover altitude you can do so with a simple sketch.
Draw a vertical and horizontal axes for a graph. The vertical axis represents altitude increasing from bottom to top, and the horizontal axis represents CAS increasing from left to right.
Draw a vertical line from bottom to top at about the middle of the horizontal axis. This line represents a constant CAS climb.
Now to draw the CAS equating to any constant Mach number we must remember that the speed of sound as a CAS decreases as altitude increases. So to represent a constant Mach climb we must draw a line sloping downwards from left to right.
The point at which the two lines cross is the crossover altitude.
Now label the lines with approriate values, let's say 260 Kts CAS and Mach 0.74.
To see how increasing CAS changes the crossover altitude, simply draw another vertical line to the right of the first. Let's say we have chosen this to represent 340 Kt CAS. You will see that this higher CAS line crosses the Mach 0.74 line at a lower altitude. So increasing the chosen CAS decreases the crossover altitude.
Now draw another sloping line (to the right of the original) to represent a higher mach number. Let's say Mach 0.78. You will find that this crosses the original CAS line at a higher altitude. So increasing the chosen mach number increases the crossover altitude.
This exercise indicates that increasing the chosen CAS will decrease the crossover altitude, but increasing the chosen Mach number will increase it. If of course we increase both the CAS and the Mach number then the change in crossover altitude will be the combined effect of both changes.
Draw a vertical and horizontal axes for a graph. The vertical axis represents altitude increasing from bottom to top, and the horizontal axis represents CAS increasing from left to right.
Draw a vertical line from bottom to top at about the middle of the horizontal axis. This line represents a constant CAS climb.
Now to draw the CAS equating to any constant Mach number we must remember that the speed of sound as a CAS decreases as altitude increases. So to represent a constant Mach climb we must draw a line sloping downwards from left to right.
The point at which the two lines cross is the crossover altitude.
Now label the lines with approriate values, let's say 260 Kts CAS and Mach 0.74.
To see how increasing CAS changes the crossover altitude, simply draw another vertical line to the right of the first. Let's say we have chosen this to represent 340 Kt CAS. You will see that this higher CAS line crosses the Mach 0.74 line at a lower altitude. So increasing the chosen CAS decreases the crossover altitude.
Now draw another sloping line (to the right of the original) to represent a higher mach number. Let's say Mach 0.78. You will find that this crosses the original CAS line at a higher altitude. So increasing the chosen mach number increases the crossover altitude.
This exercise indicates that increasing the chosen CAS will decrease the crossover altitude, but increasing the chosen Mach number will increase it. If of course we increase both the CAS and the Mach number then the change in crossover altitude will be the combined effect of both changes.
Joined: Jun 2004
Posts: 1,843
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From: Australia
26000/27000 feet for what Shaka Zulu, Vmo/Mmo, Max Rate Climb, Econ Climb, Best Angle Climb, Maximum Range Cruise, Long Range Cruise, Nominal Descent Mach/CAS, High Speed Descent Mach/CAS, One Engine Inop Drift-Down? - Changeover Pressure Height varies for each CAS/Mach schedule. I know of one aircraft type where there is about 20000 feet difference between 2 of these schedules I've mentioned, and know of no aeroplane where CAS rules below a particular Pressure Height and Mach Number above, except for a specific CAS/Mach schedule.
Can you be specific?
Can you be specific?
Joined: Oct 2003
Posts: 1,300
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From: Canberra Australia
Further up is "Coffin"s Corner"
Go to the top corner of the graphs or number crunching and you are at Mcrit at the stall.
Almost impossible to get right into the corner.
First subsonic aircraft to suffer seriously in this area was the USAF's B47.
Is there another name for the condition?
Go to the top corner of the graphs or number crunching and you are at Mcrit at the stall.
Almost impossible to get right into the corner.
First subsonic aircraft to suffer seriously in this area was the USAF's B47.
Is there another name for the condition?
