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Aircraft and Speed of Sound
Name: Christine
Status: educator
Age: 30s
Location: N/A
Country: N/A
Date: 2001
Question:
My question is about the speed of sound: (My husband and
I have been discussing this because he is a C-5 loadmaster and I am a math
teacher.) First, what is the formula for determining percentage of
Mach? Second, what is it about the speed of sound that makes it rather
than airspeed per se the limiting factor for a subsonic aircraft? For
example, a C-5 travelling at about 320 kts of indicated air speed must
slow down above about fl300 in order to avoid exceeding the plane's
capabilities relative to the Mach even though the aircraft's
weight and engine power would seem to allow that speed.
Replies:
Christine -
The Mach number is the speed of the aircraft relative to the speed of sound in
that particular density of air. (It is not truly a percent rather a ratio.)
At sea level on a standard day the speed of sound is about 760 MPH. In that
environment a speed of 380 MPH would be Mach .5. As the density of the air
changes, the speed of sound changes and therefore the basis of the Mach number
changes.
Pressure waves build up on aircraft surfaces differently at different Mach
numbers. They are built to withstand a variety of situation, but do have
limits.
Without knowing the precise formulas or the C-5, I would feel confident that
the combination of the two above factors would hold the answer to your
problem. Perhaps one of the other AAS folks will give you the actual numbers
to help you with your mathematical curiosity.
Hope this helps.
Larry Kengel
The Mach number is one of a myriad of dimensionless numbers used in
fluid flow, thermal systems, and mass transfer just to name a few.
Dimensionless numbers are ratio of various parameter that return, you
guessed it, numbers without any units. The Mach number is a
dimensionless number that is the ratio of the velocity of the fluid to
the acoustic velocity of the medium, or in equation form Mach=V/c. A
value less than 1 is subsonic flow, equal to 1 is sonic flow, and
greater than 1 is supersonic flow. OK, that is all fine and dandy, but
what does it mean. In the case of the C-5, the fluid velocity is going
to be the velocity of the air passing around the plane and over the
wings. In equation form, c=sqrt(k*g*R*T), where k is the ratio of the
specific heat of the medium at constant pressure to the specific heat of
the medium at constant volume, g is gravity, R is the gas constant of
the medium and T is the temperature. Although it may not be obvious,
this equation shows that acoustic velocity is dependent on the
temperature of the air (the medium), which is also dependent on the
pressure, which is also dependent on the altitude. So, what may be
subsonic flow at one altitude (i.e. one temperature), may be supersonic
flow at a different altitude. That is why you'll see that planes are
rated for Mach speed at sea level as opposed to another altitude. This
is all important because supersonic flow creates shock waves that can
disrupt an air foil or wing causing either damage to the wings or abrupt
changes in the flow characteristics over the foil, which is all bad if
the wings are not designed for supersonic flow. Most likely, the C-5
wings are designed to create maximum lift so that it can get those big
loads off the ground, where as a fighter has those small wings designed
to cut through the supersonic regime with no problems.
Hope this answered your question.
Chris Murphy, PE.
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Update: February 2012
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