Looking for a Formula to Calculate Mach Speed
Daniel J. Bodony
In article <rddE5G...@netcom.com>,
Daniel Smith + Joan Doglio <jdo...@ix.netcom.com> wrote:
>
>Does anyone have a good formula for calculating Mach number? I
>recently read an article that says Mach number is solely a function of
>temperature. Is this true or does air density affect Mach number at
>various altitudes as well ?
Assuming you want a calorically perfect gas, the mach number of a
vehicle moving at velocity u is:
u
M = ---
a
where a is the speed of sound and is related to temperature via
a = sqrt(1.4*1716*temp)
where temp is the temperature in degrees Rankine. The relation of
mach number with temperature is found in the equation above; however,
for a CPG, the speed of sound can be written as
a = sqrt{1.4*pres/rho}
where pres is the pressure in lbf/ft^2 and rho is the density in
lbm/ft^3. For any fluid, the speed of sound is defined as
d(p)
a = sqrt{1.4 ----}
d(rho)
Hope this helps.
Dan
Stuart Butts
In article <rddE5G...@netcom.com>, jdo...@ix.netcom.com says...
>Does anyone have a good formula for calculating Mach number? I
>recently read an article that says Mach number is solely a function of
>temperature. Is this true or does air density affect Mach number at
>various altitudes as well ?
Temperature is only variable. For the 1962 US Standard Atmosphere up 80,000
feet or so:
a_sl = 1116.45 // sea level speed of sound (ft/sec)
if altitude < 36089.24 feet
theta = 1.0 - 6.87525E-06 * altitude; // temperature ratio (ta / ta_sl)
else
theta = 0.751874; // temperature ratio (ta / ta_sl)
endif
a = a_sl * sqrt(theta); // speed of sound (ft/sec)
mach = true airspeed / a_sl; // mach number
--
=======================================
Stuart Butts
USAFA '85
stub...@cris.com
=======================================
Jack Dunn
In article <rddE5G...@netcom.com>, jdo...@ix.netcom.com (Daniel Smith + Joan Doglio) writes:
>
>Does anyone have a good formula for calculating Mach number? I
>recently read an article that says Mach number is solely a function of
>temperature. Is this true or does air density affect Mach number at
>various altitudes as well ?
For a "thermally perfect" gas, i.e. a gas which obeys
p = rho * R * T, the speed of sound can be found to be
a = sqrt( gamma * R * T).
For air this equation becomes
a = 49.0 * sqrt(T).
Jack Dunn
[Moderator's note: By now, everyone has probably figured out why some
of us just look it up in the Standard Atmosphere, usually the 1966
edition. MFS]
COSMO12365
Mach number is simply the ratio of your true airspeed and the speed of
sound in the air you are travelling in:
M=TAS/speed of sound
The speed of sound in a particular air mass is a function of
temperature. The equation for the speed of sound is the square root
of 1.4 times the gas constant, R, and the absolute temperature of the
air:
speed of sound=SQRT( 1.4*1716*T)
1.4 = ratio of specific heats for air
1716 = gas constant,R, for air (English units)
T = absolute temperature of the air (degrees Rankine in English units)
Hope this helps,
Cosmo