Question

The Lockheed SR-71 Blackbird aircraft cruises at Mach number of 3.3 at an altitude of 85,000 ft. Calculate the speed of sound and flight speed at these conditions. Compare the flight speed to the muzzle speed of a 30-06 rifle bullet (700 m/s).

Answer 1

As there is no direct relation between velocity of flight with an altitude. So first we need to derive it with few assumption.

Let,

p = pressure (lb/ft2)

T = absolute temperature = EF + 459.7

v = specific volume (ft3/lb)

w = specific weight (lb/ft3) = 1/v

R = a constant (for air: R = 53.3)

p = density = w/g = 1/gv v = 1/gD

From Boyle's law of gasses: pv = RT ,

therefore we have: p/p = gRT = (32.2)(53.3)T = 1718 T

It can also be shown that: p/py = constant; for air y = 1.4

From the continuity equation applied to a sound wave: pAVa = (p+dp)A(Va + dVa)

Expanding and dropping insignificant terms gives: dVa = -Va dp/p

Using Newton's second law (p + pVa/2 = a constant) and taking derivatives: dp = -pVadVa

So we get from above equation, Va2 = dp/dp

We get

At "Standard" atmosphere of 59E F @ Sea Level

Speed of sound

Where A= altitude (K ft)

Answer: --

From Above equation,

Put A= 85K ft

We get Speed of sound V_a = 426.35 ft/sec (=129.95148 m / s)

From equation of Mach no,

MACH NUMBER = VELOCITY OF FLIGHT / VELOCITY OF SOUND

By putting Mach no= 3.3 &

Velocity of sound = 426.35 ft/sec,

We get Velocity of flight (velocity of Lockheed SR-71 Blackbird aircraft) = 1406.957989 ft/sec (=428.840795 m / s)

Now coming on answer 2 that’s compare it with muzzle speed of a 30-06 rifle bullet (700 m/s)

Here muzzle speed is very high (700 m/s),

Lets find mach no for rifle bullet,

We get mach no for bullet is 5.386687 ( =700/129.95)

Which is larger than 3.3 Mach no In our case. So bullet speed is quite larger than flight . So its mach no is higher than mach no of Flight.

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