# The SR-71 flew at 2193 mph. Mathematically, how can this be Mach 3.3?

Virtually every time I read about the Lockheed SR-71 Blackbird (including other threads on this forum), I see that its speed record is listed as approximately $$2193$$ mph. The same blurb will invariably say this is "about Mach $$3.3$$". However, when I search for how fast Mach $$1$$ is, the number that almost always comes up is $$767$$ mph. Now, $$767 \cdot 3.3 \approx 2531$$, which is well above $$2193$$. If I take $$2193$$ and divide it by $$767$$, I get Mach $$2.85$$.

I doubt I've stumbled on something new here. So what am I missing? How can $$2193$$ mph be Mach $$3.3$$ when $$767$$ mph is Mach $$1$$?

• May 6, 2020 at 20:36
• great question, thanks @Joe - whilst I knew that mach is meant to vary depending on air conditions, I did not know the details - and now we have all the details! May 8, 2020 at 14:21
• Well you see, multiplication works differently at high altitude.. May 8, 2020 at 19:40
• Because Mach number as a function of temperature, not physical speed Feb 27, 2023 at 17:48

The SR-71 was only capable of Mach 3.3 flight at altitude. You can see the limitations in the pilot's operating handbook(POH) for the aircraft:

At higher altitudes the relative speed of sound is lower. If we use this handy NASA calculator in a standard atmosphere the relative speed of sound at 70,000 ft. is 660 MPH making your 2193 MPH equal to Mach 3.321

Its also important to note that the word "about" is often used as the SR-71 was flown to a maximum compressor inlet temperature(CIT) not a maximum Mach when doing a 3.3 run. According to the POH

Mach 3.2 is the design Mach number. Mach 3.17 is the maximum scheduled cruise speed recommended for normal operations. However, when authorized by the Commander, Speeds up to Mach 3.3 may be flown if the limit CIT of 427°C is not exceeded.

• Comments are not for extended discussion; this conversation has been moved to chat. May 10, 2020 at 7:10