Mach Numbers

This is about physics. It might also interest you if you like aviation.

What is a Mach number?

Typically, the maximum speed of (military) aircraft is expressed in "Mach".

Like many things in physics, the Mach number is named after some dude. In this case, a dude named Ernst Mach.

The Mach number is defined as the ratio between an object's speed and the speed of sound. For example, an F-16 jet fighter has a maximum speed of about Mach 2.0 (depends who you ask, I have seen numbers ranging from Mach 1.95 to Mach 2.05. Let's just round it to Mach 2).

So, since Google tells us that the speed of sound at sea level is 340.29 m/s (= 1225 km/h), this means that an F-16 can fly at 2450 km/h, right?

Umm, nope. For example, this site tells us that the F-16 can fly at 2074 km/h. A bit of a difference. So, what gives?

Well, the catch is in the speed of sound at sea level. This sort of suggests that at other altitudes than sea level, the speed of sound might be different. And so it is. And it also depends on the temperature. Which also depends on the altitude. Boy, did I open a can of worms. Let's try to close it.

So with our F-16 example, apparently the aircraft reaches its top speed at an altitude where the speed of sound equals 2074 km/h divided by 2.0, or 1037 km/h, or 288 m/s.

So, in conclusion, be careful when interpreting Mach numbers. Don't just multiply them by the speed of sound at sea level, take into account that the speed of sound at the altitude where the aircraft is flying might me quite different. The Mach number is actually the speed of the object divided by the speed of sound at the location it is traveling.

Unfortunately, I didn't close the can of worms completely. One of the consequences of Murphy's Law is that when you open a can of worms, you alwasy need a bigger can to put them back. Sigh.

I was planning on bitching about the American media and NASA, who invariably claim that the Space Shuttle flies at Mach 25. Since the shuttle typically orbits at 300 km altitude where there is no air whatsoever to speak of, this must clearly be wrong, hmmm? Obviously some dumbass took the shuttle's orbital speed (7725 m/s, or about 27810 km/h) and divided it by 340 m/s, right? Well, no, since that would result in Mach 22.7. Close, but not close enough. There must be something else going on.

So, turns out that the boys at NASA are smarter than that. This page sort of claims that the shuttle indeed enters the atmosphere at Mach 25, and it seems that it takes into account that the speed of sound is different at the altitude of re-entry. Ok, good. I have no reason to doubt them.

The page also includes a nifty calculator to calculate the speed of sound at different altitudes. For example, it shows that the speed of sound at 10000 m altitude (or ~30,000 feet) is something like 295 m/s, which is pretty close to 288 m/s which we calculated for our F-16. However, the calculator gives this value for a wide range of altitudes. Hmm. Also, it appears that the speed of sound goes down with increasing altitude, stays the same for a while, and then goes up again (!). Bummer. Now I have to try to understand why that is. Some other time, though.

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