A dimensionless number named after Ernst Mach, used in momentum transfer in general and near/ultra sonic flow and throttling calculations in particular. Mach numbers <  1 are called subsonic, Mach numbers >  1 are called supersonic.

Ma = V / Vsound

V: velocity, Vsound: velocity of sound in fluid


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For the less mathematically inclined . . .

The Mach Number is ratio of the speed of what is travelling vs the speed of sound, where both are in the same medium. Mach 1 is the speed of sound. Something that is subsonic is below the speed of sound and something that is faster is called supersonic and if something is at Mach 5 or higher it is Hypersonic.

I want to put in a bid for equality here! Everyone has heard of Mach number 1, but who ever heard about Ma=0.3? Who ever heard about Ma=0.97?

These numbers are almost as significant as Ma=1.000, but no-one ever gets to hear about them. Why not? Because that fucking unity, that isolated and arrogant number one got in the way, and made everyone think unity is the only Mach number to think about. Well let me tell you, they're Wrong!

In case you were wondering, the speed of sound in air at sea level on a normal kind of day is about 330 m/s, or 750 mph, or about 1200 kph. The speed of sound slows down at higher altitudes, because the pressure and temperature drop as you go higher in the atmosphere.

So driving along in your car at 120 kph will get you a Mach number of about 0.1. Speeding along in a train at 300 kph will get a Mach number of 0.25. Taking off in Concorde at 412 kph will get you up to a Mach number above 0.3, and that is where things start to get interesting.

At Ma=0.3, in air, the first signs of compressibility set in. We start to see the very first indications that air behaves differently from water. We all know that when you pump up a tyre, you can fill it with air, and then pump in more air, with no appreciable change in volume, but can you do that with water? Nope! Water is incompressible, and that makes a huge difference when you start to push things through it at high speed.

When you are driving along in your car at 120kph, air seems to be incompressible, because when you push at such a slow speed, the air has plenty of time to get out of he way. There is nothing—such as viscosity or inertia—holding it back, so if something is forced to travel through air at these low speeds, the air behaves just like water, and everything is fairly straightforward and easy to predict.

As your aircraft speeds up, and the Mach number gets to around 0.3, however (around 100m/s or 400 kph), the air molecules simply cannot get out of the way fast enough, so we start to see the first signs of changes in density in the air around the aircraft.

Get up to double that speed: Ma =0.6, and the compressibility becomes noticeable, but nothing really to worry about. As you speed up (relative to the air), the Mach number climbs to 0.7… 0.8…0.9 and still there is not much change in the flight performance. Around Ma=0.9 we are approaching the limit of subsonic flight, so this is the aerodynamic speed limit applied to modern, commercial airliners. That is about 1100 kph at ground level, but more like 900 kph (airspeed) at typical cruising altitudes of 37000 ft/11000m.

When the bulk Mach number gets up to around 0.95, things start to get even more interesting. This is called the trans-sonic zone, but was once called the sound barrier, A normal aircraft wing works by using geometry to make the air speed up over the top of the wing and slow down underneath. By the wonders of the Bernoulli effect, that creates a pressure differential, which gives some lift.

Now, imagine that the aircraft is flying forward at Ma=0.95 or slightly more. The air speeds up slightly over the wing, so the local airspeed might start approaching Ma=1.

What happens then?

At low speeds, the wing is rushing through the air, making a noise. This noise is sent out in all directions, radiating out from the source as a series of sound waves: little compressions and relaxations in the air pressure. However, the sound can only travel forward at the local speed of sound. This means that the sounds will pulse forward at around 330 m/s as viewed from a stationary observer, but will be less than that for someone looking out from the moving wing.

If the wing is moving forward at Ma=0.5, it will move forward 50 cm in the time the sound waves have gone forward by 1m. At Ma=0.9, the wing will go 90 cm in the time the sound waves travel 1m. At Ma=0.99, then the wing is so close behind the sound waves that even after travelling 1m, the wing is only 1 cm behind the sound wave. All the noise and pressure waves generated in the last 1m of travel are packed into a space1 cm long.

With just a little more speed, the wing catches up with the sound waves, and all the compressions get packed into zero space, That shows itself as a shock wave. A little zone of space where the pressure changes suddenly from one value to another. A discontinuity in the pressure field surrounding the aircraft.

Shock waves are strange things. Nature normally abhors discontinuities, and we humans have to work very hard to create them. They absorb a lot of energy, and as a consequence, a shock wave creates huge amounts of drag on an aircraft, a bit like suddenly launching a sail out of the top of the wing.

As the first rocket-powered aircraft speeded up beyond Ma=0.95, small shock waves started forming over their convex exterior surfaces, and the drag increased dramatically. That slowed them down again to subsonic speeds. As the engineers built in more power, to push harder, the shock waves got bigger and more powerful, creating yet more drag on the aircraft, and shaking the aircraft as they formed, collapsed and re-formed along the outer surfaces of the plane.

With more power still, the craft can be pushed up to Ma =1.05, and out beyond the trans-sonic zone, into true supersonic flight. Once the aircraft has passed into the supersonic condition, a large, primary shock wave appears ahead of the craft, centred on the nose cone, with a secondary shock forming near the tail. Once the plane is up to this speed, it is always travelling in still air, and the bumps and lurches associated with trans-sonic speeds disappear.

Modern supersonic aircraft are designed quite differently from subsonic planes. In subsonic craft, all the surfaces are rounded and smooth, designed to allow smooth airflows around the body. For supersonic flight, pointy bits and sharp edges are the norm, in order to control the formation of shock waves. So the front of a subsonic Boeing 747 is a blunt, curvy shape, but the front of a Concorde is a sharp point, designed to ensure the shock wave originates at a pre-defined place.

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