SafekipediaMach number
Adapted from Wikipedia · Discoverer experience
The Mach number is a special way to measure how fast something is moving compared to the speed of sound. It is named after Ernst Mach, a scientist who studied how things move through air or other gases. When we talk about Mach number, we are really comparing two speeds: how fast an object is moving and how fast sound travels in the same place.
If something is moving at Mach 1, it means it is going exactly as fast as sound. If it is moving at Mach 0.65, it is going slower than sound—about 65% as fast. If it is moving at Mach 1.35, it is going faster than sound—about 35% faster. The speed of sound changes depending on how warm or cold the air is, so the Mach number helps us understand motion in different temperatures and heights.
Mach number is very useful for scientists and engineers who study how air or other gases move. It helps them decide when they can treat the flow of gas as if it does not squish or change shape much, which makes calculations easier. Whether an airplane is flying high in the sky or air is moving through a special tube called a wind tunnel, the Mach number helps describe what is happening in a simple way.
Classification of Mach regimes
The words subsonic and supersonic describe speeds slower than and faster than the speed of sound. This is important because around a speed called Mach 1, the usual simple math rules for airflow change. Even if the airplane itself is moving slower than the speed of sound, the air around parts of it might actually be moving faster than the speed of sound.
The supersonic regime refers to speeds where we can use simpler math rules. In this range, we assume the air isn’t reacting chemically and we can ignore heat transfer between the air and the vehicle for calculations.
| Regime | Flight speed | General plane characteristics | ||||
|---|---|---|---|---|---|---|
| (Mach) | (knots) | (mph) | (km/h) | (m/s) | ||
| Subsonic | Most often propeller-driven and commercial turbofan aircraft with high aspect-ratio (slender) wings, and rounded features like the nose and leading edges. The subsonic speed range is that range of speeds within which, all of the airflow over an aircraft is less than Mach 1. The critical Mach number (Mcrit) is lowest free stream Mach number at which airflow over any part of the aircraft first reaches Mach 1. So the subsonic speed range includes all speeds that are less than Mcrit. | |||||
| Transonic | 0.8–1.2 | 530–794 | 609–914 | 980–1,470 | 273–409 | Transonic aircraft nearly always have swept wings, causing the delay of drag-divergence, and often feature a design that adheres to the principles of the Whitcomb area rule. The transonic speed range is that range of speeds within which the airflow over different parts of an aircraft is between subsonic and supersonic. So the regime of flight from Mcrit up to Mach 1.3 is called the transonic range. |
| Supersonic | 1.2–5.0 | 794–3,308 | 915–3,806 | 1,470–6,126 | 410–1,702 | The supersonic speed range is that range of speeds within which all of the airflow over an aircraft is supersonic (more than Mach 1). But airflow meeting the leading edges is initially decelerated, so the free stream speed must be slightly greater than Mach 1 to ensure that all of the flow over the aircraft is supersonic. It is commonly accepted that the supersonic speed range starts at a free stream speed greater than Mach 1.3. Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behavior of flows above Mach 1. Sharp edges, thin aerofoil sections, and all-moving tailplane/canards are common. Modern combat aircraft must compromise in order to maintain low-speed handling. |
| Hypersonic | 5.0–10.0 | 3,308–6,615 | 3,806–7,680 | 6,126–12,251 | 1,702–3,403 | The X-15, at Mach 6.72, is one of the fastest crewed aircraft. Cooled nickel-titanium skin; highly integrated (due to domination of interference effects: non-linear behaviour means that superposition of results for separate components is invalid), small wings, such as those on the Mach 5 X-51A Waverider. |
| High-hypersonic | 10.0–25.0 | 6,615–16,537 | 7,680–19,031 | 12,251–30,626 | 3,403–8,508 | The NASA X-43, at Mach 9.6, is one of the fastest aircraft. Thermal control becomes a dominant design consideration. Structure must either be designed to operate hot, or be protected by special silicate tiles or similar. Chemically reacting flow can also cause corrosion of the vehicle's skin, with free-atomic oxygen featuring in very high-speed flows. Hypersonic designs are often forced into blunt configurations because of the aerodynamic heating rising with a reduced radius of curvature. |
| Re-entry speeds | >25.0 | >16,537 | >19,031 | >30,626 | >8,508 | Ablative heat shield; small or no wings; blunt shape. Russia's Avangard is claimed to reach up to Mach 27. |
High-speed flow around objects
When an aircraft flies, its speed can be grouped into several categories. At speeds close to the speed of sound, some parts of the airflow around the aircraft become faster than sound while others remain slower. This happens first above the wing and is called the transonic period.
When the aircraft goes faster than the speed of sound, a strong pressure change forms right in front of it. This is called a shock wave and spreads out in a cone shape behind the aircraft, creating what we hear as a sonic boom from the ground. Inside the aircraft, this boom is not heard. As the aircraft goes even faster, the cone becomes narrower. When the aircraft is fully supersonic, the shock wave forms a clear cone, and the airflow is either all faster than sound or has only a tiny area slower than sound near the front of the aircraft.
As the aircraft’s speed increases, the shock wave becomes stronger, and the cone gets narrower. When the air passes through the shock wave, it slows down and the temperature, pressure, and density of the air increase. At very high speeds, the temperature rise can be so large that the air molecules begin to break apart.
| Regime | Subsonic | Transonic | Speed of sound | Supersonic | Hypersonic | Hypervelocity |
|---|---|---|---|---|---|---|
| Mach | 0.8–1.2 | 1.0 | 1.2–5.0 | 5.0–10.0 | >8.8 |
High-speed flow in a channel
When air flows through a channel and reaches supersonic speeds (faster than the speed of sound), something interesting happens. At slower, subsonic speeds, making the channel narrower makes the air go faster. But once the air is moving faster than sound, the opposite happens: making the channel wider actually makes the air speed up even more.
This change happens because of how mass flow rate is conserved, meaning the same amount of air has to keep moving through the channel no matter what.
Calculation
The Mach number tells us how fast an aircraft is flying compared to the speed of sound. We can find this number using a simple idea: divide the aircraft's speed by the speed of sound at that height.
For example, if an airplane flies at 340 meters per second and the speed of sound at that height is also 340 meters per second, its Mach number is 1. This means it’s flying exactly at the speed of sound.
The speed of sound changes with temperature. On a cold day, it might be slower, so the same airplane could reach a higher Mach number. On a warm day, the speed of sound is faster, so the airplane might need to go faster to reach Mach 1.
velocity
speed of sound
thermodynamic temperature
ratio of specific heat
specific gas constant
Kelvins
Bernoulli's equation
ideal gas
impact pressure
static pressure
Rayleigh
flight instruments
root-finding algorithm
septic equation
Abel–Ruffini theorem
fixed point iteration
Newton's method
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This article is a child-friendly adaptation of the Wikipedia article on Mach number, available under CC BY-SA 4.0.
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