This week's topic -- Mach numbers, and the accompanying aerodynamics.
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The Basics
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A bullet and its accompanying shock wave
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Most people, if not everyone, has heard of Mach numbers before; They are a dimensionless quantity that compares the speed of the aircraft to the speed of sound. Mach 0.94 is 94% the local speed of sound, Mach 2.75 is 275% the local speed of sound. Mach numbers are a dimensionless number, which is why the quantity follows the unit (Mach 2 instead of 2 Mach). When you break the sound barrier, a shock wave will form in front of the leading edge of an airfoil. As you increase speed beyond Mach 1, the cone will narrow down, becoming the signature shock cone.
The Catch
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Pressure map of an airfoil,
showing the pressure/speed
variations |
But there's a catch. Aerodynamics is never that simple. See, when air goes over an airfoil or any other solid, it changes velocity. That is in fact how planes and helicopters work. They generate lift through Bernoulli's law, which says that faster air has lower pressure, which generates that lift. So when air hits an airfoil it slows down, when it gets deflected, it slows down, and when it leaves the airfoil it speeds up. These speed variations along the length of the airfoil cause a number of caveats to the deceptively simple number.
Categorizing Mach speeds
There are 4 main speed categories in terms of Mach that objects operate in. Subsonic, which is the slowest and means that local air speeds over the entire vehicle are below Mach 1, no local Mach shock wave forms over any part of the vehicle, every airspeed across every surface is completely subsonic (below the speed of sound).
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| Speed map of an airfoil |
Next, is transonic, which, confusingly, goes into the supersonic regime in the conventional sense. Transonic means across the sound barrier, which is exactly what transonic aircraft do. But how? The tops of airfoils will experience a higher velocity compared to elsewhere in the vehicle and shock waves will form in these regions, starting at the critical Mach number (will be discussed later). As the speed of the aircraft increases, the supersonic shock wave will move towards as more air breaks the sound barrier on the airfoil. When the shock wave reaches the leading edge, it becomes a full shock cone, spilling below the airfoil. There are some more complicated nuances involving the critical Mach number, but what is improtant is that from M = 0.8-1.2, the aircraft is transonic, not supersonic.
But, as speed increases beyond Mach 1.2 and into Mach 1.3, all airflow becomes supersonic. At these speeds, airplane design is different. Wings must be thinner, sharper and control surfaces are often all-moving. Most supersonic combat aircraft compromise speed and performance at supersonic speeds in favor of low speed handling. Aircraft that are designed - "true" supersonic plane designs are planes like the F-104 starfighter, with extremely small and back set wings. Or, alternatively, like the SR-71, with backset, narrow wings, unique to extremely fast aircraft.
Going faster, we have hypersonic speeds, speeds in excess of Mach 5 and up to Mach 25. At these speeds, design choices and characteristics dramatically change. Wings become even smaller to reduce drag and heat induced on the vehicle. Additionally, wings become simpler and more "ideal", modeling Newtonian Flow theory. For example, take the tail control surfaces on the X-15. Leading edges must become blunter to push the oblique shock in front of and away from leading surfaces, minimizing the extreme heat that vehicles in this speed regime experience. Heat becomes a dominant design consideration and vehicle design revolves around heat shielding and prevention, rather than handling.
Critical Mach Number(s)
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Normal (top) vs Supercritical Airfoil;
A = Supersonic flow region
B = Shock wave
C = flow separation
As seen, supercritical airfoils have
smaller shockwaves and less drag |
The critical Mach number is the Mach number at which any air flowing over a vehicle reaches, but does not exceed, the speed of sound. This is the lower critical Mach number (upper critical Mach number is not too important). The critical Mach number (Mcrit) is a very important design consideration for all aircraft capable of reaching any significant speed. For example, as an aircraft exceeds Mcrit, drag dramatically increases as a result of only a local shockwave forming on part of an aircraft. Drag coefficients can jump up to an order of magnitude during this phase, as adverse pressure gradients and flow separation increase drastically as airspeed reaches the speed of sound.
Sometimes, in aircraft not designed to at or above Mcrit, dangerous things happen to the control surfaces of the airplane. Control surfaces often stall and lead to a loss of control. Sometimes, the shockwave formed on the upper part of airfoils pushes the center of pressure (or center of lift) backwards, pushing the aircraft into an uncontrollable dive, called Mach tuck.
Overtime, we designed technologies to remedy these errors and the increase in drag caused by local shock waves only increases by 2-3x. We have invented supercritical airfoils, which delay the onset of local shock waves, and made wings thinner to reduce the speed disparity across an airfoil cross-section and lessen the effect of local shock waves.
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Thanks for reading!
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