Back to Basics

The Helicopter and the Speed of Sound!
Phil Croucher
February 23, 2009
By Phil Croucher
Continuing from my last column with the theme of things you didn’t know you needed to know, have you ever wondered why some rotor blades have weird shapes at their tips? Or what possible significance the speed of sound might have for helicopter pilots? They generally only do around 100 knots, right? Well, yes, they do, but … the tips of your rotor blades may approach the speed of sound, especially when they are advancing, as the speed of the helicopter is added to their rotational speed. The classic example is the Huey, which has tip speeds over 800 feet per second (fps), only 300 fps behind the speed of sound, which is around 1,100 fps. While this may appear to be a large margin, under some circumstances, parts of the blade could still reach supersonic speeds. My point is that 800 fps (or 475 kts) is way over the margin where air density becomes significant (below about 300 knots, air is considered to be incompressible.)

Thus, compressibility effects can actually be felt well below the speed of sound. The most adverse conditions that affect this include: high airspeed; high RPM; high gross weight; high density altitude; low temperature (for example, if you take a Bell 212 to the Arctic, you will lose around four per cent of the power available due to compressibility); and turbulence (when rotating, the blades push waves of air ahead of them which bunch up as the speed of sound is reached into a Mach wave). Mach numbers denote a ratio between two speeds, namely true airspeed compared to the local speed of sound, which varies depending on the temperature. M1.0 is equal to the speed of sound.

In short, as air is compressed, its temperature increases, its density reduces, and large increases in drag and a rearward shift of the aerodynamic centre are felt, meaning that more power will be required and there will be excessive blade twisting, not to mention vibration.

The flow of air over the top of the blade initially moves into a region of lower pressure, courtesy of Bernoulli, but as it nears the trailing edge it encounters a higher pressure from the adverse pressure gradient (where higher-pressure air from underneath pushes forward over the upper surface at the trailing edge) and has to work harder, so it decelerates. If the adverse gradient becomes too great, flow separation occurs and the aerofoil stalls. When it finally reaches the speed of sound, a shock wave will form where the flow decelerates, as behind it, the pressure waves are moving forward. The shock wave forms where the two airflows meet, and its angle progressively decreases with speed. In the shock wave there is a considerable increase in density, pressure and temperature, which causes the boundary layer to separate into a shockstall. The energy required for this comes from forward speed, so it is the equivalent of a drag penalty (it is like deploying spoilers at high speed). The lower surface shock wave forms later because the lower camber is less, but this means that it ends up more forward than the upper one, which causes the centre of pressure to move aft, and further aft when the shock waves reduce the lift at the root. The resulting pitching moment only increases the airfoil’s speed and makes things worse.

At supersonic speeds, changes in velocity and pressure will take place sharply and suddenly, which is another good reason for being smooth on the controls! The Critical Mach Number (MCRIT) is the highest speed you can get without supersonic flow (about M0.72). To put it another way, it is the lowest free stream Mach number (MFS) at which a local Mach number of one will occur at any point, usually starting on the upper surface. Thus, MCRIT marks the lower end of a band of Mach numbers where a local one may be supersonic, marking the boundary between subsonic and transonic speeds. It follows that, the less air is accelerated over the wing, the higher MCRIT can be, which is done either with a lower camber (thinner) or a higher sweep, which is the preferred method with rotor blades, whose tips may have special shapes:

A swept tip is angled aft; a 30 degrees sweep will increase MCRIT up to about M0.75. The idea is to make the blade appear (to the airflow) thinner than it really is – coming at the air from an angle instead of head-on reduces the brute force effect, and allows a higher TAS without the air going supersonic. The Black Hawk and the Apache have the last seven per cent of the blade swept back by 20 degrees. In this way, control loads at high speeds are reduced, as well as the noise pattern. The BERP (British Experimental Rotor Program) tip, as fitted to the EH-101 and Lynx, has a similar effect, where its planform is swept forward, then aft.
Phil Croucher is a longtime industry expert and author of Professional Helicopter Pilot Studies.
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