Air speed and blowing pressure in woodwind and brass instruments: how important are they?
Air speed and air flow — and some values for both
To begin, let's distinguish air flow rate, measured in litres per second and air speed, measured in metres per second. Let's start with some values. First, imagine taking a deep breath and exhaling five litres in five seconds; this gives a value of 1 litre per second (1 L/s equals 10−3 m3s−1), which is a very high value for playing. For a low value, take the same volume, but exhale slowly enough to last fifty seconds: one tenth of a litre per second (0.1 L/s equals 10−4 m3s−1) is a low value. Air is compressible, but blowing pressures are usually rather less than 10% of atmospheric pressure, so air doesn't compress much in playing. Consequently, to an approximation that's good enough for now, the average volume flow out of the lungs equals that passing through the mouth, which equals that between the lips, and this rate will usually be in the range 0.1 to 1 L/s (maybe a bit lower for oboes playing softly).
The flow through a pipe increases if you increase either the speed at which the air flows, or the cross section of the pipe: the average air speed multiplied by the cross section gives the average air flow rate. (Think of a mountain stream: slow speed in a wide deep section (large cross section) leading to the nearby rapids, where the cross section is small so the speed is high, but the same average volume flow (in L/s) through each.) So let's consider a place in our mouth or throat where the cross section is about three square centimetres (= 3 × 10−4 m2). Divide this into our range of likely flows and we get a range of average air speeds from 0.3 to 3 metre per second — at that point with this relatively large cross section. Now consider a location with a small cross section, say a tenth of a square centimetre (= 10−5 m2). Such a value is small but possible for the lip aperture of a flutist, between a trumpet player's lips, or sometimes between a clarinet reed and mouthpiece. (An oboe reed opening is even smaller.) If the tongue is held near the hard palate (e.g. in an 'ee' configuration), the cross section there would have an intermediate value, say roughly 1 square centimetre, but it would vary depending on the tongue shape.
Combine our range of flows (roughly 0.1 to 1 litres per second) and these apertures (say 0.1 to 3 square centimetres): this tells us that the average air speed will usually be in the range about 0.3 m/s (a reasonably wide area of the mouth or throat with soft playing) to 100 m/s (blowing a lot of air through a very narrow aperture). It's worth repeating that dependence on aperture cross section: the average speed of the air could simultaneously be roughly 3 m/s in a flutist's throat where the cross section is 3 square centimetres and and 100 m/s where it passes through a gap of 0.1 square centimetres between the lips; both give a litre per second . (I've been talking about average values here for two reasons, First, there's the possibility of variation in speed over the cross section. But there's also rapid variation in time: we have average air motion due to the steady exhalation and rapid variations in air speed due to sound waves in both the instrument and the vocal tract. So I'm thinking of an average taken over a time of about a few hundredths of a second or more and, where relevant, a spatial average over the cross section.)
Air speed and blowing pressure
Blowing pressure is usually closely related to air speed. The exception is when you use your tongue or your lips to close the air passage – then there is no air flow and the air speed is zero even with high pressure in the mouth. But let's now consider the high air speed passing between the lips of a flutist or trumpet player, or between a clarinet reed and mouthpiece. That air has been accelerated by the difference in pressure between the inside of the mouth and the outside air or the air in the instrument, both of which are close to atmospheric pressure. So
the blowing pressure in the mouth is what accelerates the air to high speed between the lips, and the kinetic energy of the high speed air is roughly equal to the work done on it by the blowing pressure. So the blowing pressure is approximately proportional to the square of the average speed between the lips or flowing past the reed (P ≅ ½ρv 2 where ρ is the density of air and v the speed). A pressure difference of one kilopascal (1 kPa) produces roughly 40 metres per second, but for 80 metres per second, a difference of about 4 kPa is needed. Measured blowing pressures usually range between 1 to 10 kilopascals (kPa) or 1% to 10% of atmospheric pressure, though (potentially dangerous) higher pressures are sometimes recorded. This range is enough to accelerate air from rest up to speeds between very roughly 1 and 100 metres per second, consistent with our simple estimations above.
Generating and controlling that pressure is complicated and various muscles in the torso will often be coordinated to produce a smooth rise, a steady supply and a smooth fall, just for a single, isolated note. When the lung volume is near maximum, the elastic response of the distended torso tends, on its own, to contract the lung volume and expel air. This elastic response can be helped by the muscles used for exhalation, if needed. At low lung volume, however, the torso's elasticity tends to expand the lungs, which produces a small suction, so extra muscular tension is required for exhalation in this condition. Sometimes, the diaphragm (a muscle which is usually used for inhalation) can be used to reduce or to control blowing pressure, and may be used if very low pressure is required for soft playing at high lung volume.
A warning for high-range trumpeters and perhaps oboists: sustained very high pressures are reported to affect circulation in the head and neck, with reports of possible consequences including stroke and eye damage. Be careful, and try to achieve the high range with embouchure rather than pressure; oboists should avoid very hard reeds. Also, because of the small aperture, oboes require very small flow rates. However, if you are an oboist, the fact that you can play very long soft passages without breathing doesn't mean that you should: if the conductor goes blurry, you are in danger of fainting.
How important are air speed and power in performance?
Air speed at the lips or mouthpiece is often important in the operation of the instrument. For the flute, both the register and the intonation are dependent on the time that the air jet from the lips takes to reach the edge of the embouchure hole, and that time is the distance travelled divided by the air speed. For brass instruments, different speeds at different positions on the lips are related to different pressures, and this spatial variation in pressure contributes to the forces that act on the lips during their vibration. A similar effect can act on the reeds of woodwind instruments.
For the flute (or recorder), the jet leaving the lips has a reasonably steady flow. For other instruments, however, the flow varies strongly because the aperture between lips or between reed and mouthpiece varies in size.
In brass instruments and reed instruments, the aperture sometimes closes completely during the vibration cycle, so the instantaneous flow rate and the instantaneous air speed fall briefly to zero.
Air speed is difficult to sense, and what musicians mean by it is often unclear. While the blowing pressure and the air speed past the lips or reed have direct effect on the performance, the different air speeds in different parts of the mouth have less effect. Pressure and speed are correlated, so it is possible that when a teacher asks a student to 'maintain air speed', perhaps s/he means 'maintain blowing pressure'. Another possibility is that saying this has the effect of getting the student to adopt a vocal tract shape or vocal fold adjustment whose acoustic resonances have some particular values or some other subtle effect.
Controlling and varying the air pressure in the mouth is a fundamental skill in wind and brass instrument performance. Loud playing in general requires higher pressure and/or higher flow. High pressure also gives faster attacks. When starting the first note of a phrase, the blowing pressure is often increased and the tongue is released during that increase. The pressure usually falls during the end of the last note of a phrase. On many instruments (the clarinet is an exception), higher pitch requires higher pressure at the same loudness. For flutes, blowing pressure is roughly proportional to frequency, and a flute's loudness is largely determined by flow, which is controlled via the size of the lip aperture. Variations in pressure and other control parameters are are used to produce accents and to give musical ‘shape’ to a phrase. Variations in pressure can also be used in vibrato.
While we're here, we should calculate the power. Take the range above of 0.1 to 1 litre per second (10−4 to 10−3 m3s−1). Multiply this by the pressure (1 to 10 kPa) to give the range of power provided by the player's breath to the instrument: here that gives 0.1 to 10 watts. This overestimates the range in practice, however, because high notes, which require higher pressure on most instruments, are usually played with lower flow, so power over a watt is rare. Instruments have typical efficiences of only 1% or so, so the output sound power is usually measured in milliwatts. However, even one milliwatt of sound power output yields, at one metre distance, about 80 decibels if uniformly radiated, and more if radiated in a particular direction, e.g. in front of a brass instrument bell. (See How to relate power to dB).
This page grew out of a question on our FAQ in music acoustics. Let me know if it's not clear.