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How fast does air move in the airways during a cough?

The following passage is from Talley and O'Connor's Clinical examination: a systematic guide to physical diagnosis (emphasis mine):

Cough is a common presenting respiratory symptom. It occurs when deep inspiration is followed by explosive expiration. Flow rates of air in the trachea approach the speed of sound during a forceful cough. Coughing enables the airways to be cleared of secretions and foreign bodies.

The speed of sound claim is unreferenced. I have found mention of coughs approaching the speed of sound in numerous popular sources (e.g. here, here, here (where it says 1000 km/h), and here), and innumerous books (e.g. here, here, here, here, here, and here); none of these references the claim. The same claim is also here. This book has a more exact (unreferenced!) claim:

Velocities as great as 28 000 cm/s (85% of the speed of sound) have been reported, but it is impossible to determine the gas velocity at points of airway constriction, where the greatest shearing forces will be developed. During this phase there is dynamic collapse in the bronchial tree, with large pressure gradients across the collapsed segment.

That speed is just over 1000 km/h. When I have searched for research literature behind this, I've only found much lower velocities at the mouth (rather than at a narrower location like the glottis), e.g. a peak cough velocity of 22m/s, also 11.2m/s, and 28.8m/s. The closest to a reference I found was this book with the following:

A cough comprises: ... sudden opening of the glottis, causing air to explode outwards at up to 500 mph or 85% of the speed of sound (Irwin et al, 1998), shearing secretions off the airway walls.

Irwin et al isn't primary literature either, and references Comroe JH, Jr. Special acts involving breathing. In: Physiology of respiration: an introductory text. 2nd ed. Chicago: Year Book Medical Publishers, 1974; 230-31. I don't have access to this book (does anyone here?), but I expect the references only continue from there.

My question is this: how fast is a cough in the airways (I am interested because such an explosive rush of air could explain the substantial damage seen in chronic cough), and does anyone know where the 1000 km/h claim comes from, or can point me to a legitimate reference?

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    $\begingroup$ If you are asking about whether a claim is correct/or not and where it comes from, you might receive more feedback on the skeptics stackexchange. $\endgroup$
    – Ebbinghaus
    Commented Nov 9, 2016 at 6:25
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    $\begingroup$ Perhaps. I'm not a skeptic though, I'm sure the claim is probably true; I would just be interested to find a reference for it so I can see how it was measured. I thought it would be more relevant on biology.SE. $\endgroup$
    – Anon
    Commented Nov 9, 2016 at 6:29

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This reference from CHEST lists 21 clinically measured peak flow rates during various modes of coughing. Of these patients, and for unassisted cough, the highest peak flow is about 4 liters/sec. The human trachea ranges from 13 to 27 mm diameter. The relationship between velocity, $V$ and flow $Q$ is

$$ V=\frac{Q}{A}$$

Assume the 4 liters/sec = 4000 cm^3/sec and minimum diameter, 13 mm = 1.3 cm, the cross section area being

$$A = \pi (D/2)^2 = 1.3 cm^2$$

Plugging in

$$ V=\frac{4000}{1.3} = 3077 cm/sec$$

which is a far cry from 28,000 cm/sec, so at this point I'm skeptical.

Things to consider is that the data taken in the paper was from sick humans so perhaps a healthy (and athletic) person may be able to exert much higher flow rates. But then healthy people generally are not stimulated to cough as much as a sick person with an airway compromised by sputum.

Although lower airways do have smaller diameters, the flow measured at the trachea is divided among them, so you wouldn't expect to see peak velocities in the lower airways, but rather the accumulation in the trachea.

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    $\begingroup$ Nice answer +1. I did a similar calculation to you, but I thought perhaps using that size for the trachea wasn't legitimate; a cough begins with a closed glottis, so in principle the airflow in the first moments is through a very narrow opening between the vocal folds and so in principle the flow rate could be higher. The flows in your paper are at the mouth which would potentially lead to a slower pickup in velocity at the beginning (if the actual speed were actually near the speed of sound which is the maximum speed that an impulse can be transmitted in air). I agree about smaller airways. $\endgroup$
    – Anon
    Commented Mar 21, 2017 at 5:43

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