The spread of droplets originated from a cough

An Introduction to the Physics of Cough

You might have read or heard someone say this about the physics of cough: “Cough, pushes air at an extreme speed!” But what exactly happens physically to your body when you cough?

First, let’s get acquainted with the three phases of cough:

  1. Inspiratory phase – The large breathing muscle at the base of the lungs (diaphragm) contracts, bending downwards into a dome shape; the accessory breathing muscles relax. These muscle movements cause lung pressure to decrease (lower than Earth atmospheric pressure): air from the atmosphere rushes into the lungs, and a deep breath in (inspiration) occurs.
  2. Compression phase – The closing mechanism on the top of the airway (glottis) seals shut. At the same time, the diaphragm relaxes, and auxiliary respiratory muscles contract. Due to the substantial elastic effect of the relaxing diaphragm forcing it to return to a flat shape, pressure in the lungs increases sharply.
  3. Expiratory phase – The glottis suddenly opens, causing the air at supra-atmospheric pressure in the lungs to leave the lungs rapidly.

The Extreme Pressures and Speed

What kind of pressures and speed can the physics of cough achieve?

During intense coughing, pressures inside the chest cavity may reach over 300 mmHg (about three times the average normal blood pressure). Then, air rushes out through the airways at near transonic speeds (~800 km/h, or 85% of the speed of sound).

Due to the extreme airflow speeds, coughing is genuinely an explosive process. As a result, when repeated enough, it causes trauma to the upper airway (larynx) and lower airway (trachea), which is known as “cough-induced” laryngotracheitis (CILT).

Here is a list of the most common possible negative consequences of the extreme physics of repetitive cough when the body doesn’t get a chance to recover:

  • Exhaustion/Musculoskeletal pain – Due to the intense contraction of respiratory muscles during cough.
  • Self-consciousness – Coughing can often cause people to direct their attention to their respiratory muscles, distracting them from other activities.
  • Insomnia – Coughing often may directly conflict with the need to settle down for sleep.
  • Headache/Dizziness – Coughing can disturb pressure inside the skull, cerebrospinal fluid flow, and blood flow.
  • Hoarseness/mechanical trauma – the repetitive insults to the upper airway (laryngotracheal domain), caused by the blasts of air shooting out of the lungs, directly damage tissues.
  • Inflammatory response – with extended insult, a chronic inflammatory response may establish a feedback mechanism where inflammation (cellular and immune pathways) induces further propagation of cough (more mechanical trauma), which causes further inflammation.

The Surprising Blood Flow

What impacts does the physics of cough have on blood flow?

The extreme pressure changes during cough almost make the chest cavity function as a second heart. Thus, a single cough starting with a deep breath can: 

  • Pull a small amount of blood from the extremities to the thorax (inspiration phase)
  • Push about 300 mL and 700 mL of blood from the chest and toward the extremities, respectively (compression and expiratory phases).

The extreme pressure and blood flow changes during a deep cough made people wonder:

Could coughing help during a heart attack?

Figure 1: the main symptoms of a heart attack. Credit: Ivana P Dewi, Irma Maghfirah, Louisa F.K. Wardhani, Fatimah Alzahra, Ni P.A. Laksmi

If you’re experiencing symptoms of a heart attack (as illustrated in figure 1), you must immediately call your national emergency number. Before help arrives, if you can perform deep voluntary coughs, you may do so. It is potentially beneficial to enhance blood flow to the brain. However, keep in mind:

Cough alone is not enough to save you; only trained EMS/EMT/ER personnel are trained and have the means to do so.

Coughing as a CPR mechanism must NEVER delay contacting emergency services.

Since coughing might increase pressure inside the head (intracranial pressure), it can cause or worsen a headache. For example, in people with migraines, coughing is often an aggravating or triggering factor.

The Physics of the Frightening Distance Droplets Launched by Cough Can Reach

What implications does the physics of cough have on the reach of expulsion droplets? In other words, is the two-meter social distancing, as mandated by health authorities, enough? In short, the answer is: “Mostly yes indoors; but not outdoors.” An average human cough may travel up to unexpected considerable distances depending on the wind speed.

If the wind speed is zero, saliva droplets (and any infectious disease pathogen potentially within them) did not travel 2 m. However, safety can drop in windy conditions, and saliva droplets can travel beyond six meters. The figures below illustrate what happens with wind speeds of 4 km/h (slight breeze) to 15 km/h (leaves and small twigs in constant motion, wind extends light flags).

Figure 2: Cough droplet movements with no wind. Credit: Talib Dbouk and Dimitris Drikakis.
Figure 3: Cough droplet movements with a wind of 4 km/h to 15 km/h (wind direction left to right). The droplet cloud will affect both adults and children of different heights due to the vertical dispersal. Credit: Talib Dbouk and Dimitris Drikakis.

Droplets released when coughing occur in a continuum of sizes. They can amount to as much as 7 to 8 mg. Moreover, these droplets are trapped and carried forward within a moist, warm, turbulent cloud of gas (they do not travel independently on their trajectories).

Properties of droplets released when sneezing or coughing: 

  • Larger droplets:
    • Are formed by saliva.
    • Settle more rapidly than smaller ones due to gravitational forces.
    • Gradually disperse into smaller ones while moving away from the mouth.
  • Smaller droplets:
    • Are formed by the mucous coating of the lungs and vocal cords.
    • Are often invisible to the naked eye due to their small size.

Take Home Notes on The Physics of Cough

Thus, no safety measure is too much to avoid infection by a respiratory disease. And in public spaces, cough etiquette and mask-wearing are fundamental, while distancing recommendations need adjustment for outdoors. On one hand, a social distance of above two meters is effective in indoor public spaces. On the other hand, regarding outdoors, if people are not wearing masks, the risk of someone coughing and dispersing droplets beyond six meters is genuine. In this situation, avoid remaining near large groups of people.


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