Tutorial: The Building Blocks of Aerospace Physiology (Part 2)

WHAT’s THAT COMING OVER THE HILL?

The brothers Wright are often heralded as the first aviators. Whilst this holds true for heavier-than-air flight, the true acolade belongs to a different pair of siblings some 120 years earlier. On 21 November 1783 the Montgolfier brothers ascended to approximated 500ft in their hot air balloon in the first recorded episode of human flight.

But the more modest looking balloon shown here belongs to another inventor and scientist of the time – a man who is less well known, but perhaps more relevant to the field of aerospace medicine; Jacques Alexandre César Charles.

Missing out on the title of first person in the air by 10 days, Charles was arguably well ahead of his time. Inspired by the work of Robert Boyle he invented (alongside the Robert brothers – in case you thought there was a suspicious lack of siblings in this story!) the first hydrogen-filled balloon – a mean feat for 1783 that required pouring sulphuric acid onto iron filings. So alien was his achievement at the time that when his first uncrewed test landed in the French village of Gonesse, the villagers thought a monster sent by a rival village had descended upon them and took to it with pitchforks and knives.

Unperturbed, Charles prepared for a crewed mission with himself and Nicolas-Louis Robert. The first attempt saw them reach almost four times higher than the Montgolfier brothers. Excited by this success, Charles asked Nicolas-Louis is step out so he could try again. This time he reached 9,840ft before being forced to release the gas and descend. The reason why? An unforseen side effect of Boyle’s law…the first ever case of aviation related barotrauma.

But Charles’ link to aerospace medicine doesn’t end there…

As we will see over the course of this tutorial, Charles’ law looks at the relationship between temperature and volume in a gas. Whilst it was first written down by Joseph Gay-Lussac, it was credited to unpublished work by Charles and was given his name. In an odd coincidence it would go on to sit beside the gas laws of his inspiration, Robert Boyle, and his commemorator, Gay-Lussac in the combined gas law – another of our fundamental building blocks of aerospace medicine and the focus of this tutorial.

THE IDEAL LAW?

In Part 1 of this tutorial we discussed how there are some fundamental principles that come up time and time again in aerospace medicine and are worth getting to grips with. Having dealt with the hydrostatic gradient it is now time to move on to the Usual Suspects – the eponymous gas laws.

Before we get started its important to note that all of these laws apply to what are called ‘ideal gases’. Luckily for us this is good enough for most occasions we will deal with and certainly to understand the principles enough to work out what the effect may be in the aviation or space environments.

Boyle’s LAW

The most prolific of these laws is the very same one that inspired Jacques Charles; Boyle’s Law.

Boyle’s Law states that (where the temperature of a gas is kept constant) the pressure exerted by a gas is inversely proportional to its volume. This can be expressed as:

Let’s go back to our SCUBA diver in the pool. Look at the exhaled bubbles and how they get bigger as they rise to the surface. As we learnt in Part 1, there is a pressure gradient in the pool which means that the pressure increasing with depth in a linear fashion as determined by ρ x g x h. Each bubble has a set number of molecules that are moving around, exerting pressure on the outside of the bubble (lets call this P_internal) and trying to make it bigger. However, this is countered by the external pressure of the water (or P_external). The size of the bubble is determined by the equilibrium reached when P_internal = P_external. As the bubble rises, P_external reduces and the bubble can get bigger before the equilibrium is reached.

It may be easier to think about this in reverse. Like flies in a jar, gas molecules are naturally spread out and like to move around the volume of the container in which they are placed. One way to think of pressure is how many times they bump into the walls as they move. If the flies continue to move at the same rate (see Gay-Lussac’s law below) but the jar shrinks, then they will hit the walls more frequently and the pressure will go up.

GAY-LUSSAC’s LAW

Gay-Lussac’s law describes what happens if instead of changing the volume of the gas, we change it’s temperature. It states that, where volume is kept constant, the pressure of a gas is proportional to the temperature (measured in Kelvin). This can be expressed as:

A rise in temperature reflect an increase in the average kinetic energy of that substance – in this case our gas. Without getting into the complexities of thermodynamics a simple (but not wholly accurate) way of thinking of this is that the molecules in a hotter gas are moving more rapidly.

If we heat up our jar with the flies (keeping the number of flies and size of the jar constant) they become, understandably, agitated and start to move around more quickly, bumping into the sides more in the same amount of time.

CHARLES’ LAW

As mentioned earlier, this law was first published by Gay-Lussac but was credited to unpublished work by our favourite balloonist (how the theory of science as being built on the shoulders of giants isn’t quite true is perhaps a good topic for a future blog). If you know the other two laws this one might seem like common sense.

Charles’ Law states that, if we keep the pressure of a gas constant, the volume will be proportional to the temperature. This can be expressed as:

As the substance is heated the molecules move more rapidly. To keep the pressure the same we have to increase the volume of the container:

This time we have removed the flies from their jars and let them fly freely for the same amount of time. The more sluggish flies on the left fly less far than their agitated siblings on the right. If we draw a box around the distance traveled (or the volume) we can see that the cool flies have less volume than the hot ones.

The Combined Gas LAw

As is probably clear, the three laws above overlap somewhat. If you change a parameter in one then it will affect the others. Instead of running through each of these rules individually we can combine them to form a…you guessed it…combined gas law which can be written as:

This equation (with the limitations noted at the start) is relevant for a huge number of applications in aerospace medicine. Combining this with what you learnt in the previous Part of this tutorial, you can probably guess why but we will go over this in more details in our next tutorials as we discuss the aviation and space environments.

One thing to note is that the Combined Gas Law does not take into account changes to the number of molecules (or number of flies in the jar). To do this you have to include Avogadro’s Law which states that the volume of a gas is proportional to the amount of substance of the gas in moles. When added in, this creates the ‘Ideal Gas Law’ (see here for more) but the Combined Law is “ideal” for us in the majority of cases.

Some Other EPONYMOUS LAws…

Besides the Combined Gas Law there are a number of other principles that we will run into on a number of occasions. A number of these (such as Fick’s Law and Poiseuille’s Law) are predominately related to physiology and will be covered as needed in future tutorials. The two I have chosen to go into in more detail here have physiological implications but are also needed to understand the aviation and space environment.

Dalton’s LAw

Dalton’s law describes something that those working in the medical world use regularly and innately understand, but might not quite be able to put into words. Gases in the natural world are very rarely purely made up of one substance – even if breathing 100% O₂, the gas in someone’s alveoli contains CO₂ that has diffused across from the capillaries (and likely some N₂ unless they have been breathing O₂ for some time). Dalton’s law describes what happens when you combine gases and is fundamental for understanding what goes on in the atmosphere and inside our bodies.

Dalton’s Law states that the total pressure of a gas is the sum of the partial pressures of the individual gases that make it up. It defines partial pressure as the pressure that all molecules of that substance would exert if they were on their own in the same volume container at the same temperature.

Let’s go back to our jar:

This time the flies are accompanied by a couple of different types of flying insects. If we continue the metaphor then the total pressure in the jar is now made up from the times that all of the insects hit the walls (P=6 here). To work out the partial pressure of the bees or the flies we need to imagine them in separate jars…

Now it becomes quite easy to see the partial pressure of each insect. When describing partial pressures we tend to use the style of P_substance so in this case we have P_bees = 2, P_flies = 3, P_dragonflies = 1. Dalton’s Law states that P_jar = P_bees + P_flies +P_dragonflies, which it clearly does here!

For ideal gases – like our jar – the ratio of partial pressures is equal to the ratio of the number of molecules.

If we look at the gas mixes in the air at ground level we can see this become a bit more relevant. Based on the ICAO Standard Atmosphere (see upcoming lecture of the Altitude environment) air is made up of roughly 78% N₂ and 21% O₂, with the remaining 1% made up of inert gases (predominately Argon) and CO₂ (only 0.03%!). At ground level the atmospheric pressure is 760mmHg. Using Dalton’s Law we can work out that:

Henry’s LAw

This is one of those laws that is much easier to demonstrate than to describe and is one you can try at home. Go and get a new bottle or can of a fizzy drink and head outside. If you’re brave you can give it a shake*. Now open the bottle and see what happens. If it has not been opened before, you should see bubbles of carbon dioxide escaping from the liquid. If you pour it into a glass you might notice that a foamy raft of bubbles, or ‘head’, is formed. You probably didn’t need to do this to know what was going to happen as it’s something we take for granted. But with Henry’s Law we can explain why.

Henry’s Law states that the solubility of a gas in a solution is proportional to the partial pressure of the gas above that solution. The higher the partial pressure of a substance in the gases surrounding the liquid, the more of that substance that can be dissolved.

As we will come on to see in future tutorials, Henry’s Law (along with Boyle’s law) forms the basis of injury caused upon rapid decompression or exposure to extreme altitudes.

So this has rounded off our introductory piece looking into some of the fundamental building blocks of aerospace medicine. Next we will use some of these to help build up our picture of the aviation and space environments and the effect they can have on humans who, if the words of John Gillespie Magee Jr, choose to slip the surly bonds of Earth. Until then…

Yours,

JB

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