Sails as aerofoils

Much confusion surrounds our understanding of how sails propel us. This article explains some of the forces at work

How do sails work?

A simple question I’m sure you will agree but you will discover there are very few simple answers. Indeed, this is an astonishingly contentious subject on which there is widespread disagreement. I don’t want to spend too much time digging deeply into the associated wrangling but I would like to give you a taste of it.
But first let’s establish clear some basics:

• Both air and water are fluids.
• Sails, wings and rudders all foils: aerofoils and hydrofoils to be precise
• It doesn’t matter if the fluid is static (air) and the foil moving (aircraft wing) or the foil static (sail) and the air moving (wind). Yes I know all can move but it’s the interactions between foil and fluid that counts.

The most popular – and still enduring – explanation as to how sails work was founded on what’s known as the ‘equal transit time’ theory. This is best illustrated with reference to an aircraft’s wing – more precisely a wing with an asymmetric section, in some ways resembling the shape taken up by a sail seen from overhead.

The presiding guru for ETT supporters (of which I was once gullible enough to believe) was the Swiss mathematician Daniel Bernoulli (1700-1782) who conducted experiments to demonstrate that:

As the velocity of a fluid increases its pressure decreases correspondingly.

Let’s think about a conventional wing section. As is common for the type it’s asymmetric in section, being cambered on its upper surface and more or less flat underneath. Now let’s imagine two small clusters of molecules side by side at its leading edge. As the air starts to pass over the foil, one cluster takes the high road over the camber and the other the rather easier route along the underside. Clearly, the former has the longer path and, if it’s to arrive at the same time as the other, will have to move faster to make the rendezvous.
And, in line with Bernoulli’s Principle, faster results in a corresponding decrease in pressure so now there’s an imbalance in pressure between the two surfaces, essentially sucking the foil upwards – ‘lift’ in other words.

Let’s say immediately that Bernoulli was entirely right in his predictions. Unfortunately the ETT presumptions are wrong. Firstly, those molecules taking the mountain trail don’t arrive at the same time as ones underneath but actually before the others. This, of course, which would enhance the Bernoulli Effect, but unfortunately application of the great man’s formula reveals that this still doesn’t produce enough lift for flight. Also, where with sails are concerned, there is no straight path along the ‘under’ side. A sail is actually a very thin foil whose surface dimensions can be considered identical. The equal transit time theory also suggests that planes with asymmetrically shape wing foils couldn’t fly upside down – and that’s plainly not so! No, there have to be other forces at work.

And there are.

See and believe
We can learn much by observation. Watch a video clip of a helicopter landing on a dusty surface or hovering over water. You might expect those swirling blades – each one an aerofoil – to fling at least a significant quantity of air out horizontally. But that’s not the case. The helicopter is in fact riding on a column of air directed vertically downwards with very little divergence to either side.

Or look over the stern of a sailboat under power. The thrust from the propeller (the blades this time two or more hydrofoils) can be seen to extend almost straight astern. Yes, that path of churning water can be seen to fan out a little but it remains generally constrained for a considerable distance before diverging.

In both instances we are seeing what’s known in aeronautics as ‘downwash’ – commonly described as the change in direction of air by the action of a foil.

This would be a good time to introduce perhaps the most influential physicist of all time: Isaac Newton (1642-1727). His Third Law of Motion states that:

For every action there is an equal and opposite reaction

So there’s the key. Lift arises by turning the direction of a flow. Plugged into the context of aerofoils, this means that the downwards deflection of the airflow – the ‘action’ – demands an upwards ‘reaction’ that we know as lift. The combined effect of these two sources of lift and its distribution can be approximated as shown below.

Part of the problem for anyone attempting to pick apart the dynamics behind why aircraft can fly and sailboats can sail is that there is no simple or single explanation. And whereas Bernoulli and Newton played perhaps the most significant roles in enlightening the mysteries, there are a number of other heroes in the tale. So, if you delve deeper into the subject, expect to meet such luminaries as Henri Coanda, Martin Wilhelm Kutta, Nikolai Joukowsky and others. Each one has been a major contributor to the understanding of foils and deserves the credit that is undoubtedly their due.


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