I met Michael during the 2016/17 holiday season – he is a sailing instructor based in the British Virgin Islands (website) and was also part of the crew in the 1983 America’s Cup! Over the few days we had together, Michael noted that many airline pilots take up sailing and speak about the similarities between flying (air) and sailing (air and water).
Michael kindly agreed to write an article on the physics of sailing and those similarities, which I am delighted to share below today:
Everyone can easily understand how a sailboat can move downwind. The wind just ‘pushes’ against the sails and the boat moves through the water, right?
Some people understand that the same theory explains how a sailboat can sail across and against the wind—up to an angle as close as 45 degrees to the wind’s direction.
But few people understand — perhaps because its ‘unseen’ under water is the effect of keel and rudder and how they contribute to the same theory.
That’s what we’re going to talk about here: how the theory and physics of flight: the relationships between thrust, lift, mass/weight, drag, angle of attack, Newton’s laws and the Bernoulli principle.
They explain both how planes can lift off the ground and fly and how sailboats can sail against the wind. Both are pretty cool but although most people would say that flying is more complicated than sailing, there are a couple of interesting twists that might change your mind:
1) To lift the weight of the plane and its cargo off the ground, the airplane must be pushed forward through the air. Planes normally burn fuel for jets or propellers to generate forward thrust which creates a high flow of air over their wings and vertical and horizontal stabilizers—plus the other moving ‘control surfaces’ (flaps, slats, elevators, ailerons, etc) to create lift.
Sailboats are ‘green’ in that they don’t need to burn fuel to create a ‘wind’ over and under their wings. Instead, they use the actual (true) wind rushing by their sails to generates ‘lift’ and then, once moving, they can take advantage of the extra, relative (apparent) wind to sustain lift even further.
2) Planes operate with their wings, etc in air. Sailboats operate in air and water. Water and air are both ‘fluids’ to scientists and engineers. Sailboats sail at sea level and here, water is 784 times denser than air — also unlike air, water is incompressible. For airplanes flying in air alone, the air molecules resist its forward motion and this is called aerodynamic drag. For sailboats moving through light air and much, much heavier water, the air molecules create aerodynamic drag and the water molecules hydrodynamic drag.
So how can a sailboat sail upwind without fuel and in two different fluids?
A good way of visualizing this is to imagine an airplane flying straight and level but at 90 degrees to the horizon. Normally,’ the thrust of the plane’s jet or propeller creates a rush of air that flows over and under both its wings generating desirable ‘lift’ which it uses to take-off and ascend.
So with our plane now flying at a right-angle to the horizon, the force of ‘lift’ would tend to make the plane move sideways, toward the normally upper surface of its wings.
Now, suppose our plane at 90 degrees dips into the sea (its a special plane!) so that one wing is completely under water and the other completely out — with the body of the plane, its fuselage half-in and half-out like the hull of a sailboat.
Because the denser water creates much more resistance (drag) than air, it will cause our special plane to slow down quite a bit! And our propeller or jet engine designed for air won’t work in water. So with that out of commission, we may as well turn off the one remaining in the air as the asymmetrical thrust from it against the other wing immersed in the dense water would make the plane ‘cartwheel’!
So, with no thrust to make us go forward, we’ll have to change our ‘frame of reference’ — instead of thinking about the plane going forward to create airflow, think of the wings being stationary and the airflow over the wing in the air created from the ambient wind and the water over the ‘wing in the water’ created by the water flowing past it once its moving. We won’t go as fast as a plane but we will ‘go’ — and we won’t need fuel to do it.
So now we have our slowed-down plane ‘flying’ at 90 degrees to the water surface with one wing and its horizontal stabilizer vertically down in a dense fluid and another wing and horizontal stabilizer vertically up in another fluid that’s almost 800 times less dense. (The airplane’s rudder will be at sea level and effectively just part of the fuselage as far as this model is concerned.)
Now, recall that most sailboats can’t sail directly into the wind. But they can sail as close as 45 degrees. So that means that if we steer our submarine-plane to an ‘angle of attack’ of 45 degrees to the wind, our wings in the air will have an angle of attack of 45 degrees to the incoming wind/airflow.
- For above the surface wing and horizontal stabilizer think headsail and mainsail of a sailboat.
- For immersed wing and elevator/horizontal stabilizer think keel and rudder of a sailboat.
Aerodynamic engineers and pilots have tested and proved that by changing the plane’s ‘angle of attack’ to the flow of air beyond ten degrees, that ‘lift’ moves toward the leading or forward part of the wing and has a fairly large ‘forward’ component.
So while airplanes just steer to where they want to go, sailboats steer to where they want to go and steer to change their angle of attack to the true wind
The sideways force transmitted from the ‘wings in the air’ is resisted by forces from the partially immersed fuselage and fully immersed ‘wings in the water’ (think the hull, keel, and rudder of a sailboat) and so with these neutralized, the ‘net’ force on the ‘wings in the air’ causes the sailboat to move forward. If you were on the sailboat as it moves forward, you would feel the wind speed ‘apparently’ increasing relative to what it was when the boat was still. This ‘combined’ relative wind is called the ‘apparent’ wind because it’s apparently happening although the ‘true’ wind is really the same as it was before.
Underwater, something else is going on with our ‘wings in the water’ (keel and rudder).
As they resist most (but not all) of the sideways force from the ‘wings in the air’, they experience water flowing over them as the sailboat moves forward. But because the sailboat is actually going forwards and a little sideways at the same time, the dense and incompressible water is striking (‘attacking’) the leading edge of the underwater wings at an ‘angle of attack’ different to the one the wings feel in the air.
Hydrodynamics of a sailboat
Aerodynamics of a sailboat
So, and without burning any outside energy, both the wings in and the wings of the water both help ‘pull’ the sailboat toward the direction of the wind.
Pretty cool, eh?