An old mystery from my days as a sailor resurfaced this week. Does air on one side of the sail somehow know what the air on the other side is doing? Sounds strange, but it happens to be a key part of explaining how boats, birds and airplanes work, and it stumps a whole lot of people who should probably know better – including most pilots.
I was reminded of this by Bob McDonald from CBC’s Quirks and Quarks radio show. He was in town to give a talk on “The Science of Everyday Life”. It was clear that this was going to be a show for kids, but I dragged Charlie along for two reasons. First, I was planning on presenting some of my peacock research at a family science festival on Saturday; I thought it might be useful to see a master of this sort of thing in action. Fandom came into it too – the Quirks show is one of a handful of radio programs that got me through my troglobite period of 8 hour days in the darkroom last summer.
I was pretty sure what we were in for – baking soda and vinegar magic for the edification of the grade school set – but I wasn’t prepared for how quickly McDonald would put me under his spell, too. Sitting there cold and hungry in the dingy auditorium, I had forgotten all about my surroundings by the time McDonald was whirling a mop around and keeping a kid trapped in his chair using only his thumb to demonstrate centre of gravity. And he was just getting started. Although the talk was too long at nearly 2 hours, it was worth the wait to see video of McDonald’s adventures in weightless flight at the end. His imaginative pitch for the space tourism industry was another highlight. I was hooked at his concept for a giant rotating space hotel. If we put a cylindrical swimming pool smack in the middle, the water would stick to the outer walls by centripetal forces. You could literally fly around in the air at the zero-gravity centre and dive down in any direction to the water below.
McDonald mentioned something in his explanation of how to make a better paper airplane that brought up an old problem for me.
How does a sail actually work? Much like the wing of a bird or an airplane, sails are curved to generate lift. As McDonald explained, this is also the reason why early airplane designs didn’t work: they had flat wings. Most sailors learn pretty quickly that curvature can make a big difference when you’re trying to make progress upwind. In fact, once they realize this, young racers easily slide into a trap of devoting way too much attention to the sail shape puzzle. Tuning your sail won’t help when you’re headed right into the doldrums of a big lull – or sailing blindly past the next mark.
The reason curvature matters has to do with Bernoulli’s principle. This is drilled into every kid at sailing school, usually with the help of some funky lines sketched on a chalkboard: when air flow hits a curved surface or foil, it sets up a zone of high pressure on one side and low pressure on the other. According to the theory, air on the windward side of a sail is under higher pressure relative to air on the opposite or leeward side. This creates the driving force, or lift. A wing works similarly – just replace “windward side of a sail” with “lower surface of a wing” and “leeward side” with “upper surface”.
So far so good, but there’s often an extra bit tacked on. Bernoulli’s principle relates pressure to flow velocity: air in a low pressure zone can accelerate. The explanation why can get murky. Most sailors will say that the molecules on the convex (leeward/upper) side of the foil (sail/wing) speed up because they have a greater distance to travel around the outside of the curve. They have to move faster than the ones on the inside of the curve in order to come out at the other end at the same time.
This is also known as the “equal transit time theory“, and it’s passed on at sailing school chalkboards everywhere – that’s where I first learned it. McDonald is an avid sailor, so it makes sense that he would mention it when explaining the science of airplane wings. According to David Ison in Plane and Pilot magazine, the equal transit time story is widespread in aviation classrooms, too1. But do molecules on one side of a sail really know what the ones on the other side are doing, keeping in sync by some kind of quantum air flow action-at-a-distance phenomenon?
I started looking into it. It turns out that there are actually a number of hotly debated issues in aviation physics, including a longstanding controversy over whose theories best explain the force of lift, Bernoulli’s or Isaac Newton’s. Those in the Bernoulli camp argue that it all has to do with air pressure. Newtonians maintain that Isaac Newton’s third law of motion (every action has an equal and opposite reaction) best explains aerodynamic force. In the Newtonian scenario, the curved foil induces a change in the velocity of the air flow by deflecting it off of its original path; the reaction force to this change is what generates lift.
So which is it, Bernoulli, Newton, equal transit time, or some combination of the above? Unfortunately for sailing school instructors everywhere, quantum air flow is definitely more myth than reality. In fact, we know that air moving over the upper surface of an airplane wing moves much, much faster than the equal transit time theory would predict: measurements show that it beats the air on the bottom to the trailing edge by a wide margin1.
According NASA, both Bernoulli’s and Newton’s theories can be used to explain the forces generated by a curved wing or sail. In Bernoulli’s theory, the net force on a foil can be found by adding up the pressure differences over the entire object; lift is simply the component of the net force that runs perpendicular to the direction of the original flow (or wind), whereas drag is the component parallel to it. You can get the exact same result with Newton’s theory by simply adding up the changes in velocity rather than pressure. Here’s another way of thinking of this: Bernoulli’s theory frames the problem in terms of the conservation of energy, whereas Newton’s law expresses it in terms of conservation of momentum; the two are mathematically equivalent.
Birds, sailors and pilots – most of them don’t really understand the science behind their craft. Should we be worried? Perhaps, but as David Ison points out, “arguing with a pilot is like wrestling a pig in mud – after a while you begin to think they like it”. Sounds a lot like the sailors I have known. And besides, as birds so beautifully demonstrate, you don’t need to understand why in order to be able to do it.
References
From May 9, 2011