Airfoil technology helped human beings to fly. Wind turbines, gas turbines and hydraulic machines, all work on the principles of airfoil. In this aricle will unveil the physics behind the simple shape that revolutionized the engineering world.
An airfoil produces a lift force when fluid flows over it, this is illustrated in Fig 1. But what is the source of this lift? Is Bernoulli's principle or Newton's third law responsible for it? or both the effects? Some textbooks point to Bernoulli’s principle, but many people reject this claim.
Skeptics include NASA scientists and Professor Holger Babinsky of the University of Cambridge, who, in his popular YouTube video, proved both experimentally and theoretically that the equal time argument is incorrect. Anyway, we will approach this problem rationally and use computational fluid dynamics and experimentation to support our findings. We will also include an interesting brain teaser at the end of the article.
First, let's see what is the argument that uses Bernoulli's principle. From the shape of the airfoil it is clear that the upper surface is more curved than the lower surface. This means the particles on the upper surface should travel a greater distance than the particles on the lower surface. Since both particles should reach the trailing edge at the same time, the upper surface particles should have more velocity than the lower surface particles. This means that according to Bernoulli's principle, there is more pressure at the bottom and less pressure at the top surface (refer Fig 2). The difference in the pressure generates lift. This argument more specifically is known as the “equal time argument”.
The equal time argument is a beautiful way to explain lift, but it’s completely wrong. The first mistake pertains to how 2 particles starting from the same location reach the trailing edge at the same time. That is a completely absurd argument.There is no law in physics to support it. The 2 particles can leave for a completely different journey and may not meet in their lifetime!
The second mistake is that you cannot apply Bernoulli's equation between 2 streamlines. Bernoulli's equation should be applied strictly along a streamline, this is illustrated in Fig 3.
Even after pointing out these mistakes, if you still support this widespread myth, just take a look at this shape. According to the equal time argument, this surface should also produce a lift force. And this surface, the same argument indicates that this should produce an incredible amount of lift, as shown in Fig 4. Bernoulli's equation is completely right. It is just Newton's second law of motion applied along a fluid streamline (refer Fig 5). Some people applied it incorrectly and caused confusion.
Now, we will investigate the science behind lift generation by applying the laws of physics correctly. The particle approaches the airfoil and takes a curve as shown in Fig 6. But after the curve, why doesn’t it move straight?
Examine this curved motion more closely. In order to take the curve, there should be more pressure at the top of the particle than at the bottom. This will supply the centrifugal force (refer Fig 7a). The higher pressure pushes the particle downwards, which is why the flow is always attached to the airfoil. This effect is known as the “Coanda effect”. There is a simple experiment to demonstrate this fact, shown in Fig 7b.
The flow gets curved at the bottom of the airfoil as well. A curved bottom surface will make the bottom flow also curved to a greater extent, this is illustrated in Fig 8. In short, the introduction of the airfoil makes the flow curved and deflected. And this curved flow is exactly what causes the lift. Far away from the airfoil, the pressure is atmopsheric. We know in a curved flow the outside pressure should be larger. So at the top, the pressure will decrease as we move towards the airfoil (refer Fig 9).
On the other hand, at the bottom, and for the same reason, pressure should increase as we move toward the airfoil (refer Fig 10a). This difference in pressure is what causes the lift (refer Fig 10b).
Basically, the introduction of the airfoil makes the flow curved. This curvature generates the pressure difference and the lift. This means that more curvature translates to more lift. But then, why are airplane airfoils not shaped like this? (refer Fig 11a). The reason is to give structural support and a space for accommodating the fuel tanks (refer Fig 11b).
Is there any fundamental law of physics that justify the lift rather than this fluid mechanics-based explanation? Yes – Newton's third law of motion. You can see that the airfoil deflects the flow as shown in Fig 12, or it pushes the flow downward. So, according to Newton's third law, the air also should push the airfoil in opposite direction with equal magnitude. This results in lift.
In conclusion, the deflection or curvature of the flow caused by the Coanda effect generates the lift. If you find that others still support the equal time argument, ask them to generate lift from this surface (refer Fig 13a). If they are too lazy to do so, we will do it for them. For this simple geometry, 'equal time argument' and 'Newton's third law analysis' predicts direction of the lift in different ways (refer Fig 13b). We have even conducted a high-quality CFD analysis to prove the same thing.
If you understand what we have discussed so far, here's one brain teaser for you, in actual experiments, you can see that the air at the top of the airfoil moves much faster than the air at the bottom and they never meet. Why is that? If you study this pressure gradient more closely, you’ll find the answer in next article.
Thanks for reading.