A factoid is an incorrect piece of information that is repeated so often that it is believed to be a fact. This can be a dangerous thing in Maths and Science, as these can create the basis of further study that is fundamentally flawed. Thankfully, with a little thought, some of these factoids can be proved incorrect with some (relatively) basic Maths.
For my fans, this entry leads on from my previous blog about Personal Statements. For anyone new, you don’t need to go back and read it (although I, at least, thought it was good).
You may remember a brief statement about the workings of a plane wing. More specifically, “how does a plane wing generate lift?” After this I claimed the widely accepted answer to be false, but didn’t explain why. So, read on and feel the suspense no longer. For the purpose of simplicity, we will assume that air is incompressible, which is a good assumption until you reach very high speeds (0.75 Mach).
Firstly, the factoid: “The air flowing over the wing moves faster than the air flowing underneath it. Using Bernoulli’s equation, it can be shown that the airflow over the wing is therefore at a lower pressure which generates lift.”
A lovely and simple explanation that, unfortunately, is wrong. Firstly, “the air flowing over the wing moves faster”. It is claimed that the air particles have further to travel, and must reach the wing tip at the same time as those that travel under the wing.
WHY must they reach the tip at the same time? Well, they don’t. If this were the cause of lift, then sails on boats wouldn’t work as the air on either side have pretty much the same distance to travel. The air particles are separate. They don’t have to reach the same point in space at the same time (there are online videos showing smoke moving over a wing to show this).
Right, so a bit of thought shows the initial statement to be false, but that’s not the full story. Bernoulli’s equation is stated as:
Pressure (unit area) + Kinetic Energy (per unit volume) + Gravitational Potential Energy (per unit volume) = Constant
So (negating the slight change in height for the thickness of a wing), if the velocity increases (kinetic energy) then the pressure must drop. Again, this is misleading as the principle is very rarely quoted correctly. The constant changes for each stream line, therefore the velocities of two adjacent streamlines can be different, and their pressures remain the same.
So, with just a bit of logic and research, we’ve shown that this is not how wings generate lift. As planes aren’t falling out of the sky, we must deduce that they produce lift another way (that or we start believing aeronautical engineers are wizards).
What’s going on then?
This question should always leave to a sketch. What is physically happening when a plane is in flight? Before you continue reading, perhaps you’d like to see if you can work it out yourself.
Okay, so how can we figure out what is going on?
Step 1: What do you see? In this example, the most obvious thing is that the streamlines above the wing are traveling in an arc which is centred beneath the wing.
Step 2: What does this mean? This means those air particles in the streamline are accelerating towards a point below the wing. There must be a force acting on these particles that is causing the acceleration (circular motion).
Step 3: What could be causing this? The only thing in contact with the vast majority of the air particles are more air particles.
Step 4: How could it be causing this? If the force comes from the air particles, then it must be due to a pressure difference. Since the pressure 20 metres above the wing is roughly atmospheric pressure, we must conclude that the pressure on the surface of the wing is less than atmospheric. This would cause these air particles to curve.
Step 5: Does this theory work? If there is a lower pressure on the top of the wing than the bottom, we generate lift. This mechanism doesn’t require the air particles to reach locations at the same point, or tinker engineering principles.
Wings, sails and F1 rear wings work by altering the flow of the air. Introducing these curvatures introduce pressure differences making your jet fly, or your Mercedes stick to the road. You’re welcome Lewis Hamilton.
This entry has focused on a wing, but these methods of questioning should be applied towards your interview. Always think about your assumptions, and if they make sense. If you are unsure, sketch what is physically happening and then ask what is happening, and why is that happening.
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