The expression about not seeing the forest for the trees comes to mind… we have plenty of expert botanists in this thread (and for many readers, that’s what we need), but I think there are a few people who haven’t even found the forest yet! So this might be helpful to those of you who are having trouble understanding how the plane can be stationary over the ground and not fall out of the sky.
The cast of characters:
Pilot: the guy flying the airplane
Dude: some random guy on the ground, watching the airplane
Arachnicus Physicus Unnilunius*: that friendly little Spider, most commonly found in physics textbooks and who helps us understand what inanimate objects are thinking. Mr. Spider is sitting somewhere on the surface of the airplane’s wings.
For the sake of simplicity, let’s just say the plane is flying at 10 units distance per unit time, or 10 d/t. It will make things easier to explain, IMHO.
Let’s start with the scenario that we can all understand. There is no wind, and the plane is flying at 10 d/t. What do our characters see?
The Pilot sees the Dude on the ground go past at 10 d/t. The Dude on the ground sees the Pilot in the plane go past at 10 d/t. But what about the Spider? He feels wind, not from the environment (not a natural wind) but wind caused by the plane moving through the air. He feels as if there is a strong wind blowing in the opposite direction of the plane’s travel, at a speed of 10 d/t.
Pretty straightforward.
So now let’s add a headwind, but let’s make it one of only 1 d/t. What happens now?
Intuitively, we know that the plane will “slow down”, and it does, from the point of view of the Pilot watching the Dude and from the point of view of the Dude watching the Pilot. As they measure each other’s speeds, they will both come back and say that the plane is going 9 d/t. This is the ground speed; it is the speed at which the airplane will pass over the ground.
But it isn’t that simple. We can’t forget about our friend the Spider, who is still sitting on the wings (he’s very strong!). Recall that what keeps the plane up in the air is the flow of air over the wings; that’s the only thing that matters. So what are the wings experiencing; what will Mr. Spider tell us he feels?
He feels a strong wind blowing in the opposite direction of the plane’s travel, at a speed of 10 d/t.
The wind the Spider feels is caused by two different things; the actual wind, going “backwards” at 1 d/t, and the wind caused by the motion of the plane, which feels like a 9 d/t wind, also going backwards. Add them together and you get 10 d/t, which means that as far as Mr. Spider and the plane are concerned, nothing has changed. He doesn’t know that there’s now a headwind, because it feels exactly the same as when there wasn’t one.
So take it a bit further, to a headwind of 5 d/t, and again, the Dude and the Pilot will look at each other and say the plane is only going 5 d/t, but again the Spider will think that nothing has changed. 5 d/t from the natural wind, and 5 d/t from the airplane moving through the air, and so the airflow over the wings is exactly 10 d/t, just as it was before, and the plane is still flying.
If that headwind were to be exactly 10 d/t, Dude and Pilot will be looking at each other as if they were stationary, and the Spider will still say that the wind is 10 d/t over the wings, and so the plane will stay in the air. And it does, as the pilots in this thread will attest. Naturally, if the headwind were 11 d/t, the Pilot and Dude would think the airplane is going backwards, but there is now 11 d/t worth of lift over the wings, and the airplane will stay in the air (and probably climb as well… I’ll leave that to the botanists…!)
And so we have an airplane going nowhere and yet staying in the air. Isn’t physics fun?
I hope that helps!
*No Spiders were harmed in the making of this post. The Dude’s head might have exploded. We are looking into it.