7 ms·

I feel a bit silly here... but why do you keep your airspeed when you turn 180° after entering the faster-moving air? The article says "due to momentum" but tha

I feel a bit silly here... but why do you keep your airspeed when you turn 180° after entering the faster-moving air? The article says "due to momentum" but that doesn't really make sense to me. It says "the tailwind has now accelerated the glider", but if it was all down to tailwind you would only be able to reach the groundspeed of the wind, after that there can be no tailwind right?

hedgehog 3y ago
This is probably not exactly right but here's a way to think about it. Look at the diagram on the Wikipedia page. Set aside parasitic drag for a moment, and imagine the loop as four segments (up, downwind, down, upwind). Imagine the glider is headed straight up in the upward segment at speed X (air and ground for the sake of the example0, and the wind is moving at speed W. The wind pushes the glider's ground speed from 0 to W, adding momentum. Now the glider pulls into the downwind segment, translating the upward airspeed X into downwind air speed X and downwind ground speed X+W. As the glider pulls into the downward segment and into the lower region of still air the momentum translates into airspeed X+W, then it completes the loop and repeats. It's sort of like how if you push someone on a swing a little bit each oscillation you can keep adding energy even though your pushes aren't particularly fast or energetic.
mannykannot 3y ago
It's not a silly question (apparently, more than just a few pilots don't understand this), and the phrase "the tailwind has accelerated the glider" is incorrect. What actually happens in any of the turns is that the glider undergoes a change of velocity equal to twice its original airspeed, in the direction opposite to which it was originally flying. This is simply a consequence of it flying an energy-conserving path (we are ignoring drag and also assuming the turn is made in level flight, so there's no change of potential energy.) When measured in a frame of reference moving with the wind, with W as the wind speed and A as the air speed, a glider flying upwind has a velocity of -A, and after turning 180 degrees has a velocity of +A. The magnitude of both velocities is the same. From the ground frame of reference, it has gone from W-A to W+A, so the magnitude has increased, from the difference to the sum. In both cases, the change in velocity is +2A, regardless of how strong the wind speed is or whether there is any wind. The appearance of there being an acceleration when the wind is blowing but not when it is still results from considering the change of ground speeds before and after, instead of change in velocities (measured in any inertial frame of reference, as long as it is the same one before and after.) It is not easy to see intuitively how this allows the kinetic energy of the glider to keep on increasing, but perhaps this will help: the 180 degree turns are like elastic collisions (i.e. without energy loss) between the glider and the air. From this perspective, we can make an analogy with a bat and an elastic ball: if you bounce the ball between the bat and the floor, striking it downwards each time it bounces back, it will keep on picking up speed: it rebounds from each blow you give it faster than it was coming up, and it keeps that newly-acquired speed when it bounces back off the floor. In this analogy, the bat stands for the wind at altitude, and the floor stands for the still air below.
- bjackman 3y ago
  > When measured in a frame of reference moving with the wind, with W as the wind speed and A as the air speed, a glider flying upwind has a velocity of -A, and after turning 180 degrees has a velocity of +A. The magnitude of both velocities is the same. This seems to be begging the question. Why does it get a velocity of +A? It seems obvious if you assume the inertial frame of reference of the wind, but from the ground it's very surprising. Why is the frame of reference of the wind the "right one"? Perhaps a better way to ask is: when the second turn happens, why don't we go back to -A? It seems the "correct frame of reference" is now the still air? But why? It's easy for me to intuitively understand that there's a source of energy at this windspeed gradient but it's hard for me to understand that this technique can extract it.
  - mannykannot 3y ago
    I don't have time today to write a complete reply, but I hope to do so soon. Meanwhile, here are a couple of partial responses: Why is the frame of reference of the wind the "right one"? There isn't a right one in the sense of being the only one giving the right answer, it's just by far the easiest one to work with, and then you can convert the result to any other inertial frame via the Galilean transformations [1]. In the frame in which the wind speed is zero (and only in that frame) you can calculate the path of the glider while turning by using the well-known solution for uniform circular motion [2], in which the centripetal force is always perpendicular to the direction of motion, and the speed of the moving object is constant. The difference between the solution in that frame and the ground frame is nothing more than the difference between drawing a semicircle on a piece of paper, and going through the same motions on a piece of paper that is moving. It's easy for me to intuitively understand that there's a source of energy at this windspeed gradient but it's hard for me to understand that this technique can extract it. The turning glider exerts a force on the airmass it is turning in (Newton's third law), which is itself accelerated, in a direction that lessens the difference in speed between the two airmasses. Your middle question will take more time to address, and I plan to come back to it tomorrow. [1] https://en.wikipedia.org/wiki/Galilean_transformation https://en.wikipedia.org/wiki/Galilean_transformation [2] https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/04%3A_Motion_in_Two_and_Three_Dimensions/4.05%3A_Uniform_Circular_Motion https://phys.libretexts.org/Bookshelves/University_Physics/B...

hedgehog 3y ago

This is probably not exactly right but here's a way to think about it. Look at the diagram on the Wikipedia page. Set aside parasitic drag for a moment, and imagine the loop as four segments (up, downwind, down, upwind). Imagine the glider is headed straight up in the upward segment at speed X (air and ground for the sake of the example0, and the wind is moving at speed W. The wind pushes the glider's ground speed from 0 to W, adding momentum. Now the glider pulls into the downwind segment, translating the upward airspeed X into downwind air speed X and downwind ground speed X+W. As the glider pulls into the downward segment and into the lower region of still air the momentum translates into airspeed X+W, then it completes the loop and repeats. It's sort of like how if you push someone on a swing a little bit each oscillation you can keep adding energy even though your pushes aren't particularly fast or energetic.

mannykannot 3y ago

It's not a silly question (apparently, more than just a few pilots don't understand this), and the phrase "the tailwind has accelerated the glider" is incorrect. What actually happens in any of the turns is that the glider undergoes a change of velocity equal to twice its original airspeed, in the direction opposite to which it was originally flying. This is simply a consequence of it flying an energy-conserving path (we are ignoring drag and also assuming the turn is made in level flight, so there's no change of potential energy.) When measured in a frame of reference moving with the wind, with W as the wind speed and A as the air speed, a glider flying upwind has a velocity of -A, and after turning 180 degrees has a velocity of +A. The magnitude of both velocities is the same. From the ground frame of reference, it has gone from W-A to W+A, so the magnitude has increased, from the difference to the sum. In both cases, the change in velocity is +2A, regardless of how strong the wind speed is or whether there is any wind. The appearance of there being an acceleration when the wind is blowing but not when it is still results from considering the change of ground speeds before and after, instead of change in velocities (measured in any inertial frame of reference, as long as it is the same one before and after.) It is not easy to see intuitively how this allows the kinetic energy of the glider to keep on increasing, but perhaps this will help: the 180 degree turns are like elastic collisions (i.e. without energy loss) between the glider and the air. From this perspective, we can make an analogy with a bat and an elastic ball: if you bounce the ball between the bat and the floor, striking it downwards each time it bounces back, it will keep on picking up speed: it rebounds from each blow you give it faster than it was coming up, and it keeps that newly-acquired speed when it bounces back off the floor. In this analogy, the bat stands for the wind at altitude, and the floor stands for the still air below.

bjackman 3y ago
> When measured in a frame of reference moving with the wind, with W as the wind speed and A as the air speed, a glider flying upwind has a velocity of -A, and after turning 180 degrees has a velocity of +A. The magnitude of both velocities is the same. This seems to be begging the question. Why does it get a velocity of +A? It seems obvious if you assume the inertial frame of reference of the wind, but from the ground it's very surprising. Why is the frame of reference of the wind the "right one"? Perhaps a better way to ask is: when the second turn happens, why don't we go back to -A? It seems the "correct frame of reference" is now the still air? But why? It's easy for me to intuitively understand that there's a source of energy at this windspeed gradient but it's hard for me to understand that this technique can extract it.
- mannykannot 3y ago
  I don't have time today to write a complete reply, but I hope to do so soon. Meanwhile, here are a couple of partial responses: Why is the frame of reference of the wind the "right one"? There isn't a right one in the sense of being the only one giving the right answer, it's just by far the easiest one to work with, and then you can convert the result to any other inertial frame via the Galilean transformations [1]. In the frame in which the wind speed is zero (and only in that frame) you can calculate the path of the glider while turning by using the well-known solution for uniform circular motion [2], in which the centripetal force is always perpendicular to the direction of motion, and the speed of the moving object is constant. The difference between the solution in that frame and the ground frame is nothing more than the difference between drawing a semicircle on a piece of paper, and going through the same motions on a piece of paper that is moving. It's easy for me to intuitively understand that there's a source of energy at this windspeed gradient but it's hard for me to understand that this technique can extract it. The turning glider exerts a force on the airmass it is turning in (Newton's third law), which is itself accelerated, in a direction that lessens the difference in speed between the two airmasses. Your middle question will take more time to address, and I plan to come back to it tomorrow. [1] https://en.wikipedia.org/wiki/Galilean_transformation https://en.wikipedia.org/wiki/Galilean_transformation [2] https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/04%3A_Motion_in_Two_and_Three_Dimensions/4.05%3A_Uniform_Circular_Motion https://phys.libretexts.org/Bookshelves/University_Physics/B...