Pouring water in an airplane during a barrel roll
Jearl Walker www.flyingcircusofphysics.com
March 2015 First I will tease you with this image that has been widely circulated. A pilot in a military jet pours water from a bottle into a cup while the jet is upside down --- the water stream is downward in the image, away from the ground that appears at the top of the image, but that means the water flows against gravity.
Has gravity been somehow reversed? That is impossible, of course. One key to explaining the image is that the airplane is not continuing to fly upside down but instead is in a barrel roll (the airplane is rotated 360 degrees around its long axis while continuing to fly forward). That rotation might prompt you to say something like this, “The rotation is slinging the water away from the ground.” Or this, “A centrifugal force is pushing (or pulling) the water away from the ground.” I don’t think so, but I will first examine another airplane stunt that seems to be related but which is actually different. Then I will come back to this perplexing image.
Cup of tea upside down.
Here is a video of an airplane doing a barrel roll while a cup of tea is placed upright on a platform (just over the control console --- disquieting!). The tea stays nicely in the cup even when the airplane is upside down.
What keeps the tea in the cup? Or rather, why doesn’t the tea pour out when the cup goes through the upside down orientation? Those are actually two different questions, depending on whether we take the perspective from inside the airplane or from the ground.
Let’s begin to answer the second question with a common classroom demonstration. A bucket of water is rotated rapidly in a vertical plane and yet the water does not pour out of the bucket when the bucket passes through the upside down orientation. The important word in that description is “rapidly”. If the speed is too slow (or the angular speed of the rotation is too slow), the water will pour out.
Let my dot in this next drawing represent the water at the top of the vertical circle and for moment let the cup magically disappear.
As the water goes through this position at the top of the circle, it is about to be launched horizontally into projectile motion, much like you can throw a ball horizontally. The shape of its path depends on the launch speed. If the speed is slow, the water will take the more curved path. A faster speed gives a flatter path.
Now put the cup back in place. That cup is following the circular path drawn with the wide line.
Notice that the slower launch allows the water to fall away from the cup as the cup rotates along its circular path from the top. However, with the faster launch, the water runs into the cup and is force to move along the circular path. So, if the young man in the video rotates the bucket of water fast enough, the water is trapped in the bucket, but if he moves it too slowly, he will be drenched.
Some people prefer to describe the physics as seen in the rotating system, as if we could ride along with the bucket. Because the system is continuously being accelerated (to keep it in circular motion), we say that the system is non-inertial, which is a fancy way of saying that Newton’s laws of motion may not work. In this case, they do not work because an upward force seems to counter the downward gravitational force.
That upper (centrifugal) force is not real but only a convenient way of explaining why gravity does not pull the water downward and out of the bucket.
In the airplane video, we are effectively in the rotating airplane with the camera and thus are in a non-inertial system. So, a non-real force seems to keep the tea in the cup even when the cup is inverted. However, if we could see this stunt from the ground view, as we did in the water bucket video, we have no need of the non-real force and could simply say that the water is just not allowed to go into projectile motion.
Now let’s go back to the first image where water is being poured from a bottle to a collection cup. The physics here is very different because the water does go into projectile motion as it moves from the bottle to the cup. Another key point is that the portions of the water stream we see in the image did not leave the bottle at the same instant. Instead, the portion that is about to enter the cup left the bottle earliest and when the bottle was lower in its circular motion in the barrel roll.
Let’s consider the common launching of a ball and the resulting projectile motion. In my drawing here, three balls are thrown with the same launch speed but at different launch angles. The one with the largest launch angle travels the highest and along a path with the most curvature. The ball with the smallest launch angle does not travel as high and its path is flatter.
To apply those general results to the poured water stream in the jet plane image, let’s first divide the stream into five portions. Here is how they would look from a ground perspective. The bottle mouth is moving counterclockwise along the heavy circular path. Portion 1, which is about to enter the collection cup, was released when the bottle mouth was low on the side of the circular path. Portion 2, somewhat farther from the cup, was released when the bottle mouth was somewhat higher on the circular path. Portion 5 is near the bottle mouth, which is highest on the circular path.
Each portion was launched with the same speed but with different launch angles. The launch angle of portion 1 was greatest, so portion 1 will move highest (just as with the launched balls) to reach its position in the image. A short time later portion 2 was launched but the bottle had move along its circular path by then. The launch speed was the same but the launch angle was less. So portion 2 moves along a flatter path to reach its position in the image. And so. Portion 5 was launched with a small angle and has move only a short distance to reach its position in the image.
Because the image is a photograph and not a video, we don’t see any of this motion. Rather we see only the locations of the portions at the instant the photograph was taken. Visually connecting the portions at that instant we see a curved water stream. From the perspective of the camera in the jet, here is the arrangement.
The water resembles what we would see with a stream from a garden hose, and we are misled into thinking that there must be some mysterious force directing the stream away from the ground.
http://www.military.com/video/aircraft/gliders-and-parachutes/pouring-water-upside-down-in-glider/2647406994001/ very irritating music
https://www.youtube.com/watch?v=WOlEOiQvCNU Walter Lewin at MIT, go to last few minutes of this hour-long lecture
Are you looking for the stories from last four months? They are in the archives:
Loop-the-loop with cars, bikes, skateboards, and simply running, 1.270
Pub trick --- spoon into mug, 1.271
Transparent when wet, 6.86
Lethal upward streamers in an electric storm, 5.1
Floaters in your eye, 7.5
Pub trick --- musical wineglass, 3.43
Standing and walking in a strong wind, 1.227
Pub trick --- beer bottle tapping prank, 2.76
Bull riding, 1.92
Mianus Bridge collapse, 1.71
Sliding stick across outstretched fingers, 1.172
Café wall illusion, 7.58
Tire explosions, 4.114
Pub trick --- using thermal stress to open a wine bottle, 4.113
Giant Leg towers, 1.272