The Story of the Truck Canaries (also, a Drone in a Box)
I read a story online by Laura Vinersha (great-great granddaughter of Isaac Newton*). The story goes like this:
A friend of mine was driving along a narrow road up a steep mountain. Part way up he caught up to a slow-moving truck. The truck slowed down more and more as he followed, eventually just barely moving. Suddenly the truck stopped, the driver got out and banged with his fists on the side of the cargo trailer. Then he got back in the truck and resumed driving up the hill.
When the truck began moving up the hill it moved faster than before but then gradually slowed until once again it was barely moving. The driver stopped, got out, banged on the side, and began driving once more, only to have the same result as before.
When the truck slowed and stopped for the third time my friend jumped out of my car and asked, "Why do you keep banging on the side of your truck?" The driver replied, "I'm carrying a load of canaries. They are too heavy, so I can only drive very slowly up the hill. But if I bang on the side, the birds start to fly around the inside of the truck. This makes the truck lighter and I can drive faster. But as the birds land the truck gets heavier and slows down. That's why have to stop. I need the birds to keep flying around the inside of the truck or I will never get this truck up to the top of this road."
After a few moments I playfully slugged my friend on the arm. "Great story! My great great grandfather would have loved it."
In the Pivot Interactives lab, we’ve been working to recreate this scenario, not with birds and a truck, but with a small battery-powered drone in a sealed box. While we were able to reproduce the expected result, we stumbled upon a similar scenario with a surprising result. Could be that flying birds inside a truck could make the truck heavier, and conceivably more massive, than when the birds sit at the bottom?
Here’s our process. We purchased a Tello drone, and began by experimenting with flying the drone in an enclosed box. Not surprisingly, the drone was not stable in the turbulence created by the four rotors, and we had many crashes where the drone thrashed around inside the box like it was in a blender. After destroying one drone, we’d determined the minimum box dimensions to allow stable flight, and began building the box. We constructed the box of 1.5” thick foam walls, but with a transparent acrylic floor and front wall. We also purchased a scale with 22kg capacity, and ± 1 gram precision. We practiced taking off and landing the drone inside the box, which is not easy. The piloting skills of Bryson, an expert gamer, saved the day (but not the life of our first drone).
Moving to video, we started by placing the drone on the scale, flying upwards, hovering, and landing. The results were not surprising. As the drone moved around, the rotor wash (the stream of air ejected from the underside of the rotors) sometimes applied a force on the scale, and other times it did not. So the scale reading fluctuated between zero, up to a value less than the weight of the drone. (Note: by weight I mean the force exerted on the scale, converted into grams.)
Next, we sealed the box with the drone inside, placed the box on a scale, and used the tare function on the scale so the scale showed the weight of the drone only. For those of you thinking about reproducing this, consider that the scale needs to be zero-ed before the drone is placed in the box. Then box needs to be sealed airtight after the drone is placed inside. The drone needs to be turned on before the box is sealed, but has auto-shutoff, a short-lived battery, and a finicky wifi connection. If anything goes wrong, the process needs to be repeated. We found a way to circumvent the auto-takeoff function (which causes the drone to crash into the ceiling). Also, we needed to make sure the drone landed back on the same spot on the floor of the box. Flying the drone inside the box, where the rotor wash creates violent turbulence, required lightning-fast reflexes and coordination. The physics teacher on hand possessed either of those traits, so all flights were piloted by Bryson.
But for all the effort, the results were just what we expected: the scale reading fluctuates somewhat as the drone moves around inside the box, but the average scale reading appears to be very close to the value when the drone is not flying.
During the process, though, we tried a variation that surprised us. We placed the floor of the box on the scale, zeroed the scale and placed the drone on top. When the drone hovered above the floor, we were initially surprised. The scale reading was significantly higher when the drone was hovering above the floor compared to when it was sitting at rest on the floor.
Why? Here’s a hypothesis. When the drone hovers above the platform, the rotor wash rebounds off the platform, so it applies a force to the bottom that is greater than the force supporting the drone. This is similar to the effect of water rebounding from the curved-bladed Pelton water turbine shown at right. The curved blades of a Pelton water turbine cause the incoming water to deflect so the water leaves blade moving in the opposite direction. Compared to water that does not rebound, this change in direction causes a greater change in velocity and therefore it imparts a greater force. This concept makes frequent appearances on the AP Physics 1 exam, either in the form of Newton’s second law F=dP/dt, or as the impulse-momentum theorem: F∆t =m∆v.
When the drone hovers in a sealed the box, the rotor wash still rebounds from the floor, but the rebounds again from the ceiling of the box. The total average force of he rotor wash on the box is equal to the weight of the drone.
This is an example of a problem where it is difficult to predict the outcome without evidence. Its certainly possible that all the rotor wash would exit the edges of the platform horizontally, and that none of the air would rebound from the surface. In that case, the scale reading would be equal to the weight of the drone. Alternatively, its possible that some of the rotor wash would miss the platform and hit the table supporting the scale. That would result in a scale reading less than the weight of the drone. Without seeing that the scale reading increases, we’d have a hard time knowing that some of the rotor wash rebounds.
Could the truck in the story appear heavier when the birds fly? That is, would a scale placed under the truck show a higher reading if the birds were flying? Also, would the truck be more massive? That is, would the truck contain more matter if the birds were flying? In the case of a sealed truck, the answer to both questions is clearly no. But what if the roof of the truck was made of screen? Here are two reasons to consider that it in this case, the truck could be heavier, and also more massive when the birds fly. First, imagine the birds flying near this screen roof. As their wings draw air from outside the truck and force it downward between the bird and the floor of the truck, the air pressure in the space between the birds and the floor is greater than atmospheric pressure. Meanwhile the pressure above the birds is equal to atmospheric pressure. This means the truck could contain more air when the birds fly then when they don’t. This combined with the effect of the air rebound from the floor could cause the truck to be heavier, and more massive when the birds fly.
After recording these videos, we created an activity in Pivot Interactives with guided student instructions that allow them to retrace our steps and observe these events for themselves. There are over 200 activities like this in Pivot Interactives, spanning physics, chemistry, earth and climate science, and biology. Each activity allows students to explore and analyze real events using interactive video. Find out more at our website: www.pivotinteractives.com
*There are many versions of this story. The version adapted here is from the NPR radio program Car Talk. But my own grandfather, a physicist, loved this story as well, long before I heard it on Car Talk. I do not know the origin of this story. Also, Laura Vinersha is not the great-great granddaughter of Sir Isaac Newton. Credit for the clever pun goes to Car Talk, where Laura Vinersha was listed as a staff scientists, along with statistician Marge Inovera. Try saying her name out loud a few times.
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