Science fiction is not always known for hewing to scientific fact, so it will probably come as little surprise that Star Wars’ ships have terrible aerodynamics. But it’s nevertheless fun to see EC Henry’s analysis of drag coefficients of various Rebel and Imperial ships and just how poorly they fare against our own designs.
Drag coefficients really only give a tiny piece of the story, though. We don’t know what speed Henry is testing the ships at, and we get no information about properties like lift or lift-to-drag ratio, which can be even more important than just the drag when it comes to evaluating an aircraft.
There are some intriguing hints about other aerodynamic properties in the clips of flow around an X-wing and TIE fighter, though. Notice that the wake of both ships meanders back and forth. This is an indication of vortex shedding, and it means that both spacecraft would tend to be buffeted from side-to-side when flying in an atmosphere. Either the ships would need some kind of active control to counter those forces, or pilots would need iron constitutions to operate under those conditions! (Video and image credit: EC Henry)
Satellite imagery often reveals patterns we might struggle to see from the ground. Here Gaudalupe Island off the western coast of Mexico perturbs the atmosphere into a series of vortices. Air flowing across the open ocean gets deflected around and over the rocky, volcanic island, creating a line of vortices that get shed off one side of the island, then the other. The pattern is commonly referred to as a von Karman vortex street, and it appears in the wakes of spheres and cylinders, as well as islands. The two rainbow-like bands framing the vortex street are an optical phenomenon known as a glory, which NASA Earth Observatory explains here. (Image credit: NASA Earth Observatory)
Hold a buoyant sphere like a ping pong ball underwater and let it go, and you’ll find that the ball pops up out of the water. Intuitively, you would think that letting the ball go from a lower depth would make it pop up higher – after all, it has a greater distance to accelerate over, right? But it turns out that the highest jumps comes from balls that rise the shortest distance. When released at greater depths, the buoyant sphere follows a path that swerves from side to side. This oscillating path is the result of vortices being shed off the ball, first on one side and then the other. (Image and research credit: T. Truscott et al.)
Sitting at a traffic stop on a windy day, you may have noticed the beam holding the traffic lights shaking steadily up and down. This phenomenon is called vortex-induced vibration. When the wind flows over the beam, it looks something like the flow animation shown above. Airflow follows the shape of the beam until near the backside, where the air separates from the surface and creates a vortex that sloughs off into the beam’s wake. These vortices form asymmetrically on the beam – first on one side, then the other. This creates unequal pressures on either side of the beam, and those pressure differences create a force that moves the beam. Because vortices are being steadily shed off the beam, it will keep moving back and forth as long as the wind is strong enough. (Image credits: traffic light – L. Sennick, source; cylinder – Aphex82/Wikimedia)
These satellite images show Rupert Bay in northern Quebec. Sediment and tannins have stained the bay’s waters various shades of brown, which helps show the dynamic flows of the area. Rivers empty into the bay, but the tide appears to be coming in from the northwest as well. The flow is just right to create a wake of alternating vortices off a tiny island near the center of the bay. This pattern is known as a von Karman vortex street and often appears in the wake of spheres, cylinders, and, yes, islands. (Image credit: NASA Earth Observatory; submitted by Adam V.)
Today’s post is largely brought to you by the fact that I have been sick the past four days and my fiance and I have been bingeing on Star Trek Voyager. At some point, we began wondering about the sequence from 0:30-0:49 in which Voyager flies through a nebula and leaves a wake of von Karman vortices. Would a starship really leave that kind of wake in a nebula?
My first question was whether the nebula could be treated as a continuous fluid instead of a collection of particles. This is part of the continuum assumption that allows physicists to treat fluid properties like density, temperature, and velocity as well-defined quantities at all points. The continuum assumption is acceptable in flows where the Knudsen number is small. The Knudsen number is the ratio of the mean free path length to a characteristic flow length, in this case, Voyager’s size. The mean free path length is the average distance a particle travels before colliding with another particle. Nebulae are much less dense than our atmosphere, so the mean free path length is larger (~ 2 cm by my calculation) but still much smaller than Voyager’s length of 344 m. So it is reasonable to treat the nebula as a fluid.
As long as the nebula is acting like a fluid, it’s not unreasonable to see alternating vortices shed from Voyager. But are the vortices we see realistic relative to Voyager’s size and speed? Physicists use the dimensionless Strouhal number to describe oscillatory flows and vortex shedding. It’s a ratio of the vortex shedding frequency times the characteristic length to the flow’s velocity. We already know Voyager’s size, so we just need an estimate of its velocity and the number of vortices shed per second. I visually estimated these as 500 m/s and 2.5 vortices/second, respectively. That gives a Strouhal number of 0.28, very close to the value of 0.2 typically measured in the wake of a cylinder, the classical case for a von Karman vortex street.
So far Voyager’s wake is looking quite reasonable indeed. But what about its speed relative to the nebula’s speed of sound? If Voyager is moving faster than the local speed of sound, we might still see vortex shedding in the wake, but there would also be a bow shock off the ship’s leading edge. To answer this question, we need to know Voyager’s Mach number, its speed relative to the local speed of sound. After some digging through papers on nebulae, I found an equation to estimate speed of sound in a nebula (Eq 9 of Jin and Sui 2010) using the specific gas constant and temperature. Because nebulae are primarily composed of hydrogen, I approximated the nebula’s gas constant with hydrogen’s value and chose a representative temperature of 500 K (also based on Jin and Sui 2010). This gave a local speed of sound of 940 m/s, and set Voyager’s Mach number at 0.53, inside the subsonic range and well away from any shock wave formation.
Of course, these are all rough estimates and back-of-the-envelope fluid dynamics calculations, but my end conclusion is that Voyager’s vortex shedding wake through the nebula is realistic after all! (Video credit: Paramount; topic also requested by heuste11)
Happy 50th anniversary, Star Trek! Some of my earliest memories of TV are of watching TNG with my parents. Star Trek taught me that curiosity and scientific inquiry were vital and valuable, and that anyone could grow up to be a scientist, engineer, and leader. Thank you for such an inspiring and hopeful vision for humanity’s future!
And, seriously, those von Karman vortices are awesome.
Soap films can create remarkable flow visualizations when illuminated with monochromatic (single color) light. Each of the photos above shows a flow moving from left to right with a small object near the left creating an obstruction. In the top two images, the objects are cylinders; in the lower one it’s a flat plate tilted at 45 degrees. All of the objects shed vortices as the flow moves past. These vortices alternate in direction – the first spins clockwise, the next counter-clockwise, then clockwise again and so on. This pattern is known as a von Karman vortex street and can even show up in the atmosphere! (Image credit: D. Araya et al.)
Heard Island, a remote patch of rock in the southwestern Indian Ocean, peeks its head above the marine cloud layer. The volcanic island disrupts the atmosphere enough to generate a von Karman vortex street, a line of alternating vortices shedding from either side of the island. Usually these vortices would march in a straight line downstream from their source. But here strong winds from the south have blown a bunch of its vortices northward, creating an unusual kink in the island’s wake. (Image credit: J. Schmaltz/LANCE EOSDIS Rapid Response; via NASA Earth Observatory)
The wake of a cylinder is a series of alternating vortices shed as the flow moves past. This distinctive pattern is known as a von Karman vortex street. The speed of the flow and the size of the cylinder determine how often vortices are shed. Incredibly, this pattern appears at scales ranging from the laboratory demo all the way to the wakes of islands. Von Karman vortex streets can even be seen from space. (Image credit: R. Gontijo and W. Cerqueira, source video)
Von Karman vortex streets are a pattern of alternating vortices shed in the wake of a bluff body. They’re commonly associated with cylinders and can be demonstrated in simulation and in the lab. (They even show up in supersonic flows.) But they also show up in nature quite frequently, like in this cloud pattern off Central America. Such wakes often occur downstream of rocky, volcanic islands that rise above the smooth ocean surface and disrupt the atmosphere’s boundary layer. The same phenomenon is responsible for the “singing” of electrical lines on a windy day, and I’ve even heard it make the spokes on my bicycle wheel sing in a crosswind. (Photo credit: R. Mastracchio; via @BadAstronomer; submitted by jshoer)
