# Mathematical Proof The Eagle In The USPS Logo Is FAST!

The logo for the United States Postal Service is a mean-looking eagle. But a true fluid dynamics geek might look at it and realize that eagle is moving so fast it’s causing a shock wave. But just how fast is it moving? [Andrew Higgins] asked and answered this question, posting his analysis of the logo’s supersonic travel. He claims it’s Mach 4.9, but, how do we know? Science!

It turns out if something is going fast enough, you can tell just how fast with a simple picture! We’ve all seen pictures of jets breaking the sound barrier, this gives us information about the jet’s speed.

## How does it work?

Think about it like this: sound moves at roughly 330 m/s on Earth at sea level. If an object moves through air at that velocity, the air disturbances are transmitted as sound waves. If it’s moving faster than sound, those waves get distributed downstream, behind the moving object. The distance of these waves behind the moving object is dependent on the object’s speed.

This creates a line of these interactions known as a “Mach line.” Find the angle difference of the Mach line and the direction of travel and you have the “Mach angle” (denoted by α or µ).

There is a simple formula for determining the speed of an object using the Mach angle, the speed of sound (a), and an object’s velocity (v): sin(µ) = a / v.  The ratio of to a is known as the Mach number, (M). If an object is going exactly the speed of sound, it’s going Mach 1 (because v = a).

Since Mach number (M) is v / a, we can plug it into the formula from above as 1 / M and use [Andrew]’s calculation shown in the image at the top of the article for a Mach angle (µ) of ~11.7°:

$\bf \sin ( \mu ) = \frac{1}{M} \\ \\ M = \frac{1}{\sin(\mu)} \\ \\ M = \frac{1}{\sin(11.7)} \\ \\ M = \frac{1}{0.202787295357} \\ \\ M = 4.9312753949380048$

The real question is, did the USPS chose Mach 4.93 as a hint to some secret government postal project? Or, was it simply a 1993 logo designer’s attempt to “capture the ethos of a modern era which continues today”?

# Burning Propane Beautifully Illustrates How A Tesla Valve Works

When you hear the name “Tesla”, chances are good that thoughts turn instantly to the company that’s trying to reinvent the motor vehicle and every industry that makes it possible. While we applaud the effort, it’s a shame that they chose to appropriate the surname of a Serbian polymath as their corporate brand, because old [Nikola] did so many interesting things in his time, and deserves to be remembered in his own right.

Take the Tesla valve. In essence a diode for fluids, the Tesla valve uses a tortuous path to allow flow in one direction but severely restrict it in the other. Understanding how it works isn’t necessarily intuitive, though, which is why [NightHawkInLight] chose to demonstrate the Tesla valve principle with exploding propane. It’s not new territory to him; we’ve covered his propane-powered rifle in the past.

The swirling blue and green flame front in those experiments make burning propane the perfect working fluid to demonstrate how the Tesla valve works. The video below tells the tale, with high-speed footage showing the turbulence that restricts the reverse flow. The surprise discovery is that in the forward direction, the burning gas actually seems to accelerate as it moves down the valve; hypersonic Tesla plasma cannon, anyone?

We’ve seen Tesla valves before, including one made from a “Shrinky Dink”. That did a pretty good job of visualizing the flow patterns that make the valve work, but there’s a huge showmanship gap between tiny channels filled with colored water and the explosive decomposition of a fuel-air mix. It’s a bit riskier, and standard “don’t try this at home” disclaimers apply, but luckily [NightHawkInLight] still has his eyebrows, so he must be doing something right.

# When Vortex Rings Collide

Intrigued by a grainy video from 1992, [Destin] from Smarter Every Day decided to jump in and fund his own research into the strange phenomenon of vortex ring collisions.

This hack started with a scientific publication and a video from back in 1992. The paper, written by Dr. T T Lim and TB Nichols, illustrated what happens when two vortex rings collide perfectly head-on. The rings collide and spread out forming a thin membrane. Then smaller rings form at a 90-degree angle to the original collision. It’s a beautiful effect when created with multicolored dye in water. But what causes it? There are theories about the fluid mechanics involved, but not much research has gone on since Dr. Lim’s paper.

[Destin] wanted to find out more about the effect, and get some video of it. Being the guy behind Smarter Every Day, he had the high-speed photography equipment and the funds to make that happen. Little did he know that this passion project would take four years to complete.

The initial prototype was built as part of a senior design project by a group of college students. While they did show the phenomenon, it was only barely visible, and not easily repeatable. [Destin] then got an engineer to design and build the experiment apparatus with him. It took numerous prototypes and changes, and years of development.

The final “vortex cannons” are driven by a computer controlled pneumatic cylinder which ensures both cannons get a perfect pulse of air. The air pushes a membrane which moves the dye and water out through an orifice. It’s a very finicky process, but when everything goes right, the result is a perfect collision. Just as in Dr. Lim’s video, the vortexes crash into each other, then form a ring on smaller vortexes.

Destin didn’t stop there. He’s made his data public, in the form of high-speed video – nearly 12 hours worth when played at normal speed. The hope is that researchers and engineers will now have enough information to better understand this phenomenon.

You can check out the videos after the break. If you’re a Smarter Every Day fan, we’ve covered [Destin’s] work in the past, including his backwards brain bike and his work with magnets.

# Fluid Simulations In The Kitchen Sink

In an age of ultra-powerful GPUs and cheap processors, computational techniques which were once only available to those with a government-sized R&D budgets are now available to the everyday hacker. An example of industry buzzword turned desktop software is the field of “computational fluid dynamics”, which put simply allow modeling how gasses or liquids will behave when moving through a cavity under specific conditions. Extensive utilization of these fluid simulations are often cited as one of breakthrough techniques which allowed SpaceX to develop their engine technology so rapidly when compared to Apollo and Shuttle era methods.

But just because anyone with a decent computer has access to the technology used for developing rocket engines doesn’t mean they have to use it. What if you prefer to do things the old-fashioned way? Or what if, let’s me honest, you just can’t figure out how to use software like Autodesk CFD and OpenFOAM? That’s exactly where [Desi Quintans] found himself when developing GUST, his cooling duct for i3-type 3D printers.

[Desi] tried to get the big name fluid simulation projects working with his prototype designs for an improved cooling duct, but had no end of trouble. Either the learning curve was too steep, or the simulation wasn’t accurate enough to give him any useful data. But remembering that air is itself a fluid, [Desi] took his simulation from the computer to the sink in order to better visualize what his cooling duct was doing to the airflow.

[Desi] printed up a box with a hole in the bottom that would connect up to his nozzles under test. As the volume of water in the box would be a constant between tests, he reasoned that this would allow him to evaluate the different nozzles at the same pressure. Sure enough, he found that the original nozzle design he was using caused chaotic water flow, which backed up what he was seeing in his experiments when mounted onto the printer.

After several iterations he was able to tame the flow of water by using internal baffles and fins, which when tested in water created something of a laminar flow effect. When he tried this version on the printer, he saw a clear improvement in part cooling, verifying that the behavior of the air and water was close enough for his purposes.

We’ve seen other projects that successfully used fluid simulations in their design before, but the quick and dirty test procedure [Desi] came up with certainly has its charms.

# Compressed Air Levitation And The Coanda Effect

What do you want to levitate today? [Latheman666] uses his air compressor to make all kinds of stuff float in mid air. Light bulb, key chain, test tube, ball bearing, tomato… pretty neat trick to try in your shop.

It is interesting to see what physics explain this behavior. The objects do not float just because they are pushed upwards by the airflow, that would be an unstable equilibrium situation. Instead, they obtain lift in a very similar way as the wings of an airplane. Not all objects will levitate using this trick: the object has to be semi-spherical at the top.

[Applied Science] nicely shows this behavior by levitating a screwdriver first, then an identical object but with a flat top. The flat top screwdriver fails to levitate. The curvature provides the path for a smooth airflow, because of the Coanda effect, creating a zone of low pressure at the top, making the situation analogous to that of an airplane wing. Therefore, for this to work, you need an object with some kind of airfoil shaped surface. Another great demonstration is that of [NightHawkInLight], using a high speed camera.

A very impressive experiment that needs nothing more than an air compressor!, we are sure you will try it next time you work with one. For more on this topic of levitation with air streams, check the ping pong ball levitation machine.

# Peculiar Fluid Dynamics Creates Hot And Cold Air

We’re fascinated by things with no moving parts or active components that work simply by virtue of the shape they contain — think waveguides and resonators for microwave radiation. A similarly mystical device from the pneumatics world is the Hilsch Vortex Tube, and [This Old Tony] decided to explore its mysteries by whipping up a DIY version in his shop.

Invented in the 1930s, vortex tubes are really just hollow tubes with an offset swirl chamber. Incoming compressed air accelerates in the swirl chamber and heads up the periphery of the long end of the tube, gaining energy until it hits a conical nozzle. Some of the outer vortex escapes as hot air, while the rest reflects off the nozzle and heads back down the pipe as a second vortex inside the outer one. The inner vortex loses energy and escapes from the short end as a blast of cold air – down to -50°C in some cases. [Tony]’s build doesn’t quite approach that performance, but he does manage to prove the principle while getting a few good-natured jabs into fellow vloggers [AvE] and [Abom79].

We’ve covered vortex tubes before, but as usual [Tony]’s build shines because he machines everything himself, and because he tries to understand what’s making it work. The FLIR images and the great video quality are a bonus, too.