Day: March 6, 2019

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Track a Tank Shell With a Mirror and Polar Coordinates

https://www.wired.com/story/physics-tank-shell-polar-coordinates

If the internet was your online physics textbook, The Slow Mo Guys would be writing a good number of those homework questions. Of course The Slow Mo Guys are Gavin and Dan and they use a super high speed camera and look at stuff around us. OK—in this case, they aren’t looking at normal things. They are looking at the motion of a high speed shell fired from a tank.

But how do you see this tank shell if it is traveling around 2,000 feet per second (609 m/s)? You could just put the camera far enough away that the path of the projectile would be in the frame. However, in that case you could barely see the fast moving object. It would be too small in the video. OK, what about getting close to the path so that the shell looks larger? Yes, you could see it, but just for a tiny fraction of the total path.

The solution to this problem is to use both methods. Get the camera close to the path and then rotate the view as the projectile passes. The Slow Mo Guys are going to put the camera 82 feet from the path which means it would have to rotate at around 3,000 degrees per second—which is pretty much impossible. But instead of rotating a camera, they will just use a rotating mirror. The camera looks at the mirror and from that it can see the tank shell. Then the camera can stay in place while the mirror rotates. Perfect.

Here is the real question. How do you determine the angular position of a mirror so that it can track the projectile? The answer: polar coordinates. Yes, you thought they were just joking when they made you do stuff with polar coordinates in math class. Surprise. You actually need this sometimes.

Let’s do this. How about a review of two different coordinate systems: cartesian and polar coordinates. Also, how do you use polar coordinates to track a super fast projectile?

Cartesian Coordinates

This is the one you are likely familiar with. In two dimensions, there is an x-axis and a y-axis. They are perpendicular to each other. Once you pick the origin, you can describe the location of an object with an x and y coordinates.

Rhett Allain

There’s really not too much to say about this coordinate system since you’ve probably seen it before. Let me just make some comments. Don’t forget about units. It’s not just x and y numbers, these numbers have to have units to make a connection to the real world.

Now let’s say that the projectile is moving in the negative x-direction with a velocity of 600 m/s. In that case, I can write the following kinematic equations for the position of the projectile.

Rhett Allain

In these expressions, x1 is the starting x-position and x2 is the position after some time Δt. Notice that the y-position doesn’t change since it’s only moving in the x-direction.

But just because it’s easy to find the position doesn’t mean you would know where to point your camera mirror. OK, I get it. It’s possible to use the position to calculate the angle to aim the mirror—but that’s not as much fun as using polar coordinates.

Oh, I should also point out that if you move the origin of the cartesian coordinate system it’s not a big deal. Sure, you will have different starting positions but the velocity equations mostly look the same.

Polar Coordinates

If you are still dealing with motion on a flat plane (ignoring the vertical motion of the tank shell), you will need two coordinates to describe the location of the object relative to the origin. Instead of using two perpendicular distances (x and y), polar coordinates uses an angle and a distance. Here is the same object from before using polar coordinates.

Rhett Allain

Instead of x and y, we use r (the distance from the original) and θ the angle from the x-axis. Yes, if you draw the polar coordinates on top of the cartesian coordinates it’s possible to see the connection between the two systems. If you want to find the r and θ values you can use a right triangle. The hypotenuse of this triangle would be r and the angle would be θ. This gives the following conversion.

Rhett Allain

Everything looks great. But there is a problem. How do you express the velocity of an object in polar coordinates? It’s not a simple problem. If a projectile is moving in the x-direction, its velocity is just in the x-direction in the cartesian coordinate system. However, for polar coordinates both its angular value and its r value will change. You can see this if I show the coordinates of the object at two different times.

Rhett Allain

Describing the velocity in polar coordinates isn’t just in one dimension and those values aren’t constant. Why would anyone use polar coordinates? Because with polar coordinates, you get the angular position of the object. This is exactly what you need to aim the mirror. Oh, notice that if I move the origin for the polar coordinate system the values can change quite a bit.

OK, let’s just do this. Let’s get an expression for the velocity in polar coordinates. Since it involves a lot of math, I’m just going to share this video of my derivation instead of writing it out. Actually, I wrote it out too—here you go.

But in the end, you don’t get something nice and simple like you do in cartesian coordinates. You get an r and θ expression that changes with time and depends on second derivatives with respect to time. Yes, you get a differential equation. But wait! All is not lost. I know you don’t want to solve a differential equation—and you don’t have to. We can create a solution to this problem by breaking it into tiny steps and solving each step. This is the key idea in a numerical calculation. It’s easiest to do something like with a small bit of computer code.

In order to create a numerical calculation, I need the following (in polar coordinates).

  • The starting position of the object. The video states that the camera is 82 feet away (25 meters), so I will use that as my starting r value. The initial angle will be 90 degrees.
  • What about the starting velocity? Since I have two dimensions (r and θ) I need the velocity in these two directions. Here is the weird thing about the velocity in polar coordinates. As the object moves the r-direction and θ-direction change. In cartesian coordinates, the x and y-direction stay constant. OK, so let’s give this thing an initial velocity in the θ direction with a magnitude of 600 m/s.

That should be enough. With these values, I can use the differential equations to find the polar velocity and position after some short time interval. Then I just keep doing that until I want to stop or my computer explodes. Here is the code with a plot of the angular value of the position as a function of time. Feel free to edit it and rerun it. You can’t break anything.

From the plot of angle vs. time, you can see it’s not such a simple problem. You can’t just turn the camera mirror at a particular angular speed to follow the projectile. The closer the tank shell gets to the camera, the faster you have to rotate the mirror for it to stay in view.

OK, now for some questions for you (or for me in the future).

Homework

  • Use the code above. Create a plot of r vs. time.
  • In the code, use the values of r and theta during each time step to calculate the x-position of the object. Plot the position vs. time to show that it is indeed a constant x-velocity.
  • Modify the starting position (r) in the code. What happens if the starting position is closer to the tank shell? What if it is farther away?
  • What is the maximum angular velocity (in radians per second) for the mirror?
  • Suppose you put a camera that has a length of 10 cm and rotates about the center. Calculate the centripetal acceleration for the end of this camera if it was to follow to projectile. Suppose the end of the camera has a mass of 50 grams. Calculate the force needed to keep it together.
  • Estimate the power (in watts) needed for a camera to rotate to track the tank shell.

More Great WIRED Stories

via Wired Top Stories https://ift.tt/2uc60ci

March 6, 2019 at 08:06AM

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Harman patented flying robotic speakers

https://www.engadget.com/2019/03/06/harman-patent-flying-robotic-speakers/

Imagine you’re using a VR headset and as a car races past, you hear it whip from left to right. Only the sound literally moves from left to right because it’s coming from a robotic speaker that zips across the room. From the looks of a new patent, audio company Harman is dreaming up speakers that would do just that.

This week, the US Patent Office awarded Harman a patent for a "mobile speaker system for virtual reality environments." (As you might remember, Harman is the company Samsung acquired for $8 billion in 2017.) According to the patent, the company would map VR soundscapes to robotic speakers, which would either drive or fly (thanks to quadcopters) to better represent the distance, direction and movement of sounds.

Today, most VR headsets rely on headphones to create 3D audio that only gives the illusion of a sound’s location or movement. Harman wouldn’t do away with headphones altogether. The patent notes that they might be useful for internal monologues, but that this new system might make conversations, for instance, more realistic. And the idea applies more to public, group VR experiences than it does to using your own headset at home, which is good considering consumers might not be ready for a room in their house full of moving speakers.

Of course, companies patent wild ideas all the time, and it doesn’t mean we’ll ever see this one come to fruition. But this does give us a sense of Harman’s ingenuity. If it’s going to take off, they’ll have to make sure the speakers themselves are silent — a fleet of drones moving around you as you follow a VR storyline sounds pretty distracting.

Via: The Verge, Variety

Source: US Patent Office

via Engadget http://www.engadget.com

March 6, 2019 at 09:18AM

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The best games for Nintendo Switch

https://www.engadget.com/2019/03/06/nintendo-switch-best-games/

Nintendo’s Switch is on a roll. Now into its second year, the youngest of the games consoles is punching above its weight with a mix of core Nintendo games that have pushed iconic characters like Mario and Link into the modern gaming age. The Switch is also a portable console, which has injected new life into older titles and indie hits that have never made it a Nintendo device before.

The Switch’s online store isn’t the easiest to navigate, however, so this guide aims to help the uninitiated start their journey on the right foot. These are the games you should own — for now. We’ll be updating these guides regularly.

Legend of Zelda: Breath of the Wild

Switch

The Legend of Zelda: BOTW signals the biggest shift in the series since the Nintendo 64’s Ocarina of Time, and it might well be one of the best games of the past decade. It pulls the long-running series into modern gaming, with a perfectly pitched difficulty curve and an incredible open world to play with. There’s crafting, weapons that degrade, almost too much to collect and do and a gentle story hidden away for players to discover for themselves. Even without the entertaining DLC add-ons, there’s simply so much to do here and challenges for every level of gamer. MS

Bayonetta 2

Bayonetta 2

The Bayonetta series fuses together compelling (and different) character design with memorable boss battles, seemingly endless waves of monsters and a smart fighting system that’s easy enough to start with, but pulls no punches later. Originally launched on the Wii U, the Switch gives Bayonetta 2 another chance to shine (the original is also available alongside) in a portable console, with nothing lost in transition. Another reason to catch up? A third game for Nintendo’s hybrid console is already underway. MS

Mario Kart 8 Deluxe

Nintendo

Mario Kart 8 Deluxe‘s vibrancy and attention to detail prove it’s a valid upgrade to the Wii U original. Characters are animated and endearing as they race around, and Nintendo’s made bigger, wider tracks to accommodate up to 12 racers. This edition of Mario Kart included gravity-defying hover tires and automatic gliders for when you soar off ramps, making races even more visually thrilling, but at its core, it’s Mario Kart — simple, pure gaming fun. It’s also a great showcase for the multitude of playing modes that the Switch is capable of: Two-player split screen anywhere is possible, as are online races or Switch-on-Switch chaos. For now, this is the definitive edition. MS

Mario Odyssey

Nintendo

Super Mario Odyssey might not represent the major change that Breath of the Wild was for the Zelda series, Instead, we got a great Mario game that’s been refined across the last two decades. Yes, we got some important modern improvements, like maps and fast travel, and the power-stealing Cappy is a truly fun addition to Mario’s usual tricks. But that core joy of Mario, figuring out the puzzles, racing to collect items and exploring landmarks, is here in abundance. MS

Fortnite Battle Royale

Fortnite is a cultural phenomenon, responsible for popularizing a new shooting-game genre and doing it in a way that has millions playing across mobile, PC and games consoles, like the Switch — you’ll see this particular game appear in several of our lists. It all started with a simple idea: survive. (Actually it started with a tower-defense-esque game where you built a fort to protect human survivors against zombies, but hey, it evolved.) Fortnite has a low barrier to entry (it’s free!), and the sheer momentum behind the fact that everyone is playing it makes resistance futile. Parachute into the field, grab supplies, guns and ammo, build some defensive protections if you like and make it to the end. Sounds simple, but the best game ideas are. PUBG, Apex and the rest have a tough fight on their hands. MS

Mario + Rabbids Kingdom Battle

Nintendo

The visuals of this Ubisoft-Nintendo collaboration betray a sophisticated, turn-based strategy game. Mario + Rabbids‘ learning curve is perfect, with the story mode adding new characters and unlocking better, different weapons and skills as the game progresses. Skills (and weapon effects) playfully interact with each other by the middle of the game, adding dimensions to the initial cover-based shoot-out. Each level has a goal (destroy all enemies, get to this area), and you’re rated only by the survival rate of your three fighters and the number of turns it takes to fulfill said goal. Parts of the single-player mode are weaker, but the core game is equal parts entertaining and slick. There’s also a rich multiplayer mode to add to the longevity. MS

Rocket League

Rocket League

Rocket League could have been a short-lived novelty title, a game that mashed together soccer and vehicular combat to make a few million in its launch year before fading quietly into obscurity. Instead, developer Psyonix has consistently innovated since 2015, and in the process, it’s pushed the broader video-game industry toward a more inclusive future. Rocket League was one of the first games to call for and implement cross-console play, and today it’s one of just two titles (the other one being Fortnite) to support play among PlayStation 4, Xbox One and Switch. JC

Splatoon 2

Nintendo

The original Splatoon, released on the underselling Wii U, didn’t get the love it deserved. On the Switch, the sequel is even better, with plenty to offer both new and returning players. This squid-ink shooter divvies up players into teams of four and asks them to cover as much turf as possible — by dousing it in paint. Splatoon 2 adds even more weapons, cool clothes and even a few new battle modes, including Salmon Run, which pits your team against a series of unusual sea-creature-inspired bosses. There’s always something to do in the game, making it more than worth the Nintendo Online subscription needed to play with your ink-shooting friends (and foes) online. KN

Stardew Valley

Sometimes all you want to do is just water some plants, drink a beer and pet a dog, and Stardew Valley has all that and more. When you escape your mundane office job to the valley, you’re given a small farm to shape as you see fit with crops and livestock. If you get tired of that, explore the nearby Pelican Town, get to know your neighbors and hopefully woo one lucky one into marriage. Or, you can take your chances in the caves at the edge of town to mine for gems and metals — at which point the game becomes more dungeon crawler than simple farming sim. You can play Stardew Valley at your pace, so you can spend hours on it and never get bored, or put it down for months and pick it up again and just start watering your crops again like no time has passed. KN

Celeste

Celeste

Celeste is a lot of things. It’s a great platformer, but it’s also a puzzle game. It’s extremely punishing, but it’s also very accessible. It puts gameplay above everything, but it has a great story. It’s a beautiful, moving and memorable contradiction of a game, created by Matt Makes Games, the indie studio behind the excellent Towerfall. So, Celeste is worth picking up no matter what platform you own, but its room-based levels and clear 2D artwork make it a fantastic game to play on the Switch when on the go. AS

Contributors: Jessica Conditt (JC), Kris Naudus (KN), Mat Smith (MS), Aaron Souppouris (AS)

The best games
Explore our top picks for every system


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via Engadget http://www.engadget.com

March 6, 2019 at 08:36AM

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Uncovering Earth’s Orbital History Buried in Ancient Rock Deposits

http://blogs.discovermagazine.com/d-brief/?p=32441

Our solar system is a chaotic place – literally. Rewinding orbital possibilities quickly becomes too complex and too numerous for astronomers to calculate. That means we only know the orbital movements of Earth and the other planets over the past 60 million years or so. To look further back, scientists are pulling core samples from deep under Earth’s surface to examine long-ago climate change and learn about how the planets moved hundreds of millions of years ago.
Scientists used two core

via Discover Main Feed https://ift.tt/1dqgCKa

March 5, 2019 at 05:54PM

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NASA visualizes supersonic shockwaves in a new, awe-inspiring way

https://arstechnica.com/?p=1469125

  • Using the schlieren photography technique, NASA was able to capture the first air-to-air images of the interaction of shockwaves from two supersonic aircraft flying in formation.

    NASA

  • In order to acquire this image, originally monochromatic and shown here as a colorized composite image, NASA flew a B-200 at around 30,000 feet while the pair of T-38s remained in formation and flew at supersonic speeds at the precise moment they were directly beneath the B-200.

    NASA

  • When aircraft fly faster than the speed of sound, shockwaves travel away from the vehicle, and are heard on the ground as a sonic boom.

    NASA

It wasn’t an easy shot to get, but the end results of NASA’s efforts to capture air-to-air images of supersonic shockwaves sure seem worth it.

To take these unprecedented photos, the space agency updated the imaging system on one of its Beechcraft B200 Super King Air aircraft. NASA scientists upgraded the camera so that it could capture a wider field of view, improved its connection to data storage, and increased its frame rate to 1,400 frames per second.

Then, the B200 flew up to about 9,100 meters. Meanwhile, two T-38 jets flew in formation, less than 10 meters apart, only about 600 meters away from the B200 aircraft. All three planes had to be in the right place, and a result, the camera system took exceptionally high-quality images of shockwaves created by the two T-38 aircraft and the interaction of the shockwaves between the two jets.

“We never dreamt that it would be this clear, this beautiful,” J.T. Heineck, of NASA’s Ames Research Center in Mountain View, said. “I am ecstatic about how these images turned out. With this upgraded system, we have, by an order of magnitude, improved both the speed and quality of our imagery from previous research.”

Quieter sonic booms

An aircraft traveling faster than the speed of sound creates a shockwave, essentially a pressure front that pushes into the surrounding air. In this case, flying the B200 aircraft above the T-38s provided a new vantage point for observing shockwaves, as well as their interaction. Ground-based observers perceive a sonic boom as the shockwave from a supersonic aircraft crosses their location.

This photography effort wasn’t a project to create art, even though the resulting images are stunning. Rather, scientists want to better understand the formation of shockwaves and their resulting sonic booms as part of a NASA project to develop quieter supersonic aircraft.

NASA and Lockheed Martin are developing a “low boom” flight demonstrator, the X-59 aircraft, to test technologies for lower-impact sonic booms. This aircraft may be ready for test flights in 2022, and NASA wants to have equipment ready to measure its capabilities. By then, NASA wants to have perfected its use of the schlieren imagery technique that captured these new images and data.

With this kind of data, NASA or commercial companies may be able to convince regulators to permit over-land, less-disruptive supersonic air travel. Although the Concorde was done in by a number of factors and stopped flying in 2003, one of its biggest limitations was the fact that it could only fly from coastal destinations to coastal destinations above the speed of sound.

Listing image by NASA

via Ars Technica https://arstechnica.com

March 6, 2019 at 08:26AM