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Elliptical-blade NACA airfoil propeller

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You don't see aircraft with elliptical wings anymore. The most famous aircfaft with such wings is probably the Supermarine Spitfire fighter aircraft from World War II. Elliptical wings have the most uniform theoretical distribution of lift and therefore the least induced drag. In the case of the Spitfire, the gentle taper of the ellipse near the wing root also provided more room to mount weapons internally than a straight-taper wing, while providing an overall thinner, low-drag cross-section. However, with all curved edges, elliptical wings are expensive to construct. Of all the kinds of drag that a wing or propeller blade experiences, induced drag is an unavoidable price for lift. Induced drag has nothing to do with the drag created by surface area, surface roughness, or thickness of the airfoil. Induced drag depends on the planform shape of the wing. It is also inversely proportional to aspect ratio (the ratio of wing length to airfoil average chord length). The optimal and
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Whose hands are biggest? You may be surprised.

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A recent project to create an ergonomic handle for 3D printing led me down a path that introduced me to anthropometric measurements of the human hand, which in turn revealed some interesting facts about hand sizes. I had no idea that hand size is dependent on nationality, but I found a number of research articles on this topic. For those who don't want to read further, the answer to the title question is: Based on the data found, Filipino males have the biggest hands, by a significant margin. In fact, the margin is large enough that this population may be considered an outlier from the general human population with respect to hand size. Even Filipina females have larger hands than most males of other nationalities. On the other end of the spectrum, Vietnamese females and Indian females have the smallest hands. Now you can read on for the whole story, or you can skip down to the chart at the end. Idea for a toy My unintentional investigation into hand sizes started while de
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It seems I created a meme

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Back in July 2005 I became intrigued with crafting weird and improbable magical items for the amusement of my Dungeons and Dragons gaming group. At the time, I had also been employed in the defense industry for about half my life, working around various weapons systems. Naturally, these things came together in creating a couple of D&D weapons, one of which became a meme in both D&D and in engineering circles . It started like this. Gary, one of the other players in our group, sent out an email to the other players warning about a possible dirty trick that Ian (our Dungeon Master) might play on those of us playing characters who rely on magic and magical items: Conventional D&D wisdom states that placing a rod of cancellation into a bag of holding, handy haversack, or portable hole will destroy both items in a massive explosion. I dunno if Ian is going to spring this to annoy folks who are carrying too much equipment, but you may want to store unidentified wands outs
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My favorite mathematical card trick

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I learned this card trick in the fourth grade, decades ago, before the World Wide Web existed. I have never seen it written about, and anyone to whom I have shown it has never seen it either. This is surprising given how long I've known this trick. Did a brilliant classmate (or a parent) invent it? I'd love to know the origin. This is a mathematical card trick. Meaning, there is no sleight of hand, no actual trickery, just manipulation of playing cards that gives a surprising, final result. You can find many examples of mathematical card tricks on the internet; some of them appear downright magical and quite impressive. What the audience sees Here is how this trick appears to the audience. It looks like many steps, but they are easy to remember after you've practiced the trick even once: Starting with a deck of 52 cards (no jokers), you ask a volunteer from your audience shuffle the deck. You deal out the cards into seemingly arbitrary face-up piles, handing t
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Legitimate uses of loaded dice

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This is why, as a game master / dungeon master (DM), I would never allow a player to bring 3D printed dice to a game. However, I would supply them to players, for certain purposes. In this article I examine the characteristics of "most fair" and "most unfair" designs of d20 dice, which I made in a CAD program and 3D printed for experiments. A fair and balanced d20 (white), a d20 biased to 20 (bronze, with the ☺ on the 20 face), and a d20 biased to 1 (purple, with the F for "fail" on the 1 face). A d20 is a twenty-sided icosahedron with faces numbered from 1 to 20. In the game Dungeons and Dragons , the d20 is ubiquitous. It determines success or failure of an action. It is the first thing rolled any time a player takes an action. The result of the d20 roll, with some modifiers added based on the player's character abilities and skills, determines whether the player's action succeeds or fails, with appropriate consequences. Advantage a
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Simulating erosion

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I decided to create a procedurally-generated 3D landscape in a CAD program, and wrap it around a globe, which led me to an investigation of erosion algorithms. I include a JavaScript erosion demo at the end of this article for you to play with. As an aside, let me say that I like OpenSCAD in spite of its idiosyncrasies. Other CAD programs can do many things that OpenSCAD can't, but OpenSCAD is the only 3D modelling software I know of that makes it easy to create procedural or algorithmic parametric designs. It runs on all my computers: Windows, macOS, and Linux — and it's freeware. Its main idiosyncrasy is that it uses a declarative language that requires familiarity with functional programming , a different programming mindset in which all values are evaluated at compile-time instead of run-time, meaning that all "variables" are effectively constants. Even so, one still has conditional branching, looping, and recursive functions, so one can get stuff done. For exa
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Syncing Office 365 Outlook to Google calendar using Power Automate

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When my employer switched over from the Google office suite to Microsoft's Office 365, it caused unexpected disruption in my family. I had been sharing my work calendar with my wife (sharing no details, just busy times). It became an integral part of her calendar, to help her coordinate (between her job and my job) who picks up and drops off my son from school, and to let her know when I was free to take a phone call during my work day. Since the switchover to O365, my ability to share a calendar externally was eliminated. Based on documentation I could find, it should be possible, but the option doesn't appear in my employer's implementation of Outlook. I can view my personal Google calendar in my work Outlook calendar, but I can't share it the other way. Microsoft's Power Automate provides a way to solve this problem. It lets you create flows of data, triggered manually or automatically by events, to move data around, not only among the Microsoft products but
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The water rocket: Thrust from water

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Launch tube thrust Thrust from air Once the rocket has left the launch tube, the water thrust phase of the flight begins. But before we begin those calculations, we need to have equations for ballistic flight, which is the last step described in the introduction . Why? Because during ballistic flight (coasting through the air), the only forces acting on the rocket are gravity and wind drag — but these are acting on the rocket during the thrust phase too. Ballistic flight is exactly the same, just without the thrust. Ballistic flight We need to know how gravity and drag affect acceleration, velocity, and ultimately altitude during all thrust phases as well as the ballistic trajectory afterward, so we'll start with the ballistic flight equations. Air resistance First we need to get the ambient air density. Denser air results in higher drag, and dry air is more dense than moist air. To get the density, we first need to know the partial pressure of water vapor in the air. T
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New approach to screw threads in OpenSCAD

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This is an intellectual exercise with a practical end-result. There are better approaches to this problem, but the approach I describe here is interesting. A screw thread from a stack of discs Imagine a stack of 50 coins, stacked so that each coin is slightly offset from the one below it, with the offset moving around in a circle with each new coin. Here is what it looks like for fifty coins 20 mm in diameter and 0.5 mm thick, offset by 2 mm from a center of rotation, and stacked with a rotation offset of 30 degrees per coin ( click to enlarge any image in this article ): Obviously, this is a spiral stack of coins. But it also approximates screw threads. The thread profile looks like a sinewave rather than the trapezoidal profile of machine screw threads. Indeed, others have observed this, and used the freeware parametric CAD program OpenSCAD to make screw threads by extruding an offset circle while twisting it, as in this model on Thingiverse , for example. From a distan
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