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Blog Entries posted by oxy126

  1. oxy126
    I attend the local Rochester parkour gym (http://www.rochesterparkour.com/) on a weekly basis. I also tend to struggle to come up with topics for my physics blog posts. But today, I had a revelation: why not combine the two. So I introduce my new series, the physics of parkour. First up is the "top-out".

    A top-out is essentially a way to go from a hanging position on a ledge (a "cat"), to having your upper body above the ledge with your palms supporting you, without clambering up with your elbow in between. Here's a mock up of it:

    And a video (if you only want to watch the top-out, and not all the instruction, you can go to 5:12):

    It relies on three things: a solid footing, a good knee drive with the hanging leg, and of course maintaining a solid grip with your arms. When done properly, it requires a lot less upper body strength then you might imagine.

    For a brief overview, it consists of three parts: building upwards momentum with your legs, building a bit of forward (but mainly rotational) momentum with your arms (the reason why they play more into rotation more than anything will be discussed), and finally transitioning to the support position resting above your palms. First, and most important, is the legs. One is planted firmly, and the other is supposed to drive upwards, in order to build momentum which will later be transferred to the rest of your body. However, friction can be tricky: the tendency of your planted leg is to slip and slip, because most people will "paw" at the wall as if they were running up it. As we know, frictional force is proportional to normal force, so you actually want to kick/jab your foot into the wall, because this will allow it to stay in place. As you're doing this, you can drive your hanging leg up, generating some momentum.

    During this, you should also be pulling up/in with your hands. Simply, you want to counteract/overcome the force of your leg pushing away from the ledge, and also gather a bit more upwards momentum. However, simply due to the weaker nature of our arms, it won't contribute quite as much as our legs, which can be surprising. What is helpful, though, is the torque it creates on the body: while it is counteracting the linear momentum from our legs, it is working with the force from our legs to rotate our body over the lip, which is more beneficially, seeing as we right next to the wall to begin with. Now, with momentum built up from our knee drive and arms, and a slight rotation, our upper body will pop up and over the ledge, and rotate us into a position where we can easily re-position our hands to rest on our palms.

    From there, it is usually pretty easy to swing/climb up the rest of the way. But without proper training, this technique is very difficult, because people usually rely on their arms way too much. Yet again, it's an example of something made easier through physics.
  2. oxy126
    Why do bicycles stay " up"? Physics, that's why. Bicycles rely on the concepts of angular momentum and precession to prevent tipping over when. When a wheel is spinning fast, it tends to resist changes in it's angular momentum. This is called 'precession', and is an important concept in bicycles and unicycles alike. When gravity tries to tilt a wheel, it is effectively trying to alter the angular momentum of the wheel. In reaction, the wheel will turn only slightly, and gain a slight 'wobble' as one side of the wheel juts out above the rest, which is usually resolved by dampening forces 'n' stuff. So bikes work because of physics, and that's pretty cray.
  3. oxy126
    High-speed trains have always been a fascinating concept. While they have achieved high popularity in other corners of the world (primarily Japan), they have been mostly absent from American travel. We continue to rely on trains, automobiles, and other forms of public transport, which, while quite fast, are not always the most efficient. Planes in particular use a lot of fuel, and are very costly to travel on (which is, in part, just due to the monopolistic tendencies of airlines). The hyperloop, however, would be America's first step into land-based intercontinental travel.

    As most people can imagine, it relies on magnetism and vacuum tubes - nothing new to thoughtful people. However, on interesting thing about the design is it's reliance on only a partial vacuum (not clearing out as much air as they could), and instead compressing the air the shuttle encounters and pushing it underneath, providing an air cushion for the device. Other than that, it would still use induction principles to accelerate the train, but I find the partial vacuum interesting. Whether it stems from the difficulty of maintaining a higher vacuum, or simply trying to use what remaining air is left after what they can (feasibly) do to make it more efficient, I don't know, but there are trade offs for each.

    Outside the simply physical realm, there are issues to deal with. One is cost - you're building a giant vacuum tube thousands of miles long. Another would be safety against hijack. While a plane, when hijacked, provides a much greater threat to bystanders, the presence of a giant, above ground tube is easy to sabotage. While it would be hard to cause casualties this way (a broken pipeline would most likely just have the trains slow to a stop), and if casualties were incurred they would be much smaller than those suffered on 9/11, limited to passengers, it still poses a threat, and there is no realistic way of keeping a vigilant eye over thousands of miles of tubing. So there are still a few logical kinks to work out. Not to mention that, with the forces of supply and demand in play, fares for this "tube" could potentially be inflated to near the price of airplanes, if not higher.

    Regardless, I think it is a cool technology, one that I hope is applied in at least some scale. Hopefully the day when we can ride the hyperloop isn't too far away.
  4. oxy126
    Recently I came across this article ---> http://www.popsci.com/article/technology/rise-insect-drones <---, detailing the success of engineers/researchers to mimic insect flight, for potential application in insect drones. In short, the article details how the flight of insects was previously misunderstood - based on our conventional notions of flight they were unable to generate the lift to stay aloft - and now, with better study into concepts into "wake absorption" and other fancy flying terms, we're able to mimic an insect's flight to produce the highly efficient lift that they create. I would recommend reading it.

    The topic on it's own is fascinating. Personally I think robotic bugs are cool. But I also think that the potentials for the new forms of flight they're able to reproduce are also quite interesting. Who knows: modifications on stuff like this could be used in larger scales drones, or maybe even better human powered flight. This all may be unfeasible - I'm no aeronautic engineer - but it's cool to think about nonetheless.
  5. oxy126
    From the beginning of time, this world has been governed by the laws of physics. Which makes sense, because the laws of physics were created to model the patterns of our world. Its actually fairly tautological. But despite this obvious comparisons, it remains an important topic of study, because at its core it is a continuing quest for understanding of the natural world, and it allows us to do great things with that knowledge. While most of my blog posts describe physics, because I wanted to use a post title with no actual relation to any subcategory within physics, I have decided to discuss the merits of the field and the reasons it is worthwhile to learn, not just for the engineers but for everyone.

    I, personally, feel the merits of physics are obvious. Unlike certain other fields of study, physics has immediate applications into our modern lives. In our digital world devices like computers, planes, cars, skyscrapers: these all are made possible by the past research of physicists and other scientists. But what isn't as clear to most people is why they need to learn physics, as potentially someone whose desired career path will have little to nothing to do with the inner workings of our world. And in some part I agree: you simply won't need the technical details surrounding how to calculate the various values associated with certain things, as physics teaches us to do. But there is value in having simply a general understanding of thinks regardless its eventual impact on your future. Personally, I find the ability to be able to look at something and say "I understand that" is valuable. However, what I find most important in my study of physics is the "scientific culture", as you may call it: the fact that what we learn is founded on a desire for knowledge, a willingness to test and experiment to find the truth. This is the true value of physics, to non-physics people: the root philosophy of curiosity and a desire to expand one's knowledge is entirely transferable to other fields, and can be applied in day-to-day life.

    Essentially, physics, even to me, a prospective scientist, is as much about the mindset as it is the content. The sense of wonder and amazement scientific observations impart to me is the reason why I enjoy it so much. It's a return to the roots of human nature and understanding, to our innate desire to learn and inspect. For me, it allows the childhood feelings of mystery and intrigue and wonder to resurface, and it expands the possibilities of our world further and further until they're only limited by our imaginations.

    A few hundred years ago, had I looked up into the night sky, saw the stars, and said "That's nice". These days, on warm, clear nights, when I've looked into the sky, I've seen the stars, and knowing the sheer distances that light has traveled, the immensity of the stars they came from, and the vast swathes of time that have elapsed during their journey has only made them more amazing. Moments like that is why I find physics so amazing.
  6. oxy126
    During webassign time I tend to let my mind wander, though it often doesn't wander too far. So I chanced upon the effect Earth's magnetic field has on spacecraft, and the properties a coil of wire in space will have with the aim of spacecraft orientation while in orbit. Digging a bit further, I learned that these devices are called magnetorquers, and so I decided to write about spacecraft orientation and attitude control, both from magnetorquers or reaction wheels or gravity or whatnot.

    First there's the magnetic torquers, which are in their simplest form imagined as a coil of wire through which induced current can flow through. As the spacecraft turns, the flux due to Earth's magnetic field changes, inducing a current in the coil and creating a restorative force (with the magnetic moment and all that stuff). Hence, while in orbit, it will tend to maintain maximum flux, which makes it tend towards a certain orientation.

    Reaction wheels are a bit simpler. Basically, they are just rotating discs which a control system will apply and impulse to to give the craft something to "push" against, so that it spins opposite the direction of the discs. Nothing too complicated.

    One interesting thing though is "gravity-gradient stabilization", which is a manipulation of tidal forces (the force of gravity being weaker further away from a large body) to orient a spacecraft. Because the portion of a craft closer to the planet feels a greater force, it will "swing" downward (very slowly, of course), with a tendency to keep pointed downwards. Using longer rods or beams, this effect is amplified, but it does technically work regardless of shape. This effect is the reason why the moon's orbital period around the Earth is equal to it's rotational period - over time, the portion of the moon closer to the Earth tended to face us, so the same side of the moon is always facing us.

    Space flight is cool, but I also believe that the engineering put into making it more reliable, effective, and precise is also quite exciting. Hopefully you found this to be somewhat cool.
  7. oxy126
    I'm here today to discuss the possibility and implications of time travel...

    ...Just kidding. Time travel isn't real, kids, and you'll just have to get over that. But there is one thing which I think you'll find equally fascinating: PLUMBING.

    Plumbing is pretty insane. Water flowing through pipes and stuff, the transportation of liquids, at times I've found it too much to handle. As many physics students have already learned, Bernoulli's equation and stuff. It all applies to plumbing, and making sure everything flows right.

    Bernoulli's equation is important for things like constricted pipes or transporting water to the tops of tall buildings. For example, when your hose gets kinked, the water through that kink must flow faster in order to maintain the same flow rate, which requires more energy. Using Bernoulli's equation, we can see that this means the flow rate must diminish in order for energy to be conserved, causing the water in your tubing or hose to slow down, which can be a problem especially with a low-pressure water supply. On an entirely different semi-aquatic semi-plumbing topic, the venturi effect, or the effect of a fast moving stream to create low pressure areas, is used in aquariums to bring air into the marine environment while only using a water circulator to do so.

    So yeah. Plumbing.
  8. oxy126
    Magnetic brakes are pretty cray. With them, you're able to stop stuff from moving WITHOUT EVEN TOUCHING IT. Which really isn't too interesting, but still. It's interesting enough.

    As I already stated, no mechanical contact is required for these to work, which means a significantly smaller amount of wear and tear on the braking system. Because of this and their convenience for certain applications, they're used in things like roller-coasters, or industrial applications, and with design modifications they can be used for regenerative braking in electric automobiles.

    How does it work? Conducting plates typically have a current create in them due to the movement of magnets, as a result of magnetic induction, which according to Lenz's law, will create a magnetic field opposing the rate of change of flux through the surface. This tends to oppose the motion of the magnet, slowing the device down, and when used properly (such as in regenerative braking), the current induced can be harnessed to recharge batteries. It does also oftentimes produce a lot of heat, which can be negative, but sometimes this can be used to your advantage. If you need to heat something (for example, in pipe soldering), creating an "inductance situation" within something like a copper pipe can heat the pipe until it is ready to be soldered. Or burn stuff.
  9. oxy126
    For the most part, humans have good sight. A lot of time and effort during our modern era is put into making TV and computer screens at a higher and higher resolution in order to make things look as "real" as possible - that is, to make the pixels onscreen indistinguishable from what we would normally see. But how good are our eyes really? Lets find out.

    Before all of this, I'll direct you to a nice, short, but informative link (https://xkcd.com/1080/), courtesy of xkcd. A good representation of how we see, it outlines the many different parts of vision very nicely. Focusing primarily, however, on the "resolution" of our field of vision, that is, how many "pixels" we can see, we can see it varies. Right in the center few degrees, in the foveal region, we can see stuff quite clearly, which makes sense, because we're looking at it. However, the blurred characteristic of the surrounding areas isn't just because we aren't focused on it, but because there simply isn't as much data provided there - much less, in fact. While our center of vision is comparable to a high-res camera, the surrounding areas are much worse quality, with the entire area outside of the center ~10 degrees containing a fraction of the data that the center area does. Our brain just fills in the gaps.

    So while at times our vision is quite good, other parts could use some work. And even with the high detail of our foveal region, you still might not need that new HDTV. Based on how far away you're sitting, it might not even be noticeable, so don't waste your money.
  10. oxy126
    There's been a lot of news this past year surrounding NSA surveillance of personal communications. While I'm not here to debate the politics involved with that issue, I am here to describe how they do (part) of it, that way you can do your own surveillance if you really wanted to.

    With copper cabling, one of the flaws with using it for communications is the fact that it produces a magnetic field, essentially broadcasting the data within the wire to anyone within short range. Through the hall effect - the tendency of a magnetic field to push charge carriers in a wire to one side of the wire, creating a difference in voltage - this magnetic field can be measured accurately, allowing people to survey communications without disrupting the actual data. Simply, a person just needs a current gun, or something equivalent, to clamp around the wire to get precise B-field readings.

    That is just yet another benefit of fiber optic cables. While they have a much higher data throughput, they also prevent to a significant degree this style of wiretapping, because the line would have to physically be broken to monitor data. It won't stop the NSA, but still...
  11. oxy126
    This past week it has gotten pretty cold up here in the (somewhat) North. With windchill, temperatures have dropped below zero, and with weather like that it can always be a struggle to stay warm. But with the proper clothing, one can still brave the harsh climate and still have a good time. We might often take it for granted, but how exactly does this insulating process work?

    Heat travels in three ways: conduction, convection, and radiation. Conduction is simply the transfer of heat by colliding molecules, like when a pan will get heated along its full surface instead of the bottom, and this form of energy transfer is the reason why things like microwave burritos often tell you to wait a few minutes before eating, to let the heat distribute itself evenly. In more conductive objects like metal, it is a good way of transferring heat, but in less conductive things like air (air is, in fact, a poor thermal conductor, which seems counterintuitive), it doesn't exactly do much. Radiation is simply the transfer of heat energy through electromagnetic radiation (primarily thermal, or infrared radiation), such as with sunlight or tungsten light bulbs, and for most common objects it doesn't play a big role in the transfer of heat. In fact, if you wound up stranded in space, one half of you would not freeze as the other side boils, as is popular belief. While space is technically very cold, through radiation along heat leaves your body very slowly. The real issue would be (still) your blood boiling, not due to temperature but due to the vacuum of space, and of course the lack of oxygen. But nonetheless, radiation for cooler objects doesn't transfer heat too well.

    The real reason why winter is cold is because of convection: the movement of air molecules in our atmosphere, the reason for our weather and the reason why open doors have "drafts". While air is a poor conductor, it convects very well, and with colder air being denser and of a higher pressure, cold air will flow into warmer areas, like when a cold front blows in, or you feel a "blast" of cold from your freezer. So in order to combat this flow of air, we bundle up, putting on layers to protect us from the wind and these currents. However, just one layer to stop the wind won't cut it - the transfer of heat itself will generate convection. The real secret to staying warm is a measure of "dead air", or the pockets of gas within our coats or mittens that are too small to give rise to convection currents but still present as to slow conduction. It's the measure of these microscopic packets of air that allow our clothes to be warm without being unnecessarily expensive. While we can certainly cut out these small pockets of air altogether (certain jackets do), the benefits of using dead air maintain warmth at a lower physical cost, and usually make a coat thicker and more resilient to tears.

    With that, now you know not only how to stay warm, but how staying warm works. So don't forget to bundle up.
  12. oxy126
    Below the atmosphere, we have a little problem called global warming, or just in general high levels of pollution for you non-believers, which is the general degradation of our atmosphere and lakes and oceans due to excessive amounts of waste, brought on by agregious practices and poor waste management. In space, there's Kessler syndrome, the hypothetical scenario where, when the amount of space debris orbiting our planet becomes over-saturated, various "leftovers" from spacecraft will collide and split apart, going on to hit even more debris creating a cascade of small but dangerous shrapnel that will make travelling through low-earth orbit an unfeasible, and at the very least highly difficult, affair.

    Just like below our atmosphere's limits, we need to be concerned about pollution. While space pollution has a much smaller influence (space is big, and the chances of hitting something are slim), it is still dangerous and costly, but much of the time preventing this pollution is difficult, as it requires a lot of energy to bring a empty fuel tank or decoupler back down into the atmosphere. But, for the moment, it isn't too serious, so in case any of you were actually planning a mission into the grasps of space, don't get anxious.
  13. oxy126
    While it may not be necessarily very physics related, it is an interesting point on the topic of networks, both social and otherwise: the average facebook user is only 4.74 "connections" away from any other average facebook user. The article https://www.facebook.com/notes/facebook-data-team/anatomy-of-facebook/10150388519243859, while from 2011, illustrates the concept that, when the correct pathways are taken, we can all be very closely related. Building on Stanley Milgram's famous experiment trying to assess the validity of "six degrees" of separation between anybody else, this facebook analysis shows how the exponential nature of going from friends to friends of friends puts us all in a strangely close social proximity to one another. In my opinion, it is fairly astounding stuff.

    Networks, internet related or otherwise, are essentially complex structures built from basic components. Whether it is a vast array of *almost* symmetrical distributions of elementary particles giving way over the years to for stars, nebulae, planets, and even life, or just the movement and flow of a bunch of water molecules through your faucet, they are simple yet complicated, where even, as the social network experiment shows, the tiniest part of the system can have an influence on another part completely separate, influences which happen frequently and, as a result, make the prediction of these systems very difficult. Our whole physical world, everything we learn, is based on combinations of the same few elementary particles responding to elementary forces, and things like centripetal force and the laws of thermodynamics are just (often slightly simplified) mathematical models to explain the ways all of these forces and particles interact with each other. So while you can blame the weatherman for getting the forecast wrong, or just wonder why no physics engine to date has implemented a fast yet accurate fluid modelling system, just remember that the world can be a very complex, interconnected place.
  14. oxy126
    It's common knowledge that a blue flame is hotter than a red/orange frame. While I'm not entirely sure that is true, having never tested the fact with my own appendages, many reliable sources seem to say it's true. But why, really, is a blue flame hotter? The answer lies with a bit of science on the nature of "light".

    Light with higher frequencies (towards the blue/violet end of the spectrum) contains more energy than light towards the other end of the spectrum, the red/orange end (light in this case refers to all electromagnetic radiation - from gamma to radio waves). And when objects are heated, they radiate energy in the form of light. As you can see in the attached image, this pattern of radiation follows a predictable function dependent upon temperature and wavelength. While certain materials emit certain wavelengths better than others, the general trend is that, the hotter the object the is, the more power it will output at higher and higher frequencies. In other words, a blue flame is emitting more energy at higher frequencies because it is hotter. Theoretically, purple flames would be even hotter, and would most certainly look cooler.

    The big lesson is that there are plenty of ways to quench your curiosity about flammable objects with your eyes, and not your various limbs. Although I guess you can always try.
  15. oxy126
    'Twas only yesterday that I took my inaugural ski run, traversing the trails of Bristol, and as I cruised down the mountain I began to reflect on the nature of skiing, particularly waxing. My skis weren't particularly well waxed for the day, so I wasn't going quite to fast, but I did have experience waxing skis beforehand (mostly with nordic skiing - for that it was a weekly affair). When one considers the purpose of wax, it's natural to assume that all it does is make the ski smoother, filling in the tiny holes of the ski so that there is less (dry) friction involved. However, while that is part of what makes a certain type of wax good, a bigger influence is the creation of a thin layer of water underneath the skis caused by contact with the snow. This thin liquid layer allows an even lower coefficient of friction to be achieved, and has to be taken into consideration when waxing your skis (or snowboard).

    Ideally, only a very thin layer of water is created, because too much will create suction due to the fluid nature of the water, while too little will mean there is still too much dry friction. So the relative propensity of the snow to turn into water on contact has to be taken into account in order to create this balance, and this relative propensity is determined largely by temperature, which is why different conditions require different waxes. Colder temperatures make it harder to create a liquid layer, meaning a stiffer, harder wax is needed, because a harder wax will melt more of the contact layer. On the other hand, warmer temperatures work best with a softer wax. For competitive racers, this means that wax is often reapplied before every race in order to get the optimal conditions. However, for the less enthusiastic, a mid-range wax will often work fine.

    In case you're every feeling slow on the slopes, take this waxing knowledge into consideration. Soon you'll be zipping around like no one's business.
  16. oxy126
    This week has not been the best week for driving. It's been very snowy, and so cold that road salt has been working very poorly, making the roads a slippery mess. Loss of traction can cause serious accidents, so it is best to drive slowly. In the end, it all comes down to friction. Whether you're fishtailing, or stuck in a rut, or have gone into a full on skid, too little friction can cause serious problems.

    Most commonly people will end up fishtailing more in snowy weather, usually while going around turns. This is characterized by a loss of control in the rear wheels, where they begin to slide as the car continues to turn, even when you try to straighten out. The scary part about sliding is, however, that it is harder to stop than it is to prevent. Once you've started to slide, frictional forces tend to oppose you, and your best bet is to point your front wheels in the direction of the skid and wait until you've regained traction. A similar problem occurs when your drive wheels are spinning out, skidding without a solid connection with the ground. A result of accelerating too fast, it is best remedied by easing up and taking it a bit slower next time. But worst of all is when your front wheels begin to lose control, preventing you from steering and often sending you into a spin. Like with all other winter driving problems, you just have to easy up and "go with the flow", until you can regain control.

    Proper winter driving requires a gentle touch, and grace under pressure when the inevitable happens. On bad days it is almost unavoidable to have some slipping here and there, but as long as you don't try to overcompensate the issues will stay minor and not wind up getting much, much worse. So drive safe, and try not to panic.
  17. oxy126
    One of the "hot" news stories over the past few months has been discussion of the growing impotency of antibiotic treatments for disease and infection. Due to widespread use of antibiotics over (primarily) the last century, antibiotic-resistant bacterial strains have started to emerge, making hospitals more and more dangerous, filled with diseases that are harder and harder to treat.

    What this represents is a very serious problem. A large part of modern medicine succeeds due to the prevalence of antibiotics, and as they become less and less effective, disease related mortality will continue to rise even with access to adequate resources. Aware of these problems, research is being done into alternative solutions, such as anti-adhesion medication or probiotics, but until those methods are properly developed, developed countries will have a blind spot in the war against disease.
  18. oxy126
    The second-largest moon in our solar system, Titan, orbits around Saturn, about 8.5 AU (the distance from Earth to the Sun) away from us, making it a very chilly place. A fairly massive moon (80% more massive than our moon, according to Wikipedia), it has the unique characteristic of having an atmosphere that obscured views of the surface until the launch of the Cassini-Huygens mission in 2004, designed to chart out primarily the Saturn system.

    A moon with an atmosphere is strange, and interesting. But what makes Titan truly intriguing is the presence of a liquid cycle, akin to our water cycle, in it's atmosphere and on it's surface. An average temperature of -179.5 degrees Celsius means that this liquid isn't water - it's methane. The atmosphere and oceans of Titan are composed of liquid methane, which, under the conditions on the surface, acts similarly to water. It evaporates, precipitates, and forms liquid bodies and oceans, just like on Earth. Deeper down below the surface, there is, in fact, liquid water too, at higher temperatures and pressures beneath an icy "crust".

    Titan is a strange planet, but interesting in it's composition. With a thicker, denser, and "taller" atmosphere than our own, it has some unique properties, and manages to be Earth-like in strange ways, by substituting life-giving water with a whole lot of poisonous (to us) hydrocarbons. But it is interesting nonetheless.
  19. oxy126
    Water is strange. Unlike most compounds, its solid form is (normally) less dense, and of a larger volume than its liquid form. Because of this, its very difficult to compress water, because normally there isn't really anything to compress it into. But the story of ice is a bit different from the snow and hail we see falling outside of our windows during these winter months. In fact, ice has many different forms, depending on the conditions it forms in.

    The ice we commonly know is called Ih - a common ice type with a hexagonal structure. But as you can see from the picture, there are many different types of ice. Ic is also a (relatively speaking) common ice type, with a cubic structure that can be present in the upper atmosphere. In total there are 15 different types of ice, all forming at different pressures and temperatures, all with different crystal structures, densities, and electrical properties. For example, while water is hard to compress, when put under great enough pressure at normal temperatures, can form into ice IV (not pictured), a denser form of ice. While most variations are just density and structure based, certain forms (like ice XI) have ferroelectric properties, which is something I looked up and failed to understand, but it sounded interesting. And noticing the lower pressures, below ~1 kPa (about 1/100 of normal sea pressure), liquid water fails to exist, and water vapour will undergo deposition straight into ice below this point.

    As we head into winter, it's interesting to note the complexities of such a common substance. It can take on many forms with many properties, and I think that's pretty cool.
  20. oxy126
    I'm a big fan of sound. Music for me is a nice blend of science and art, and I take strides to better my understanding of it occasionally. And occasionally, I enjoy listening to chiptune songs - 8-bit music, as you may call it. A typical sound wave is sinusoidal, meaning it looks like a sine/cosine curve. This is the natural state of a pressure fluctuation that is sound. However, sound waves are (obviously) not all sine waves. Because of the constructive/destructive interference of waves, waves with a new shape - or timbre - like with a square or saw wave, essentially keeping the dominant frequency (pitch) of the note while still changing how it sounds.

    What is really happening when this is going on is that, in some ways, the frequency is changing, but just not the dominant frequency. In music, an octave occurs when one note has double the frequency of another, and by changing the amount of sound energy contained in a certain frequency that is an integer multiple of the base frequency (be it an octave or a different multiple), you can change the timbre without distorting pitch. This is the fundemental basis lying behind the Fourier transform, a method for breaking down a period function into an (often infinite) sum of sine waves with different frequencies. With bar-based music visualizers, the same things is happening, with wave shapes being analyzed for the frequencies they contain. But this phenomenom is what makes music sound the way it does, and it demonstrates that wave interference can have some interesting and melodic effects.
  21. oxy126
    A lot of games let you fly planes, but when was the last time one let you fly a rocket? While if that has been what you've been looking for in your time-wasting pursuits, wait no longer, for Kerbal Space Program lets you do just that. As the director/god of the aptly named Kerbal Space Program, you have the ability to launch probes, satellites, landers, space planes, and a whole plethora of fancy little stuff. But behind all of this glamour comes (simplified) rocket science. Much like real rocket scientists, you have to design a craft with fuel and power constraints in mind. Going to the Mun may not be as trivial a task as some may hope.

    If you prefer fast paced action, this game probably isn't for you. But if you're willing to think a bit, ponder questions about choosing an engine with a larger thrust to weight ratio versus one with a higher specific impulse, or how you should stage your creation to successfully land on Minmus and return home safely, this might just be your cup of tea. I recommend checking it out.
  22. oxy126
    The trebuchet is an old art. Last time it was seriously used, people were assaulting castles and pillaging the countryside (for the most part). But oddly enough, for a time period associated with such little scientific innovation, is the trebuchet really so complex? It isn't hard to think why it works: it pulls a sling, that sling releases, and so away it flies. But for accurate predictions and optimization, it is actually a fairly complex beast.

    You may expect me to explain how it works. Well, I won't. It's complex enough where few definitive outlines exist for their ideal mathematical operations, and presently I don't have the time to take a crack at all that math. But I mention it because I feel as though it is a good example of complexity generated not by subject matter but rather the amount of subject involved. You have the sling, rotating around the end of the lever arm. You have the counterweight and beam, a first class lever, and in the real world, that beam has a linear mass density as well. You have friction around the fulcrum, friction in the chute, and a need for precise timing with the release of the ring from the end of the payload side of the beam (NOTE: if none of this makes sense to you, I would advise checking out http://www.redstoneprojects.com/trebuchetstore/how_a_trebuchet_catapult_works.html - it gives you a basic overview of how it all works). While this is all stuff we've covered, concepts we know, the fact that they are all combined in a complex system makes it much more difficult to be precise with.

    So just take note that, while solving problems using these concepts may seem easy, similar problems can become much harder with just a few things added in. Me, personally, I like this. It means there are always new things to try and explore.
  23. oxy126
    Boomerangs to some can be quite mysterious. One may ask, "why do they fly the way they do?" But fear not, for I'm here to explain them to you.

    At first glance, a boomerang might appear flat to the unsuspecting eye. But alas, for a boomerang to return to your hand, it must actually act a bit like a helicopter rotor, with one side angled up one way and the other the other way, so that when it spins it creates lift.

    But when you think of a helicopter, you think of something going up and down, not around in a circle. What you don't consider is that lateral movement of the boomerang cause air to flow past one side of the boomerang faster than the other as it rotates, create unequal lift, causing it to turn (this means two things: one, boomerangs are thrown vertically/almost vertically as opposed to horizontally, because that would cause more of a loop-de-loop, and it also displays one of the major shortcomings of single-rotor helicopters: they suffer from this same issue). It continues to turn as it flies, eventually creating the loop we all know and love.

    So if you're making a boomerang, keep this in mind: angle the fins. And for legal purposes I do not support the use of boomerangs as a projectile weapon. Thank you and goodnight.
  24. oxy126
    If a random star were to appear in our skies, and you asked an astronomer how far away it was, they couldn't give you an immediate answer. One thing I always took for granted was how these scientists were able to map the night sky, give us a detailed perspective on what was out there in the final frontier. Some of these methods (like how to determine how far away a star is) can be somewhat interesting.

    Using the right math, many people could triangulate the position of an object, as long there are a few known variables and objects in the field of view. However, on Earth, to calculate how far away a star is, through distances spanning hundreds of light years, it is very difficult, because the angles which are being dealt with are very small, and hence prone to error. However, given a 6-month span, our orbit around the sun gives us a much better distance to do this calculation with. Knowing such things as the precise time, radius of orbit around the sun, and the positions of other stars in the sky, we can calculate relatively well star distances.

    However, this only really works up to 400 light years (thanks, HowStuffWorks), because, while the 150 million kilometer difference in our position is a lot, with a star 10 light years away (still fairly close), the difference in angle is still miniscule, clocking in at just a few hundred-thousandths of a degree. Which is to says, that while the distances we get aren't perfectly accurate, for what they're worth they are pretty dang good.

    There are different, more spectroscopic and more accurate methods of determining a star's distance, that rely on standard gathered data for stars that work at all distances. But before this data was collected, really the only way to gather this data was through triangulation. That, simply put, means that olden astronomers, those like Galileo, were the ones doing all this tricky math. Cool stuff.
  25. oxy126
    The gravitational two-body problem is a popular concept in the study of planetary bodies. In essence, it models the paths taken by two massive objects orbiting around each other. Earlier today, I was thinking about our Earth's orbit around the sun, and how while it is easy to think that the Earth doesn't move the sun, it does. So while our solar system surely doesn't have only two bodies, I decided to assume it did (and with a perfectly circular orbit), and calculate just what the orbital radius of the sun is.

    Beginning this, I actually had no idea the gravitational two-body conundrum existed, so I tried to solve for part of it myself. Knowing the force of gravity on both objects (Gm1m2/r^2), and the centripetal force necessary to maintain said orbits (mv^2/r - note, however, that the r in both equations is not the same: the r for gravity is the sum of the radius of both bodies around the barycenter, or center of the orbit). Using this knowledge (and I won't bore you with the steps), I arrived at Ea/w^2 = Sb/v^2, with E=mass of earth, a=distance from Earth to barycenter, w=velocity of the sun, S=mass of sun, b=distance from sun to barycenter, and v=velocity of the Earth. However, I felt this required too many known values, and could be simplified.
    From there I looked into the laws of momentum. Knowing that the force of gravity was the same on both bodies, and that it acted (obviously) over the same time period, I deduced that the momentum imparted to both was equal. However, momentum is also mass times velocity. Using that knowledge, with my previously derived equations, I could further simply and eliminate my velocities, netting me, eventually, the distance of each mass to the barycenter (equivalent to the mass of the object times the radius between objects, divided by the sum of the masses).

    While you may not think this is too exciting, I found that deriving this, and then finding out I was actually right was interesting. All of these equations that were used were simple, but when applied together in the correct situation, they have the ability to solve more complex problems.

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