Comment Re:MIT and MythBusters busted it (Score 1) 83
Some of this is sort of true-ish but it ignores a lot of stuff on the other side of the equation, too. The most prominent is that the best mirror available to Archimedes was almost certainly a sheet of burnished bronze. He definitely didn't have modern silvered-glass mirrors; the process for making clear glass was not discovered for well over 300 years after his death. If it's touch-and-go doing it with modern mirrors, it's not possible with ancient ones.
Firstly, it's an assumption that bronze mirrors were the best available to Archimedes. Since well before Archimedes, people have been making mirrors out of polished metal. Yes, usually bronze, but other metals were available. Notably silver, which is very nearly as reflective as aluminum (and is notably _more_ reflective in infrared ranges). The obstacle for silver was obviously the cost, but, although modern silver plating did not exist, silver leaf did. While applied silver leaf would not be an ideal surface for a mirror intended for admiring ones reflection, it could potentially work quite well in one merely intended to reflect sunlight. Then of course there are other materials that were available such as pewter that could have been used for an improved mirror surface.
Of course, even if only bronze was available, there is still room for improvement in the shaping of the mirror so that it can focus the light to more of a point at the appropriate range. Bear in mind that I am not saying that Archimedes did any of these things. There is simply no evidence that he could not have. Suitable materials existed and were known at the time, even if they were not commonly used in vanity mirrors of the time. Not to mention that historical discoveries keep showing us that many inventions that we think of as modern have actually been invented in the past, then vanished into the mists of history: flushing toilets, steam engines, electric batteries, clockwork, etc.
I think that your discussion of dragons is also based on a complete failure to understand what gliding is. Of course a dragon has to generate lift equal to its weight to remain airborne; that is just Newton's second law, that an object with a net force applied accelerates in the direction of the force (in this case, downwards). This is what gliding is: gravity accelerates the wing down; the wing is angled so that downward movement is deflected by air pressure into forward movement; the lift on the wing is proportional to the square of the forward velocity; so the forward velocity increases until the lift equals the gravitational force and the wing stops being accelerated by gravity. In order for the drag not to slow it down again, this has to include a steady downward velocity to generate enough forward force to cancel out the drag.
Ironic for you to accuse me of a failure to understand when you clearly either have a serious reading comprehension problem or you do not understand the difference between lift and thrust. To clarify, I wrote: "...a dragon with certain characteristics would not be able to generate downward thrust equal to its body weight." Note please that I said "thrust". You replied with "Of course a dragon has to generate lift equal to its weight to remain airborne". This sentence is technically true, but does not relate to my sentence about thrust. Thrust and lift are different concepts in aerodynamics. Thrust can be used to generate lift, but most heavier than air flying machines and animals use significantly less thrust than their own body weight to stay aloft because aerodynamics allows them to generate lift greater than their body weight. That you go on to say " that is just Newton's second law, that an object with a net force applied accelerates in the direction of the force (in this case, downwards)." suggests that this was not mostly a reading comprehension fail, you just really do not understand aerodynamics. Or, at least you do not understand the role of thrust in aerodynamics.
So, my point stands, the author in the magazine in question was incorrectly assuming that a flying thing needs thrust equal to its weight to stay aloft. Your explanation about gliding entirely misses the point that gliding works without any thrust. A gliding object is capable of falling slower than acceleration due to gravity would demand because lift is countering that acceleration, not thrust. Now, gliding is not flying, but it is part way there. By also applying thrust to a gliding object, you can turn a gliding object into a flying object that can stay in level flight indefinitely (at least until the thrust runs out). The cost in thrust to do that is, under normal circumstances, less than the force of gravity that applies to the object and is generally approximately equal to the difference between the lift it gets as a glider and the force of gravity. Sure, that's a simplification. Once again, the main point still stands: you do not need thrust to equal or exceed weight in order to make something fly!
Supposing that the average dragon depicted in art had a body density similar to other animals, that is indeed a pretty good argument that they would be unable to fly because their tiny wings imply such an enormous forward velocity to be able to glide that it is clearly ridiculous. Your intuitive model is based on the flawed (and fairly ridiculous) idea that something gliding isn't being held up by its wings.
I'm not sure where you got your nonsense analysis of what I wrote. You seem to have made the error of thinking that I am trying to defend the idea that a dragon would be able to fly. That's missing the point entirely on your part. My point was that the argument they made for why a dragon would not be able to fly was nonsense. It was back of the envelope stuff by someone who was not considering the physical realities, just their little math problem.
You see this kind of stuff all the time. People claiming that, according to the math, bumblebees can't fly or kangaroos or sturgeon use more energy than they consume as food. All based on flawed models of aerodynamics or hydrodynamics or, in the case of kangaroos, ignoring that bounding is elastic and most of the energy from a jump is recycled in the next jump. Other fun examples are those people who insisted that large sauropods would have had to spend their entire lives in ponds because there's no way an animal that size could walk around without its leg bones fracturing. The ironic counterpoint to that ridiculous argument was that sauropods could not have stayed submerged because the pressure would have crushed their windpipes. That also ridiculous argument used a comparison between a sauropods neck and a garden hose, ignoring the fact that the garden hose is very, very thin and a sauropods neck would have been very, very thick and made of bone and very solid muscle.
So, that's the problem I have with so many Mythbusters episodes and other people who think that they have "disproven" things with simplistic methods and math. The problem is that they are not generally disproving the thing itself, they are disproving a model. If the model is wrong, then their proof is meaningless. That does not mean that the thing they are trying to disprove is actually real, it just means that they need to work harder to convincingly disprove it.