This site is populated by some way smarter than average folk. Thought a physics brainteasers thread might be fun.
I'll start:
Is it possible (theoretically or real world, either one) to build a wind powered vehicle which can travel directly downwind, faster than the wind, powered only by the wind, steady state?
Is it possible (theoretically or real world, either one) to build a wind powered vehicle which can travel directly downwind, faster than the wind, powered only by the wind, steady state?
I'm going to say 'yes', either by use of a special sail (which I think I've seen demonstrated, or at least tested) that allows the car to pick up speed; or perhaps with a wind power generator (though I don't know how that would work, but might involve concentrating the reconverted kinetic energy on the drive wheels: not getting more total energy but just using the energy available more efficiently).
If you are being driven by a tailwind, with a sail, as your speed increases the tailwind lessens and eventually stops as you reach the same speed as the wind. Your sail becomes useless.
Try a propeller. As you exceed the tailwind speed you are now in a headwind. But, there is secret to how the propeller is used, how it is powered before the transition and what it powers after.
Try a propeller. As you exceed the tailwind speed you are now in a headwind. But, there is secret to how the propeller is used, how it is powered before the transition and what it powers after.
Not really. If we had just the initial tailwind spinning the blade like a turbine it would spin in the opposite direction we would need after the transition to headwind. And, again, as the tailwind dropped so would the spin.
Clarification. If set up properly the propeller stays facing and spinning in the same direction throughout the full run.
Edited by AZPaul3, : No reason given.
Edited by AZPaul3, : No reason given.
Edited by AZPaul3, : Wow. I can really mess this up for someone if I get lazy.
I probably should have noted that while it's as "physics" brainteaser, it only requires simple Newtonian physics to solve it. It was included as a model physics problem in the 2013 International Physics Olympiad for high school students so entry level college physics knowledge will certainly do.
For now I'm only going to facilitate discussion rather than give out the answer. Also know that simple explanations that use terms like "energy" often include assumptions that may require diving deeper to get on the same page.
As to the ideas so far:
1: If attached rigidly to the vehicle chassis/hull, any mechanism that extracts energy from the wind by slowing the wind relative to the extraction mechanism itself will fail. As AZPaul3 notes above, once the vehicle is at windspeed there is no more relative wind to slow and thus no energy to extract.
2: The problem with the term "sail" is that most folk (even long time sailors) don't realize that a sail can function both as bluff body - catching air and slowing it down relative to the sail, and as an airfoil that is used to *accelerate* air relative to the sail. This change in function or mode need not include a change in sail shape (though it can include such), but can be achieved merely by changing the angle of attack (AOA) of the sail. To be clear, one must differentiate between the two states in which the sail operates. For simplicity (it's terms people already know) I prefer to call them "turbine mode" and "propeller mode".
In the simplest terms I can come up with:
A: in turbine mode, the sail slows the air relative to itself and from that exchange of momentum, energy can be extracted. B: in propeller mode, the sail accelerates the air relative to itself and to facilitate that exchange of momentum, energy must be input.
(Remember that while the typical applications of turbines and propellers have the blades spinning on a shaft, that's merely a practical issue and both would function the same aerodynamically in a linear fashion.)
I'm unsure if your question relates to the natural wind direction (across the ground), or the relative wind direction (across the vehicle chassis).
When the brainteaser refers to "downwind", it's referring to the natural wind direction. To go faster than the wind, directly downwind, there will need be a relative headwind to the vehicle once the vehicle exceeds the natural speed of the wind.
Since it has been done, I'm going to go out on a limb here and say, yes, it can be done.
how
Attach the rear wheels to the prop. As the tailwind moves the cart the wheels transfer power to the prop causing it to spin. The faster the tailwind pushes the cart the faster the prop spins. The spinning prop creates a negative air pressure to the front and a positive pressure to the rear adding additional forward momentum to the cart AND transferring additional power to the wheels. As the tailwind lessens and drops away the prop has picked up the slack and becomes the motive power to the wheels and the cart. The inertia of the cart takes it right through the transition from tail to headwind. The (now) headwind adds to the action of the prop which transfers additional power to the wheels. Eventually you run out of drive space, run into a tree, and crash.
would such a vehicle violate the laws of physics?
Hmmm, tricky.
Unless there is a new god whose name is not Newton I'd have to go with, no.
Since it has been done, I'm going to go out on a limb here and say, yes, it can be done.
Well certainly IF it's been done, then it can be done, but I'm wondering why you're so sure it's been done?
OK. For the cookie:
First off, the brainteaser specifies "steady state" which precludes the usage of stored energy to accelerate the vehicle. Your description violates that clause so no cookie quite yet. sorry.
But generically let me see if I have your description correct: The wheels turn the prop which motivates the prop forward which drags the chassis along with it thus forcing the wheels to turn which turns the prop which pulls the chassis forward which turns the wheels which turns the prop which turns the wheels ... ... ...
Relating to the 'It's been done so of course it's possible' take, many people (including physics professors and at least on Nobel prize winning physics professor) say it hasn't been done and will never be done as it violates the law of conservation of energy.
Here is a link to a physics professor from Louisiana who writes a physics blog and articles for Wired magazine who gives his reasons as to why it is impossible.
On the same "Can it be done" topic, these are the words of Science author and blogger Mark C Chu-Carroll written on his science blog (good math / bad math) when someone suggested he look into the topic (more on Mark later).
To summarize his argument, I'll quote the last paragraph of his blog entry:
quote:Everyone should be able to understand the physics involved here. My third grade daughter can understand this. This isn’t difficult. There’s nothing tricky or subtle about it. If you have a vehicle moving at the same velocity as the wind, the wind cannot possibly exert any force on the vehicle. No force, no acceleration. Period. How can supposedly intelligent, educated people not know this?
And here is the entire entry:
This has been quite the day for the bad math; I’ve encountered or been sent a bunch of real mind-numbing stupidity. Unfortunately, I’m too busy with work to actually write about all of it, so as I have time, I’ll pick out the best tidbits. Today’s example is a fascinating combination of perpetual motion and wrong metrics.
Via BoingBoing comes a bunch of bozos who believe that they can create a wind-powered vehicle that moves faster the wind that powers it.
This is, obviously, stupid. Wind power isn’t some kind of magic: you generate power by the motion of air pushing against some surface. And there’s the catch: the power comes from moving air pushing. The air has to be moving relative to the surface being pushed — or there’s no way for the air to push it.
The idea that somehow wind moving in the same direction as a vehicle can make the vehicle accelerate when it’s moving faster than the wind. There’s no mechanism by which the air can push. It’s actually really remarkably simple: the force of a wind pushing on a surface is (roughly) proportional to the speed of the air relative to the surface, and in the same direction as the motion of the air relative to the surface. Once you’ve got that much, then it’s just good old F=ma.
So, you start with the vehicle at a standstill, and the air moving relative to it at 7mph. So you’ve got an air speed relative to the vehicle of 7mph. This pushes the vehicle, so it accelerates. After some amount of time, it’s been accelerated up to 3.5 mph. Now the relative speed of the air relative to the vehicle is down to 3.5mph. The force of the wind against the vehicle is now half what it was when it was stationary. And so on, until friction becomes dominant, and you get a stable speed.
What would happen if you went faster than the wind? Like, say, 10mph? The speed of the air relative to the vehicle would then be -3mph. So the force from the wind would be in the opposite direction — that is, the air will now be decelerating the vehicle. There’s just no way for a wind moving more slowly than a vehicle to accelerate that vehicle in the direction of the wind — the wind isn’t moving from the viewpoint of the vehicle anymore.
But that’s not the end of the stupidity of this. We haven’t gotten to the error of measuring the wrong thing.
A couple of bozos decided that they wanted to test the vehicle under controlled laboratory conditions. They cite relativity to make the claim that a vehicle moving relative to the ground is equivalent to the ground moving relative to the vehicle — they’re just different, but equally valid frames of reference. And they’re absolutely right about that, as far as it goes.
Using that reasoning, they make a model of the vehicle, and put it on a treadmill. And, suprise! — when they do that, the propeller spins and accelerates the vehicle towards the front of the treadmill — the propeller on the vehicle accelerates it forward, so that it’s moving faster than the treadmill.
Anyone with a clue should see the problem here.
If you’re testing a wind powered vehicle, then in a closed, windless room, putting the vehicle on a treadmill moving at 10mph is not the same thing as putting the vehicle on a stationary surface in a 10mph wind.
You see, they didn’t actually preserve the original reference frame. In the original reference frame, you had a stationary vehicle with no motion relative to the ground, with the air moving in a forward direction relative to vehicle, and with no other forces acting on it. In the treadmill experiment, you had a vehicle that was moving forward relative to the ground beneath it, but stationary relative to the air. There is no wind relative to the vehicle when it’s put onto the treadmill. That might seem like a problem — but in the outdoor experiment, once the vehicle accelerates to windspeed, it’s really the same situation as in stationary air with the treadmill moving under it.
But the treadmill reproduction isn’t an accurate reproduction of the original outdoor demonstration of the vehicle. There’s a force operating on the vehicle on the treadmill that isn’t there in the outdoor demonstration. The treadmill isn’t level.
If you want to accurately reproduce an experiment under controlled conditions by producing an equivalent reference frame, you actually need to perform the experiment in an equivalent reference frame.
In the real world, we obviously can’t perfectly reproduce everything. But you can look at the experiment you’re performing, and ask what the key, relevant factors are to accurately reproduce it.
In the case of this wind powered vehicle, the most crucial thing is the forces operating on it. What the experiment is trying to do is demonstrate that wind can exert a force on the vehicle even when the vehicle is moving faster than the wind. So it’s crucial to make sure that your controlled experiment includes the forces from the original demonstration, and doesn’t add any forces that weren’t present in the original.
The reason that I say this is a problem of metrics is because the bozos in question believed that they were creating an equivalent reference frame because the ground speed in the two reference frames were equivalent. Speed is one metric — that is, one measurable quantity in the experiment. But it’s not the important one. If you can reproduce the experiment using a windspeed of 10 mph instead of 7mph, no one is going to claim that you’ve changed anything important. Velocity is an important metric for measuring the outcome of the experiment. But all that you really care about is the difference between the velocity when the experiment started, and the velocity when it finished. On the other hand, force is the key metric: what the experiment really wants to test is if wind can exert a force on the vehicle under the correct conditions. That’s the key.
Their results are rubbish for exactly that reason. There’s a force present in their controlled experiment that wasn’t present in the original. And that force is being channeled through the mechanism of the device to provide some apparent forward acceleration.
Whenever I point out a perpetual motion machine, I get people insisting that while the device in question might violate the laws of physics, it’s not a perpetual motion machine. So I’ll address that criticism before anyone even raises it. What this device claims is that if you start the vehicle in a wind, once it’s started, if it’s placed it in non-moving air (that is, the situation which is equivalent to when it’s accelerated to windspeed), it will continue to move, and even to accelerate. That’s classic perpetual motion.
Finally, I’ve got to say that I’m incredibly disappointed in how utterly clueless about things like this most people are. In the original post on BoingBoing, the author says:
quote:I admit that I don’t understand the physics involved, so I don’t really know whether DDFTTW is possible, but I am siding with Charles on this because I’ve never known him to be wrong when it comes to math, physics, or electricity.
Everyone should be able to understand the physics involved here. My third grade daughter can understand this. This isn’t difficult. There’s nothing tricky or subtle about it. If you have a vehicle moving at the same velocity as the wind, the wind cannot possibly exert any force on the vehicle. No force, no acceleration. Period. How can supposedly intelligent, educated people not know this?
ThinAirDesigns' quote of Mark C Chu-Carroll writes:
There’s nothing tricky or subtle about it.
There is a little bit of trickiness to it, though.
My initial thought out-of-the-gate was "nah, can't be done... otherwise it would continue to gain speed and there would be no 'steady state.'"
My second thought was:
But ThinAirDesigns is a smart man, and he himself is stating that he thinks the people here are smart... if he's so smart, and he thinks people here are smart... why would he ask such a non-question?
This idea makes me second guess myself (as I haven't actually taken a physics course in over a decade now).
Really, "your reputation proceeds you" and no matter how many times you (or anyone else) says "there's nothing tricky here..." the way the question is proposed in and of itself belies a certain amount of tricksy magics
...which led me to belief that maybe there was some fancy way of handling Newtonian physics that I was immediately unaware of (such a thing has happened many, many times).
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