(NOTE: It appears that I really blew it with this one. I’m the bozo in this story. After lots of discussion, a few equations, and a bunch of time scribbling on paper, I’m convinced that I got this one wrong in a big way. No excuses; I should have done the analysis much more carefully before posting this; looking back, what I did do was pathetically shallow and, frankly, stupid. I’m sincerely sorry
for calling the guys doing the experiment bozos. I’ll follow up later this weekend with a detailed post showing my analysis, where I screwed up, and why this thing really works. In the meantime, feel free to call me an idiot in the comments; I pretty much deserve it. I’m leaving the post here, with this note, as a testament to my own stupidity and hubris in screwing this up.)
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:
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?