Introduction
By Mark Frauenfelder
In 2007, MAKE projects editor Paul Spinrad sent me a link to a YouTube video of a wind-powered cart, made by a Floridian named Jack Goodman, that seemed to be able travel directly downwind faster than the wind. How could a wind-powered cart outrun a tailwind, we wondered? Intrigued, Paul and I asked contributing editor Charles Platt to repeat the experiment and report on the results for MAKE.
Charles built a small cart, but was unable to get it to outrun the wind. Charles wrote in his article (which appeared in MAKE Volume 11 in August 2007), “Perhaps Jack Goodman has some clever explanation for this. Perhaps I didn’t build my version exactly the same way that he built his. Perhaps you should build your own, just to make sure.” In the end, Charles suspected Goodman had played a prank.
As soon as the issue hit the newsstands, our message boards (here, here, here, and here) began to boil with impassioned arguments over the theoretical and practical possibility of travel “DDWFTTW” (Directly Downwind Faster Than The Wind). Several people emailed me, including a fellow named Rick Cavallaro, about errors in MAKE’s wind cart design. I soon came to the conclusion that we had likely misunderstood the design of Jack Goodman’s cart. I told Rick I would like to publish a follow-up article (authored by him) in MAKE, but not until I’d conducted more research, and not until Rick had developed a convincing DDWFTTW demonstration. Rick happily obliged, and in the months to follow, he kept me apprised of his impressive research efforts.
Meanwhile, I began corresponding with wind cart enthusiasts, skeptics, physicists, and Jack Goodman. There was no clear consensus — even some physicists told me DDWFTTW was impossible — but I was starting to side up with the proponents.
Then, in July 2010, Rick informed me that he and his colleagues had taken a downwind cart they’d built onto the El Mirage Dry Lake Bed in southern California and had achieved a speed 2.8 times faster than the wind. They carried out the test in front of authorized representatives of the North American Land Sailing Association (NALSA). It was very convincing, and I asked Rick to write an article about it, which you can read below.
Is DDWFTTW possible? In 2007 I didn’t think so. In 2010, I think so!
—Mark Frauenfelder, editor-in-chief of MAKE
The Little Cart That Did
By Rick Cavallaro
Is it possible to build a wind-powered vehicle that travels directly downwind, faster than the wind, powered only by the wind, continuously?
This is a question I asked myself several years ago. After working out a few vectors, I decided it should work just fine. But since this is pretty clearly counterintuitive, I figured I’d pose the question as a brainteaser on a kitesurfing forum and a
radio-controlled helicopter forum.
To my surprise, very few people believed my claimed answer was correct. They simply didn’t accept my vector analysis.
But more surprises were in store. It turns out that an aeronautical engineer by the name of Andrew Bauer built exactly such a vehicle in the 1960s. There exist a few still photos of Bauer standing next to his cart, but little other evidence. There’s no compelling documentation beyond Bauer’s own claim that he beat the wind speed briefly, and by a modest amount.
The next surprise came when a man by the name of Jack Goodman built a working model of such a cart to settle the now raging debates taking place across the internet. Goodman intended only to prove to his sailing buddies that the feat was possible, but one of those buddies posted Goodman’s proof (in the way of a video) on the internet.
This only fanned the flames. The video went viral. There were claims it was a hoax — that it was being pulled by a string, that it was going downhill, the wind wasn’t directly at its back, the wind wasn’t steady, and on and on. Goodman could have made additional videos addressing these concerns but, as we learned the hard way, doing so would not be trivial, and still few would be convinced.
In 2007, MAKE published an article titled “The Little Cart That Couldn’t” by Charles Platt. This article specifically addressed Goodman’s video, and concluded that Goodman had hoaxed us all.
Small demonstration wind cart. Photo: Rick Cavallaro
Learning the Hard Way
After more than a couple of years debating this on the internet, my old hang gliding buddy, John “JB” Borton, convinced me we would have to build our own cart and address the skeptic’s concerns if we hoped to convince them. And so we did.
To address the issues of whether the road was level, the wind was constant, the cart was going downhill, or being pulled by a string, we decided to perform (and document) carefully controlled tests. If this were an airplane, we’d use a wind tunnel. But since this vehicle is intended to go downwind — rather than into the wind — the appropriate instrument for our tests was a garden-variety treadmill.
Rather than move the air over the road, we’d move the road beneath the air. Galileo, Newton, and Einstein have assured us (and it’s now one of the most basic and accepted principles in physics) that these two situations should be identical from the point of view of the cart.
If our cart could hold its ground on a level, moving treadmill, it would be a demonstration of going directly downwind at exactly wind speed. If it could advance, against the motion of the belt, it would be an ideal demonstration of going directly downwind faster than the wind.
Of course there are those that argue there’s no wind in the room, so the treadmill test is not valid. But it’s really just a matter of looking at it from the cart’s point of view. If you ride your bike downwind at exactly wind speed you won’t feel any wind either.
Video footage of the first run of the two days spent on the lakebed in Ivanpah, NV
So, the little cart did as we predicted. Not only did it hold its own on a level treadmill, but it advanced against the belt consistently. In fact, we inclined the treadmill to its maximum angle, and the cart climbed the treadmill against the motion of the belt.
Still, most of the skeptics remained … skeptical. So we invited them to submit tests they’d like to see. We panned the camera to show there were no fans or strings. We hung streamers over the belt, in front of the cart, and behind. We placed a fan in front of the cart to create a headwind (as requested). But still the doubters (including Platt as well as some noted physicists and aero engineers) remained unconvinced.
Ultimately, we posted a detailed set of build videos (watch part 1 | part 2 | part 3) so that anyone could build their own working model of our cart and prove it to themselves for about $40 in parts. In Texas, group of high school students on a budget followed our plans and improvised them to keep the price below $20! The result? They won the science fair with
their demonstration.
Going Full-Scale
But with the skeptics still unconvinced, and the hang gliding and kitesurfing seasons winding to a close, JB convinced me we’d have to build a full-scale, manned cart that could operate outdoors in “natural” wind and be witnessed by trustworthy experts. And so we did.
With funding from Joby Energy and Google, we proceeded to build a cart that weighs 450 lbs and stands 23′ tall to the top of its 17′ propeller. We approached the North American Land Sailing Association (NALSA) to develop a record category specifically for wind-powered vehicles designed to go directly downwind faster than the wind. We worked with NALSA over the next several months, and ultimately established a world record by going 2.8 times the wind speed directly downwind on the 2nd of July 2, 2010 on the El Mirage Dry Lake Bed in California’s Mojave Desert.
Blackbird wind cart. Photo: Emilio Castaño Graff
Some skeptics still remain, but then there are still those who believe the Earth is flat and man never stepped foot on the moon. So we’ve decided to be satisfied with the evidence we’ve produced and the minds we’ve changed. And we’d certainly like to thank MAKE magazine for giving us the chance to set the record straight regarding “the little cart that did.”
Blackbird wind cart. Photo: Steve Morris
In the spirit of MAKE and the scientific method, we truly hope some of you will follow our build videos and make one of these carts for yourselves. It’s not difficult to do, and if you have a hard time accepting that a wind-powered vehicle can go directly downwind faster than the wind, you owe it to yourself to see it firsthand.
Videos
Video shot by Richard Jenkins from the back of JB’s truck at El Mirage during the NALSA runs
Discovery Channel segment on the Blackbird
Official NALSA announcement of world record run
Up next: On Monday, Make: Online will run my piece about wind carts and their proponents and detractors, and on Tuesday, you can read my interview with Jack Goodman, the wind cart designer who captured the attention of so many people. –Mark Frauenfelder
Editor’s note: We gave Charles Platt, the author of the wind cart article in MAKE Volume 11, the opportunity to respond. His response is below. Rick Cavallaro asked to respond to Charle’s statement, which is also below.
I have never denied that a vehicle may be designed that will move into a headwind if the propeller is geared appropriately. What I do not believe is that this vehicle can start from rest with the wind behind it, accelerate until it is moving at the same speed as the wind, and then continue to accelerate faster than the wind, i.e. into a net headwind, without any fluctuations in wind speed, and without any gear-shifting along the way. That is what the original video from Florida purported to demonstrate, and is where all the arguments began. I have always suspected that the Florida video was faked.I know very little about Rick Cavallaro’s cart, and am not very interested, partly because Rick has been extremely abusive, obnoxious, and condescending to me, and partly because, as I say above, I am quite willing to believe that his vehicle can move into a headwind. Indeed, the very primitive cart that I built for my original MAKE article did succeed in edging forward into a strong blast from a large fan. Again, what I do not believe is that his vehicle or any other can start with a steady wind behind it, accelerate to a speed equal to that of the wind, and then continue to accelerate so that it is moving faster than the wind, in one uninterrupted process.
I have repeated myself in an effort to make this clear. — Charles Platt
Mr. Platt seems to suggest that he refuses to consider real-world evidence because he feels I’ve been “abusive, obnoxious, and condescending” to him. This strikes me as being ironically similar to our differing position on reference frames. From where I stand, Platt established the pattern of abuse and condescension in his emails to me. Perhaps we’re both right (or wrong) on that count.
Unfortunately, Platt wrote an article presenting an unfair attack on an honest man (Jack Goodman), without even contacting Goodman or making any reasonable attempt to reproduce Goodman’s results. To me this seemed unfair. My only hope here is to set the record straight. I can live with the fact that Platt, and many others, may never accept these results that have been ratified by NALSA (a qualified, independent, and disinterested organization). I hope that we can agree to leave it at that, and not attack each other in public any further. — Rick Cavallaro
Rick and JB are great guys and good friends, I was there helping out on the record days and shot some photos:
http://picasaweb.google.com/davidhglover/DDWFTTWJuly3RecordDay
http://picasaweb.google.com/davidhglover/DDWFTTWJuly2RecordDay
http://picasaweb.google.com/davidhglover/DDWFTTWJuly1
When will he admit his mistake? He just does not get it.
I recently learned, from a source whom I trust, that Rick’s vehicle has a ratchet that allows the propeller to spin freely (i.e. not driving the wheels) when the wind blows from behind. The observer told me that there was “no easy way” to disconnect this ratchet, and it was used in every run that he observed.
This is a violation of the conditions that I set when I first issued a challenge. The challenge was to build a cart that behaves as Goodman’s cart allegedly behaved. It must begin by accelerating in response to a following wind, must reach a speed equal to that of the wind, and must continue to accelerate into the wind–without any kind of gearing or other transmission that changes the mechanical relationship between the propeller to the wheels during this sequence.
A ratchet allows the propeller to spin freely without exerting a reverse force via the wheels when there is a following wind. It is an obvious way to get around the problem that a propeller which is angled to drive the wheels and move the cart forward into a headwind will have the opposite effect in a tail wind. This is the same old, same old problem which I raised at the very beginning, and which Rick told me was merely a reflection of my stupidity and lack of understanding of aerodynamics.
I look forward to an admission from Rick that he had to add the ratchet to make the cart work. I also look forward to the $10,000 he pledged, although not with much expectation.
Lastly I understand that the propeller on the cart has variable pitch. This, too, is a violation of the terms that I set out.
You completely misunderstand the function and use of the ratchet. This video has no ratchet nor variable pitch: http://www.youtube.com/watch?v=EEuAqq8FINw
By what you wrote I think you still don’t understand how the vehicle works.
Then you say: ” It must begin by accelerating in response to a following wind, must reach a speed equal to that of the wind, and must continue to accelerate into the wind–without any kind of gearing or other transmission that changes the mechanical relationship between the propeller to the wheels during this sequence.”
That is exactly what Blackbird does. It works – I was there at El Mirage. You have a fundamental blind spot to the claim and the reality of what is happening. Some day you will see the error and I hope you blame yourself because many people have tried to explain it to you, but I think you are unwilling to listen.
>> Violation of the original terms of the challenge
Wrong again – in so many ways. First of all, you never accepted my challenge, nor did you offer me a challenge. Secondly, our ratchet exists to allow us to push and tow the cart around without the prop spinning. The ratchets were engaged during the runs. Our model carts have no ratchets (because we can pick them up and carry them around) – yet they still work just fine. These ratchets are a convenience for handling the cart and to allow us to brake at the end of the run without putting reverse loads on the transmission. They have nothing to do with the terms of the challenge you had with a different person.
>> … which Rick told me was merely a reflection of my stupidity and lack of understanding of aerodynamics.
Perhaps I should post the entire email thread between you and I. I’m pretty sure I never used that word. You’re the one that seems intent on making this abusive – and on getting it wrong at every turn.
>>I look forward to an admission from Rick that he had to add the ratchet to make the cart work. I also look forward to the $10,000 he pledged, although not with much expectation.
You simply refuse to read anything at all on this topic – huh? The arrangement between you and I was to be a bet. I offered you $100K against your $10K (as Mark Frauenfelder noted in his article). You refused the bet for reasons that only you know and we can only guess – even though it was 10:1 in your favor.
You’re darn right that you’ll get no admission from me that I had do use a ratchet – because I did NOT have to use a ratchet. If you even made an honest attempt to understand this thing you would understand that.
Instead I get exactly what I got throughout our email chain – evidence that you didn’t even read what I wrote. Instead you asked what made me so arrogant as to think I could write an article. What I wrote was an article to correct the article you wrote. And unlike you, I did my homework. What you did was to attack a man that you never even bothered to contact. That’s not journalism!
>>Lastly I understand that the propeller on the cart has variable pitch. This, too, is a violation of the terms that I set out.
There are three problems with that:
1) You did not set out any terms for me. You’re in no position to do so. You refused to take my bet.
2) Variable pitch is not required – we proved that with the small carts and with the manned cart in Ivanpah.
3) If you understood this cart you would understand that this doesn’t violate the terms you set out for YOU to give $10K to Peslel. The only terms involving me paying anyone were based on a bet that you refused – and would have lost.
If you insist on continuing to misrepresent our conversations I will post our entire email exchange here.
>> If you understood this cart you would understand that this doesn’t violate the terms you set out for YOU to give $10K to Peslel. The only terms involving me paying anyone were based on a bet that you refused – and would have lost.
@ myself
I blew it here. Platt offered Peslel $1K if Peslel could demonstrate DDWFTTW under Platt’s terms (which Peslel did).
The arrangement between Platt and I was to be a 10:1 bet in Platt’s favor – my $100K against his $10K.
I simply made an error when I spoke of Platt’s arrangement with Peslel being $10K.
Even if Rick’s vehicle did need a ratchet to work (which it doesn’t) how would that invalidate it as a DDWFTTW vehicle?
Yowza Charles — through your lack of research on the vehicle you just continue to dig your hole deeper.
I can only assume that this lack of research is willful since rather than simply asking us questions about the vehicle (like you should have done with Goodman to start), or read the extensive construction blog (that you are well aware of), you just continue to make stuff up. There are so many things fundamentally wrong in your comments that it’s hard to know where to start.
Charles:
>>I recently learned, from a source whom I
>>trust, that Rick’s vehicle has a ratchet …
The ratchet in question is no secret — it’s fully documented on the construction blogs, pictures and everything.
http://www.fasterthanthewind.org/2010_04_01_archive.html
http://www.fasterthanthewind.org/2010/05/higher-torque-upgrades.html
Let me point something very important here — the ratchet has absolutely *nothing* to do with normal operation of this craft. The ratchet has *not once* released and gone ‘click, click, click’ during the running of the vehicle. Easily demonstrated physics dictates this and video documentation shows it.
Here’s the purpose for the ratchet on the prop shaft — if the driver of the Blackbird has to make a panic stop, the spinning mass of the propeller would try to keep it spinning while the brakes (on the drive axle) try to bring it to an immediate stop. For safety reasons, the brakes are much more powerful than the propulsion system (just as on any car). We wanted strong brakes (for obvious reasons), but we don’t want our transmission to snap just because the driver had to slam on the brakes.
Without the ratchet, the mass of the prop would backdrive the transmission and overload it. With the ratchet, in a panic stop the vehicle can be brought to zero quickly, while propeller can at its own pace, coast to a stop independent of the vehicle movement — just going ‘click, click, click’ until it RPMs are zero.
As an additional plus, the ratchet allows us to tie the prop down and push the vehicle around by hand (backwards) without the prop spinning and getting in our way or hitting something.
Again, since under normal operation the torque on the shaft is always in the same direction and the ratchet is FORCED by this torque to remain engaged the entire time during and run.
We’ve never had to make a panic stop so it’s never even been used for it’s primary purpose.
Charles:
>> [this ratchet] allows the propeller to
>> spin freely (i.e. not driving the wheels)
>> when the wind blows from behind.
First, the prop NEVER tries to drive the wheels forward under ANY circumstances other than panic stop, so this parenthetic notion you put forth above (i.e. not driving the wheels) is ALWAYS true — no ratchet needed to influence that.
Second, since I’m familiar with every single observer who was at every one of our tests, I can assure you that you are misundstanding whatever it was that they told you.
Ask ANY of those observers this question:
“Before and during each run that you observed, when the Blackbird was sitting still in the tailwind or running below windspeed (i.e. “wind blowing from behind”):
A: was the propeller spinning freely as Charles Platt asserts the ratchet allowed?
or
B: was the propeller’s rotational speed directly tied to and spinning directly proportional to the rotational speed of the wheels?”
In other words, “did the prop every spin freely in the early stages of the run, or was the propeller always tied directly to the wheels?
Their answer to a man will be “B”.
I also know that each of them is willing to talk publicly about their observations and they know we would encourage them to do so and actually hope that they would.
In light of that I encourage you to email your observer that question and ask him to respond with “A” or “B”. and post the answer here. Thanks.
Let’s be clear — I’m not accusing you of lying here, but I am most assuredly stating that just like your continued misunderstand of the fundamental operation of the craft, you have misunderstood the operation of the ratchet. You owe it to yourself, your readers, Pelesl (whom you owe $1,000 to as he fulfilled your original requirements, word for word btw) and especially the observer you have just misrepresented to get and post the observers answer to that above question. What it will show is that again are attempting to defend yourself through lack of knowledge and understanding.
Additionally, as someone else already posted, there is plenty of video around showing NALSA observed runs (in Ivanpah) where the prop shaft ratchet was NOT installed (it broke just before we left — again documented in the construction blog) and there was NO variable pitch hub in use (not built yet — again documented in the blog) and still we went near 3x the speed of the wind from a standstill. These points themselves demonstrate the fallacy of your position.
Your lack of knowledge on this topic, and your willingness to make stunningly false assertions based on that lack of knowledge is a serious setback to any credibility you might wish to have as a journalist. You really should step up to the plate, do the sort of research the your Editor-in-Chief did and return wiser and accurate. Your not doing yourself favors at this point.
JB
@Charles Platt:
>>> “I recently learned, from a source whom I trust, that Rick’s vehicle has a ratchet that allows the propeller to spin freely (i.e. not driving the wheels) when the wind blows from behind. The observer told me that there was “no easy way” to disconnect this ratchet, and it was used in every run that he observed.”
In my earlier post, challenged you to email a specific question to your observer source. The purpose of this clearly worded question (see bottom of post) is for YOU to find out for youself if the assertion you make above is actually true, or if you simply misunderstood what the observer told you.
http://www.nalsa.org/BlackBirdDDWSR/Observers%20ReportNALSA%20C4BlackbirdJuly2and%2032010.pdf
You will notice that the official Observers Report from NALSA includes a section/paragraph listing everyone who was at the runs. Attending folk were asked to ‘sign in’ and leave their info in case there was a need to refer to them later (like perhaps someone who wasn’t there later makes claims that aren’t true).
To put it bluntly, I have no faith that you will actually email that question to your observer source on your own initiative and post the answer here, so in the spirit of Make Magazine (a go out and do it yourself if you want it done publication) I will be performing that service here, in this public forum.
So here’s how it’s going to work — one by one each of the observers on that list are going to read that question and respond with their A/B answer (and any other comments they may wish to add). I will post their answers here as I receive them. They will all respond and will give me permission to post their answer because that’s the kind of folk that they are – all of them took the time out of their busy lives to travel to a god-forsaken spot in the desert to observe the tests. Most drove for hundreds of miles, some flew for thousands, all on their own dime and they will not shy away from such a challenge I am sure.
The way for you to look your best would be for you to FOR ONCE, get ahead of the curve on this mistake you’ve made and to return here with a statement saying that it’s a simple mistake that you’ve made in this case and that even if you don’t understand how the ratchet was integrated and used, what you DO know is that contrary to your assertion, the propeller wasn’t “freewheeling” when the vehicle had a following wind but rather was tied directly to the rotation of the wheels.
Here is a reprint of the relevent question:
“Before and during each run that you observed, when the Blackbird was sitting still in the tailwind or running below windspeed (i.e. “wind blowing from behind”):
A: was the propeller spinning freely as Charles Platt asserts the ratchet allowed?
or
B: was the propeller’s rotational speed directly tied to and spinning directly proportional to the rotational speed of the wheels?”
In other words, “did the prop every spin freely in the early stages of the run, or was the propeller always tied directly to the wheels?
Richard Jenkins shoots unedited video, and read his write up – very funny – RIchard is the world land speed record holder for a land yacht. http://www.fasterthanthewind.org/2010/07/video-from-richard-jenkins-world-land.html
I find it more than a little ironic that Platt thinks I’ve been abusive, obnoxious, and condescending. I’ll be more than happy to post the email exchanges between Platt and myself so that people can decide form themselves who has been abusive, obnoxious, and condescending.
I think people will find that Platt’s version of reality in that respect is similar to his unfounded denial of the facts shown clearly in these videos – which he was invited to witness for himself.
But I guess I can understand his refusal to accept the obvious since he has a $1000 incentive to not understand. Platt offered another reader $1000 of his own money if that reader could demonstrate DDWFTTW. He did. Platt did not pay.
I see a link but the word “vector” doesn’t appear over there.
I see now that that link has multiple pages. Page two does mention vectors. There’s even a broken img tag that I guess used to have a drawing. I’d be interested in a page dedicated to the mathematics of this (in pictures and equations, which are harder to argue with than hand-waving explanations).
Platt:
>>
Again, what I do not believe is that his vehicle or any other can start with a steady wind behind it, accelerate to a speed equal to that of the wind, and then continue to accelerate so that it is moving faster than the wind, in one uninterrupted process.
>>
And yet that is what exactly what the Blackbird has done scores of times in front of dozens of independent witnessess. This including Officials from NALSA while 18 recording sensors were documenting the easy to achieve feat.
Charles, when the evidence disproves your theory, it’s time to admit you were wrong and come up with a new theory.
JB
>> I see a link but the word “vector” doesn’t appear over there.
Which link did you follow? I don’t know that my initial vector analysis is on-line, but I’ll be more than happy to post it.
“I figured I’d pose the question as a brainteaser on a kitesurfing forum and a radio-controlled helicopter forum.
To my surprise, very few people believed my claimed answer was correct. They simply didn’t accept my vector analysis. ”
The helicopter thing is a link. Since they “didn’t accept” a vector analysis, I assume one was given in that thread.
Yes, I’d very much like to see it. For one thing, I can’t follow any of these YT videos. I can’t even tell what is being claimed, let alone what is really happening (i.e. wind directions or speeds, rotation directions or speeds, etc).
Hi David,
I’ll let Rick get you the vector analysis you are looking for, but I wanted to responsed to this:
>> I can’t even tell what is being claimed,
Here’s the claim:
“Directly downwind, faster than the wind, powered only by the wind, steady state”.
JB
Has anything new happened since July?
What prompted this article now?
Make originally published an article which contained incorrect conclusions. Fortunately, the editor of the magazine has been following the progress of the Blackbird project and decided to to the right thing by publishing an article with made the appropriate corrections.
Kudos to Mark Frauenfelder and any editorial staff involved.
JB
We are running Rick’s article in MAKE, but since we are a quarterly, we wanted to run it online before the story got too old.
My take on the wind wagon:
The prop drives the wheels, but the wheels also drive the prop. The wind spins the prop, but the prop also provides lift. Think of it as an autogyro on its side.
This cart operates in 3 states:
1. Starting downwind, the wind pushes on the prop (and cart) causing the prop to spin, transmitting power to the wheels and off she goes. The lift from the prop increases and pulls the cart along.
2. Matching wind speed, the prop freewheels and begins to receive power from the wheels. The lift from the prop is still pulling the cart forward.
3. Exceeding the speed of the wind, there is now a headwind. The momentum of the cart is causing the prop to continue rotating, causing it to act like an airplane prop and pull the cart along. Friction enters the scene (fah, it was always there!) and eventually slows the cart back below windspeed.
disclaimer: I am not coming to this as a scientist, but as a sailor and model airplane builder.
Hi Rhudson:
>>> 1: . Starting downwind, the wind pushes on the prop (and cart) causing the prop to spin, transmitting power to the wheels and off she goes.”< <<
There is never any power transmitted to the wheels from the prop. From the very first moment of movement, the rolling wheels force the propeller to turn.
There is even a ratchet on the prop shaft that ensures the prop can never drive the wheels.
http://www.fasterthanthewind.org/2010/04/not-this-time.html
http://www.fasterthanthewind.org/2010/05/higher-torque-upgrades.html
>>> 2. Matching wind speed, the prop freewheels and begins to receive power from the wheels. The lift from the prop is still pulling the cart forward.”< <<
As pointed out above (and by Neuropulse), the prop never freewheels, but rather recieves power from the wheels at *all* times and *all* speeds.
>>> 3. Exceeding the speed of the wind, there is now a headwind. The momentum of the cart is causing the prop to continue rotating, causing it to act like an airplane prop and pull the cart along. Friction enters the scene (fah, it was always there!) and eventually slows the cart back below windspeed.”<<<
The vehicle will continue to travel steady state, well wind speed as long as there is wind and a surface to run on. It does not repeatedly cycle above and then below wind speed, but rather exceeds wind speed and stays there.
JB
Well, I never claimed to be a physicist
I hope at least one of my points was right though.
No worries Rhudson — I wasn’t trying to come of a critical of you personally, just trying to set the record straight on how it works.
JB
I wonder if acceleration could be increased (or matched) by using the variable pitch on the propeller to drive the vehicle at below wind speeds (that is use the rotational energy of the propeller to drive the wheels). As the car approaches wind speed the blades are flattened acting as a sail (The vehicle is simply being pushed by the wind). Lastly to go beyond wind speed, the pitch is altered to provide the air cushion acceleration (The same method they employ now). I understand that this would not increase there top speed, but it would be interesting to hear if this method would work also.
That method would absolutely work. We originally ran with a fixed pitch prop, and later went to a variable pitch (which was planned from the start), but for several reasons we opted not to let the prop drive the wheels (we used ratchets to prevent the possibility). This was partly due to the design of our drive-train, and partly to prove to NALSA that we could not make any use of stored momentum or energy to accelerate.
So we did start out with a flat pitch and increase it as our speed increased, but we never ran a negative pitch.
Thanks for your reply. I was also wondering about the plausibility of an electrical drive train v the mechanical one you are using. I believe that generators and hub motors can provide around a 95% efficiency of transfer, though I do not have any figures to back this. I guess that weight is critical to you, but it may be a simple way of varying your wheel speed without a mechanical CVT.
Actually weight isn’t all that critical. It affects our acceleration, but has relatively little impact on our top speed as rolling resistance is a small piece of our overall losses.
Also, we don’t currently do any gear changing. We have a gear cluster for finding the optimal ratio, but we haven’t changed it since our early experiments. Once you’re in the neighborhood on gearing you can achieve the same effect to first order by adjusting prop pitch.
For a larger vehicle a generator and electric motor could make sense for a number of reasons. On Blackbird our drive is pretty simple, and I think higher efficiency than we could achieve electrically.
Thanks for the comments, I think it is a fascinating project and wish you the best.
And thank you.
@Rhudson:
Sorry, but this will be my second attempt at answering your post — my answer just above somehow got delivered mangled and incomplete.
Here goes round 2:
“1. Starting downwind, the wind pushes on the prop (and cart) causing the prop to spin, transmitting power to the wheels and off she goes.”
The prop *never* transmits power to the wheels. Not at any speed nor at any time. In fact, there is a large ratchet on the prop shaft that ensures that this can never happen:
http://www.fasterthanthewind.org/2010/04/not-this-time.html
http://www.fasterthanthewind.org/2010/05/higher-torque-upgrades.html
“2. Matching wind speed, the prop freewheels and begins to receive power from the wheels. The lift from the prop is still pulling the cart forward.”
The propeller was recieving power from the wheels the entire time and at all speeds — see above.
“3. Exceeding the speed of the wind, there is now a headwind. The momentum of the cart is causing the prop to continue rotating, causing it to act like an airplane prop and pull the cart along. Friction enters the scene (fah, it was always there!) and eventually slows the cart back below windspeed.”
The vehicle will continue to travel steady state, well wind speed as long as there is wind and a surface to run on. It does not repeatedly cycle above and then below wind speed, but rather exceeds wind speed and stays there.
JB
(Hope the formatting works this time — crossing fingers)
It appears to me that understanding this involves getting past an initial assumption. I had initially assumed that it was wind rotating the propeller that drove the wheels. Once I saw your note correcting this, the entire system makes sense. Initial acceleration depends on the wind pushing the cart in general, not on wind rotating the propeller.
Would I be correct in concluding that at the point where the speed of the cart equals the wind speed, it is the momentum of the cart spinning the wheels driving the propeller to accelerate the cart? What would then be the theoretical maximum speed for the cart?
Would this principle work on a windless day, with an external vehicle getting the cart moving in the first place?
?? Would this principle work on a windless day, with an external vehicle getting the cart moving in the first place?
No. It relies entirely on a difference in speed between the air and the ground to work. If it could work in still air, starting from a push, you would have a form of “perpetual motion”, which we all know is impossible.
>> Would I be correct in concluding that at the point where the speed of the cart equals the wind speed, it is the momentum of the cart spinning the wheels driving the propeller to accelerate the cart?
No. We never make use of stored momentum or energy. Even at exactly wind speed the cart could pull a trailer all day long and then accelerate to beyond wind speed.
>>What would then be the theoretical maximum speed for the cart?
There is no theoretical maximum speed as a multiple of wind speed. There is however a maximum practical absolute speed. Once your prop tips get into the range of about 200 mph you’re pretty much done because of compressibility effects of the air.
>>Would this principle work on a windless day
No
Rick,
Isn’t it more correct that upon reaching steady state, Blackbird does not make use of any stored energy or momentum.
I would have though that the initial losses incurred by the propeller are “borrowed” from the accumulated kinetic energy of the cart (as accumulated from the initial apparent tail wind) until they are paid back from the net momentum transferred from the airmass by the propeller itself.
In other words, during the initial “pushed by the wind” phase, the cart travels slightly more slowly with the propeller engaged than it would if it was disengaged.
jon.
>> Isn’t it more correct that upon reaching steady state, Blackbird does not make use of any stored energy or momentum.
Nope. In a stead wind the vehicle would accelerate monotonically until it reached its max speed. At no time would we take use any of the momentum of the cart or spinny bits for any reason. In fact we just keep *adding* momentum until we reach steady-state. But it’s just there – it can’t be avoided, and we don’t make use of it.
>>
I would have though that the initial losses incurred by the propeller are “borrowed” from the accumulated kinetic energy of the cart
< <
Nope. To borrow from the kinetic energy of the kart the kart would have to slow down - which it doesn't do until I apply the brakes.
>>
In other words, during the initial “pushed by the wind” phase, the cart travels slightly more slowly with the propeller engaged than it would if it was disengaged.
<<
That’s quite true. That’s simply a battle of forces and torques. The wind is trying to push the propeller CCW (as viewed from behind) while it’s also trying to push the whole thing downwind (which is trying to turn the prop CW). The greater torque prevails.
Ok, so the propeller is engaged from the start of the run?
Would it be true to say that _if_ the propeller was engaged later in the run, one might expect to see a transfer of kinetic energy from the translational components to the propeller and hence a drop in velocity?
jon.
>> Would it be true to say that _if_ the propeller was engaged later in the run, one might expect to see a transfer of kinetic energy from the translational components to the propeller and hence a drop in velocity?
Sure, if you “dropped the clutch” on the prop very abruptly, it might slow the vehicle down just a bit. That is *if* we had a clutch – which we don’t.
I just want to remind folks here, as this conversation continues, that we have a “be nice” policy here on Make: Online. You can read the guidelines on the link below.
As this is a controversial subject and there are strongly opposing views, things can easily get personal and ugly. Please try and keep comments productive and about the experiments themselves and the science involved, not personal. Thanks!
The treadmill is not a valid test. Put the cart in a wind tunnel since it is wind-powered. Let it run on rollers. It will never exceed the wind speed in the tunnel. I guarantee it!
>>The treadmill is not a valid test
The world record wasn’t set on a treadmill — it was set on a perfectly level dry lake bed in a steady wind with 18 recording sensors on vehicle and course placed by an independent testing organization and witnessed by noted sailing contest officials and writers.
@Prang
It is important, crucial, that one understands that the vehicle does not accelerates because the wind spins the prop which spins the wheels. It accelerates because the ground is moving relatively beneath it spinning the wheels which spins the prop which propels the vehicle.
@Rhudson
“1. Starting downwind, the wind pushes on the prop (and cart) causing the prop to spin, transmitting power to the wheels and off she goes.”
I think it starts moving because the wind is pushing on it as it would anything wheeled, prop or no prop.
“2. Matching wind speed, the prop freewheels and begins to receive power from the wheels. The lift from the prop is still pulling the cart forward.”
The energy goes from the wheels to the prop the entire time.
“3. Exceeding the speed of the wind, there is now a headwind. The momentum of the cart is causing the prop to continue rotating, causing it to act like an airplane prop and pull the cart along. Friction enters the scene (fah, it was always there!) and eventually slows the cart back below windspeed.”
It does not slow down. It goes about 3 times faster than the wind and continues at that speed.
I’m sure I would have gotten a different impression had I seen it operate in person. I was wrong about the steady state thing.
I’m still fairly sure that the propeller’s lift enters into the equation.
@Rhudson
“I’m still fairly sure that the propeller’s lift enters into the equation.”
Yes, the propeller *pulls* the vehicle through the air just as a plane propeller pulls the plane through the air. A plane will move forward regardless of whether or not the plane is going slower or faster than the wind.
What causes so much confusion is the source of the power is the same thing that is propelling the vehicle, the propeller.
The propeller is acting both as a sail and a propeller. The wind pushes on the propeller like a sail. This moves the vehicle over the ground turning the wheels. The turning wheels turn the propeller and provide more thrust.
What you describe is infact the basis of many perpetual motion machines.
The most reasonable cause is the following:
Like a wind turbine extracts kinetic energy from oncoming wind, the propeller (when the cart is moving faster than the downwind) will act as a turbine and should drive the wheels in order to take the cart forward. This does however require the coefficient of Drag to be less than the total energy gain from the prop,which I can make no conclusion on.
@edgertronics
>>> “The most reasonable cause is the following:
Like a wind turbine extracts kinetic energy from oncoming wind, the propeller (when the cart is moving faster than the downwind) will act as a turbine and should drive the wheels in order to take the cart forward.”
Edger — *you* may find your described “cause” as the most reasonable, but since the design of the machine makes your theory impossible, there’s not much ‘reasonable’ about it.
There is a ratchet on the prop shaft which specifically prohibits the propeller from ever being able to drive the wheels forward.
http://www.fasterthanthewind.org/2010/04/not-this-time.html
http://www.fasterthanthewind.org/2010/05/higher-torque-upgrades.html
This ratchet had to be included and functioning (confirmed by NALSA observers) to meet the NALSA rules that no stored momentum from the propeller could be used to drive the vehicle.
Very interesting experiment, but I am even more amazed at how bullheaded people can be. If they can’t accept it with this much evidence then I guess they never will.
I’ve ran into naysayers like that before (regarding a different subject) and it is terribly frustrating. I offered to do any reasonable demonstration to prove my point, but luckily they were honest with me and flat out told me that they would assume any demonstration on my part was faked. Although I still did an experiment to prove it to myself. I just couldn’t believe how unwilling people were to accept an idea different than their preconceived notions.
Anyway, great work Rick. You’ve definitely proved your idea to any reasonable person.
While I don’t necessarily believe this to be impossible. One ridiculous factor riles me so.
Richard, you obviously have a very interesting concept of reference frames. I would suggest that you go back and ask you first science teacher about it as it is really rather tragic. Your treadmill experiment is not only non-sensical but embarassing, the test is only valid if the cart is moving in relation to the air surrounding it. ipso fact if the carts not moving relative to the ground and neither is the air then you’re doing sweet fa, and miraculously you seem to have created a cart that can roll up hill!!!!!!!! If only if only. I would suggest taking the cart to your local university with a wind tunnel and asking the engineering department to test it, for currently you have NO PROOF whatsoever nor any scientific basis for your “invention.” I must also add that your “vector analysis” is also BS
Please don’t resort to telling people to go back and query their grade school science teacher (or similar insulting comments). That’s really unnecessary to arguing your points or refuting others. Thanks. – The Mgt.
If make is going to be a sensible proponent of citizen science I would suggest that the treadmill test never have been mentioned. It is both the fact that it found publication, AND that it is touted as meaningful that I take issue. The very topic of this is personal as we have one man, who has shown no formal analysis the theory behind the cart, allowed to publish his thoughts on the subject when it appears that his underlying knowledge is flawed. I do not refute the operation of the cart, simply that Richard has offered no solid grounds for why it does, nor a particular disposition for meaningful experimentation.
I watched the video on youtube with the model/treadmill as well as the video on Vimeo with the fullscale test. If they would include just a few more items it would strengthen the evidence much more….Include a few sensors!
On the treadmill video if they just had a handheld wind speed meter showing how fast the wind was going and then give us a readout as to what the treadmill is doing…this would solve everything! Of course the cart will go faster than the treadmill if there is a 10mph wind while the treadmill is going 7mph.
On the fullscale video, how do we know there isn’t a gust of wind pushing the cart to go faster? They obviously invested a lot of money building the cart, trucking it out there and video taping it…why wouldn’t you invest in some simple sensors to be done with it???
Unfortunately posting videos of something just “working” is not enough. You can search youtube for plenty of videos of perpetual motion machines just “working”. Here is one: http://www.youtube.com/watch?v=epLOEaoPMFU&feature=channel
I’m still skeptical…hopefully Mythbusters will come to the rescue. They’re always pretty good with setting up sensors and showing some actual numbers.
We had a total of 18 recording sensors for our record setting run. I believe you can see the data at http://www.NALSA.org
Regarding the wind over the treadmill, the air in the room was still. We demonstrate this in some of our youtube videos. The wind in that experiment is the relative motion of the treadmill belt at 10 mph below the still air of the room.
There is no relative motion of the cart to the air however. This is the problem, because the cart is not moving in the room, and in still air on flat ground it cannot move unless it is propelled by another means
@greg:
>>They obviously invested a lot of money building the cart, trucking it out there and video taping it…why wouldn’t you invest in some simple sensors to be done with it???
NALSA oversaw the installation and data collection of 18 recording sensors during the record runs. These were installed on the vehicle itself, on chase vehicles and on the desert floor. They used the data from these sensors to determine the outcome of the runs.
http://picasaweb.google.com/davidhglover/DDWFTTWJuly3RecordDay?feat=flashalbum#5490178307451061170
http://picasaweb.google.com/davidhglover/DDWFTTWJuly2RecordDay#5489555438988192866
http://picasaweb.google.com/davidhglover/DDWFTTWJuly2RecordDay#5489555487020943538
http://picasaweb.google.com/davidhglover/DDWFTTWJuly2RecordDay#5489555272027178082
Etc.
How many more sensors might you need?
JB
The number of sensors are not the problem.
The lack of mathematical proof or presentation of the true physics is the issue.
The prop and wind speed are a red herring if I understand correctly.
A quick gust of wind would be enough to get it moving and then the wind could disappear completely and the craft would continue to accelerate?
First, the comment about there not being any sensors was in regards to the video as being proof enough that this concept works. The video alone does not show any sensors.
Now onto the paper posted at NALSA. Here are my comments:
For any paper of this type to hold any weight, an extensive report on the measurement setup must be given. Location of sensors, brands/models of sensors, accuracy of sensors, method of recording data, method of manipulation/calculations of recorded data. The GPS sensors were mentioned, however any wind sensors present were not described in any real detail. The one plot-Chart 6 shows the true wind speed measured at the chase vehicle. No indication was given as to how these numbers were arrived at.
Get an outside non-invested party to evaluate this. You should be able to find some grad student up at Berkley who needs funding. Have them write up a real research paper detailing the necessary items for a paper to hold up against scrutiny.
So, to begin with, the propeller acts like a sail, driving the thing forward through the mast. Then, as speed increases, the wheels are driving the propeller, keeping momentum going kind of like a flywheel. The wind continues to act on the propeller, providing more ‘sail’ power through the mast, and the cart keeps building speed to it’s ability to slip through the headwind and other friction factors.
Is that anywhere close to how it actually works?
The frustrating part of this article, and even the proof, is the lack of real hard physics/math proofs of what is really happening. The trick is all in the gear/screw ratios. As you can assume – minimizing/maximizing friction in all areas is the key to maximizing the gains (and therefore top speed)
To start(t=0), the wind nudges the cart forward, as any wheeled object. The prop is a non-factor at t=0
Once underway, (for the purpose of this example I’ll use made up numbers) We have a wheel, with a 1 ft circumference, rotating at 20 rpm, connected to a shaft & prop. The wheel is driving the prop (through friction of the wheel on the ground, driven by the wind behind to over come initial conditions)
At this point we have a vehicle moving at 20 feet per minute. Driving a prop at 20 RPM.
Here’s the fun part; each revolution of the prop (it’s an airfoil, like a plane’s wing, and produces forward thrust) produces enough forward thrust to PULL the cart 1.5 ft. There are a lot of things going on, but for the sake of the example, shaft friction, vehicle drag and other items are non factors. Essentially, picture the prop being driven by an engine, we can agree that faster spinning produces faster speeds of travel.
So the prop is pulling forward at 30 feet per minute, while spinning at 20 RPM (with that connected shaft). There’s some slippage with this, but the net effect is to speed up the whole craft.
At this point, if there were no drag, only friction to the wheel/ground system; we could accelerate infinitely.
The only thing stopping infinite acceleration is the drag on the rest of the craft. Initial wind speed plays a key role in that it shifts the equilibrium point of the whole system. A faster initial wind speed, will add more ‘push’ to unity, and less drag afterward. By unity, I mean the point at which the vehicle is moving at the same speed as the wind (and therefore with 0 drag force)
I hope this makes it a little clearer than the vagueness I’ve seem so far. If it really comes down to it, I could run the actual numbers, but in reality these numbers should suffice.
@edgertronics:
>>> “The very topic of this is personal as we have one man, who has shown no formal analysis the theory behind the cart, … ”
edger, you might want to check around a bit before you make claims that no “formal analysis” has been shown. That assertion is totally and completely false.
In addition to many, many formal treatments published by Rick, here is a nice set from world renoun MIT professor Mark Drela.
http://www.boatdesign.net/forums/attachments/propulsion/28167d1231128492-ddwfttw-directly-downwind-faster-than-wind-ddw2.pdf
http://www.boatdesign.net/forums/attachments/propulsion/28168d1231128492-ddwfttw-directly-downwind-faster-than-wind-ddwe.pdf
In the past Dr. Drela has been very responsive to interested folks like you who email him with questions. I suggest that you might wish to do so and what you will find is that Drela’s understanding of frames of reference are the same as Rick’s and that Drela will tell you that the treadmill experiment is absolutely valid.
Give it a shot, but publish his response please — it would be educational for the others here to see whether your understanding is correct or not according to one of the most noted and accomplished aero professors of our time.
JB
When writing about your own technological feat, for a fairly technical blog (and with the intense debate that has followed this one), perhaps including a link to your research and proof would be a wise idea to avoid some of this.
If you would at least link to your proofs, there would be half as many comments, and they would be much more toned down.
@Slapyak:
Slapyak, we were not asked by Make to submit an article containing comprehensive technical proofs. That is not even the normal content of Make Magazine. We were asked to submit an article telling the story of the Blackbird and link to instructions on how readers could build their own correctly (to make up for Platt’s incorrect instructions/plans).
I have happily included links (directly above) to extensive proofs from a noted source.
JB
Greetings,
I thought I understood how this works, and have tried to help explain it. But, now I am confused again.
When the vehicle is traveling at say 2.8 times wind speed, where does the energy come from to maintain that speed? Energy must be put into the vehicle’s system for it to maintain that speed in the face of air resistance and friction. The energy can not be coming from wind pushing on the vehicle from behind if it is going faster than the wind.
Thanks
@NeuroPulse:
>>> “The energy can not be coming from wind pushing on the vehicle from behind if it is going faster than the wind.”
I will give you a short thought experiment that will show your above assertion to be flawed:
Grab an ordinary bicycle. Have someone hold it upright. Place your finger halfway down the upper most spoke on the wheel of the bike (either one). Push forwards with your finger.
You will find that the bike will move forwards twice as fast as your finger is pushing forwards on the spoke.
Now to take it a step further, imagine replacing your finger with a sail sticking out from the spoke at that same point. Imagine a mechanism that would retract this sail at the bottom and deploy it at the top. Now equip each spoke with the same.
It’s quickly apparent that even with the wind coming from behind and the bike going faster than the wind, the sail will be moving slower than the wind and there will still be wind pushing on the deployed sail and spoke, just as your finger pressed on the spoke.
The above would require a very complicated (and lossy) mechanism to retract and deploy its sails, so I’m not presenting it as anything other than an example showing that energy *can* still be harvested from the wind even when the vehicle is traveling faster than the wind DDW.
The trick is to use a mechanism that is more efficient in it’s use of the harvested energy than the lossy one described above — the wheel driven propeller is that mechanism.
JB
Without sounding crass, you either need to pick up your Nobel Prize or admit that either this is a mistake or fraud.
Your thought experiment doesn’t work when the bike is traveling 2 times the velocity of the wind the “sail” will have net drag and not thrust. The thrust comes from the relative velocity difference between the sail and the wind.
This is the same kind of garbage that you hear from people who hook a generator up to a motor and claim to have net energy.
We have warned everyone not to use insulting language (“garbage”). In order to keep this discussion focused on the science (and not the personalities involved) I’m going to start deleting comments that use insulting words. This is a second warning. There will not be a third warning.
Fair enough. I knew I was being crass and I should have shown more restraint.
It is difficult to talk about a concept that explicitly violates Newton’s Second Law and conservation of energy. Simple mechanical analysis precludes their explanation. Where do we go from there?
If their explanation holds any water then there is another experiment they could run to validate this concept.
-In absolutely still wind conditions pull the car up to 5 to 10 mph.
-The linkage between the wheels and the turbine should get it going just like in the video
-Cut the line and have the vehicle continue driving for say another couple miles.
This will not work. If it did, it would cause quite a stir.
/Their machine looks cool!
>> It is difficult to talk about a concept that explicitly violates Newton’s Second Law and conservation of energy.
There is no basis at all for that claim. Please try and explain exactly how you think our vehicle (or explanation) violates this law.
>> Simple mechanical analysis precludes their explanation.
Then please give us this simple analysis.
>>If their explanation holds any water… Cut the line and have the vehicle continue driving for say another couple miles.
There is nothing about our explanation that suggests that our vehicle will work in zero wind.
If you want to understand the claims and how the vehicle works, I strongly recommend you join the discussion. Simply trying to ridicule our results and explanation will not get you there.
I am not ridiculing your design. My first instinct was/is that your explanation violates the aforementioned principles. You clearly built a car that goes really fast with the wind and appeared to do just what you claim. I am not taking that away from you. However, your explanation is still way short of satisfying my questions.
Maybe this would all be cleared up if you told us how your use of a turbine is different than a sail.
>> If their explanation holds any water then there is
>> another experiment they could run to validate this
>> concept.
>>
>> -In absolutely still wind conditions pull the car up
>> to 5 to 10 mph.
>>
>> -The linkage between the wheels and the turbine should
>> get it going just like in the video
>>
>> -Cut the line and have the vehicle continue driving for
>> say another couple miles.
>>
>>This will not work. If it did, it would cause quite a
>> stir.
This assertion is 100% correct .. but irrelevant.
There is no claim that the DDWFTTW vehicle can move at any speed in still wind. It requires a relative difference in speed between the air and the surface over which it travels to work. Consider this little experiment http://www.youtube.com/watch?v=k-trDF8Yldc which is a direct analog of the DDWFTTW vehicle (in which the ruler is equivalent to the wind and the large rotating wheel is equivalent to the prop.) Your “thought experiment” would suggest that just because the ruler can push the little cart in a particular direction faster than the ruler is moving itself that the cart could somehow be coerced to move under a stationary ruler by starting it with a push – which is obviously impossible. Again: the ruler has to move relative to the surface for the cart to move at all : And in the case of the DDWFTTW vehicle the wind has to be blowing at least strong enough to overcome friction for the vehicle to begin to accelerate to a speed at which the prop (driven by the linkage to the wheels) can drive itself by pushing against the air, faster than the air flowing over it, in exactly the same way as the big wheel of the little cart in the video, driven by its contact with the small wheels) drives itself by pushing the ruler, faster than the ruler moving over it.
@B_Petschel
>>> “Your thought experiment doesn’t work when the bike is traveling 2 times the velocity of the wind …”
Correct … that’s why I never said it *would* work at “two times the velocity of the wind” — I merely said with bike going “faster than the wind”
>>> “…the “sail” will have net drag and not thrust.”
Contrary to your assertion, there will be neither drag NOR thrust on the sail with the bike at 2x wind speed.
With the sail positioned on the spoke 1/2 of the way between the tire and the hub (as prescribed in the thought experiment), the deployed sail will be traveling exactly 1/2 the speed of the bicycle. This means with the bike at 2x, the sail will be traveling exactly the speed of the wind and thus no drag OR thrust.
If you wish to insert the requirement of “two times the velocity of the wind” into my thought experiment, you are welcome to do so — it merely requires that we adjust the point along the spoke where the sail resides.
Let’s push with our finger at a point 3/4 of the way down the spoke towards the hub. Now obviously when we push at that location on the spoke, the bike goes 4x the speed of our finger. Now replace your finger with the previously prescribed sail at this same point.
With the above adjustment, when the bike is going 2x the speed of the wind, the deployed sail is going only 1/2 the speed of the wind and thus can extract energy from the tailwind even with the bike going 2x the speed of the tailwind.
>>> “The thrust comes from the relative velocity difference between the sail and the wind.”
Yep — and I just demonstrated in a very simple way that there is still a velocity across the sail of 1/2 the speed of the tailwind.
QED.
JB
I don’t think this thought experiment works.
The point of the wheel in contact with the ground is traveling at speed zero. The hub of the wheel travels at the speed of the cart. The top of the wheel travels at twice the speed of the cart. Any point above the hub travels faster than the cart and any point below the hub goes slower.
You would need to push on a point below the hub, near the ground, but this would slow the cart down as this force works against the rotational motion of the wheel.
That said, I don’t need a mathematical proof to see that it works.