Editor’s note: Few topics we’ve covered have generated as much debate among readers as Rick Cavallaro and his colleagues proving a wind-powered vehicle can travel downwind faster than the wind. Although we don’t expect this to quell the debate, Cavallaro and John Borton recount their adventure here.

Brainteaser, n — A puzzle that requires mental/cognitive activity to solve and generally includes thinking in unconventional ways with given constraints in mind.

What are the moments when a challenger meets a problem and classic brainteasers are born? Who would have imagined that a plane and a treadmill would end up as inextricably linked as PB&J? Did Monty Hall ever dream the dreams of mathematicians? And if a wind-powered vehicle races a floating balloon and wins are physics texts made obsolete?

Tracing the path of this last riddle leaves a line that passes through moments of competent genius followed by years spent in the stubborn pursuit of absolute silliness. Add a counterintuitive solution and a bunch of name calling amongst academic elites and you have the perfect recipe for an intellectual disaster.

Directly downwind faster than the wind, n — a.k.a. DDWFTTW. An idea that 99 percent of people declare impossible. Ninety-nine percent of the rest can’t figure out how it’s done.

In 2001 a friend asked Rick Cavallaro whether a sailboat could tack downwind such that it could beat a free-floating balloon to a point directly downwind. They both knew sailboats can sail faster than the wind, but can they do well enough to beat the wind to a destination directly downwind? It would seem obvious it is not possible, but Rick knew things aren’t always as they seem. He did a quick vector analysis and convinced himself it should be possible. It certainly would be in an ice boat due to its very low drag, but could it be done with a sailboat?

As it happens, Rick’s boss at the time was legendary ocean racer and sailing navigator Stan Honey. Rick asked Stan if it had been done. Stan had recently raced PlayStation, the one boat he knew had the performance to (theoretically) do it, but Stan wasn’t sure PlayStation actually had done so.

Rick is known to tease brains to a point well past reasonable annoyance, while John Borton’s best (and worst) trait is having no clue when to give up and no sense of scale. Rick has faith in the theoretical, but JB trusts his eyes more than equations scribbled on the back of an envelope. In fact, it was a brainteaser posted at a hang gliding forum that brought them together more than a decade ago. Given a challenge, be it intellectual or physical, the two of them generally can sweet-talk it into submission or beat on it until it succumbs.

Rick, being an aficionado of brainteasers, realized this could be a great one. If this principle could be used to make a wind-powered vehicle that can go directly downwind faster than the wind without tacking, it would really bend some brains. So he gave it some thought.

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Rick initially took up the riddle as a thought problem. He imagined PlayStation on a broad reach and realized that if the world were a cylinder rather than a sphere with the wind blowing along its axis, the boat would trace one long spiraling path as it circled the cylindrical Earth. If racing a neutrally buoyant balloon drifting with the wind, PlayStation would get further ahead of the balloon with each rotation.

Except for scale, in this scenario PlayStation‘s sail was simply the blade of a propeller. Put a second PlayStation opposite the first — on the other side of this cylindrical Earth — and you have the blades of a propeller. Rick realized it was just a matter of making a device that would constrain its prop blades to follow the same path as the two PlayStation sails. In theory this would be as simple as mounting the prop blades to a nut that can wind its way down a coarsely threaded rod. This would ensure the blades of the prop would make one foot of “sideways” movement for each foot they went downwind – just like PlayStation on a broad reach.

If a solution is posted on the internet and everyone calls you an idiot, is it still a solution?

Rick figured that although a nut traveling DDWFTTW might be the simplest form of such a device, replacing the threaded rod with a wheeled vehicle would be more compelling – and possibly even less intuitive. He conceptualized replacing the device’s keel nut with gearing from a drive axle to a propeller shaft that would replicate the kinematic constraint perfectly. With the problem solved as far as he was concerned, he posed the new brainteaser on two internet forums, one for radio controlled helicopter pilots, the other for kitesurfers. Given the solution, Rick imagined people would find this clever.

Instead they considered him an idiot for ever imagining such a thing to be possible.

This is where the pointless brainteaser took on a life of its own. Science, physics and aerodynamics forums exploded. Sailing forums exploded. Flying-related forums exploded. It was silliness traveling at the speed of electrons. Turns out it’s serious business when someone is wrong on the internet, and boy did the internet ever believe Rick was wrong.

One interesting factoid emerged from the chaos. We learned that a Michigan University student posed this same non-problem – and a solution identical to Rick’s — in the 1940s. The student’s paper surfaced at Douglas Aircraft in the 1960s. Apollo M.O. Smith, the company’s chief aerodynamics engineer, and wind tunnel engineer Dr. Andrew Bauer went at it like Rick vs. the Internet. Bauer said it would work. Smith wasn’t convinced. Bauer bet Smith a dollar and went to work.

Unfortunately, documentation for Bauer’s project is scant. We learned much of the history by talking to his wife, colleagues, friends and relatives. Bauer did write a paper outlining his analysis (.pdf) and his claim to have just barely, and briefly, achieved what the Michigan University student said was possible. Witnesses we found tell us Smith paid up. We find the story credible, compelling and consistent — and we belive Bauer briefly beat the wind in a downwind race. But we are part of a tiny minority. Few on the internet believe the story, and naysayers consider Bauer, pictured standing next to his contraption, just another whack job.

Others also have attempted to put this riddle to bed.

Five years ago, retired machinist Jack Goodman found the controversy highly overrated. He had a simple idea: “Just freakin’ build it already and shut up.” He did just that. His machine was the size of a lawn mower, it was remote controlled and it worked.

Depending upon who you asked, of course.

Most on the internet considered it just another YouTube hoax with a hundred thousand hits. The video was never meant to appear online. Goodman tackled the project and documented it to settle a debate among friends. But a friend posted the video, fanning the flames of the controversy.

It didn’t help that others tried and failed to go directly downwind faster than the wind.

Make published an article by science fiction writer and frequent contributor Charles Platt, who after building a crude copy of Goodman’s device declared the whole thing a hoax. Looking at the pictures of Platt’s hapless creation, one could imagine him building a miniature Wright Flyer with two-by-fours and logging chain and declaring powered flight a hoax as well. His article ended, “…. if you decide to fake it and post a video that makes it seem to work, causing excitement and argument while spreading delusionary ideas, that is not what I would call education.”

Others made better attempts but had no better results. The skeptics appeared to be winning.

Seeing these failed attempts was too much for JB. He told Rick he was tired of watching others fail but knew vectors and equations would never convince the skeptics. Clearly it required building a working model and providing comprehensive documentation.

Forget “plane on a treadmill,” what about DDWFTTW on a treadmill? It turns out that if you want to test this device in a wind tunnel you turn the wind off. No, really. When the vehicle reaches the exact speed of the wind, there is no wind whatsoever across its chassis. Of course even though the wind has stopped, the floor needs to continue moving because even at wind speed the wheels still turn. We figured finding such a set-up wouldn’t be difficult because moving floor wind tunnels are pretty much the standard in automotive research these days. But we didn’t need NASA or even an automaker for that. A moving floor wind-tunnel with no wind is just a treadmill. Place a DDWFTTW vehicle on a garden-variety treadmill set at, say, 10 mph and if the vehicle moves forward against the treadmill it is moving faster than the wind.

This should be easy.

Naive, adj. — deficient in worldly wisdom or informed judgment.

So we built several vehicles. They all performed as expected, which is to say they all went faster than the wind. They all climbed the treadmill. You could restrain them and they would pull forward indefinitely. You could prove there were no strings attached, no fans blowing, no magnets pulling. It was the perfect controlled environment. Put it all together and it spelled quod erat demonstrandum. Of course we didn’t expect the commenters on YouTube to speak Latin, but academia?

A friend following our progress online commented, “Someday one of these will hang from the rafters of the Air and Space Museum with a plaque which will read, ‘In the early part of the century, this device caused physics and aero professors everywhere to storm out of their classrooms in absolute frustration.’” When we had only equations to present, we were nearly universally ridiculed. When we built and demonstrated a manned cart beating the wind, people complained we had no theory to back it up. To this end another friend offered, “Sure it works in practice – but can you prove it works in theory?”

The reaction from the academic world caught us by surprise, but it especially stunned Rick. Even faculty at his own alma mater attacked us (though we recently received a letter of congratulation from the university president). According to notable aerodynamicists, physicists and professors, DDWFTTW was not only impossible but our moving-floor wind tunnel was not equivalent to the real world and thus proved nothing. Somehow they missed the memo Galileo sent some 400 years before. Perhaps he’d used the wrong cover sheet.

Ultimately, noted aerodynamicist and M.I.T. professor Mark Drela weighed in with his own analysis. Interestingly, it was the exact analysis we’d offered many times, but with Greek letters and subscripts formatted in really nice equations. His analysis would be familiar to a practicing aerodynamicist, but it certainly was less accessible to the general public. Drela’s conclusion? DDWFTTW should be rather trivial with a wheeled vehicle and perhaps still possible on water.

Of course, few were convinced.

But just how trivial would this be for a wheeled vehicle? Following our build videos, and with a bit of personal guidance, three high school students built a DDWFTTW vehicle for less than 20 bucks and won their regional science fair. Of course, skeptics said the science fair judges were idiots just like us.

The story of Blackbird, our full-scale DDWFTTW vehicle, and its ratified world record has received a lot of coverage lately. In short, we hooked up with the aerospace engineering department at San Jose State University, found two exceptionally generous and open-minded sponsors — Joby Energy and Google — and put more than a thousand hours into building the best DDWFTTW vehicle ever built. It’s big, too, standing nearly 25 feet tall with a propeller 17 feet in diameter.

There are several ways to explain how the vehicle works. We’ve already described how it is equivalent to a high-performance sailboat circling a cylindrical planet. But we can look at it from an energy point of view as well. In this view we can think of the craft as a simple lever. As with any lever, we can trade a small force moved through a large distance (the long end of the lever) for a much larger force moved over a shorter distance (the short end of the lever). But how does this relate to our DDWFTTW cart? Let’s not worry about how the cart gets up to speed for now, but instead see what happens if we tow it up to speed. For this purpose we’ll tow it to 55 feet/second (about 37.5 mph), and we’ll do that in wind moving 44 feet/second wind (about 30 mph). Of course with a tailwind of 44 feet/sec the cart only feels an 11 feet/sec (7.5 mph) headwind when it goes downwind at 55 feet/second.

So let’s put a generator on the axle that creates 100 pounds of drag where the wheels meet the road. Thus the load of this generator is trying to slow the cart down – but it’s also producing exactly 10 horsepower to use however we want (55 feet/second x 100 lbs – 5500 feet-lbs/sec = 10 H.P.). If we want the cart to continue at the speed we towed it up to, we’d better provide 100 pounds of thrust to counter that 100 pounds of retarding force created by the generator. We’ll do that by turning the propeller with an electric motor powered by the generator. Remember the cart is feeling a relative headwind of only 11 feet/sec because it’s only going that much faster than the tailwind. If we want our propeller to put out 100 pounds of thrust we’ll have to give it 2 horsepower (11 feet/sec * 100 lbs = 1100 feet-lbs/sec = two h.p.).

Now, in this analysis we’ve assumed absolutely no real world losses, while in the real world the generator might be only 85 percent efficient, the propeller only 85 percent efficient and the electric motor only 85 percent efficient. But we generated 10 horsepower and only needed two for the cart to maintain its speed faster than the wind. Even with real world inefficiencies (plus aerodynamic drag and rolling resistance) we’d still generate more power than needed to maintain speed. This means we will continue to accelerate from this point – but not indefinitely. It’s easy to calculate the point at which the real-world losses equal the excess energy and the vehicle stops accelerating. This is the top speed for the given vehicle and conditions.

Of course everyone knows that you can’t power a propeller from a generator that’s hooked to your wheels and hope to come out ahead. That’s as silly as pointing a fan into your sail and hoping it will propel you forward. And if not for the wind we couldn’t actually power our cart this way. The cart is basically a lever acting between the ground and the wind – where the long end of the lever pushes us downwind faster than the wind.

Blackbird did its job in July when it unofficially and repeatedly exceeded three times the wind speed. Under the watchful eye of the North American Land Sailing Association it set a well-documented record of 2.8 times the speed of the wind. [Ed. note: Application here (.pdf), observers’ report here (.pdf) and the observer’s report appendix (Excel) here.]

It’s been a great experience. We’ve gained faith in some and lost faith in others. We were honored to speak at Stanford and San Jose State universities and the St. Francis Yacht Club. We were entertained to learn that a student at UC-Berkeley wanted to invite us to speak there but was refused after the director of the Lawrence Berkeley National Laboratory insisted such a vehicle would violate the laws of physics.

Certainly one of the most exceptional experiences that came out of all of this was attending the 2010 Science Foo camp hosted by Google, Nature magazine and O’Reilly Media. In its own words, the camp invites “200 leading scientists, technologists, writers and other thought leaders for a weekend of discussion, demonstration and debate.” We were stunned and honored to be invited and warmly received by the real big brains. Though we were challenged many times, it was refreshing to be among thoughtful people who, even when skeptical, kept open minds and carefully considered our explanations.

One of our favorite moments came when the publisher of Make, which is published by O’Reilly Media, approached JB. This gentleman excitedly asked if we’d write an article about Blackbird. “Make already did an article on this device,” JB replied. The fellow’s expression turned quizzical, and JB told him Make declared it a hoax. Watching the color drain from his face was priceless. To be fair, Make graciously invited us to write a follow-up article.

When we returned from Science Foo, our little cocoon of rational thought, we learned of course that some things never change. Reviewing the contents of our overflowing e-mail inboxes reminded us we are still, a thousand times over, idiots.

Editor’s note: This story was written by Rick Cavallaro and John Broton.

Cavallaro is chief scientist at Sportvision, the company that created the FoxTrax hockey puck. He earned a bachelor of science in aerospace engineering degree from Georgia Tech University in 1984 and a master of science in aerospace engineering degree from UCLA in 1988.

Borton is director of manufacturing at Sportvision and a longtime pilot who holds several medals in soaring aircraft. He was a designer and builder of Blackbird.



Photos courtesy Rick Cavallaro.

Video: Richard Jenkins.

Video: Discovery Channel / YouTube