DDWFTTW Vehicle Ananlys. Dead down wind faster than the wind.

# DDWFTTW Vehicle Analysis.

## Dead Downwind Faster Than the Wind.A conceptual conundrum.

When the average person hears that it is possible to have a wheeled cart with its wheels spinning a propeller, and the wind on the propeller providing the power to drive the vehicle, it sounds like a Rube Goldberg idea. When you tell him that such a vehicle has indeed been clocked moving directly downwind faster than the wind, as fast as 2.8 times the wind speed, he's likely to think someone is perpetrating a hoax. And if you refer him to some published papers, dense with equations, that conclude this is not violating physics laws, his eyes glaze over. This is the DDWFTTW (dead downwind faster than the wind) vehicle.

We may convince the skeptic by letting him see the vehicle in action, and clock it himself. Or refer him to the experts who have clocked such performances in officially controlled and verified tests. But still the skeptic will shake his head and say "It seems like magic, like getting something for nothing. It smacks of so many over-unity and perpetual motion machine proposals we have seen, that have been shown to be unworkable in practice and proven to be impossible by using the known laws of physics."

So is there any simple way to convince someone that this works? We'd have to (mostly) avoid equations or appeals to physics laws that our skeptic barely understands and may only grudgingly accept.

## A simple device with a complex analysis.

I think most will acknowledge that windmills can harvest energy from the wind, to pump water, generate electric power, and do other useful tasks. This works only when the wind speed is non-zero at the windmill (or wind turbine). So, our skeptic asks, could a propeller-driven wheeled vehicle accelerate, starting from rest in a dead calm, with zero wind speed? The answer is clearly "No."

But the skeptic wonders whether on a calm day the vehicle could perform if we towed the propeller-on-a-cart to some ground speed so that there was relative motion between air and propellor, capable of driving the wheels when we cut the tow line? Could the cart then sustain motion, powered only be the relative air speed at the cart?

No, it would not. The towed vehicle would begin to decelerate as soon as it was cut free and quickly slow to a stop when the kinetic energy we gave it (by towing) was "dissipated".

That is a clue. For this device to work, the wind speed over the ground must be non-zero.

Not all of the skeptics are saying the DDWFTTW performance isn't possible. Some are only saying, "You haven't given me a convincing argument why it is possible. Don't blind me with equations, just help me make sense of it in terms of what I know about how the world works."

Physicists often scoff at such relatively non-mathematical arguments, and rightly so, for they often are analogies, and analogies can be misleading. They always break down if taken too literally. Yet such simple arguments can successfully reveal why the classic perpetual motion machines don't work. Can they persuade us why this crazy contraption does work?

The flaw in thinking about this is usually the feeling that the propeller drives the wheels and the wheels drive the vehicle. This sounds like circular reasoning, and it is. The wheels do not drive the vehicle's forward motion, but they do drive the propeller's rotation. The wheels act as brakes on the vehicle, exerting forces on the vehicle's axles—opposite to the vehicle's direction of motion. The only force acting forward on the vehicle is that due to air interacting with the propeller. The wheels do drive (maintain) the propeller rotation. If the belt linkage to the wheels were disconnected, the propeller would stop spinning. But it is the forward force that air molecules exert on the propeller that gives the thrust to drive the vehicle.

The belt (or chain) drive between propeller and wheels maintains the propeller rotation. The propeller acts like a large screw, slicing through the air and pulling the cart through the air. Even in calm air a rotating propeller can provide thrust—if something is powering its rotation. Airplanes do that, but they have gasoline engines to rotate the propeller. This vehicle does not.

But how does the vehicle ever get started from rest in a dead calm? That sounds like the Baron Munchausen boostrap principle (lifting yourself by pulling up on your bootstraps).

We could argue that if there's a wind speed relative to the ground, the wind will start the cart moving downwind even if the propeller is disengaged from the wheels and prevented from rotating. Then engage the propeller so its rotation is driven by the wheels. The propeller blades now slice through the air, providing additional thrust due to air molecules rebounding from the blades. Eventually the cart could reach a speed equal to the ground speed of the wind. The relative air speed is then zero at the cart. But the wheels, still driving the propeller, keep the propeller spinning, and still providing thrust, and the cart begins to exceed the wind speed.

## What's the energy source?

To understand what's going on, we must first convince ourselves that there's enough wind energy to propel the vehicle, even faster than the wind. There's a continual supply of energy from the wind's speed relative to the ground. We are actually tapping the kinetic energy of this differential speed to drive the vehicle. If the wind speed were zero relative to the ground, this simply would not work. This is the sole source of energy for the vehicle. As the vehicle moves through the air it continually harvests energy from the wind.

Sometimes analogies are persuasive. The best I can think of is the old "climbing monkey" toy. The monkey is on a vertical string suspended at its top end. By pulling on the upper end of the string, the monkey climbs the string faster than your hand that's doing the pulling. Of course, in this case, the monkey moves in the opposite direction than you pull. But fasten the bottom end of the spring to a solid support, and the monkey climbs up to reach your hand, moving faster than your hand and faster than the string. You could also fasten the top string to a fixed support and pull on the bottom string. Again, the monkey moves opposite to your hand that's doing the pulling.

For another version of this in action, see this video: climbing monkey. This toy uses a different principle than the one in the previous picture.

Some of these toys operate by a clever friction mechanism; some work by a system of pulleys with a mechanical advantage.

This is a simple differential pulley—two pulleys of different diameter fixed to a common shaft. It is suspended as shown. When the two strings are put under tension (by pulling up on the upper string, or down on the lower string, or both), the pulleys climb the upper string. When the tension is removed the pulleys move downward under their own weight. When climbing they overtake the upper end of the string. This same mechanism is used in the magic trick called the "golden rising ball". The mechanism is concealed in a hollow ball, and it appears as if the ball is a solid ball with a hole drilled through it, on a single string. But there are two strings, with two pulleys inside the ball. The upper string (A) is attached to the smaller pulley. A counterweight (C) is fastened to the inside of the ball to balance the weight of the pulleys. To make the ball rise you can pull down on B or up on A. It is the string tension that makes the ball rise. You can see it in action here.

The differential pulley may be demonstrated with a simple yo-yo toy. Sit the yo-yo on edge on a horizontal flat surface, with the string wrapped around the axle and coming out the bottom side of the axle. Pull the string horizontally, and the yo-yo will roll toward your hand, faster than your hand is moving. Think of the string as the air. If you don't have a yo-you, wrap a ribbon around any spool that's handy. The yo-yo, spool, or propeller driven cart uses the energy due to the difference between speeds of two things.

Rick Cavallaro suggests an even simpler demo. Fasten and wrap a ribbon or string around the stem of a wineglass, and use it instead of the yo-you. In any of these demonstrations you can confirm that in the "faster than you pull" performance the wheels do not drive the vehicle, but only act as brakes, supplying a force to the vehicle that opposes its motion.

This model is made from Meccano and Erector parts. The gear rack below the gear pinion can be pulled along the table. If pulled to the right, the wheels move to the right faster than the rack. If pulled to the left, the wheels move to the left faster than the rack. The whole thing contains only nine parts plus nuts and bolts. Think of the geared rack as the wind.

But, these devices simply show that a system may have mechanical advantage that allows it to move faster than the agent exerting force on it. They still leave questions unanswered. Also, the details of the mechanism for these devices are necessarily different foom each other.

For more about such systems, see my puzzles page.

## Other systems with similar behavior.

The obvious system that can move faster than the wind is a sailboat. The force due to wind on a sail is roughly normal to the surface of a flat sail, so if the sail makes a small angle with the wind, the force the wind exerts on the sail can have a significant component in the forward direction of the boat's motion. The water acting on the boat's keel prevents sidewise motion.

Sailboats can move up or downwind by "tacking", moving at an angle to the wind, or zig-zagging. This depends on the fact that the hull moves easily across water only in its forward direction, but to move laterally the hull and keel provide considerable resistance. Without this resistance sailboats wouldn't work. Catamarans can achieve 2.79 times wind speed tacking downwind.

The land-yacht vehicle that has wheels and sails operates on the same principle. The wheels roll easily in the forward direction, but resist sliding sidewise. Simon Stevin (1548-1620) invented this vehicle around 1600. They were used on smooth beaches.

Sailboats can sail directly downwind, but not directly downwind faster than the wind. To sail upwind, or to sail downwind faster than the wind they tack at a substantial angle to the wind, typically greater than 20 degrees. Then how can the propeller-cart travel directly with or against the wind? The moving propeller blades act something like sails, their pitch providing the tacking angle; their rotation providing the relative speed between the blades and the air molecules.

Iceboats have achieved 5 times wind speed tacking downwind.

## Directly upwind performance?

Someone is sure to ask, "If this seemingly miraculous performance is possible downwind, can a wind powered vehicle also travel upwind? Can it travel upwind faster than the ground speed of the wind?"

This has been done. Rick Cavallaro achieved 2.1 times wind speed upwind in 2010. See The Wikipedia.

For upwind travel a windmill or wind turbine works better than a propeller. Imagine a windmill on wheels, at rest, with a drive belt from windmill to wheels. Clearly even at slow speeds the windmill can drive the wheels and, in turn, the vehicle. It can initiate motion from rest. As the vehicle gains speed the relative wind speed at the windmill blades is even greater. The maximum speed will, of course, be limited by the usual inefficiences of the mechanism and the windmill blades.

B. L. Blackford proposed an interesting device in a 1978 American Journal of Physics paper, The physics of a push-me pull-you boat.. (The title is clever, though a bit misleading.) A boat has a windmill linked to a water propeller under its stern. Like the land yacht with propeller, this one at first seems to defy common sense. But it works anyway, and isn't violating any physics in the process.

## Summary.

Downwind vehicles:

The energy powering the vehicles comes from the kinetic energy of the wind, taking advantage of the velocity difference between air and ground (or water). This velicity difference is the only source of energy.

The mechanism must have a mechanical linkage between air and ground (or air and water).

For downwind travel the propeller's rotation is driven by the wheels—always. The propellor drives the vehicle forward, just as the propellor of an airplanie moves it forward.

The wheels do not drive the vehicle; the wheels are driven by the cart's motion over the ground, and this is what turns the propeller .

Friction of the wheels on the ground is essential for all of this to work.

The air acts on the propeller to provide forward thrust, and also provides a force component opposed to the propeller's rotation. This "drag" on the blades isn't sufficient to overcome the driving force on the propeller due to the wheels. Compare the sailboat, where one component of wind forces on the sail moves the boat forward, but the other component acts on the water through the hull and keel, effectively a "drag" force. But this force does very little work. Work is he product of force and distance, and the sidewise force on ground (or water) doesn't cause much motion in that direction.

Upwind and crosswind vehicles:

The "directly upwind" vehicle uses a windmill to drive the wheels, which in turn drive the vehicle. This requires a different mechanical linkage ratio, and differently shaped windmill blades.

I figured that making and upwind wind powered vehicle would be a simple matter. So I got out my collection of steel construction set parts. Here's the finished model as a stereo picture for cross-viewing.

I wanted to see how far I could get with unsophisticated engineering. For the turbine blades I used sections cut from an old venetian blind, properly positioned and angled. I know that the profile could be made more efficient, but I would test it first and worry about such details later. Rubber band belts are inefficient, so I used a secton of coiled spring belt, salvaged from a discarded slot machine I acquired many, many years ago. And, surprise, it worked just fine in the air stream of a room fan.

Now (May 2015) I see that a toy model of this sort is available many places on the web, for prices ranging from \$18 to \$40. It is made in China, and sold under the name "Wind Power Car". It is an assemble-it-yourself plastic kit for ages 10 and up. This model may be assembled and adjusted for light breezes or strong winds. It can move with the wind from any direction, but faster than the wind performance is unlikely.

Don't pay the inflated prices online. The very same model can be bought for \$5.00 at "Five Below" mall stores where everything is five dollars or less (in 2016). Assembly is supposed to require no tools, but I found getting the tiny plastic gears onto the very slender hexagonal steel shafts required a hammer and a vise. This part of the assembly might challenge youngsters. The finished model seems fragile and easily susceptable to irreparable damage. But it does work and it looks good.

The clever feature of this toy is the "tailfin" that rotates the turbine blades so they continually face into the wind.

## Afterthoughts.

Thinking about why this DDWFTTW vehicle baffles many persons, my hunch is that it is one of many devices that seems to violate naive "common sense". After a career in teaching I am sensitive to how common sense often stands in the way of understanding. Since common sense is formed from everyday experiences, it will often fail when applied to something new that we have never experienced. Learning physics is largely a process of abandoning such naive common sense and developing a better and more powerful model for understanding the world and how it works—a model that works even for unfamiliar situations.

So when A pushes on B and B moves faster than A, or B moves opposite to A, we are surprised and baffled for it goes against our common sense. We encounter a similar situation when we push on a spinning gyroscope and it moves perpendicular to the direction we push it. Likewise people who play with magnets think the magnets are doing something "magical".

For another simple mechanism that defies common sense, see contrary springs.

Examples:

Common sense tells us that the earth under our feet is solid and unmoving. So we conclude that the sun, moon, stars and planets must move around the earth. Copernicus and Kepler had some trouble convincing us otherwise.

Common sense tells us that when we exert a force on something (pushing or pulling) it moves in the direction of our force, and never moves faster than the object doing the pushing nor does it usually move opposite to the push. I doubt that this naive feeling arises from energy considerations, but from a more basic level of naive common sense.

## References:

[1] Blackford, B. L. The physics of a push-me pull-you boat. AJP, 46, 1004, Oct. 1978.

[2] Md. Sadak Ali Khan, Syed Ali Sufiyan, Jibu Thomas George, Md. Nizamuddin Ahmed. Analysis of Down-Wind Propeller Vehicle. International Journal of Scientific and Research Publications, 3, 4. (April 2013) ISSN 2250-3153. (www.ijsrp.org) This paper has many good references.

A website, Downwind Faster Than The Wind, has a much longer discussion, with videos of mechanisms of this type.

Thanks to Rick Cavallaro for very helpful discussions on this subject. Also, Brian Beasley enligtened me on several points about sailboats. However, any remaining errors are mine alone.

—Donald Simanek, July, 2013, Dec. 2013, Dec. 2017.