Improbable Wind (and Other) Propulsion Systems

Can a wind-driven vehicle go straight down wind faster than the wind speed?  Derek Muller’s YouTube channel “Veritasium”, and the image above show Rick Cavallaro’s brilliantly designed “Blackbird” propeller-driven cart.  They say it can be done.  See  https://www.youtube.com/watch?v=jyQwgBAaBag  and Google, Wikipedia, etc. for more details.  
My intuition suggested otherwise: to ‘sail’ downwind faster than the wind one would need a machine which could first accelerate from stationary up to wind speed – no problem – but then to go faster than the wind, one would have to keep accelerating from that point in time and space where the apparent wind on your craft had dropped to zero.  Sounds impossible!  
UCLA Astronomy and Physics prof. Alex Kusenko, while claiming he has sailing experience, lost a bet of $10,000, as witnessed by Bill Nye and Neil deGrasse Tyson.  Alex claimed it could not be done saying that wind gusts and a higher wind speed at the prop height, rather than as measured at the cart, explained an observed momentarily high cart velocity.  I’m sorry I cannot find any comment on the outcome of the wager from Nye or Tyson. 

 

Nov 28, 2021.  Deep apologies to all – The following analysis is in great error!  The twist in the drive belt in the Figs. 13 and 16 is reversed and so the conclusions are very wrong.  Revision no. 16 is coming soon.
SeaBee

 

After much thought I suggest the following analyses might illustrate what is actually happening in a clear manner without resorting to plots of trig functions, etc.

General Physics Principles:

Figure 2

1.  A balloon in a steady wind surely only travels at exactly wind speed and exactly in the wind’s direction.
That great old movie “Around the World in 80 Days” showed a global circumnavigation of approximately 24,000 miles in 80 days (averaging about 12.5 avg. mph).  But did Niven and Cantinflas beat the laws of physics by doing it in (spoiler alert) 79 days, or just over 1% faster than the wind, when crossing the date line was included in their calculations?

Figure 3

2.  A balloon drifting low over a flat desert, in a 10 mph West wind, could lower a wheel-driven electrical generator (G) which could power a tow cart (M) driven by an electric motor.  But due to the second law of thermodynamics (Entropy always increases), and ever-present frictions in the generator and motor, the magnitude of the backwards (Westward direction) drag load of the generator will always be a little greater than the pulling power of the motor towards the East. This would result in our complex balloon actually travelling a little slower than the 10 mph speed of the West wind, showing us that you cannot go downwind faster than the wind, at least when using a balloon, with or without, electrical) propulsion devices. 

3.  Energy is needed to propel a wind driven craft.  Such propulsive force can come from tapping into the kinetic energy available when there is a difference in velocity between the air and the ground (or water).  That velocity difference can come from moving air (wind) over stationary land or water, or from stationary air over a moving body of water (river or ocean stream).  A dramatic example of this by Artemis Racing is shown in:     https://www.youtube.com/watch?v=q2il8Fagbyk  
where the Amazon River, flowing at 10 mph on a still air day, creates an apparent wind sufficient to drive a foiling catamaran up river (against the current) at 30 mph! 

But I ask: where can one find the potential or kinetic energy difference needed for further acceleration when a craft is travelling straight downwind at 10 mph in a 10 mph wind? 

Sailing Theory 

At age 16 Alen MacW and I canoed the River Shannon and tributaries for a month in a homemade craft, using a bed sheet for a sail when there was wind.  We sadly discovered, as did the square rig sailors of old, that we could not sail upwind at all.  We could sail: 90 degrees across the wind (“beam reaching”); at 45 degrees angle off the wind direction (“broad reaching”); and straight downwind (“running”).  To make any progress in an upwind direction in a canoe or sailboat requires a keel (or centerboard, or a good skeg) and an airfoil section sail.  The Egyptians seemed to have discovered this thousands of years ago with their elegant lateen-rigged feluccas on the River Nile, but they kept the details a secret for a long time. 

The answer to the Blackbird question lies in the application of Bernoulli’s principle

From energy conservation laws: the faster air or liquid moves, then the lower its pressure becomes. For sailing, and flying, you see this principle demonstrated in the use of a curved foil-shape cross-section of a wing, sail, or propeller. 

Figure 4 

Fluids (air, water, etc.) flow faster over the curved top of a foil shape than across the bottom when the flow is laminar, or non-turbulent.  Some think that is so the upper fluid can “catch up” with the slower medium underneath which only had to move a shorter distance across the bottom of the foil.  The faster speed of the fluid on top, perhaps surprisingly, results in it having a lower pressure according to Bernoulli.   See:    https://en.wikipedia.org.wiki/Bernoulli%27s_principle    and others. 

Including an ‘angle of attack’ of 10 to 20 degrees between the airfoil section and the wind adds the effect of an increase in pressure below the foil to that of the low pressure on top.  In optimum conditions this results in a lift force, red, of greater magnitude than the drag force, blue, shown below. 

Figure 5

A flat surface could be used instead of an airfoil section but it is not nearly as effective – see the flat fan blades on cheap cooling fans: they create noise from turbulence and don’t move the air as efficiently. 

A beautiful and simple demonstration of the Bernoulli reduced pressure lift process is had by delicately suspending a spoon near a stream of laminar flowing (non-aerated) water from a faucet.  Move the spoon towards the stream so that the back of the spoon just contacts the water.  If the water is turbulent it will splash off the spoon and push the spoon away, but when the water flow is smooth and laminar the opposite happens: Bernoulli’s low pressure draws the spoon into the stream.  The spoon’s bowl is strongly ‘sucked’ towards the water, as indicated by the red arrow in the lower photo below.

Figure 6 

This low pressure is what keeps aircraft aloft, allows sail boats to sail upwind, and lets ice yachts travel at high speeds (up to at least 5 times the wind velocity!). 

Sailing Downwind Faster than the Wind 

Using known values from existing high performance craft let us look at the details of an ice yacht, land-cart, or foiling catamaran, blue triangle in the diagram below, speeding along on a NE broad reach at about 25 mph, or two and a half times faster than the wind, in a 10 mph West wind, white arrow.  
The following diagrams use Vectors (arrows) to illustrate, by their length and direction, the magnitudes and orientations of wind speeds, forces, and boat speeds: 

Figure 7

The velocity vectors above show that even though the sail only ‘feels’ an apparent wind of about 19 mph from the NNE, the ice yacht is traveling at a speed of 25 mph. 

The wind force vectors on the sail are shown below.  The red arrow (vector) is the resulting force from the apparent wind acting at right angles to the center of the sail.  It can be resolved into a lateral force (blue) to the SE resisted by sharp skates on the ice, wheels on the sand, or a keel in the water, plus a forward driving force (green) which propels the craft to the NE. 

Figure 8 

The velocity vectors below show that when the craft is travelling to the NE at 25 mph, it is making progress due Easterly, straight downwind, at about 18 mph, or about 8 mph faster than the 10 mph West wind, (and at the same time it is making similar progress Northward at 18 mph). 

Figure 9 

But, of course, if the fixed-sail craft itself tries to sail straight downwind then the sail will stall and the Bernoulli effect will no longer apply.  With a stalled sail it becomes like our earlier balloon and could only travel due Eastward at close to 10 mph at most. 

 

A Thought Experiment

To address the main question of how to sail straight downwind faster than the wind let us imagine a (triangular shape) land cart, heading due East on the flat desert floor, with a steady 10 mph West wind blowing.  On this cart we have a hypothetical horizontal supporting beam, blue line, with a track mechanism holding an ice yacht sail (same as the one used above) vertically on a sliding track which allows the mast and sail to be moved laterally in a North-South direction relative to the cart axis.  If the sail is moved to the left, on the cart, at a speed equal to the forward speed of the cart then the sail ‘feels’, for a few moments, the exact same wind, force and direction, red, as the ice yacht sail felt, with its fixed sail, when it was travelling to the NE, in the previous case. 

Figure 10 

An observer looking down from a balloon above would see, for a few moments at least, the sail moving in exactly the same direction as the ice yacht’s sail, and therefore generating the same lift and drag vector forces. 

Figure 11

The picture above shows the initial position of the cart (in blue, left) with the sail amidships.  The later position (green), shows the cart a few moments later, moving to the right (Eastward) and with the sail moving left (Northward) on its track, while the sail traverses a NE path over the ground. 

The net driving force on the land yacht will be somewhat less than that of the ice yacht because of the energy needed to move the sail on the imaginary track.  

Rather than having the complex imaginary supporting track for the mast why not let the sail simply be a blade of a propeller?  As this propeller revolves around its horizontal fore and aft axis the airflow will be very similar to the sails in the two cases above.  By considering a short period of time we can ignore the small change in tilt angle of the sail as it rotates in its new propeller-like configuration.  As the propeller blade rotates through its upper quadrant our overhead viewer would once again see air flowing over an airfoil similar to both the ice yacht and sand cart examples above.   Add a second blade to the prop so while the upper blade is behaving as shown above when in the top quadrant of its rotation, the other blade is in the lower quadrant and supplies a similar Eastward direction driving force, but with an opposite direction (Northward) lateral force. 

As the professor so often says, “I leave it to the student to resolve the details for the prop blades when they are travelling through the side quadrants (3 o’clock and 9 ‘-clock)”.  The answer is simple: when the prop blade (sail shape) is travelling up or down, through the side quadrants, the resultant horizontal forces will similarly drive the craft forward, while the lateral vertical drag component, upward or downward, subtracts from or adds to the craft’s weight on the ground. 

So now we can have a real cart going straight downwind (due East) at 18 mph with a propeller whose sail-shape blades move across the wind in a very similar manner to that of the fixed sail of the ice yacht travelling at 25 mph in a NE direction, in the same 10 mph West wind. Even though at 18 mph Eastward cart speed the apparent wind at the land cart body is 8 mph against it from the East, the propeller blades are still ‘feeling’ an appreciable, and useful, apparent NNE wind. 

The propeller is turned towards the apparent wind by the belt drive connecting the prop shaft and the wheel axle.  The drive force from the propeller provides a forward push to the top of its supporting mast, in the same manner that an airplane’s propeller ‘propels’ an airplane forward.  The forward movement of the cart over the ground drives the wheels which turn the axle and puts tension in the belt to turn the prop. 

An ice yacht, having the least drag resistance (from its skates) to forward motion of the three craft types considered, should have the greatest velocity of the three craft types considered here.  A foiling catamaran, with a similar sail, should be the next fastest given that the drag of the foils through the water would be greater than that of sharp skates on ice.  Our land-cart has low rolling resistance but it does have to supply energy from the rotating wheels to turn the prop against the apparent wind and so could be expected to have the slowest vehicle velocity of the three. 

The magic of the Blackbird rotating propeller is that the blades can ‘feel’ an apparent NNE wind of about 19 mph even though the craft is running straight downwind, Eastward, at 18 mph in our 10 mph West wind.  Note that the ice yacht and foiling cat, with their fixed sails would feel a direct head wind if they turned straight downwind and so they could never find the power needed to sustain their speed. 

But can the Blackbird propeller generate enough forward drive power after overcoming the drag of the drive belt on the wheel axle which has to rotate the propeller against the apparent wind?   Work done is the force multiplied by the distance moved.  For the ice yacht the lateral force is simply resisted by the skates on the, with no ‘distance’ moved on the ice and so no work is done. But in Blackbird work is done equal to the distance the prop is moved against the drag of the wind.  The solution lies in the force vector diagram, Figure 10 above, which shows the driving force, green, is greater than the blue drag force when the vehicle is travelling at 25 mph.  The details of Blackbird operation in the pages below show the drag force, blue, meeting the drive force, green, in the drive belt.  As long as the magnitude of the drive exceeds the magnitude of the drag the craft can continue to accelerate. 

 Can Blackbird function in Zero Apparent Wind? 

The thought experiment above reasonably demonstrates how Blackbird can travel straight downwind faster than the wind, but to get to that velocity, if it is travelling in a straight line, and starting from a standstill, it must first accelerate from zero speed to the velocity of the wind, and then exceed it.  If the wind is 10 mph from the West then when the Blackbird has reached a speed of 10 mph to the East there will be zero apparent wind velocity as measured on the cart.  How could the propeller mechanism create a drive force in zero apparent wind?  A closer examination is needed of the cart and its operation while it accelerates straight downwind, starting at zero velocity. 

Step by Step Detail from Zero to Twice Wind Speed Straight Downwind in a Prop Driven Land Cart 

The cart’s propeller blades are continuously pitch-adjusted, by the sailor, to an angle of attack of about 20 degrees to their apparent wind to optimize the Bernoulli lift effect.  

  1. The sketch below shows a 10 mph West wind with about 1 mph Eastward cart speed.  An apparent West North West wind, light blue arrow, is felt by the rotating prop. The resulting wind force, red, on a single blade of the prop (black cross section) drives the prop around, and drives the cart forward. The wind force shown can be divided into two component parts, or vectors, (green and blue) in two different directions, at 90° to each other.

                        Figure 12

Figure 13

The green arrow shows the drag force component of the wind on the prop pushing it against the bearings in a hub at the top of its support mast (not shown). This green arrow force is countered by an equal and opposite direction force at ground level against the drive wheels, making them rotate. The blue arrow shows the lift force on the prop, in this case driving it ccw (when viewed from behind) around its axis.  That force pulls the aft side of the drive belt up adding to the forward driving torque on the axle 

 With the cart at slow speed the wind turns the prop and propels the cart downwind, like a balloon, whether there is a drive belt or not, up to a speed approaching that of the wind, but no further. 

2.  At about 5 mph cart velocity the propeller blades are turning  with a velocity of say 5 mph at the middle point of each blade as they are driven by the wind and the belt from the wheel axle, assuming a 1 to 1 drive ratio.  The apparent wind felt by the blade in the upper quadrant will be coming from NW. The prop pitch angle is adjusted to keep laminar flow over the blade as the cart velocity increases. 

At 5 mph speed the cart is still being accelerated.
Figure 14 

3.  When we reach the very interesting speed of 10 mph the land cart’s propeller generates more thrust. The center of each blade is travelling in a vertical North-South plane at the same 10 mph speed.  This gives an apparent wind on the blade from the North of about 10 mph while it is passing through the top quadrant of its circular path, even though the apparent wind velocity on the cart body is zero!  Note that the blue drag force vector is now colored blue because it has reversed direction and is working, through the belt action, against the green drive force (now colored green).
 Figure 15

Figure 16

It is worth examining this step in more detail as the conundrum centers here where the apparent wind on the craft body is zero and a reason for its continuing acceleration must be found. 

To drive the cart there must be an available source of energy. This can be found when there is a velocity difference potential between two locations.  While there is no velocity difference available between the 10 mph wind and the cart body moving at 10 mph, there is a spot at the middle of the propeller blade (moving around the prop axis at about 10 mph) where there is a velocity difference of about ph between the resultant apparent N wind and the blade, see Figure 15.  Tapping into this potential creates lift, and drag, on the propeller.  As long as the lift force is greater than the drag there will be a net drive force available to push the craft forward and accelerate it. 

4.  At 15 mph craft speed to the East, the nose of the land cart feels an apparent wind of 5 mph from the East.  This starts to create drag resistance.  

 Figure 17 

But each blade of the rotating propeller feels a stronger wind, say about 16 mph (from the NNE for the blade passing through the top quadrant) and supplies a greater forward thrust (green) than the drag (blue) so the craft can continue its acceleration. 

5.  At say 25 mph cart velocity, the apparent wind on the prop moves more towards the East, the wind drag (blue arrow) of the propeller increases until it matches that of the forward thrust of the propeller (green arrow) and the craft no longer accelerates. 

 6.  If the wind strength were to increase above 10 mph then then the West wind vector would lengthen. This would cause the apparent NW wind on the prop to move more towards NNW. With the prop pitch re-adjusted a new drive force greater than the drag could result in new acceleration.

 Figure 18

  Other Thoughts 

Could there be a way to exploit the power generated by the wheel driven propeller in zero wind seeing that this was almost done when the apparent wind on the cart was zero in the 10 mph example above? 

Towing the cart Eastward at any speed, in a zero wind velocity, and then releasing it, at first sounds similar to the above situation of 10 mph cart velocity Eastward in a 10 mph wind from the West.  But plotting the vectors quickly shows the apparent wind on the prop now comes from the NE.  With a 20° angle of attack the forward drive vector to the East, green arrow, is much smaller than the lateral drag force Southward, blue arrow, and so when they pull the drive belt in opposing directions, the craft will quickly come to a halt.
Figure 19 

 It would be interesting to see what speeds Blackbird could attain as it started to turn towards the wind.  I have since read that Cavallero did alter Blackbird a little – he widened the axle for stability against the torque of the propeller- and reportedly travelled straight upwind at twice the wind speed.   

 

  Other Unlikely Propulsion Methods:

 1. Straight downwind sailing, faster than a very low wind velocity, can be done on flat water, by experienced racing windsurfers who vigorously ‘pump’ the sail back and forth.  But this is adding energy (human) from an exterior source and cannot be accepted in our case. 

2.  I remember clearly, about 45 years ago, looking with my young son at our first skateboard on the smooth varnished floor of the Algonquin Island clubhouse and wondering if there was any way it could be propelled without putting one’s foot to the ground.  I erroneously concluded that was impossible, but not long later others showed us how to do it with a “tic-tac” motion, pumping the board forward by twisting it back and forth, while simultaneously popping the front wheels forth and back. 

3.   Perhaps the hardest is to levitate oneself by standing in a bucket and pulling up on the handle (which principle may come to mind when you first hear of the Blackbird story).  But even that improbably could work, at least momentarily, by performing an energetic series of hops.  Or have I just invented a ‘Pogo Bucket’?

4.  In my year (1965) of wandering through India I did watch out for the infamous rope trick and actually met these great characters who appeared as though they might be keepers of the secret:
 Sadly I never did see the rope trick performed. 

 5. I close with my disappointment in the late but brilliant magician Doug Henning who long ago told us from the stage of Ryerson Theater in Toronto, on his return from visiting the Maharishi Mahesh Yogi in Switzerland, that he would soon be genuinely levitating.  He failed to truly do that. Photos similar to the one above were created by the Yogi’s followers bouncing on trampoline-like devices.  Doug tragically died too young of a liver problem which he falsely believed (according to Wikipedia) could be cured by his faith in the Maharishi’s “Transcendental Meditation” methods.

 

 

 

Sea-Bee  (OH-10)
V15  2021/11/05 

Under the Outskirts

Driving again to Chicago last week I passed under the edge of a dense cloud bank. I always expect some dramatic weather at the skirting line between blue and black sky but it never happens.  Are these the places where those bumpy or jagged frontal lines occur on weather maps?

 

A few years ago I flew over one such edge at sunrise while descending into Philadelphia – even more dramatic in appearance but surprisingly not bumpy

It was a little more concerning to sail under one such cloud skirt edge in the middle of the empty Atlantic early one morning years ago with Tony on Taonui, but again nothing dramatic happened

But right now in Chicago tourists are much more interested in being photographed while standing under the skirts of Marilyn’s huge new statue

 

 

 

 

Cape Hatteras, North Carolina

The island is slowly recovering from hurricane Irene at end of August. Bridge to Salvo is only open again this week. Much debris – including large propane tanks – and many mosquitoes in the bushes. Fortunately they are not out on the beautiful water.
The twisted dock (just visible in the bushes on the left) was 4 ft lower when we used it 2 years ago.

On the ocean side shore waders eat the sand fleas, but the little crabs are too swift for all except Nat.


The crab was happy to be returned home

 

Meanwhile back on the Sound, thanks to Jim’s magic waterproof cameras:

 

The barometer crashed down bringing rain and big wind. Then it shot up:


bringing sun with the same big wind: Glen took this great shot of my 3.2.sq.m. ‘Pin-Head’ storm sail (with Ron close astern) that I’d bought from Karen M about 26 years ago.

If every picture is worth a thousand somethings then this one cost me even more when I dashed off to Andy’s Sail NC to convert my rigs to the current era. The improvement in sail stability & control is startlingly significant. Notice the 3 very short battens in my old green sail vs. Ron’s 5 full length ones and you can imagine how the green sail wobbled when the wind was 30 + mph.