Blackbird Land Yacht "DDWFTTW" 2

[LuckyDuc]

Did anyone follow this back in 2010? Somehow I missed it until I read where the craft was for sale:

http://autos.yahoo.com/blogs/motoramic/wind-powered-blackbird-sale-rewriting-physics-134230233.html

Wikipedia page is here:

http://en.wikipedia.org/wiki/Blackbird_(land_yacht)

There was a great deal of "Its a hoax and you are an idiot if you think otherwise" internet banter going on until they proved it. I am a mechanical engineer, but have not had to commit calculus or draw a free body diagram in YEARS! I've always enjoyed mindbenders like this and wouldn't mind discussing a few "nuances" and details of the project if anyone is game???

LD

 

[Compositepro]

I had to re-read my explanations from the other thread to remember how this works. It is not easy for most people, including me, to visualize how this works. But it does work, and it is well worth the effort to come to an understanding of how it works because it is so counter-intuitive.

Think of the propeller as a sail with aerodynamics that changes with rotational speed. When not rotating it does not present much sail area to the wind, but enough to start the cart rolling. The rolling cart drives the wheels, which drives the propeller opposite to how the wind would drive the propeller. As the propeller rotates faster it can still push back against the wind even though the cart is going faster than the wind. So the wind is still pushing the cart downwind.

 

[MintJulep]

Sorry, this:

With the balance speed being where red, blue and green sum to zero.

 

[Alsee]

Here's some calculations showing how the cart works. Start with the cart going 30 meters per second to the left, and a wind at 20 meters per second to the left. So the cart is going downwind, faster than the wind. The cart sees an apparent headwind of 10 meters per second.

Now we put a load on the wheels, a drag force of 1 newton trying to slow the cart down. How much power can obtain? Power=force*velocity. The force is 1 n, and the velocity of the wheels over the ground is 30 m/s. So the power is 30 n m/s.

Now we use that power to drive the propeller. How much thrust force do we get? If we flip the power equation to isolate force, we get force=power/velocity. And note that the prop is pushing against the air, and the air is passing through the prop at a velocity of 10 m/s. So force = power (30 n m/s) / velocity (10 m/s). This yields force = 3 n.

Drag is 1 newton, thrust is 3 newtons, net thrust is 2 newtons. The cart is going downwind, faster than the wind, and accelerating.

A real world cart is going to have inefficiencies and friction losses, but our ideal prop thrust is three times as much as we need. An overall net efficiency of 34% is enough to still yield an accelerating cart.

Note that if you recalculate things using a zero windspeed then you always wind up with prop thrust exactly equal to wheel drag. In the ideal case, with zero wind, the cart neither gains nor loses energy, it simply inertial coasts forever at 20 m/s. In the real world friction and inefficiencies kick in, and prop thrust will always be less than wheel drag. In the real world, with zero wind, the cart inherently slows to a halt. Exactly like any other wind-powered vehicle does.

 

[rb1957]

aren't there a lot of asusmptions in that ...

"Start with the cart going 30 meters per second" ... it'd be more rational to start with the cart at 0 ? why can the cart be assumed to be going downwind faster than the wind ? if the apparent wind is "on the nose", how does the cart generate power to overcome aerodynamic drag ?

getting 30Nm/s of power from the propeller is (sorry) fiction. the propulsive efficiency of a propeller is never much above 80%.

"Note that if you recalculate things using a zero windspeed" ... i'll take that as nett windspeed ... "then you always wind up with prop thrust exactly equal to wheel drag." ... BS ! you'll Always wind up with prop thrust < wheel drag (IMHO) 'cause otherwise you've got perpetunal motion, haven't you ?

and another way to read that statement is "the cart cannot go faster than the wind" 'cause if prop thrust = wheel drag then the propulsion system isn't accelerating the vehicle and you're already at "zero windspeed".

if the initial motive force of the cart is windage against the propeller (going downwind), so now the wheels are turning, then you can take power from the wheels (slowing the cart). for the propeller to produce thrust (ie downwind force) from a following wind, it'll have to decelerate the airflow (i think ... ??) but this is the mechanism for the vehicle to be moving in the first place (you're taking the drag of the prop as a driving force for the cart, the drag is created by slowing the wind ...


Quando Omni Flunkus Moritati

 

[Alsee]

"'Note that if you recalculate things using a zero windspeed' ... i'll take that as nett windspeed "

Nooooo.... When I said "if you recalculate things using a zero windspeed" I really did mean "if you recalculate things using a zero windspeed". If you consider the case of NO WIND BLOWING, you get the same sort of result that you expect to get for any sail craft. At zero true wind your sail generates zero force. (In this case we have a pair of funky-looking sails, the two blades of the prop.)

"'then you always wind up with prop thrust exactly equal to wheel drag.' ... BS ! you'll Always wind up with prop thrust < wheel drag (IMHO) 'cause otherwise you've got perpetunal motion, haven't you ?"

First, I'm doing a theoretical calculation for the ideal case where friction and other losses are taken as zero. So your "prop thrust < wheel drag" should be written as "prop thrust less-than-or-equal-to wheel drag".

Second, when you jump to the obvious "prop thrust less-than-or-equal-to wheel drag" conclusion, you're doing so with certain unstated and unnoticed assumptions. If those assumptions don't hold you'll jump to a conclusion which doesn't hold. This particular problem trips up all of the usual assumptions, causing lots of people to reach mistaken conclusions. We're all well familiar with with law of conservation of energy, and the general principal that you can never get more out than you get in. But there's a related pair of oversights here. The first is, the law is conservation of ENERGY, not "conservation of FORCE". There is no conservation of force. A simple lever demonstrates this... on the long arm of the lever you can apply a small force through a long distance, and on the short arm of the level you obtain a large force moving a small distance. The second oversight here is that there is a wind blowing. You can nail a windmill to the ground and obtain forces and extract energy. The wind is a potential INPUT of energy and forces. If you quickly jump through the problem and forget to *explicitly* address the wind you're going to get a wrong result. And in this case it's mentally tricky... the typical reaction is to jump into the reference frame of the cart an think "what happens when you're at windspeed", and in that frame you see zero apparent wind. And the natural reaction is to think that you have accounted for the wind, that you've gotten it to zero and removed it as a factor. Except what you've actually done is merely turned the problem "upside down". By jumping into the reference frame of the cart at windspeed, you have reduced the apparent windspeed and apparent wind-kinetic energy to zero, however you have merely transferred that speed and that apparent kinetic energy into the ground. You have not actually accounted for the wind... if you now fail to account for the ground motion then your assumptions and your conclusions conclusions will still be be wrong. All you did was turned the problem upside down, you are now "standing in the wind" and the ground is "blowing". The true wind exists, it just looks like a "blowing ground" now. In this reference frame you can replace a "windmill" with a "groundmill". You can nail a "groundmill" to the air to harness the apparent kinetic energy of the ground. If you are in a blimp floating in the wind, you can lower a wheel to the ground, you can drag that wheel behind the blimp causing the wheel to spin, and you can attach a generator to that wheel to extract power. That is a "groundmill". Note that, standing in the blimp, you feel zero airspeed. From your point of view it seems like the generator is being power by the ground rushing past.

"aren't there a lot of asusmptions in that
it'd be more rational to start with the cart at 0 ?"

My goal was show that the cart works, with the calculations implicitly showing how/why it works. Generally everyone understands that it's easy for a wind-vehicle to head downwind at upto windspeed, I merely addressed the part that is hard understand. I described a machine that can be constructed, and I showed that such a machine can still accelerate even in the counter intuitive range above windspeed. So I assumed a cart already above windspeed.

If you were able to follow the calculation, you can simply re-do the calculations filling in any starting speed you wish. You will find that, for any speed above zero, the cart will experience an acceleration in the downwind direction. The speed of zero is a corner case. At zero speed the wheels are not turning, the prop is geared directly to the wheels, so the prop isn't turning. This part of the machine isn't (yet) doing anything, so this portion generates zero force. However as you noted, a real cart will experience aerodynamic drag. A cart parked in the wind will experience a simple drag trying to pull it downwind. This gets the initial speed above zero. In the range between zero and windspeed, simple aerodynamic drag is pulling it faster and faster downwind PLUS the wheel-prop system helps push it faster downwind. When you reach exactly windspeed the apparent wind becomes exactly zero and any aerodynamic drag becomes exactly zero. Note that at this point there is *zero* aerodynamic drag resisting any attempts to go slightly faster. Any non-zero net thrust gets you above windspeed. If you check the calculations for a cart at exactly windspeed you find the wheel-prop system is generating a large forwards acceleration. (Actually you'll find infinite force, this is a corner case, a real prop has losses and inefficiencies, a prop with zero airspeed will generate a very large but finite force.) The cart smoothly accelerates from below windspeed to above windspeed without noticing anything significant at windspeed. As you go faster above windspeed you get a headwind and aerodynamic resistance will begin to increase in proportion to apparent windspeed squared. This means wind drag is vanishingly small when you are going only a little faster than the wind, and wind drag becomes increasingly nasty at larger speeds. The cart speed will increase, and the aerodynamic drag will increase, up until the the point where aerodynamic drag equals the net thrust being produced by the wheel-prop system. This will be the peak speed, and it will be significantly faster than the wind. The peak speed is determined by the efficiency of your wheel-prop system and by how aerodynamically you design the cart. These are "merely" engineering issues. In principal the cart has no maximum speed. The cart can collect energy from the true wind to drive the cart to speeds limited only by your drive chain efficiency and aerodynamic design.

This cart has been built as passenger size vehicle named Blackbird. It has been tested, reaching slightly over 3x windspeed in unofficial runs, and has been certified in an official test as reaching 2.8x windspeed by the North American Land Sailing Association (NALSA). NALSA has extensive experience running conventional land-sail-cart races, and they are the foremost organization in the world for preforming and certifying world record speeds for conventional land-sail-cart designs. The Blackbird's 2.8x speed has also been certified by Guinness World Records as a world record speed for wind craft sailing on a directly-downwind course. The Blackbirds design has even been included as a model physics problem in the 2013 International Physics Olympiad for highschool students. MIT Professor professor in aerodynamics Mark Drela published a paper analyzing and confirming this sort of design works (although his paper laid it out as a boat going downwind faster than wind, rather than a land cart.)

"getting 30Nm/s of power from the propeller is (sorry) fiction. the propulsive efficiency of a propeller is never much above 80%."

If you look, you should see I directly addressed this. I pointed out that the calculated prop thrust was 3 newtons, where any force greater than 1 newton was enough to accelerate the cart. As I noted, the cart and the calculation work even with a dismal 34% overall efficiency. Citing an 80+% prop efficiency is not an obstacle. That leaves a real-world engineered cart abundant of headroom for other losses, and allows it to reach speeds significantly higher than the example speed. As the Blackbird demonstrates, a skilled two man team with a five-digit financial budget can reach over 3x windspeed. A more aerodynamic design, with a bigger more efficient prop and a more efficient drive chain, could certainly reach 4x speed or higher. There's no theoretical limit, but getting to 6x windspeed and above would involve increasingly unrealistic engineering constraints. Aerodynamic drag in that range becomes a very severe challenge.

"for the propeller to produce thrust (ie downwind force) from a following wind, it'll have to decelerate the airflow (i think ... ??)"

That raises an interesting and important point. Note that the meaning of "decelerate the airflow" is reference-frame dependent!
From the point of view of the cart, to generate thrust we need to push the air faster toward the back of the cart. From the point of view of the cart, we extract energy from the wheels, and we spend that energy accelerating the air faster towards the back. Energy is flowing from teh cart to the air.
But now look at it from the ground. We see the wind blowing, the wind has lots of kinetic energy. The propeller is turning in a direction that SLOWS the wind down. The propeller is pushing backwards against the wind. And here is the key point.... we see the air slowing down.... which means we see the air losing kinetic energy. And by the law of conservation of energy, we know this energy MUST be going somewhere. And if you think about it, there is only one place this energy could be going. This energy is transferred into the cart. In the calculations this energy shows up in the form of "extra" thrust at the prop, accelerating the cart, increasing the cart's kinetic energy. This is where the "extra" thrust comes from... it's from the kinetic energy that the wind is losing.

Conservation of energy is absolute, however the apparent *direction* of energy flow can be reference frame dependent. From the point of view of the ground, wind energy is going into the cart, part of that energy drives the prop to spin, the rest accelerates the prop. From the point of view of the cart, energy is going the other way, from the cart into the air. The cart sees the ground as the source of energy which drives the prop and accelerates (transfers energy into) the air.

Energy is conserved in all frames, but the direction of energy flow is subjective to particular frames.

This cart problem is so fascinating because it highlights certain tricky cases where we instinctively apply invalid assumptions, and how it highlights unintuitive aspects of physics like how the direction energy flow can be subjective to particular frames.

 

[1gibson]

This is how I see it:

1) Starting from a dead stop (this is important to some people, not sure why, we aren't talking perpetual motion here...)
2) Wind pushes vehicle forward slowly (aerodynamic drag on the vehicle body and prop)
3) Rolling wheels turn the prop so it pushes air backwards (towards rear of vehicle)
4) This is met with resistance from the wind, making the vehicle increase speed
5) More wheel speed, more prop speed, more thrust, more vehicle speed


Forget the wind for a second, it is dead calm, and assume the vehicle has already started moving (I know I know, just stay with me for a second.) Now chase it with a big sheet of plywood, holding the plywood very close to the propeller. The vehicle speed will continue to increase because the prop is pushing air against the plywood, and some lunatic is chasing after it continually pushing the plywood closer to the prop.

Now, remember the wind, and take away the plywood and the lunatic. You get the same results, without the unwanted side effects (neighbors thinking you are crazy.)

 

[rb1957]

if there's no wind then there's no motive power to start the wheels turning.

if there's no wind what's causing the thing to move ? it's own velocity ?? now you do have a perpetual motion machine !

(and btw, i did post reading your long post after the first sentence)

Quando Omni Flunkus Moritati

 

[77JQX]

Thanks Alsee! I learned something today.

 

[Compositepro]

Nice explanation, Alsee. Your second post does clarify your first post, which I was not quite prepared to agree with, but now makes sense.

 

[Alsee]

Correction. I meant to say:
"From the point of view of the ground, wind energy is going into the cart, part of that energy drives the prop to spin, the rest accelerates the CART".
I accidentally wrote the last word as "prop" instead of "cart".


rb1957:
if there's no wind then there's no motive power to start the wheels turning.

Correct. Any wind-powered vehicle only operates when there is a true wind blowing.
Just be careful not to confuse "true wind" with "apparent wind". When a True Wind exists the sails on this cart (the prop blades) never see an apparent wind of zero. The rotation of the prop moves the blades cross-wind like a sailing ship moving crosswind on a tack. This imposes an apparent wind over the sails (over the prop blades), maintaining lift. It is well established that high performance sailing craft can achieve an average downwind speed greater than windspeed by tacking back and forth across the wind.

 

[Compositepro]

" It is well established that high performance sailing craft can achieve an average downwind speed greater than windspeed by tacking back and forth across the wind. "
I was not aware of that, but I guess the same logic applies.

 

[rb1957]

i am well aware of true and apparent wind (see my earlier posts).

1) "high performance" sailboats can go faster than the wind without tacking, a beam reach is usually the fastest point of sail, and apparent wind effects are all a Hobie 16 needs to get the wind to clock around.

2) i don't see this cart tacking downwind ...

Quando Omni Flunkus Moritati

 

[Alsee]

rb1957:
i don't see this cart tacking downwind

That's the neat part of this design. There's no need for the *entire cart* to tack. The only thing that truly need to be tacking across the wind is the *sail*. On a conventional sailcraft the sail is mounted directly to the body of the craft, and this means that to get the sail to tack you need to tack the entire craft. In this design we have a pair of sails mounted on opposite sides of an axle. If you think about it carefully, that's exactly what a propeller is, a pair of airfoils mounted on an axle. To get a sail to tack we impose a sideways force on it using the keel. On a conventional sail craft this means the keel pushes the entire craft sideways across the wind. In this design we use the keel (the wheels) to push just the sails sideways across the wind.... specifically we impose a rotational force on the prop. This causes the sails to alternately tack to the right, tack down, tack left, and tack back up. The sails follow a constant corkscrew tack downwind. In sailing terms, the prop blades are on a broad reach. The exact same kind of tack that a high performance sailcraft uses to achieve a net downwind speed greater than the wind. To reach a goal in the directly downwind direction a convectional sailcraft needs to alternate left and right tacks, just like the prop blades are alternately tacking left and right.

 

[rb1957]

i was replying to Compositepro's post ... and as i say "i don't see this cart tacking downwind"

IMO, this design requires the propeller to be fixed dead ahead, since the propeller is providing thrust for the cart (to go forward). and i don't see these propeller blades as being on a "beam reach", i see them as airfoils with pitch control and twist to maximise thrust. a problem i have is that the blades are doing two, very different, jobs ...
a) they're stopping the wind (to create the inital motive force), and
b) they're rotating (driven by the wheels which are already turning) to create thrust.
now, ok, you might say that ...
a) initially the propeller is locked and the blades are closed (opposite of feathered) to maximise the drag (= thrust), and
b) once the cart is moving the propeller changes role (unlocks and starts to turn) and starts to create thrust; thrust driven by the wheels ... so drag on the wheels is turned into thrust on the propeller ...

Quando Omni Flunkus Moritati

 

[Alsee]

rb1957:
this design requires the propeller to be fixed dead ahead
the propeller is providing thrust for the cart (to go forward)

Right and right.

rb1957:
i don't see these propeller blades as being on a "beam reach"

Right. It's a broad reach. (For the non-sailors, "broad reach" means the sail is traveling diagonally. It's going downwind and across the wind.)

rb1957:
a problem i have is that the blades are doing two, very different, jobs ...
a) they're stopping the wind (to create the inital motive force)

Ok, you're looking at it starting from a dead stop there. If it helps, just look at the wind drag on the cart frame for the moment. This will tend to drag the entire cart down wind and get things started. Examining the stopped situation is rather unimportant, all the interesting questions are about the moving cart. How does a moving cart work? How fast can a moving cart go?

rb1957:
b) they're rotating (driven by the wheels which are already turning) to create thrust

Right.

rb1957:
now, ok, you might say that ...
a) initially the propeller is locked and the blades are closed (opposite of feathered) to maximise the drag (= thrust)

We don't do that. Everyone knows it's easy to sail downwind at less than wind speed, so as we don't care about performance here. The cart operation is already pretty difficult to understand, and equally difficult to explain. We keep things as simple as possible. The last thing we want to do is mess with gear changes or variable angle props. This means the typical cart design has absolutely dismal startup performance. In the boring range below windspeed we make zero effort to maximize thrust. Basic wind drag plus lousy thrust efficiency at the low end is enough to get us close to wind speed, which is where things get interesting. The prop is set up for decent performance at exactly windspeed and maximum thrust when above windspeed.

rb1957:
b) once the cart is moving the propeller changes role (unlocks and starts to turn) and starts to create thrust; thrust driven by the wheels ... so drag on the wheels is turned into thrust on the propeller ...

Right, and I assume your "..." represents the common reaction that you see things going in a circle. The prop pushes the cart forwards, which makes the wheels spin, which drive the prop, which pushed the cart forwards, which makes the wheels spin, which drive the prop. This looks like your standard perpetual motion machine loop. And you're right, it basically is your standard perpetual motion machine loop.... with an important difference. Firstly, it is perfectly legal to *assemble* a "perpetual motion machine design".... and it will sit there doing exactly nothing. However if you plug it into an electric wall socket the machine will run. A machine with a loop is a red flag of bogus physics, but a loop is not in itself illegal. You need to check very carefully whether or not there is a power input. Powered machines work, unpowered machines don't. In this house we obey the laws of physics

The wind contains kinetic energy. If you consider a windmill, the propeller blades slow the air down. This reduces the air's speed. The slower air now contains less kinetic energy. The law of conservation of energy, this energy had to go somewhere. This energy went into the windmill. That energy is now available for our use.

Now consider the moving cart. If you look at the direction the prop is turning, it's blowing like a fan... it is blowing backwards against the wind. If you look at it from the ground, this wind has been *slowed down*. The wind was blowing 10 MPH, but the air coming out of the propeller is only going 5 MPH. This means the air contains less kinetic energy. By the law of conservation of energy, we know this energy *must* be going somewhere. It can be a bit of a brain bender getting a handle on what happens at this point, but we clearly have the air losing energy and we know it's going somewhere. And the only place for it to be going is into the cart. So how is this energy getting into the cart? If you do the physics calculations it turns out that this energy shows up in the form of an increased thrust force at the prop.

The fact that the wind exists means that the air speed at the prop is going to be different than if there were no wind. Ordinarily you would expect a cart going at 10 MPH to feel a 10 MPH headwind. But a cart going downwind at 10 MPH in a 10 MPH wind feels still air. The fact that the prop feels still air instead of fighting a 10 MPH headwind means the prop can generate more thrust. A cart going faster than the wind, a cart at 20 MPH in a 10 MPH wind only feels a 10 MPH headwind instead of the expected 20 MPH headwind. Even when the cart is going slower than the wind, the fact that the wind exists still changes the airspeed seen by the prop. This has an effect on the prop thrust.

If there's no wind, the prop thrust will always be less than or equal to the wheel drag, just like any underpowered perpetual motion machine. With zero (wind) power input it wouldn't work, it would grind to a halt. But in this case the wind is losing energy. In this case the existence of the wind is modifying the airflow and the thrust at the prop. In this case the physics calculation show that the prop trust winds up being greater than the drag at the wheels. There is no "over unity" here.... the energy for this extra prop thrust comes from the wind. *This* is exactly where the wind energy is vanishing to. This energy takes the form of extra thrust appearing at the prop. *This* energy pushes the cart forwards. *This* energy forces the wheels to turn. And *this* energy forces the prop to spin.

There is a loop, but it's a loop with energy flowing into it. And as the energy flow into and around that loop it forces the prop and the wheels to spin faster. The speed will increase until the friction losses and aerodynamic drag losses equal the energy input. For the large man-piloted Blackbird cart, this top speed is approximately three times windspeed. Friction losses are minimal, it's the increasing apparent headwind striking the cart-body that limit your top speed. And note that that pathway of energy loss doesn't even exist until you're already above windspeed.

 

[JStephen]

Okay, read up on the Flettner Rotors. Interesting, but not really related- they are using a powered rotor, for one thing, and basically function as an improved sailing ship. "and the rotor ship could tack (sail into the wind) at 20-30 degrees, while the vessel with its original sail rig could not tack closer than 45 degrees to the wind." But, not straight into the wind, and no propeller in the water involved.

 

[Walterke]

let's start with a few assumptions:
(I'm thinking this up as I type)
1) frictionless world (except for the wind of course)
2) Surface A= surface which catches wind=surface of the propeller
3) 100% efficiency between wheels & fan rotor.

As soon as the wind is blowing, the cart will accelerate until Vcart=Vwind.
wheels will make the fan rotate creating a backwards wind Vfan
The "speed" of the air right behind the fan will as result be Vcart-Vfan or Vwind-Vfan
Since there is a difference in wind speed between the "bag of wind" behind the fan and the actual wind, there will be an accelerating force relative to dV=Vwind-Vfan, causing the cart to accelerate to Vwind+Vfan
This, in turn, will increase Vfan to Vfan2, making the cart accelerate to Vwind+Vfan2, and so on.

So in a "perfect" world, you have an energy surplus, making it more than a perpetuum mobile, meaning that, provided all energy losses (friction, gear efficiency, etc.) are small enough, the cart will accelerate.

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