Understanding DDWFTTW: Exploring Its Principles and Addressing Common Questions

[Opus_723]

I know there have been several other threads about this, but I couldn't find answers to my specific questions, so as much as I hate to stir this up again, I'm hoping someone will take pity on a newbie and talk me through this. I would like to say that I have no doubts that these vehicles work, and I'm simply trying to understand the principles involved.

First, what I think I understand so far:

At first I couldn't understand how the propeller could deliver enough thrust to overcome the friction on the wheels, if the friction was providing the power. But then I realized that the propeller doesn't move as far through the air as the wheels travel across the ground since there is a wind. So for the same amount of power, the propeller can apply more force. So once at wind speed, thepropeller can accelerate the cart to faster-than-wind speeds. It can continue to accelerate until the headwind is strong enough to balance out the additional thrust, where it then reaches a constant, faster-than-wind speed.

But what confuses me now is this:

If you assume that the wind delivers its maximum amount of power to the cart when it travels at wind speed, as happens with a sailboat, you have a problem. At faster than wind speeds, the wheels have even more power, since they are moving faster. But at this point the wind should be applying negative power in the form of a headwind.

I thought maybe the negative power from the headwind might simply balanced out the additional frictional power from the wheels, so that the cart as a whole has the same amount of power as it does at windspeed. But in order for this to be the case, the drag would have to be constant and equal to the frictional force. But drag changes with velocity, so this can't be.

So my assumption that the wind is delivering max power to the cart at wind speed might be wrong, or else I am wrong about something else. How does the cart harvest additional power from the wind at faster-than-wind speeds?

One other question:

I read in one explanation that the propeller can act as a windmill to drive the wheels at slower-than-wind speeds, and then be turned by the wheels at faster-than-wind speeds. But after playing with a fan for a few seconds, I realized that if this were the case, the thrust provided by the prop in the second stage would be in the wrong direction. Could someone clarify how the prop acts at slower-than-wind speeds?

Thanks in advance for your patience, and I apologize if I've made any particularly annoying mistakes in my first attempts.

 

[rcgldr]

... then I realized that the propeller doesn't move as far through the air as the wheels travel across the ground since there is a wind. So for the same amount of power, the propeller can apply more force.

That is the key aspect. There is effective gearing to increase force and decrease speed, enough so that inspite of power losses due to inefficiencies, there's still more force (but at a lower speed) at the prop than at the wheels.

If you assume that the wind delivers its maximum amount of power to the cart when it travels at wind speed. ... At faster than wind speeds, the wheels have even more power, since they are moving faster.

AT responded to this in the following post.

How does the cart harvest additional power from the wind at faster-than-wind speeds?

Power is extracted from the wind when the wind is slowed down by the thrust from the propeller. This occurs as long as the thrust speed from the propeller is greater than the relative (wrt cart) headwind. If I recall correctly, the effecting gearing of prop thrust speed : ground speed is about 4:5 for the blackbird cart. Say the max speed is 3x wind speed (one test run was 2.8x), then thrust speed would be (4/5 x 3 =) 2.4 x wind speed, and relative headwind speed would be (3 - 1 =) 2 x wind speed, so thrust speed would be 1.2 x relative heawind speed, and the wind would still be slowed down.

Could someone clarify how the prop acts at slower-than-wind speeds?

With a fixed pitch propeller which is what these carts use, at startup and at slow speeds, the prop acts as a bluff body, simply blocking (and slowing) the wind which pushes against the prop, pushing the cart forward. The initial acceleration is relatively slow. As speeds increase, the propeller starts to spin fast enough to start producing significant thrust, and then it's the thrust that slows down the wind as opposed to the propeller itself.

 

[A.T.]

But what confuses me now is this:

The best way to avoid confusion is to be precise:

- Make clear which reference frame you are analyzing (power/kinetic energy are frame dependent quantities)
- Distinguish between "air" with "wind" (movement of air relative to something)
- Distinguish between true wind (relative to ground) with relative wind (relative to cart)
- Distinguish between work done by the cart chassis on the air, with work done by the propeller on the air.

Being precise in formulating the questions, often makes the answer obvious.

If you assume that the wind delivers its maximum amount of power to the cart when it travels at wind speed,

That is not necessarily true. Depending on the propeller pitch the acceleration can be not maximal at WS but rather above it. So the increase in KE (seen from the ground frame) is maximal there. But the power transmitted though the vehicle always increases with speed. Here I posted some simulated values:

https://www.physicsforums.com/showthread.php?p=3352297

But at this point the wind should be applying negative power in the form of a headwind.

From the ground frame: Some of the air is doing negative work on the cart chassis. But there is more positive work done on the propeller blades by the air.

How does the cart harvest additional power from the wind at faster-than-wind speeds?

The propeller always slows down air relative to the ground. The faster you go, the more volume of air you encounter, that you can draw KE from. But that increase is linear, while chassis drag and transmission inefficiency increase non linearly with speed.

I read in one explanation that the propeller can act as a windmill to drive the wheels at slower-than-wind speeds, and then be turned by the wheels at faster-than-wind speeds. But after playing with a fan for a few seconds, I realized that if this were the case, the thrust provided by the prop in the second stage would be in the wrong direction. Could someone clarify how the prop acts at slower-than-wind speeds?

Have a look at the table below that shows different settings for a variable blade pitch propeller, coupled to the ground via wheels. What you describe above is starting out in CASE A (that gives you maximal initial acceleration) and then at some point below 1WS switching to CASE C that allows you to go faster than wind.

Note that the Blackbird didn't have that ability (even when it had variable pitch later). They didn't want the ability to turn the wheels with the prop, to avoid confusion about using stored energy. They used CASE C only.

But Andrew Bauer was using his propeller as a turbine below windspeed. Here is video where you can see him starting in "windmill mode" and change the blade pitch later.
http://www.fasterthanthewind.org/2010/09/sad-news-in-world-of-ddwfttw.html
See also the graphs on page 15 in Bauer's paper.
http://projects.m-qp-m.us/donkeypus...aster-Than-The-Wind-The-Ancient-Interface.pdf

 

[rorix_bw]

Sorry for coming late to this. I don't know what DDTWFFTW is but as a sailor i can tell you that sailing faster than the wind is easily possible, both upwind and downwind, using only sails (and I can explain how to do it if needed). Can some person please give me a quick summary of what this thread is about?

 

[rcgldr]

Can some person please give me a quick summary of what this thread is about?

DDWFTTW - directly downwind faster than the wind. This means a vehicle that doesn't tach like a sailcraft in order to achieve faster than wind speed. Instead, the propeller is linked to the wheels of the vehicle. The wind pushes the vehicle, while the wheels drive the propeller, which produces a thrust that opposes the wind. Since there are losses involved in the conversion, power output at the propeller is smaller than power consumed by the wheels, plus there is rolling resistance and aerodynamic drag to overcome when the vehicle is going directly downwind faster than the wind.

There is effective gearing from the wheels to the propeller that multiplise torque and divides speed, which allows the propeller to generate more force (but at a lower speed) than the opposing force from the wheels, in spite of the reduction in power due to losses.

This only works when there is a tailwind, because the ground speed (relative to the vehicle) is always greater than the (head) wind speed (relative to the vehicle), which allows for the effective gearing.

Recent threads about this include links to videos of a full scale model. For a while, there was some debate about whether such devices would work.

https://www.physicsforums.com/showthread.php?t=390801

https://www.physicsforums.com/showthread.php?t=421733

 

[Antiphon]

Directly Downwind Faster Than The Wind

 

[rorix_bw]

Interesting concept, never seen that before.

We can exceed wind speed on a sailboat so long as the wind isn't directly ahead or directly behind.

 

[rcgldr]

We can exceed wind speed on a sailboat so long as the wind isn't directly ahead or directly behind.

The sailcraft equivalent would be for the downwind component of speed to exceed wind speed. This is possible with land or ice sail craft. Ice boats like the Skeeter class can achieve vmg downwind about 3x wind speed in light winds.

http://en.wikipedia.org/wiki/Ice_boat#Modern_designs

http://www.nalsa.org/Articles/Cetus/Iceboat Sailing Performance-Cetus.pdf

 

[A.T.]

The sailcraft equivalent would be for the downwind component of speed to exceed wind speed. This is possible with land or ice sail craft. Ice boats like the Skeeter class can achieve vmg downwind about 3x wind speed in light winds.

http://en.wikipedia.org/wiki/Ice_boat#Modern_designs

http://www.nalsa.org/Articles/Cetus/Iceboat Sailing Performance-Cetus.pdf

To visualize this comparison:

https://www.youtube.com/watch?v=UGRFb8yNtBo

Here the vectors for a sailcraft constrained to a fixed course:

http://img253.imageshack.us/img253/6694/downwindvectorsen3.png

Here an example airfoil of a propeller blade, that is coupled to the wheels. The coupling constrains the airfoil to a helical path which also means a fixed angle to the true wind direction:

http://img811.imageshack.us/img811/4922/propellervectors.png

 

[rorix_bw]

@rgcldr

I do not understand this.

I have never sailed an ice boat but in your link they are shown to have triangular rigs (sails) that look similar to sailing yacht rigs. I think they will handle in the same manner. The boat would be heading 0 degrees and the wind coming from around 150 degrees (each boat is different). This is downwind. In this position you can exceed the wind speed.

Directly downwind means the boat is heading 0 degrees and wind coming from 180 degrees. A triangular rig cannot exceed the wind speed in that position using only power from the wind. The movie of the propeller car shows that it does it easily.

PS: I must add this applies only to triangular rigs. Tall ships like the ones of old had square sails and are different.

 

[rcgldr]

To visualize this comparison ... sailcraft ... propeller blade, that is coupled to the wheels ... helical path ...

The helical path isn't a requirement. It could be possible to construct a DDWFTTW vehicle using a tread mill with bluff bodies similar to a paddle wheel. The wheels would drive the treadmill and it's vanes upwind. The vanes would collapse when going downwind. A paddle wheel is not as efficient as a propeller, and the losses in the treadmill would be greater, and I don't know if an actual model could be made to work, but the basic concept would remain the same, the advance ratio would be set so that the treadmill speed would be less than the wheel speed.

Ice boats like the Skeeter class can achieve vmg downwind about 3x wind speed in light winds.

ice boat ... The boat would be heading 0 degrees and the wind coming from around 150 degrees. This is downwind. In this position you can exceed the wind speed.

Directly downwind means the boat is heading 0 degrees and wind coming from 180 degrees.

I didn't mean to imply the ice boat was heading directly downwind, only that it had a downwind component of velocity greater than the wind. In the pdf file from the second link in my previous post, there is a diagram showing 3 vectors, 18 mph wind speed, 70 mph boat speed, and 55 mph apparent wind speed (relative to boat). This translates into a situation similar to what you decribed, boat heading of 0° at 70 mph, true wind heading of 30° at 18 mph. VMG downwind for the boat would be cos(30) x 70 mph = 60.6 mph, about 3.37 x true wind speed. (That diagram shows beta as 8°, but it should read 9° (beta ~= 9.2°)).

 

[A.T.]

Directly downwind means the boat is heading 0 degrees and wind coming from 180 degrees. A triangular rig cannot exceed the wind speed in that position using only power from the wind. The movie of the propeller car shows that it does it easily.

Look at the "Sail to Prop" animation above. The propeller blades are not moving directly downwind even if the car does. This is equivalent to a sail-craft on a broad reach.

 

[rorix_bw]

Thank you to rcgldr and AT. This is understandable now.

Now I ask about his propeller. If he is exceeding true wind speed, he has effective head wind. Putting the propeller on the back, or behind the supporting post for it, would cause the body of the craft to disrupt airflow reaching it? But I don't understand propellers! (They point forwards now on ships with pod drives)

edit - Wait, I see now the other, newer DDWFTTW have forward pointing propellers. I'm OK now with that. I also have no idea how it steers but I do not think it's supposed to! :-)

 

[rcgldr]

I also have no idea how it steers but I do not think it's supposed to!

In the case of the black bird, the small tire at the front is steerable.

http://www.fasterthanthewind.org

In the case of the small DDWFTTW models, they were not steerable.

http://www.youtube.com/watch?v=kWSan2CMgos&hd=1

This device went around on a turntable instead of on a treadmill:

http://www.youtube.com/watch?v=MCB1Jczysrk&hd=1

 

[A.T.]

In the case of the black bird, the small tire at the front is steerable.

http://www.fasterthanthewind.org

In the case of the small DDWFTTW models, they were not steerable.

http://www.youtube.com/watch?v=kWSan2CMgos&hd=1

This device went around on a turntable instead of on a treadmill:

http://www.youtube.com/watch?v=MCB1Jczysrk&hd=1

The one by Jack Goodman was radio controlled:

https://www.youtube.com/watch?v=aJpdWHFqHm0

That is the video that sparked the internet debate, and was initially declared a hoax by MAKE magazine.

 

[rcgldr]

The one by Jack Goodman was radio controlled: ... embedded link not allowed ... That is the video that sparked the internet debate, and was initially declared a hoax by MAKE magazine.

I had forgotten about that video. I also think the more recent debate started at myth busters, but I'm not sure. There were a few threads here, some of the early ones were locked. The youtube link wasn't allowed to be embedded, so here is the url:

 

[rorix_bw]

Having now looked at this I arrive at the conclusions that even though the machines work, they are not sailing ... the prop is linked the wheels (sometimes) and they have no sails. They should rename this.

 

[A.T.]

Having now looked at this I arrive at the conclusions that even though the machines work, they are not sailing

Define "sailing".

the prop is linked the wheels

On a conventional sailing craft the sail is also connected to the keel, via the structure.

they have no sails.

Define "sail".

They should rename this.

The North American Land Sailing Association has no problem calling it an "unconventional sailing craft".

 

[mrspeedybob]

Has anyone tried to build a boat version of this? A prop in the air geared to a prop in the water. Obviously the losses would be greater but It would be interesting to see a proof-of-concept prototype.

 

[kmarinas86]

To visualize this comparison:

https://www.youtube.com/watch?v=UGRFb8yNtBo

This video above (which you can also view on its YouTube video page ) does *not* explain DDTWFTTW. In the video, Scenario 1 shows the sailboats clearly moving DTWFTTW, but not DDTWFTTW, and it shows in Scenario 2 the propeller moving DDTWATSSATW (directly down wind at the same speed as the wind).

The correct explanation:

We have terms for the net power of the vehicle (i.e. ΔKE / Δt)

force    velocity  power    source
+v^2	 +v        +v^3     propeller thrust (v>0)
+(w-v)^2 +(w-v)    +(w-v)^3 parachutic thrust (v<w) or parachutic drag (v>w)
-(w-v)^2 -(w-v)    -(w-v)^3 wind2propeller2wheel drag (v<w) wind2propeller2wheel thrust (w>v)

This can be represented as the sum of two cubic equations. Say for example:

net power = x(v^3) + (y-z)(w-v)^3

Where:
x, y and z are coefficients,
v is the vehicle speed, and
w is the wind speed.

If y-z>x, then one can have a system of equations that looks like this:

 

[rcgldr]

Having now looked at this I arrive at the conclusions that even though the machines work, they are not sailing ... the prop is linked the wheels (sometimes) and they have no sails. They should rename this.

The terminology most commonly used for DDWFTTW carts is "wind driven", not sailcraft. Both DDWFTTW carts and sailcraft are different types of "wind driven" vehicles. Wind driven is then defined as a device that intefaces between two media, the air above and the ground, water, or ice below (as opposed to an object on a frictionless surface which would (eventually) move at wind speed).

It is then noted that true wind speed (wind speed versus ground, water, or ice speed) is independent of an ideal (no losses) wind-drven vehicle's speed, and that the actual top speed of a wind driven vehicle is liimited only by effeciency, not true wind speed, which allows efficient wind-driven vehicles to have a down-wind component of velocity that exceeds true wind speed.

Has anyone tried to build a boat version of this? A prop in the air geared to a prop in the water. Obviously the losses would be greater but It would be interesting to see a proof-of-concept prototype.

Instead of air and water, a Brennan torpedo used water (instead of air) and wires (instead of water). The Brennan torpedo was a device that used retracting wires to drive propellers that drove the torpedo forwards. If water was flowing downstream relative to some "fixed" set of posts, then with it's wires connected to the posts, the Bernnan torpedo would move faster downstream than the water. Wiki article:

http://en.wikipedia.org/wiki/Brennan_torpedo

 

[rorix_bw]

@rgcldr

Call it sailing if you wish, then place an advert for crew and see what happens. :-) "Wind driven" or "land sailing" might work.

@mrspeedybob

I like the idea and hope one day technology from this becomes applicable for general use.

However there is a big difference between a speed record boat that can attain 60 knots under perfect conditions, and an ocean racing yacht that can cover 6500 nautical miles with a peak speed of up to 600 nautical miles in 24 hours, and do it despite 7 meter high seas and 50 knot winds.

Addition: 1 nautical mile = 1.15 statute miles. 1 knot = 1.15 mph therefore.

 

[rcgldr]

@rgcldr - Call it sailing if you wish, then place an advert for crew and see what happens. "Wind driven" or "land sailing" might work.

What post are you referring to? I don't recall calling a DDWFTTW a sailcraft, only a wind powered vehicle. I did make a comment that a DDWFTTW cart does not tach like a sailcraft such as an ice boat.

... ocean ...

A bit off topic - wasn't there some ocean crossing record set a few years ago by a very large catamaran or trimaran?

 

[A.T.]

https://www.youtube.com/watch?v=UGRFb8yNtBo

This video above ... does *not* explain DDTWFTTW. In the video, Scenario 1 shows the sailboats clearly moving DTWFTTW, but not DDTWFTTW,

The sailcraft in Scenario 1 is not moving directly to downwind, but the directly downwind component of its velocity (downwind VMG) is greater than true wind speed.

and it shows in Scenario 2 the propeller moving DDTWATSSATW (directly down wind at the same speed as the wind).

Nope, the downwind VMG of the airfoils doesn't change between the different scenarios shown in the animation. It is always greater than true wind speed, so the center of the propeller moves directly downwind faster that the wind, at exactly the same speed as the downwind VMG of the sail craft in the first clip.

See the vector diagrams in post #9.

We have terms for the net power of the vehicle (i.e. ΔKE / Δt)

force    velocity  power    source
+v^2	 +v        +v^3     propeller thrust (v>0)
+(w-v)^2 +(w-v)    +(w-v)^3 parachutic thrust (v<w) or parachutic drag (v>w)
-(w-v)^2 -(w-v)    -(w-v)^3 wind2propeller2wheel drag (v<w) wind2propeller2wheel thrust (w>v)

Two things:

1) If you are considering the power (ΔKE / Δt) of the cart as seen in the ground frame, then all forces on the cart should be applied at v (the carts velocity in the ground frame)

2) The "wind2propeller2wheel" is never a "thrust" on a simple fixed pitch DDWFTTW cart. The wheels are always braking the cart, even below wind speed. With variable pitch it would be possible to turn the wheels with the rotor at v<w, but that is not what happens on the Blackbird. See post #3.

 

[rorix_bw]

@rglcdr: I am sorry, it was AT's post near the top of this page. BTW you are correct that multi-hulls are indeed quicker through the water (when they don't break).

@AT: See my comment to rglcdr about why I don't regard this as sailing. Like: it has no sails. Yes you could fix the definitions, but there's accepted standards for these sort of things.

I'm sort of getting off topic here. We could take this to private, I guess.

 

[A.T.]

@AT: See my comment to rglcdr about why I don't regard this as sailing. Like: it has no sails.

That is a circular argument. I asked you how you define "a sail".

I'm sort of getting off topic here. We could take this to private, I guess.

Of course it is just semantics how you call it. But the point is that when you try to define "sailing" or "a sail" in terms of physics and function, you will find that your defintion also fits this vehicle. Try it.

 

[ThinAirDesign]

@AT: See my comment to rglcdr about why I don't regard this as sailing. Like: it has no sails. Yes you could fix the definitions, but there's accepted standards for these sort of things.

rorix, you may wish to have your own definition of "sail", but if that definition allows for a 'hard sail' (airfoil/wing) as is used in say the America's Cup races, then the Blackbird does indeed have the same sails use in the same manner.

Literally, the only functional difference between the sails on an AC boat on a broad reach and the BB sails on DDW run is the diameter of the circle being carved. The AC boat's sail is carving a circle the diameter of the Earth while the BB's sails are carving a circle of significanly less diameter.

There truly is NO difference in the way the two sails function.

JB

 

[mender]

Happy New Year, JB!

 

[ThinAirDesign]

Hey Mender -- same to you.

JB

 

[rorix_bw]

@thinairdesign:

Are you saying Blackbird - if it floated - would qualify for Americas Cup? I would like a citation on that if possible. Is there a separate Americas Cup for land?

It's not just a rigid wingsail: it's a set of them on a rotating mount, like windmill. Further, some of those designs link them to wheels or propellers. I don't know to call it.

 

[A.T.]

Are you saying Blackbird - if it floated - would qualify for Americas Cup? I would like a citation on that if possible. Is there a separate Americas Cup for land?

Whether rotating-sail-craft would be allowed to start along with traditional ones in some Regatta is more a organizational question than one of physics.

It's not just a rigid wingsail: it's a set of them on a rotating mount, like windmill. Further, some of those designs link them to wheels or propellers. I don't know to call it.

The linkage to the wheels forces the rotating sails to move against (some components of) the aerodynamic forces acting on them. In terms of physics this is the same as the function of a keel on a sailboat.

 

[kmarinas86]

Two things:

1) If you are considering the power (ΔKE / Δt) of the cart as seen in the ground frame, then all forces on the cart should be applied at v (the carts velocity in the ground frame)

2) The "wind2propeller2wheel" is never a "thrust" on a simple fixed pitch DDWFTTW cart. The wheels are always braking the cart, even below wind speed. With variable pitch it would be possible to turn the wheels with the rotor at v<w, but that is not what happens on the Blackbird. See post #3.

The DDTWFTTW at v greater than w cart experiences a direct headwind when going DDTW. There is more to lose than to gain from the headwind. Note that in my attached diagram, the cubic function that relates to the tailwind and headwind effects is zero at v equals w. This combines the y and z cofficients. When v is greater than w, the z coefficent adds to the power and the y coefficent detracts from it. My "wind2propeller2wheel drag/thrust" (z) coefficient (rotationally-induced) was treated as a separate entity (and is significantly smaller) than the (non-rotationally induced) "parachutic thrust/drag" (y) coefficient although technically they both involve power transfer to and/or from the wheels. Therefore, when combined, they detract from the power at v greater than w but add to the power at v less than w. v and w are both evaluated with respect to the ground. The steady state thrust causes v to exceed w due to the initial tail wind storing up inertia and mechanical impedance in the propeller and the slipstream. The only reason it goes faster is the building up of this propeller thrust due to inertia and flow coupling with the wind. A sail boat whose velocity made good exceeds wind speed uses water as a reaction mass to attain this excess speed (for all one must do with that is to turn the vehicle, after it exceeds wind speed, toward direct downwind), but that option does not exist for the Blackbird DDTFTTW sand yacht. On top of this, many of your videos (the ones showing the gears) apparently depict the tailwind as providing a steady thrust when actually that tailwind is replaced by an unmistakable headwind. The sailboats simply cannot exceed windspeed downwind without changing the angle of the apparent wind either by turning the boat (requiring a reaction mass) and/or the wind itself. Thus, your analogy with sail boats is flawed.

 

[jduffy77]

The DDTWFTTW at v greater than w cart experiences a direct headwind when going DDTW. There is more to lose than to gain from the headwind. Note that in my attached diagram, the cubic function that relates to the tailwind and headwind effects is zero at v equals w. This combines the y and z cofficients. When v is greater than w, the z coefficent adds to the power and the y coefficent detracts from it. My "wind2propeller2wheel drag/thrust" (z) coefficient (rotationally-induced) was treated as a separate entity (and is significantly smaller) than the (non-rotationally induced) "parachutic thrust/drag" (y) coefficient although technically they both involve power transfer to and/or from the wheels. Therefore, when combined, they detract from the power at v greater than w but add to the power at v less than w. v and w are both evaluated with respect to the ground. The steady state thrust causes v to exceed w due to the initial tail wind storing up inertia and mechanical impedance in the propeller and the slipstream. The only reason it goes faster is the building up of this propeller thrust due to inertia and flow coupling with the wind. A sail boat whose velocity made good exceeds wind speed uses water as a reaction mass to attain this excess speed (for all one must do with that is to turn the vehicle after it exceeds wind speed toward direct down wind), but that option does not exist for the Blackbird DDTFTTW sand yacht. On top of this, many of your videos (the ones showing the gears) apparently depict the tailwind as providing a steady thrust when actually that tailwind is replaced by an unmistakable headwind. The sailboats simply cannot exceed windspeed downwind without changing the angle of the apparent wind either by turning the boat and/or the wind itself. Thus, your analogy with sail boats is flawed.

You have misunderstood how the ddwfttw cart works. The thrust generated by the prop is not dependent on the direction of the wind with respect to the cart. It is the relative motion between the air and the ground which is the power source.

 

[kmarinas86]

You have misunderstood how the ddwfttw cart works. The thrust generated by the prop is not dependent on the direction of the wind with respect to the cart. It is the relative motion between the air and the ground which is the power source.

You did not even properly read my point. In my model, the power of the thrust*velocity of the prop is repesented by x*v cubed, where v is the speed of the craft over the ground. The propeller in a fixed-gear DDTWFTTW land yacht is proportional to wheel rotational speed. The propeller's power has nothing to do with a w and its movement over land. In fact w can be zero, as is the case with the treadmill demonstration. Realize that the power of the prop is associated with x, not y or z, The latter two coefficents in my model have something to do with the relative motion between the wind and the cart and corresponding headwind and/or tailwind.

 

[jduffy77]

You did not even properly read my point. In my model, the power of the thrust*velocity of the prop is repesented by x*v cubed, where v is the speed of the craft over the ground. The propeller in a fixed-gear DDTWFTTW land yacht is proportional to wheel rotational speed. The propeller's power has nothing to do with a w and its moment over land. In fact w can be zero, as is the case with the treadmill demonstration.

I read it, I guess I did not understand it. Could you elaborate on why you think the sail to prop video is a flawed analogy? I agree that in scenario 1 we see a sail tacking faster than the wind but not directly down wind. It is in scenario 2 that we seem to disagree. If we tack around a cylinder we are clearly going directly downwind, faster than the wind.