How Does DDWFTTW Work and What Are Its Key Principles?

[rcgldr]

alpha ... beta

Can you swap the name alpha and beta in your post and diagram(s)? This would allow beta in your diagram to correspond to the term "beta" as used by the sailing world (where beta is the angle of apparent wind relative to boat's heading).

 

[kmarinas86]

Can you swap the name alpha and beta in your post and diagram(s)? This would allow beta in your diagram to correspond to the term "beta" as used by the sailing world (where beta is the angle of apparent wind relative to boat's heading).

It would be helpful them for sure, but this is not really my diagram, and I have no interest in swapping the alpha and beta terms in the image. One can replace alpha and beta with x and y if they like. They will just have to think a little bit harder when observing the diagram, that's all.

 

[rcgldr]

Therefore, as soon as the boat overtakes the true wind, the apparent wind applies a force component on the boat against the direction with respect to the true wind.

Split up the apparent wind into components perpendicular and parallel to the boat's heading. An apparent headwind applies an aerodynamic drag to the boat, while an apparent crosswind is diverted to produce thrust by the sail. Note that apparent crosswind is independent of the boats speed: apparent crosswind = true wind speed x sin(boat heading - true wind heading). As long as the thrust to drag ratio is high enough, a boat can achieve vmg downwind greater than true wind speed while tacking at some angle (around 30° to 40°, depending on circumstances).

 

[kmarinas86]

Split up the apparent wind into components perpendicular and parallel to the boat's heading. An apparent headwind applies an aerodynamic drag to the boat, while an apparent crosswind is diverted to produce thrust by the sail. Note that apparent crosswind is independent of the boats speed: apparent crosswind = true wind speed x sin(boat heading - true wind heading). As long as the thrust to drag ratio is high enough, a boat can achieve vmg downwind greater than true wind speed while tacking at some angle (around 30° to 40°, depending on circumstances).

The components you mentioned were already in the original picture and had nothing to do with the force directed parallel to the direction of the wind.

Instead of projecting the apparent wind onto axes parallel and perpendicular to the boat speed, I split up the apparent wind into components perpendicular and parallel to the wind's heading in lime green.

Your components:
* x = Boat speed - cos(beta)
* sin(beta)

My components:
* apparent wind speed*cos(alpha+beta)
* apparent wind speed*sin(alpha+beta)

In the second image below, I split up your two components into four, shown in red.

 

[A.T.]

It is possible for them to exceed VMG, but not if VMG is dead downwind (and stays that way!).

They don't "exceed VMG". They achieve a downwind VMG greater than true wind, steady state, on constant course, in constant true wind.

downwind VMG = boat velocity component pointing directly downwind.

 

[kmarinas86]

They don't "exceed VMG". They achieve a downwind VMG greater than true wind, steady state, on constant course, in constant true wind.

I didn't fix the typo in time. I meant this:

It is possible for VMG to exceed windspeed, but not if VMG is dead downwind (and stays that way!). If you are able to travel a straight line and "beat the wind" with a sail, then the wind has to be changing direction over time.

downwind VMG : boat velocity component pointing directly downwind.

Project the apparent wind speed vector over the boat speed vector component parallel to the true wind speed vector:

That is not steady state. It is obvious that the craft will slow down.

 

[A.T.]

I didn't fix the typo in time. I meant this:

It is possible for VMG to exceed windspeed, but not if VMG is dead downwind (and stays that way!).

Well, that is wrong. They achieve a downwind VMG greater than true wind, steady state, on constant course, in constant true wind.

downwind VMG = boat velocity component pointing directly downwind.

Project the apparent wind speed vector over the boat speed vector component parallel to the true wind speed vector:

Why should I do this? It is utter nonsense.

https://www.physicsforums.com/attachment.php?attachmentid=42386&stc=1&d=1325539649

Nope, this makes no sense at all. Acceleration is determined by forces, not velocities. Where are the forces in your diagram?

That is not steady state. It is obvious that the craft will slow down.

It is steady state. And it is obvious that the craft will accelerate if the L/D ratio of the sail is good enough. L/D must be at least tan(90°-alpha), but since we have hull drag it must be better than that.

 

[kmarinas86]

Nope, this makes no sense at all. Acceleration is determined by forces, not velocities. Where are the forces in your diagram?

None, as this was not a force diagram. It is a velocity diagram. The red text I added was not identify the red vectors as forces. The vectors are obviously velocities as none of them are forces. The text "This affects d'' / t' of the boat[,] and it causes d' t' to change." is a description of the consequences of the red vectors in question, not of the red vectors themselves. Two of three red vectors are components of the apparent wind velocity. The third and longest one represents the apparent wind velocity itself. The consequences (not depicted graphically here) are the forces which vary by the square of the vector magnitudes here depicted and the power which varies by the cube of the vector magnitudes here depicted, so taking that into consideration, it is clear that decomposing them in the same way as the velocity vectors would result in a diagram where the angles have no physical relevance to path of the boat other than its derivative with respect to time, and indeed I have not done so with the above modified diagram, as it is only a velocity diagram applicable for an instant of time. The force on the sail is not even balanced here without incorporating friction. Once you do that, then you would have explain how friction would act against the apparent wind, when it is obvious that the apparent wind is able to push as a result of the fact that it is itself a source of friction providing a force on the craft.

 

[A.T.]

None, as this was not a force diagram. It is a velocity diagram.

Then it cannot tell us if the boat will accelerate. Acceleration is determined by forces, not velocities. And the force vectors say it can accelerate:

 

[kmarinas86]

Then it cannot tell us if the boat will accelerate. Acceleration is determined by forces, not velocities. And the force vectors say it can accelerate:

The deflection of the apparent wind off the sail means that the apparent wind does not maintain the same direction when approaching versus leaving the sail. Any deflection at an exact right angle to the sail's momentum direction does not add energy to the boat. It simply redirects the direction of the boat. Any force component at a right angle to a momentum direction only deflects it, leaving its norm unaffected. Does this deflection add to the kinetic energy of the boat? No. It can only deflect whatever kinetic energy is already there. Only forces parallel or anti-parallel to the motion in question will allow for the kinetic energy of the boat to change.

 

[A.T.]

Only forces parallel or anti-parallel to the motion in question will allow for the kinetic energy of the boat to change.

Yes, and the "accelerating sail force" is parallel to the boat velocity. It will accelerate the boat until the hull drag matches it. Here all the vectors for constant velocity (net force = zero):

 

[kmarinas86]

Yes, and the "accelerating sail force" is parallel to the boat velocity. It will accelerate the boat until the hull drag matches it. Here all the vectors for constant velocity (net force = zero):

There is probably more to this system than meets the eye.

The sail drag and lift can be further broken down into components either parallel, anti-parallel, or perpendicular to the sailboat velocity. The part of the sail lift that is parallel doesn't quite make sense though (at first), but I think there might be an account for the energy involved in doing that. I just don't agree that it comes from the wind though.

I will now concede that in this there is a source of energy that would make for the illusion that the apparent wind can accelerate a sail craft in the opposite direction that it is blowing, so such likely has deeper origins in the energy in motion of the atoms and molecules of the craft itself. If this is indeed what is going at a deeper level, then I take back some of the things which I have said. It seems to me that if the matter's energetic motions were somehow deflected internally as a result of external pressure, then that deflection would be sufficient to explain the observational fact (which I have until now have downplayed) that indeed, as stated by A.T., that sailboats can "achieve a downwind VMG greater than true wind, steady state, on constant course, in constant true wind". If so, then some of this phenomenon could be related even to the General Relativistic corrections to Special Relativity (which drop the assumption of "inertial motion only"), as it appears that the fundamental microscopic non-inertial, vibratory/rotational motions involved must some how have changed course to some small degree (even though this is a non-relativistic scenario) as a result of the force interactions involved.

Indeed, General Relativity would predict that the sailboat would undergo an additional "gravitational time dilation" due to the non-inertial motion induced by the deflection of both the apparent wind and the sail, which perhaps could be explain sometime in the future as increasing the effective internal wavelengths that result from "spreading" paths of highly-curvatured motions inside the mass of the sailboat over longer traces of distances with respect to the grid of "spacetime", consequently leading to a decreases in corresponding frequencies and thus decreasing the overall rate of time at the sailboat relative to an external observer.

 

[ThinAirDesign]

If so, then some of this phenomenon could be related even to General Relativity, as it appears that the fundamental microscopic non-inertial, vibratory/rotational motions involved must some how have changed course to some small degree (in this non-relativistic example) as a result of the force interactions involved.

Nothing fancy -- simple straightforward fluid mechanics involved and it's not even anything new, having been done for hundreds (thousands?) of years. A simple flip of the environment (viewed from the perspective of a fish for example) easily shows that the keel of the very first boat to ever tack its way upwind was achieving a downfluid VMG faster than the fluid, absolutely steady state.

JB

 

[A.T.]

I will now concede that in this there is a source of energy that would make for the illusion that the apparent wind can accelerate a sail craft in the opposite direction that it is blowing

It is not "an illusion". It is a well verified empirical fact and in full agreement with Newtonian physics. The "source of energy" is the velocity difference between the air & surface which is always being reduced.

...matter's energetic motions were somehow deflected internally ... some of this phenomenon could be related even to General Relativity...fundamental microscopic non-inertial, vibratory/rotational motions involved ...

LOL. It's just simple mechanics as the vectors diagrams show.

 

[kmarinas86]

Nothing fancy -- simple straightforward fluid mechanics involved and it's not even anything new, having been done for hundreds (thousands?) of years. A simple flip of the environment (viewed from the perspective of a fish for example) easily shows that the keel of the very first boat to ever tack its way upwind was achieving a downfluid VMG faster than the fluid, absolutely steady state.

JB

It is not "an illusion". It is a well verified empirical fact and in full agreement with Newtonian physics. The "source of energy" is the velocity difference between the air & surface which is always being reduced.

LOL. It's just simple mechanics as the vectors diagrams show.

Without positing pre-existing "hidden" momentum inside the mass of the apparent wind and/or the craft itself, I cannot at all see how something that blows at you can pull you forward. It seems to make more sense to imagine that the apparent wind is simply allowing this "hidden" momentum (which we know exists in the form of the \vec{p} in the equation (m_{whole}c^2)^2=E_{whole}^2=(m_{parts}c^2)^2+\left\|\sum \vec{p}\ c \right\|^2 to appear visible to a human observer, than it is to believe that apparent wind would be gaining energy by doing work on the sail. After all, if the apparent wind is moving to the left and pushes the sail to the right, this would mean that the apparent wind would have to accelerate both itself and the sail, which would violate the conservation of energy, if it were not for this hidden momentum. It is no coincidence to me that so many think incorrectly that the DDTFTTW craft is impossible. They see the apparent wind as a source of energy, and they cannot imagine how it would increase speed relative to the craft by being thrusted by the propeller tailwards while at the same time having that power of the propeller being explained by the same incoming headwind. The reason why this is so prevalent is that there is something wrong with apparent wind being able to do that with the cart, if you don't accept that there is a hidden source of energy! Yes, the forces can explain conservation of momentum, but from the inertial frame of the craft at time t, it is very clear that without a hidden source of energy, we cannot explain why the head wind and the craft with increase respect to the frame once t has passed. In this case, it is not hidden because of deception, but rather, it is hidden because the energy is that of atoms and molecules. So the skeptics of DDTFTTW are not entirely wrong in their skepticism. There must be a hidden energy source (It's nature's energy!). :)

 

[A.T.]

I cannot at all see how something that blows at you can pull you forward.

Sailors use this of ages.

...hidden momentum...

Very creative, but there is no need for such obfuscatory nonsense. All the momentum is clearly visible all the time and is being conserved.

 

[ThinAirDesign]

I cannot at all see how something that blows at you can pull you forward.

Before I respond I really must clarify something.

Sailboats sail upwind all the time. They can leave a point downwind and readily arrive at a point directly upwind of where they were by simply sailing towards a point situation to the right (or left) of the upwind goal, and then once halfway there, they turn and sail directly towards that point.

A: If taken literally and without context, your above quoted statement would make it seem as though you don't see how a boat can sail upwind such as the above. I'm pretty sure that's not what you mean but I do want to ask the question.

B: If you believe boats can make upwind progress by sailing at an angle to the wind, but are having difficulty believing that *anything* wind powered can make steady state progress directly into the wind using basic Newtonian physics then I need to know that.

A or B or other?

Thanks

JB

 

[kmarinas86]

Sailors use this of ages.

Very creative, but there is no need for such obfuscatory nonsense. All the momentum is clearly visible all the time and is being conserved.

The net momentum is indeed conserved.

2 + (-2) = (3) + (-3)... etc.

That makes it look like there is no mystery.

What does not make sense to many still-skeptical skeptics is how would the Blackbird DDTWFTTW sand yacht conserve energy. Neither you, nor them, seem to have the explanation.

Note that:

(2)^2 + (-2)^2 is not (3)^2 + (-3)^2... etc.

Would you mind explaining where the energy comes from to allow the wind to do work on the DDWFTTW vehicle (in the time between t and t+\epsilon) at the same time the DDWFTTW vehicle accelerates, with respect to the initial inertial frame of the vehicle at time t? The work is done in opposite directions, conserving momentum even macroscopically, but not the kinetic energies of both (both increase as far as the initial inertial frame is concerned). My "very creative" resolution addresses this problem by bringing up the point about the true and factual existence of the below-macroscopic energy of atoms and molecules as being the entity that accounts for this apparent gap.

My explanation is not that of a hidden net momentum, but a hidden set of vector momenta which sums to zero in the frame being evaluated (i.e. the momentum whose energy is identical to the rest mass of a body, as evaluated from the system frame in question, times the speed of light squared). I have a hunch that somehow this is either the static P-V energy that was already present in the air mass prior to vehicle operation, and/or the vibrational and rotational energy of the vehicle's particle makeup. Probably both.

 

[kmarinas86]

Before I respond I really must clarify something.

Sailboats sail upwind all the time. They can leave a point downwind and readily arrive at a point directly upwind of where they were by simply sailing towards a point situation to the right (or left) of the upwind goal, and then once halfway there, they turn and sail directly towards that point.

A: If taken literally and without context, your above quoted statement would make it seem as though you don't see how a boat can sail upwind such as the above. I'm pretty sure that's not what you mean but I do want to ask the question.

B: If you believe boats can make upwind progress by sailing at an angle to the wind, but are having difficulty believing that *anything* wind powered can make steady state progress directly into the wind using basic Newtonian physics then I need to know that.

A or B or other?

Thanks

JB

Neither. Potential energy must be extracted from the system. Either the static P-V of the wind and/or the energy from the particle make-up of vehicle (and/or even that of the ground, if need be). A correct explanation cannot be found by trying to conserve "kinetic energy+heat" while ignoring potential energy.

The quote (taken out from a sentence after a comma) is taken too far out of context. It doesn't even relate to what I am saying.

 

[ThinAirDesign]

Neither.

<snip>

The quote (taken out from a sentence after a comma) is taken too far out of context. It doesn't even relate to what I am saying.

Ok, got it. I was pretty sure from your previous posts that "A" wasn't what you meant, but didn't want to move forward without confirmation.

Thanks.

It appears that what you are saying the examples I have in that post can and do happen, you just don't believe they can be explained through simple Newtonian physics.

Would that be a fair representation of your position?

JB

 

[rcgldr]

Potential energy must be extracted from the system.

For a fluid or gas, potential energy is used to describe the gravitational potential energy of a gas or fluid. For a wind driven vehicle, the energy extracted from the air affected by the wind driven vehicle corresponds to the reduction in kinetic energy (wrt ground) of the affected air. (Pressure effects are short term and only exist in the immediate vincinity of the propeller.)

 

[kmarinas86]

Ok, got it. I was pretty sure from your previous posts that "A" wasn't what you meant, but didn't want to move forward without confirmation.

Thanks.

It appears that what you are saying the examples I have in that post can and do happen, you just don't believe they can be explained through simple Newtonian physics.

Would that be a fair representation of your position?

JB

I guess that depends on what you call simple, what you call Newtonian, and what you mean by explain. You can explain things using forces without highlighting the apparent non-conservation of "kinetic energy+heat". That is simple (to me), but ignoring where this kinetic energy comes from doesn't do it for me, so I would disagree that it is somehow an adequate explanation. (If a claimed-to-be explanation is inadequate, does it really explain what needs to be explained?) Potential energy latent inside matter isn't exactly something that I would call part of "Newtonian" physics. It's not included in most of the (simple enough to be convincing to most) analyses that have been offered to explain the Blackbird. Certainly it can be explained using classical physics.

The lack of significant mention of potential energy when discussing how tacking can allow sails to move ahead of the wind, in addition to the absolute absence of this point in many of the videos that I have seen that try to explain DDTWFTTW, has (I bet) contributed much confusion for people (including skeptics and naysayers) who wonder where the energy comes from and who, like myself, have for a time not been able to see how tacking would be of any benefit to it.

 

[ThinAirDesign]

The lack of significant mention of potential energy when discussing how tacking can allow sails to move ahead of the wind, in addition to the absolute absence of this point in many of the videos that I have seen that try to explain DDTWFTTW, has (I bet) contributed much confusion for people (including skeptics and naysayers) who wonder where the energy comes from and who, like myself, have for a time not been able to see how tacking would be of any benefit to it.

If by "potential energy" you mean something other than the mass of one fluid moving relative to another (or surface) and the kinetic energy contained thus, then the reason it isn't used in an explanation or video is that it would be flat wrong. There is NO other energy involved in accelerating the craft.

If by "potential energy" you mean the mass of one fluid moving relative to another (or surface) and the kinetic energy contained thus - meaning the power of the wind, I can't imagine how you have missed such explanations.

JB

 

[rcgldr]

where this kinetic energy comes from

You could consider the source of energy for the true wind to be the heat from the sun.

Potential energy latent inside matter isn't exactly something that I would call part of "Newtonian" physics.

I don't recall any mention of potential energy in the descriptions of how wind driven vehicles operates (sail boats, DDWFTTW vehicles, DUW vehicles, ... ). Extracting potential energy within matter involves a chemical or nuclear reaction, which doesn't occur with the wind powered vehicles being discussed here.

The lack of significant mention of potential energy when discussing how tacking can allow sails to move ahead of the wind. ... where the energy comes from

I'm not sure what you mean by potential energy. Wind driven vehicles extract kinetic energy from the wind (using a ground or water based frame of reference).

how tacking would be of any benefit to it.

Tacking isn't required for a DDWFTTW vehicle. A DDWFTTW vehicle could connect the wheels to a treadmill geared so the upper surface of the treadmill moves upwind at some fraction of the vehicles speed, for example 1/2 of the vehicles speed (an advance ratio of .5). The treadmill could pull parachutes along the upper surface and then collapse them (perhaps pull them through a tube) along the lower surface. It wouldn't be as efficient as a propeller, but if the losses could be reduced enough, it would work.

A sail can't generate thrust from an apparent headwind component, so it needs an apparent crosswind component which it diverts to aft of the boat's heading to generate thrust, which is why a sail boat needs to tack in order to achieve vmg downwind greater than true wind.

 

[kmarinas86]

I'm not sure what you mean by potential energy. Wind driven vehicles extract pressure energy and kinetic energy from the wind (using a ground or water based frame of reference).

Pressure energy to me is a form of potential energy, though I tend to look at it from a "molecular" perspective where electric forces reign supreme over gravitational ones.

 

[spork]

Pressure energy to me is a form of potential energy, though I tend to look at it from a "molecular" perspective where electric forces reign supreme over gravitational ones.

Even pressure energy doesn't come into the equation. The vehicle simply slows down the air relative to the ground beneath it. That's all. For pressure energy to benefit the cart it would have to leave a volume of air in its wake that has been expanded to greater volume and lower pressure. It doesn't do this.

 

[rcgldr]

Even pressure energy doesn't come into the equation.

There's a pressure differential in the immediate vincinity of the propeller, but eventually the affected air's pressure returns to ambient and it's velocity is changed. From a DDWFTTW vehicle's frame of reference, the pressure and flow near the propeller corresponds to the description in this NASA article:

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

From a ground frame of reference, the pressure differential at the propeller results in the affected air from the true wind to be slowed down.

 

[spork]

There's a pressure differential in the immediate vincinity of the propeller...

Of course there is. But you said: "Wind driven vehicles extract pressure energy and kinetic energy from the wind"

And this isn't the case. Sure they create a lower pressure in front of the disk and a high pressure behind the disk, but ultimately, they don't take any "pressure energy" from the wind. That would be equivalent to saying that an airplane's exploits the "pressure energy" of the air to stay aloft. The fact that it has a local effect (both positive and negative) on air pressure does not imply that it extracts pressure energy from the wind.

 

[rcgldr]

But you said: "Wind driven vehicles extract pressure energy and kinetic energy from the wind"

Yeah I worded that badly and corrected my previous posts. The pressure effects are short term and only exist in the immediate vicinity of the propeller.

 

[spork]

Yeah I worded that badly. The pressure effects are short term and only exists in the immediate vicinity of the propeller.

I figured it was a simple mis-statement. That's one of the reasons I didn't mention it when you posted it, but only when kmarinas86 talked about it as potential energy. I got the distinct idea he saw it as something it's not.