## Downwind faster than the wind

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gmalivuk
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### Re: Downwind faster than the wind

Tass wrote:(By the way, the gearing in the "under the ruler" video is in not in the big wheel / small wheel, but in the ratios between the cottong reels' edge and waist diameter.)

Yeah, this took me a bit to figure out, too. Since all the action on the big wheel is happening along its edge, its size doesn't actually matter except inasmuch as that's what allows it to separately touch the two spools at once, allowing the whole contraption to be stable sitting on the ground.

And if it were the big center wheel with edges farther out than its waist, and its waist were in contact with the two wheels sitting on the ground, then something moved along its edge on top would make the car as a whole move in the opposite direction. This would be somewhat analogous to changing some of the details of the cart to make it go directly upwind (this time using the prop as a turbine to drive the wheels, instead of the other way around).
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cobra bubbles
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### Re: Downwind faster than the wind

when the cart is outside moving at a speed hypothesized to be greater than the wind there is only one source of energy--the wind. there is not any other source of mechanical energy.

all other forces acting on the cart are dissapative forces. they will only remove mechanical energy from the cart, which will act to reduce the kinetic energy of the cart.

if we look at the forces acting on the cart we find there are only three that are essentially non-zero while the cart is accelerating.

there is the normal force of the ground pointing upward. there is the weight of the car downward and there is the thrust from the propeller in the forward direction. drawing a free body diagram will show you that the normal force and weight are equal, since there is no acceleration in the vertical direction. in any case, this is uninteresting since the motion of the cart is horizontal.

that leaves only the force due to the wind acting in the forward direction.

since, F=ma, the cart will accelerate under the force of the wind. so at first, the cart feels some forward force and experiences some accleration.

however, in the videos, the cart, after some initial acceleration, eventually reaches a terminal velocity.
at this point the net force on the cart must be zero in the horizontal direction, since the velocity is constant. since there are no other horizontal forces, this means that the force on the cart due to the wind/propeller has decreased to zero as the cart reached the final velocity. the propeller force is therefore proportional to the velocity of the cart and some other velocity. the other natural velocity scale in this situation is the wind velocity, so:

F=f(v-w)

the force from the prop is some function of the difference of the wind and cart speed.

(where v= cart velocity and w= wind velocity)

for F=0, f(v-w) = 0 which implies that v=w.

therefore the cart, can at best, only go the speed of the wind.

if you take into account rolling friction and air resistance of the cart body and wheels, these forces act opposite the propeller force, which means that actually v<w. so the cart cannot even go as fast as the wind.

note:
gear ratios, propeller advance ratios, wheel diameters etc will only change the shape of the force vs. velocity curve (if you plot the force as a function of v). this will effect how long the cart takes to get to terminal velocity only. if you are clever in design, the gears/props/wheels will be maximally efficient, which will allow the cart to get closer to wind speed in a shorter time, but it won't let you pass it.

cobra bubbles
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### Re: Downwind faster than the wind

sailboats travel with a speed that is faster than the wind. they do it by harnessing the forces involved in a manner different than sailing in the same direction as the wind.

here is a quick hand wavy explanation:

ignore the vertical forces (bouyant force and weight.) the forces acting on the sailboat in the horizontal direction are the force of the wind on the sail, the force of the keel and the friction forces. if you draw a free body diagram of these forces with components parallel to motion and perpendicular to the motion you will find that the perpendicular force of the wind and the force of the keel oppose one another. the keel effectively keeps the boat going in a straight line.

in the direction of motion, you will still have a component of the force due to the wind in the same direction of motion and friction forces in the opposite direction. the force due to the wind is constant, but the friction forces increase proportional to boat velocity. at some point the friction force opposing the forward motion is equal to the force of the wind. at this point the boat reaches a constant velocity. by minimizing friction forces, you can attain a velocity that has a magnitude higher than that of the wind.

for motion in the direction of the wind, the net force on the boat is proportional to the difference of the boat speed and the wind speed. as the boat approaches wind speed, the propulsive force goes to zero. this limits a boat travelling with the wind to a max speed equal to the wind.

summary:

travel with the wind is limited by windspeed. the propulsive force goes to zero as boat speed approaches wind speed.

travel at angle to wind and the speed is limited by friction. the propulsive force does not approach zero.

Fallible
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### Re: Downwind faster than the wind

cobra bubbles wrote:F=f(v-w)

the force from the prop is some function of the difference of the wind and cart speed.

Hi Cobra bubbles,

I must admit, this is what I thought as soon as I looked at this. However, a bit more thought will show that this critical statement isn't true.

Your statement would be true if the cart had a sail. The function of a sail (in straight downwind motion) is to take air moving at wind speed, and slows it down to the speed of the cart. In this situation, it would be impossible to exceed windspeed.

However, what the propeller does is take air and slow them down to slower than the cart speed. Instead of stopping wind (like a sail), the air is reflecting wind. If the cart is reflecting wind, then it can continue to gain energy and momentum after it has exceeded windspeed.

Of course, there are still friction and air resistance forces to be taken into account, so eventually the cart will reach some equilibrium speed. This speed can be faster than the wind though.

spork33
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### Re: Downwind faster than the wind

>>
if you take into account rolling friction and air resistance of the cart body and wheels, these forces act opposite the propeller force, which means that actually v<w. so the cart cannot even go as fast as the wind.
<<

As a good friend of mine says - "sure it works in practice, but can you prove it works in theory".

I find it "interesting" that your quick analysis shows that my cart cannot do exactly what I witness it doing. Normally we use science to explain that which we observe. The reason for this is that it's so much harder to get nature to cooperate with how we think it should behave.

That being said, there are several perfectly clear explanations of how and why this vehicle DOES in fact go directly downwind faster than the wind, powered only by the wind, steady-state.

But if you're sure its not possible I won't waste your time.

>>
gear ratios, propeller advance ratios, wheel diameters etc will only change the shape of the force vs. velocity curve (if you plot the force as a function of v). this will effect how long the cart takes to get to terminal velocity only. if you are clever in design, the gears/props/wheels will be maximally efficient, which will allow the cart to get closer to wind speed in a shorter time, but it won't let you pass it.
<<

Thanks. I'll make a note of it. In the meantime, I feel a little silly having built a cart that violates your basic physical principles. I'll try and make sure it doesn't happen again.

Tass
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### Re: Downwind faster than the wind

Cobra.

I would go through your post and explain the rather basic mistakes you are making, but it has been done to death in this thread allready and I am getting tired of it. So for now I will just wish you a happy yule.

scikidus
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### Re: Downwind faster than the wind

So I've read throught he entire thread, and my eyes have glazed over. However, I came up with a different method to move DWFTW.

MS Paint FTW!
DWFTTW.GIF (7.68 KiB) Viewed 4902 times

I know it's really unclear, but here's the concept:

1. The propeller and the main car are on two separate carts. The propeller is hooked up via wires to a motor that runs the wheels in the front car. The back cart, meanwhile, is set up to only move when the dark green string is pulled, which will cause it to move until a certain distance bwteen the carts is reached again.

2. When the wind blows, it spins the propeller, which runs the motor and accelerates the front car forward. There is some slack in the wire connecting the carts, so the front car is moving faster than the wind by the time the wire becomes taught.

3. WHen the wire becomes taught, it pulls the dark green string, allowing the back cart to be tugged forward. The front car has momentum, so it keeps going, but is slowing down. Eventually, the system resets itself, and the cycle begins again.

------------

It's essentially an accordion design: a propeller on the back cart drives the front cart, until a certain distance is reached, when the back cart uses the front cart's momentum to tug it forward.

Better yet, you could wire the assembly so that when the back cart was moving, it used the propeller to push it forward (slower than the wind), allowing for more efficency.
Happy hollandaise!

"The universe is a figment of its own imagination" -Douglas Adams

cobra bubbles
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### Re: Downwind faster than the wind

Hello Fallible,

if you use some basic fluid dynamics, energy conservation and momentum conservation, you can show that the ideal efficiency of a propeller is:

e= 2/(1+vs/v0)

where vs is the speed of the air in the slipstream and v0 is the speed of the air entering the propeller. you can also show that the speed of air right at the propeller is

the maximum efficiency e=1 is attained when vs=v0.

this means that the air entering and leaving the propeller has the same speed if the propeller is 100% efficient.

since the propeller will not be 100% efficient in a real situation, this implies that vs>v0. the air coming out of the propeller is moving *faster* than the air entering the propeller.

so, a real propeller does not slow down the air, as you said, it actually speeds it up.

(a wind generator on the other hand, slows down the air)

cobra bubbles
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### Re: Downwind faster than the wind

Hello spork33,

All the explanations that i have seen have included some misinterpretation or misapplication of physics. many explanations ignore conservation laws or mix up power and work, force and momentum etc.

for instance, the only source of energy to power the cart is wind energy. the ground cannot supply power at all.

in order for some object to due work on another object, there must be some force acting between the 2 objects. when the cart is rolling at it's final constant velocity, the only forces acting between the cart and the ground are gravity and rolling friction.

the definition of differential work done on an object by a constant force is:

dW=F.dx (where the "." is the dot product between the force F and displacement dx)

since gravity is perpendicular to the carts motion on a level surface, the dot product is zero, so gravity can do no work.

since rolling friction is opposite the motion of the cart, the dot product is negative, and rolling friction does negative work. i.e. it removes energy from the cart, causing it to slow down, not speed up.

any proposed theory of how the cart can go faster than the speed of the wind that also talks about energy being supplied by the ground is incorrect.

i don't deny that the cart can move under wind power. it clearly does in your videos. i simply do not see any conclusive evidence that it is moving faster than the wind.

so far, the evidence i have read has been some simple, incorrect force analysis on the cart.

what would convince me?

average wind speed measurements and cart speed measurements, repeated lots of times with proper calculation of the uncertainties of the measurements. then if these calculations with uncertainties show the cart is consistently moving faster than the wind, i would agree.

Tass
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### Re: Downwind faster than the wind

cobra bubbles wrote:All the explanations that i have seen have included some misinterpretation or misapplication of physics. many explanations ignore conservation laws or mix up power and work, force and momentum etc.

Yes there has been plenty of misconceptions. Lets try correcting yours.

cobra bubbles wrote:so, a real propeller does not slow down the air, as you said, it actually speeds it up.

Yes. Relative to the cart.

But since the cart is going faster than the wind, the wind is actually slowed relative to the ground. Never forget your reference frame.

cobra bubbles wrote:for instance, the only source of energy to power the cart is wind energy. the ground cannot supply power at all.

Once again, this depends on the reference frame. The energy is contained in the relative motion of the air and ground.

cobra bubbles wrote:in order for some object to due work on another object, there must be some force acting between the 2 objects. when the cart is rolling at it's final constant velocity, the only forces acting between the cart and the ground are gravity and rolling friction.

No. There are normal force and regular friction as well.

cobra bubbles wrote:the definition of differential work done on an object by a constant force is:

dW=F.dx (where the "." is the dot product between the force F and displacement dx)

since gravity is perpendicular to the carts motion on a level surface, the dot product is zero, so gravity can do no work.

since rolling friction is opposite the motion of the cart, the dot product is negative, and rolling friction does negative work. i.e. it removes energy from the cart, causing it to slow down, not speed up.

True...

cobra bubbles wrote:any proposed theory of how the cart can go faster than the speed of the wind that also talks about energy being supplied by the ground is incorrect.

Not in the carts frame of reference.

cobra bubbles wrote:i don't deny that the cart can move under wind power. it clearly does in your videos. i simply do not see any conclusive evidence that it is moving faster than the wind.

Neither do I. But I believe it because I understand the phycics.

cobra bubbles wrote:so far, the evidence i have read has been some simple, incorrect force analysis on the cart.

Don't be so quick to label others analysis as incorect. There is the possibility that it is you who is making the mistake.

spork33
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### Re: Downwind faster than the wind

cobra bubbles wrote:All the explanations that i have seen have included some misinterpretation or misapplication of physics.

Interesting. I have both written and read many explanations that are spot on.

>>for instance, the only source of energy to power the cart is wind energy. the ground cannot supply power at all.

That all depends on the reference frame in which you do your analysis.

>> when the cart is rolling at it's final constant velocity, the only forces acting between the cart and the ground are gravity and rolling friction.

Wrong.

>> any proposed theory of how the cart can go faster than the speed of the wind that also talks about energy being supplied by the ground is incorrect.

Wrong.

>> i simply do not see any conclusive evidence that it is moving faster than the wind.

Your conclusion then is that we are somehow cheating? Or is it that you simply don't understand inertial reference frames?

>>so far, the evidence i have read has been some simple, incorrect force analysis on the cart.

I'm beginning to realize - it's not that you haven't found accurate information. You simply aren't able to understand it.

what would convince me?

average wind speed measurements and cart speed measurements, repeated lots of times with proper calculation of the uncertainties of the measurements. then if these calculations with uncertainties show the cart is consistently moving faster than the wind, i would agree.

I've been around this problem long enough to know that would never convince you. You would never even accept that such measurements were properly carried out.

cobra bubbles
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### Re: Downwind faster than the wind

sorry. correct, there is a normal force i ignored, but it is a third law pair to the gravitational force, and also does no work, so i left it out.

no, energy analysis of the cart does not depend on the reference frame. if you choose an inertial reference frame moving at velocity V relative to the object, the total energy of the object can be written in terms of the center of mass motion and the frame motion:

KE(total) = KE(C of M) + KE(frame)

or KE (total) = KE(C of M) + 1/2 mV^2

by changing to a different reference frame, with different speed V', you can re-write this equation. only the KE(frame) part will change. the kinetic energy is therefore only defined to within a constant which depends on the motion of the frame chosen relative to the motion of the center of mass. since kinematics depends on changes in kinetic energy, the constant KE contributed by the choice of reference frame will not matter. when you look at changes in kinetic energy, the constant drops out. also, you can see that kinetic energy is smallest with a choice of frame that moves with the object, V=0, so often the center of mass frame is the easiest frame in which to analyze motion.

as for the forces, they do not depend on the choice of reference frame either (as long as it is inertial.) if you choose the reference frame of the ground or the center of mass reference frame, the forces are still the same. the external forces acting on the cart are the thrust due to the wind, the normal force and the gravitational force. there are no other forces that can act on the cart. (i ignore friction in either frame. it makes the analysis easier, and in this case, ignoring friction yields an upper limit on the final velocity. if i included friction forces, they are dissipative and lower the final velocity.)

in either reference frame, the normal force and gravitational force are perpendicular to the carts motion. (assuming v<<c)
since they are perpendicular to the motion, they do no work on the cart and can be ignored. (assuming motion on level ground) this leaves only the force due to the wind left to act on the cart.

thus, the only force you have to consider for the motion of the cart is the force of the wind. the only energy input you have to consider is the change in energy due to the wind.

one last thing, my motivation is not to say that it cannot possibly work. it's cool. my motivation is to find out how it does work, and what the final velocity depends on. so far, i have only calculated that the propeller, like a sail, is limited by the difference of the wind speed and the cart speed.

^.*
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### Re: Downwind faster than the wind

cobra bubbles wrote: when the cart is rolling at it's final constant velocity, the only forces acting between the cart and the ground are gravity and rolling friction.

Hmm view it this way:
Okay the car is a fast as the wind.
If we take the car as reference point, there is no wind but there is still something beside friction and gravity. In fact the earth is moving in comparsion to the car.(Without wind the ground wouldn`t move in comparsion to the car.=> no miraculous movements without any wind. Yeah stating the obvious^^)
=> The same situation as the treadmill. (Though I didn`t look at the video with the treamill.) Now the only question is: "How do you use the movement of the earth to move the car in the opposite direction?":
The ground moves the wheels, the wheels move the propeller, the propeller accelerates the car.

Now could someone tell me if me try at an simple explanation was actually correct?^^
Just some random quote till I find an better signature.
Hawknc wrote:This is the easiest question ever asked on the forum, and you guys turn it into a two-page debate.
(i think this describes this forum pretty well.)

spork33
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### Re: Downwind faster than the wind

one last thing, my motivation is not to say that it cannot possibly work. it's cool. my motivation is to find out how it does work, and what the final velocity depends on. so far, i have only calculated that the propeller, like a sail, is limited by the difference of the wind speed and the cart speed.

If your motivation is to understand how and why the cart DOES work and understand it's theoretical maximum speed you're going about it all wrong. I'd try leading with that rather than "proving" that we're all wrong. It just so happens that many of us can answer all your questions - most likely to your complete satisfaction.

spork33
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### Re: Downwind faster than the wind

^.* wrote:Now could someone tell me if me try at an simple explanation was actually correct?^^

Your explanation is correct, but incomplete. You're absolutely right that the object is to exploit the energy available at the ground/air interface - even when there is no wind relative to the cart. We can talk about this from several perspectives - force, energy, and momentum being the most common. My preference is to start with the analogy of an ice-boat on a 45 degree downwind tack. As it happens:
- An ice boat can maintain a downwind velocity component of 3X the true wind speed or more.
- The blades of the prop on our prop cart are EXACTLY analagous to the sail of the ice boat on this downwind tack. The transmission and wheels simply provide exactly the same kinematic constraint the skates provide on the ice-boat.

scikidus
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### Re: Downwind faster than the wind

Does anyone know if my idea above works?
Happy hollandaise!

"The universe is a figment of its own imagination" -Douglas Adams

Mr. Smiles
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### Re: Downwind faster than the wind

Forgive me, I'm struggling to get through all five pages of this. But if I may add something: If the device in question is lighter than the wind that pushes (i.e. hits) it, won't it accelerate more quickly than the wind?

spork33
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### Re: Downwind faster than the wind

scikidus wrote:Does anyone know if my idea above works?

Yes, your idea can work. But it's not "steady-state". Still with a few more words it serves as a good intuitive proof that you can beat the speed of the wind directly downwind - even if in spurts. Once this is accepted most people will have an easier time accepting the fact that it can be done steady state.

spork33
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### Re: Downwind faster than the wind

Mr. Smiles wrote:If the device in question is lighter than the wind that pushes (i.e. hits) it, won't it accelerate more quickly than the wind?

I think there are two problems with this:

1) It's less a question of how rapidly the vehicle accelerates, and more a question of whether it can achieve and maintain a steady state direct downwind speed faster than the wind (yes an arbitrarily light vehicle can accelerate arbitrarily quickly - but it's top speed typically will still be slower than the wind when traveling directly downwind)
2) For a traditional sailing craft (sailboat, ice boat, land yacht) it's not possible to go directly downwind faster than the wind steady state - no matter how light the vehicle. What some of these vessels CAN do however is to maintain a downwind velocity component that's well above wind speed. This means they can still beat the wind directly downwind by tacking.

mikeonsixstrings
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### Re: Downwind faster than the wind

Although I probably wouldn't have conceived a vehicle that moves faster than the wind, after analyzing the mythbuster suggestion footage I think I can visualize it conceptually.

First, the scenario has to be broken down into two situations: When the vehicle is moving slower than wind speed and when the vehicle is moving at (and potentially faster than) wind speed.

In the first situation, the wind hits the propeller, causing it to spin. The kinetic energy is then transferred to the main axle, causing acceleration. The physics is straightforward so far.

After accelerating to wind speed, however, it becomes less intuitive. If the vehicle is moving at wind speed one could simply alter the frame of reference so that the vehicle and the wind would appear to be stationary. There is one hitch, however. In this frame of reference the road is moving opposite to the direction of the wind with the same speed. This causes the wheels to continue to spin, which in turn spin the propeller. If the force exerted by the propeller on the "still" air is greater than the force exerted by the road on the vehicle in the opposite direction, the vehicle would accelerate further. Hence, faster than wind speed travel. The force exerted by the road on the vehicle would be negligible if the axle had very low friction with the wheel; one could imagine a super-massive "cart" of sorts sitting still on a treadmill moving backwards if the wheels were lubricated enough simply as a result of its inertia.

The vehicle would reach maximum speed once it reaches velocity such that the force exerted by the propeller on the air in a rearward direction is equal to the sum of the force of the air moving against it and frictional force:

[math]F_P=F_a + F_f[/math]

I hope my explanation was clear, perhaps pictures would be of aid.

lightvector
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### Re: Downwind faster than the wind

For those who are still doubters, here is the energy/momentum perspective (again), showing that a DWFTTW vehicle is possible.

As abstractly as possible - we have three objects, car, wind, ground. Forget about the design of the car completely. The actual cars designed and shown in the videos are not nearly as simple (they make additional momentum/energy transfers so as to keep the propeller turning fast enough, etc), but we are interested only in the abstract, theoretical possibility of such a vehicle. The following demonstrates that this is possible. We show that a car moving at wind speed can experience a net acceleration forward.

Ground frame:
(Ground stationary, car and wind moving at initially equal speeds to the right)
• Car exerts backwards force on wind.
• Wind loses (rightward) momentum. It's absolute speed is reduced as well, so it loses energy.
• Car gains energy and momentum.
• As needed, the car transfers enough momentum to the ground and disappates enough energy through internal friction to preserve its proper momentum/energy relationship (energy = momentum^2 / mass). Because the wind provided both energy and momentum, it is always possible to make these transfers such that the car's final momentum is greater than the initial, by disappating one or the other as needed.
• Result: Car accelerates rightward over time, and exceeds wind speed.

We can also look at the same event from a different reference frame.

Initial Car frame (inertial reference frame of the car, prior to any accelerations it experiences):
(Car and wind stationary, ground moving at some speed to the left)
• Car exerts backwards force on wind.
• Wind loses (rightward) momentum. It therefore accelerates to the left, gaining energy.
• Car gains rightward momentum. Car transfers a portion of this momentum to the ground.
• Ground gains (rightward) momentum and therefore slows down infintesimally. In the process, it loses energy, which the car gains.
• Car retains part of the rightward momentum gained from the wind, and uses the energy gained from the ground to supply for the energy lost to the wind, and some additional, so it can begin moving to the right.
• We know that the energy released/needed per unit momentum is proportional to its current velocity of the object. (as before, E = p^2/m. Therefore, dE/dp = 2p/m = 2v, where E = energy, p = momentum, m = mass, v = velocity). Since the ground is moving faster than both the car and the wind (neither are moving at all, initially), it releases enough energy per unit momentum so that the car need not transfer all its momentum to the ground to get enough energy to power both itself and the wind. Any excess energy is disappated in the car's internal friction.
• Result: Car accelerates rightward over time, and exceeds wind speed.

spork33
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### Re: Downwind faster than the wind

mikeonsixstrings wrote:First, the scenario has to be broken down into two situations: When the vehicle is moving slower than wind speed and when the vehicle is moving at (and potentially faster than) wind speed.

In the first situation, the wind hits the propeller, causing it to spin. The kinetic energy is then transferred to the main axle, causing acceleration. The physics is straightforward so far.

Most of what you say is correct. However, there is no magical switching point at wind speed. At all speeds the prop is operating as a propeller, not a turbine. In other words the torque on the prop-shaft turns the prop rather than the other way around.

Tass
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### Re: Downwind faster than the wind

cobra bubbles wrote:no, energy analysis of the cart does not depend on the reference frame. if you choose an inertial reference frame moving at velocity V relative to the object, the total energy of the object can be written in terms of the center of mass motion and the frame motion:

KE(total) = KE(C of M) + KE(frame)

or KE (total) = KE(C of M) + 1/2 mV^2

No. This is where you are mistaking. That works for momentum, but not for energy since energy depends on the velocity squared.

cobra bubbles
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### Re: Downwind faster than the wind

tass:

check out this site at Duke physics:

http://www.phy.duke.edu/~rgb/Class/intr ... ode65.html

or even wikipedia, under the "frame of reference" section:

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

these sites show that while the measured kinetic energy does depend on the reference frame, the kinetic enrgy between different inertial reference frames will differ by a constant--when studying the dynamics of an object, this constant term does not matter.

here is a quote from the same Duke site above, under the "work-kinetic energy" section:

"Physics is the study of dynamics and forces that change the velocity (and hence the kinetic energy). The work done on a mass changes its kinetic energy by a certain amount independent of what it was to begin with. We thus start to see that dynamics (that is, our analysis of the effects of the forces involved) will not depend upon any constant we add to the energies being studied, as they depend only on the difference in energy between one state and another. "

since the frame of reference does not matter when we study the dynamics of an object, we might as well pick a frame of reference that is easy to write an objects kinetic energy in and one that it is easy to visualize the objects motion. for the cart, the simplest choice is the frame of reference of the ground. then the cart will have a kinetic energy of 1/2 mv^2, where v is the velocity of the carts center of mass with respect to the ground.

Tass
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### Re: Downwind faster than the wind

Okay. I see now what you meant.

cobra bubbles wrote:sorry. correct, there is a normal force i ignored, but it is a third law pair to the gravitational force, and also does no work, so i left it out.

no, energy analysis of the cart does not depend on the reference frame. if you choose an inertial reference frame moving at velocity V relative to the object, the total energy of the object can be written in terms of the center of mass motion and the frame motion:

KE(total) = KE(C of M) + KE(frame)

or KE (total) = KE(C of M) + 1/2 mV^2

by changing to a different reference frame, with different speed V', you can re-write this equation. only the KE(frame) part will change. the kinetic energy is therefore only defined to within a constant which depends on the motion of the frame chosen relative to the motion of the center of mass. since kinematics depends on changes in kinetic energy, the constant KE contributed by the choice of reference frame will not matter. when you look at changes in kinetic energy, the constant drops out. also, you can see that kinetic energy is smallest with a choice of frame that moves with the object, V=0, so often the center of mass frame is the easiest frame in which to analyze motion.

Okay. So far that is correct.

cobra bubbles wrote:as for the forces, they do not depend on the choice of reference frame either (as long as it is inertial.) if you choose the reference frame of the ground or the center of mass reference frame, the forces are still the same.

Yes, that is true as well.

cobra bubbles wrote: the external forces acting on the cart are the thrust due to the wind, the normal force and the gravitational force. there are no other forces that can act on the cart.

That is wrong, there is a breaking force on the wheels as well.

cobra bubbles wrote: (i ignore friction in either frame. it makes the analysis easier, and in this case, ignoring friction yields an upper limit on the final velocity. if i included friction forces, they are dissipative and lower the final velocity.)

Fine. But keep in mind only to ignore the dynamic dissipative frictions. There is static friction as well (such as the all important traction on the wheels) which does not dissipate energy but only transfer forces.

cobra bubbles wrote:in either reference frame, the normal force and gravitational force are perpendicular to the carts motion. (assuming v<<c)
since they are perpendicular to the motion, they do no work on the cart and can be ignored. (assuming motion on level ground) this leaves only the force due to the wind left to act on the cart.

thus, the only force you have to consider for the motion of the cart is the force of the wind. the only energy input you have to consider is the change in energy due to the wind.

Here it went wrong. The traction on the wheels extract energy from the motion already present. (In the frame of the ground it comes from the motion of the car, in the frame of the car the cars kinetic energy is at the minimum but in this acounting it comes from the motion of the ground.)

This energy is used to power the propeller to generate thrust.

In the ground frame the energy goes to make the car go faster, the wind is pushed back and therefore loses energy in the ground frame, this acounts for the extra energy to give a net acceleration on the car or to overcome the dissipative friction.

In the car frame there is a head wind. Since the wind is pushed back it gains energy in this frame. But the apparent winds motion is slower than the grounds (because of the actual wind present) it therefore takes less energy to compensate from the momentum lost at the wheels, again giving a net surplus of energy.

cobra bubbles
Posts: 10
Joined: Wed Dec 24, 2008 8:29 pm UTC

### Re: Downwind faster than the wind

tass:

you wrote: "Here it went wrong. The traction on the wheels extract energy from the motion already present. (In the frame of the ground it comes from the motion of the car, in the frame of the car the cars kinetic energy is at the minimum but in this acounting it comes from the motion of the ground.)

This energy is used to power the propeller to generate thrust."

not true. when the wheels are rolling without slipping, the spot the wheel is contacting the road is instantaneously at rest relative to the road. since there is no relative motion, by the definition of work = force * displacement, the work is zero because the displacement is zero. here is a quote from the wikipedia friction article that says this same thing:

"In the reference frame of the interface between two surfaces, static friction does no work, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does negative work."

so, the traction of the wheels does not do work, therefore the kinetic energy of the cart does not change due to the traction. since the KE of the cart stays the same, there is no change in KE that can be harnessed to generate thrust.

cobra bubbles
Posts: 10
Joined: Wed Dec 24, 2008 8:29 pm UTC

### Re: Downwind faster than the wind

this leaves us in a seemingly weird situation.

we can ignore rolling friction, gear friction, air resistance, static friction etc. either because they do not directly affect the cart's motion, or because they are so small, or because they are dissipative, and will have the effect of reducing the maximum attainable cart velocity.

if we draw a free body diagram that shows all the forces acting on the cart in the direction of motion/against motion, there is only one--the thrust.

when the cart is at it's final velocity, we know that acceleration is zero because there is no change in velocity. this means that the net force is zero, which implies that the thrust is zero when the cart is at it's terminal velocity.

let me repeat--the thrust is zero when the cart is at it's final velocity.

(kinda of counter-intuitive.)

therefore, neglecting small dissipative forces, the cart's final speed is not primarily determined by the magnitude of forces opposing motion, it is actually determined by when the propulsive force, the thrust, goes to zero.

i.e. the thrust is proportional to the difference in the magnitude of the wind speed and the cart speed. when the cart reaches wind speed it stops acclerating.

dwfttw carts, with the wheels connected to a propeller, are really just acting like fancy sails.

Tass
Posts: 1909
Joined: Tue Nov 11, 2008 2:21 pm UTC
Location: Niels Bohr Institute, Copenhagen.

### Re: Downwind faster than the wind

You misunderstand again.

cobra bubbles wrote:not true. when the wheels are rolling without slipping, the spot the wheel is contacting the road is instantaneously at rest relative to the road. since there is no relative motion, by the definition of work = force * displacement, the work is zero because the displacement is zero.

By this logic the forces between a wire and a truck it drags does no work because the relative velocity is zero. Or what about a car accelerating or braking without the wheels slipping?

You are switching back and forth between refference frames, could we please maybe choose one and stick to it? In the cars reference frame the interface between ground and wheels are indeed moving.

But yes, the whole point is that the static friction does not dissipate energy, only transfer force.

cobra bubbles wrote:"In the reference frame of the interface between two surfaces, static friction does no work, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does negative work."

so, the traction of the wheels does not do work, therefore the kinetic energy of the cart does not change due to the traction. since the KE of the cart stays the same, there is no change in KE that can be harnessed to generate thrust.

Once again: Then how does a train manage to save most of the kinetic energy when braking and store it for using to start up again?

cobra bubbles wrote:this leaves us in a seemingly weird situation.

we can ignore rolling friction, gear friction, air resistance, static friction etc. either because they do not directly affect the cart's motion, or because they are so small, or because they are dissipative, and will have the effect of reducing the maximum attainable cart velocity.

No. We can not ignore the static friction. It is there. It brakes the car, meaning that even under perfect disipative-friction-less conditions, the cart will still have propeller thrust at terminal velocity.

cobra bubbles wrote:if we draw a free body diagram that shows all the forces acting on the cart in the direction of motion/against motion, there is only one--the thrust.

No

cobra bubbles wrote:when the cart is at it's final velocity, we know that acceleration is zero because there is no change in velocity. this means that the net force is zero, which implies that the thrust is zero when the cart is at it's terminal velocity.

Again no, see above.

cobra bubbles wrote:therefore, neglecting small dissipative forces, the cart's final speed is not primarily determined by the magnitude of forces opposing motion, it is actually determined by when the propulsive force, the thrust, goes to zero.

No as said the maximal speed is reached before that.

cobra bubbles wrote: i.e. the thrust is proportional to the difference in the magnitude of the wind speed and the cart speed. when the cart reaches wind speed it stops acclerating.

Where did you get that from? The propeller is rotating!

cobra bubbles wrote:dwfttw carts, with the wheels connected to a propeller, are really just acting like fancy sails.

False conclusion based on the false asumptions above.

Though the "fancy sails" has some truth. Do you acknowlegde that iceboats can tack downwind and get an average directly downwind speed exceeding the windspeed? Then remember that the propeller blades has this sideways motion maing it work in exactly the same way.

cobra bubbles
Posts: 10
Joined: Wed Dec 24, 2008 8:29 pm UTC

### Re: Downwind faster than the wind

By this logic the forces between a wire and a truck it drags does no work because the relative velocity is zero.

correct. a wire pulling an object does no work, because there is no relative motion. the force acting on the wire does the work. the wire simply transfers the force. static friction simply transfers force also.

Or what about a car accelerating or braking without the wheels slipping?

cars can brake without the wheels slipping. kinetic energy is removed via kinetic friction between the brake pads and the discs, not by the static friction between the tire and the road. this is why you don't want to brake so hard that the tires skid. kinetic friction is typically less than static friction between two surfaces. so you get more braking acceleration by *not* slipping.

accelerating cars are different. static friction is defined as F=< uN, the magnitude of friction is less than or equal to the coefficient of friction times the normal force. static friction can change in response to the force opposing it, up to the maximum value, when slippage starts, and the kinetic friction regime is entered. to accelerate a car, the engine applies torque to the tire, which interacts with the road via static friction, up to some max value when the wheels start to slip. since the tire is pushing on the road backward, the road pushes the tire forward by newton's third law, causing a net force in the forward direction. this does not mean that the static friction force did work on the car. it does not. the torque of the engine turning the tires through an angle is the source of the cars kinetic energy.

You are switching back and forth between refference frames, could we please maybe choose one and stick to it? In the cars reference frame the interface between ground and wheels are indeed moving.

i am not switching reference frames. i am keeping in the frame of the ground. as the cart moves by the ground at speed v, the rim of the wheel is at speed -v, so the net speed of the wheel with respect to the ground is v + (-v) = 0. there for displacement is zero and work is zero. i did not change reference frames.

so yes, we *can* ignore static friction. it is simply a mechanism to transmit force. it does not transmit energy.

Where did you get that from? The propeller is rotating!

yes, the propeller is rotating. but it is a necessary consequence of newton's second law. at terminal velocity, the propeller is unable to transmit energy to the cart.

sure, iceboats and sailboats can acclerate to a speed faster than that of the wind. they do it by exploiting the forces involved in a different manner. for those boats, the final speed is determined by a constant wind force and a slowly increasing resistive force. if the resistive forces increase slow enough as a function of velocity, they will balance the force due to the wind, giving net force zero at a higher terminal velocity.

the dwfttw wind cart operates on a different principle. the friction forces are very small, and don't effect the final velocity much. the main effect is that the propellers thrust drops to zero, preventing any more acceleration.

ice boat: constant wind force, speed limited by resistance.
dwfftw cart: decreasing propeller force, speed limited by when thrust goes to zero.

so, the ice boat/sailboat comparison is really not a good one. the situations are subtly different.

cobra bubbles
Posts: 10
Joined: Wed Dec 24, 2008 8:29 pm UTC

### Re: Downwind faster than the wind

one thing i would like to have proponents for the dwfttw travel answer is:

what limits the final speed of the cart?

the carts, by design, have small profiles, so air resistance is negligible. the gears and axles are low friction, so the forces involved there are small. rolling friction is small. static friction between the wheels and ground cannot affect the motion. these dissipative forces all waste energy, mainly through generation of heat, leaving less energy from the wind to end up as kinetic energy of the cart. a free body diagram of the cart will only have the thrust of the propeller acting in the horizontal direction that can possibly affect the motion.

since the only kinetic energy left to exploit for motion is the kinetic energy of the wind, the thrust of the propeller must depend on it.

then, as the cart speeds up, the relative amount of kinetic energy available decreases, since the air is moving slower relative to the cart as the carts speed goes up. thus, it is natural to suppose the magnitude of the thrust goes as some power of the difference between the wind and cart speeds. it may go as the difference squared, or cube or something. (actually, i think my calcs show it goes as the cube of the difference) but in any case, as the cart goes faster, the thrust will drop, until wind speed = cart speed and thrust available from the wind decreases to zero.

in order to have a speed faster than the wind, the thrust must then be something like T= f(w-v) + g(v) + C.

boundary conditions dictate that C=O, since when the wind is zero, and the cart is not moving, there is no thrust. i.e. the cart does not start to move from rest if wind is zero.

so T=f(w-v) + g(v). as the carts speed goes up, the f(w-v) portion goes to zero, leaving T=f(v). the thrust is then only dependent as some function of velocity, which is eventually counteracted by the resistive forces. this could allow the cart to go faster than the wind.

this is the point that i am puzzling over now. is f(v)=0 or not? my gut says it is zero, which is why i think the cart will not go faster than the wind.

i am trying to think of some mechanism by which to show what this extra component of thrust could be.

lightvector
Posts: 224
Joined: Tue Jun 17, 2008 11:04 pm UTC

### Re: Downwind faster than the wind

cobra bubbles wrote:As the cart goes faster, the thrust will drop, until wind speed = cart speed and thrust available from the wind decreases to zero.

This is the key misconception. If the wind speed and the cart speed are equal, then because the propeller is still rotating, it is still pushing air backwards. Let me repeat - when the wind and car speed are equal, the propeller is still rotating and pushing air backwards.

Therefore, the car experiences a thrust forward, even at wind speed. In the ground frame, the wind's rightward speed is reduced. Therefore, it loses energy when it interacts with the propeller/car system. Therefore, it is possible that the car gains energy both to increase its speed and the rate of its propeller spinning, to accelerate forward, if energy loss is small enough. Because (again, in the ground frame), the ground is not moving, it provides an unlimited momentum sink. The car pushes forward against the ground so that it can get rid of excess forward momentum down to the amount consistent with its current speed and the amount of energy it recieves.

I admit, the mechanics are complicated enough that I'm not completely confident to explain how this occurs for this specific propeller/axle/wheel vehicle design.

Roughly, it goes like this:

Propeller pushes car forward and does positive work on the car, at the cost of some of it's own rotational momentum.
But the forward thrust is resisted by the wheels, since the wheels cannot slip against the ground and the wheels are connected to the propeller.
So the wheels, resisting against the ground, experience a torque.
This torque drives the propeller, keeping it spinning, restoring the rotational momentum it loses when pushing against the wind.

The forward thrust from the propeller must exceed the resistive force of the wheels that is needed to resupply the lost rotational momentum of the propeller. This apparently, can be accomplished through excellent propeller design and gearing.

spork33
Posts: 29
Joined: Mon Dec 15, 2008 4:39 pm UTC

### Re: Downwind faster than the wind

Cobra,

I applaud you for trying to get your head around how this cart works. But it seems you're missing at least one or two very critical points. Others have alluded to them. Most important of all is the fact that this cart exploits the energy of the wind relative to the ground on which the cart rolls. The cart is basically no more than a clever "lever" that trades some of the force available at that interface for velocity. For a mechanical analog see the following excellent videos (which I think may have already been posted).

what limits the final speed of the cart?

Our cart has a fixed "advance ratio". This is the theoretical distance the prop would advance in one rotation divided by the distance the wheels will roll in that same single rotation of the prop. If this number is below one we have a cart that will go downwind faster than the wind. As the number approaches one the theoretical speed of the cart becomes greater multiples of the wind speed - but at the cost that we must have a more efficient cart. There is a very simple relationship between advance ratio and theoretical max speed as a function of wind speed. In the real world the cart's steady-state speed will always be less than that speed due to frictional losses.

let me repeat--the thrust is zero when the cart is at it's final velocity.

In the theoretical case this is true (and it happens well above wind speed). In the real-world case there is definitely thrust, and a braking force on the wheels. The energy harvested at the ground/wind interface is ultimately spent on frictional losses.

i.e. the thrust is proportional to the difference in the magnitude of the wind speed and the cart speed. when the cart reaches wind speed it stops acclerating.

And this is the heart of the brain-teaser. The cart takes advantage of the speed of the wind over the ground, not over itself. Without gearing the prop to the wheels this would not be possible.

so, the ice boat/sailboat comparison is really not a good one.

The prop blades on the cart experience exactly the same dynamics as the sail of an ice-boat on a continuous 45 degree downwind tack. The transmission and wheels provide precisely the same kinematic constraint on the blades that the skates of the ice-boat provides for its sail.

...which is why i think the cart will not go faster than the wind

This leaves us with the niggling problem that my cart DOES go DDWFTTW quite repeatably - just as yours could do for \$40.

lightvector
Posts: 224
Joined: Tue Jun 17, 2008 11:04 pm UTC

### Re: Downwind faster than the wind

the thrust must then be something like T= f(w-v) + g(v) + C.

boundary conditions dictate that C=O, since when the wind is zero, and the cart is not moving, there is no thrust. i.e. the cart does not start to move from rest if wind is zero.

so T=f(w-v) + g(v). as the carts speed goes up, the f(w-v) portion goes to zero, leaving T=f(v). the thrust is then only dependent as some function of velocity, which is eventually counteracted by the resistive forces. this could allow the cart to go faster than the wind.

this is the point that i am puzzling over now. is f(v)=0 or not? my gut says it is zero, which is why i think the cart will not go faster than the wind.

i am trying to think of some mechanism by which to show what this extra component of thrust could be.

The thrust from the propeller is a function of the wind speed relative to the car and the rotation rate of the propeller. The rotation rate of the propeller is determined by the speed that the wheels are turning - which is determined by the speed that the car is moving.

Boundary conditions dictate that thrust = 0 when the wind is not moving relative to the car and the the propeller is not turning. But if the car is moving at some positive speed forward along with the wind, the wheels are spinning, so the propeller attached to the wheels is spinning. A spinning propeller in still air produces a thrust.

Tass
Posts: 1909
Joined: Tue Nov 11, 2008 2:21 pm UTC
Location: Niels Bohr Institute, Copenhagen.

### Re: Downwind faster than the wind

Once again: Could you please not double post? It is annoying having to edit to answer you posts.

(Changed to red, because this is an actual forum rule which should be followed by everyone anyway. - gmalivuk)

cobra bubbles wrote:
By this logic the forces between a wire and a truck it drags does no work because the relative velocity is zero.

correct. a wire pulling an object does no work, because there is no relative motion. the force acting on the wire does the work. the wire simply transfers the force. static friction simply transfers force also.

Or what about a car accelerating or braking without the wheels slipping?

cars can brake without the wheels slipping. kinetic energy is removed via kinetic friction between the brake pads and the discs, not by the static friction between the tire and the road. this is why you don't want to brake so hard that the tires skid. kinetic friction is typically less than static friction between two surfaces. so you get more braking acceleration by *not* slipping.

Fine so the static friction makes it possible to extract energy from the motion of the car so stop ignoring it.

cobra bubbles wrote:accelerating cars are different. static friction is defined as F=< uN, the magnitude of friction is less than or equal to the coefficient of friction times the normal force. static friction can change in response to the force opposing it, up to the maximum value, when slippage starts, and the kinetic friction regime is entered. to accelerate a car, the engine applies torque to the tire, which interacts with the road via static friction, up to some max value when the wheels start to slip. since the tire is pushing on the road backward, the road pushes the tire forward by newton's third law, causing a net force in the forward direction. this does not mean that the static friction force did work on the car. it does not. the torque of the engine turning the tires through an angle is the source of the cars kinetic energy.

Thanks for this nice breakdown of how a car manages to accelerate. Al I was saying was that just because a force produces no work, you can't just ignore its presence when summing up the resultant force at maximum speed.

cobra bubbles wrote:
You are switching back and forth between refference frames, could we please maybe choose one and stick to it? In the cars reference frame the interface between ground and wheels are indeed moving.

i am not switching reference frames. i am keeping in the frame of the ground. as the cart moves by the ground at speed v, the rim of the wheel is at speed -v, so the net speed of the wheel with respect to the ground is v + (-v) = 0. there for displacement is zero and work is zero. i did not change reference frames.

Oh no! You claimed that the air moves faster after it has passed the propeller than before. That is true in the car frame, not in the ground frame.

cobra bubbles wrote:so yes, we *can* ignore static friction. it is simply a mechanism to transmit force. it does not transmit energy.

Not when summing up the resultant force.

cobra bubbles wrote:
Where did you get that from? The propeller is rotating!

yes, the propeller is rotating. but it is a necessary consequence of newton's second law. at terminal velocity, the propeller is unable to transmit energy to the cart.

Sure a force of magnitude zero cant do work. But it is not zero at maximum velocity, it is still counteracting the braking on the wheels.

cobra bubbles wrote:sure, iceboats and sailboats can acclerate to a speed faster than that of the wind. they do it by exploiting the forces involved in a different manner. for those boats, the final speed is determined by a constant wind force and a slowly increasing resistive force. if the resistive forces increase slow enough as a function of velocity, they will balance the force due to the wind, giving net force zero at a higher terminal velocity.

the dwfttw wind cart operates on a different principle. the friction forces are very small, and don't effect the final velocity much. the main effect is that the propellers thrust drops to zero, preventing any more acceleration.

ice boat: constant wind force, speed limited by resistance.
dwfftw cart: decreasing propeller force, speed limited by when thrust goes to zero.

so, the ice boat/sailboat comparison is really not a good one. the situations are subtly different.

No. Not a constant wind force. It is tacking down wind, beating the wind to its goal. The component of the force going forward diminishes as it goes faster, but it can still move with a downwind velocity component faster than the wind. The propeller cart is completely analogous, the blades going around in a circle just removes the need to change direction all the time.

cobra bubbles wrote:one thing i would like to have proponents for the dwfttw travel answer is:

what limits the final speed of the cart?

Under perfect conditions the final speed of the cart is given by the gearing ratios. It is when the thrust of the propeller equals the braking on the wheels. It could in theory be made as high as one wanted, just like the "under the ruler" video. But the faster you gear it to go, the harder it will be to overcome the real friction whci hcan never be fully avoided.

cobra bubbles wrote:the carts, by design, have small profiles, so air resistance is negligible. the gears and axles are low friction, so the forces involved there are small. rolling friction is small. static friction between the wheels and ground cannot affect the motion. these dissipative forces all waste energy, mainly through generation of heat, leaving less energy from the wind to end up as kinetic energy of the cart. a free body diagram of the cart will only have the thrust of the propeller acting in the horizontal direction that can possibly affect the motion.

Once agian you are forgetting the braking on the wheels in your free body diagram.

cobra bubbles wrote:since the only kinetic energy left to exploit for motion is the kinetic energy of the wind, the thrust of the propeller must depend on it.

then, as the cart speeds up, the relative amount of kinetic energy available decreases, since the air is moving slower relative to the cart as the carts speed goes up.

Now you again switched back to car frame. In the ground frame the kinetic eneregy of the air is constant.

cobra bubbles wrote:thus, it is natural to suppose the magnitude of the thrust goes as some power of the difference between the wind and cart speeds. it may go as the difference squared, or cube or something. (actually, i think my calcs show it goes as the cube of the difference) but in any case, as the cart goes faster, the thrust will drop, until wind speed = cart speed and thrust available from the wind decreases to zero.

No. Again the propeller is rotating. It pushes back on the air, even if that air is stagnant relative to the car.

cobra bubbles wrote:in order to have a speed faster than the wind, the thrust must then be something like T= f(w-v) + g(v) + C.

boundary conditions dictate that C=O, since when the wind is zero, and the cart is not moving, there is no thrust. i.e. the cart does not start to move from rest if wind is zero.

When the cart is at rest in no wind there is no rotation and no thrust. It obviously cant work without wind, nobody said it could. So yes, of course, C=0

cobra bubbles wrote:so T=f(w-v) + g(v). as the carts speed goes up, the f(w-v) portion goes to zero, leaving T=f(v). the thrust is then only dependent as some function of velocity, which is eventually counteracted by the resistive forces. this could allow the cart to go faster than the wind.

this is the point that i am puzzling over now. is f(v)=0 or not? my gut says it is zero, which is why i think the cart will not go faster than the wind.

i am trying to think of some mechanism by which to show what this extra component of thrust could be.

No f(v) will not be zero. Because the faster the car goes, the faster the propeller is forced to rotate because of the coupling to the wheels.

Now I think we are getting there

roflcopter
Posts: 26
Joined: Thu Nov 13, 2008 2:14 am UTC

### Re: Downwind faster than the wind

But onto the SCIENCE!!!

Okay I sail too much for my own good and I know that for a fact you can go faster than the wind downwind, the key is not to start going downwind...

If you start off on a close reach(wind coming from the side but slightly more from the front) as you accelerate up to the wind speed the wind angle moves forward to the front(apparent wind angle) from your perspective as opposed to the true wind direction, and your speed is added to the true wind speed due to the movement and the directional change(apparent wind speed).

So as anyone who sails knows you can not sail directly upwind and must maintain an angle off of the wind, and since a close reach normally will produce the most speed you will slowly change your actual angle of movement more downwind as you accelerate and as you accelerate the wind speed across your sails will increase allowing for more speed and more wind angle change allowing for more wind across your sails, etc.

So as you accelerate you will eventually be going downwind or even slightly past straight downwind and will be working with an ever increasing(in an ideal setup) wind speed which would allow an ever increasing speed of movement.

You must remember that the true wind speed that a still observer would see is not what the moving windpowered vehicle will see, and to end this here is a video of an ice-boat(they regularly top the windspeed whichever way they are going) here, a video of the speed record on a windsurfer here, a video of a hydrofoil trimaran that goes over 40kts here, and an article about getting past the 50kt barrier in a boat and with kiteboarding(still wind powered no?) here.

If anyone sees anything wrong with what knowledge I have hopefully imparted please feel free to tell me what I did wrong!

Tass
Posts: 1909
Joined: Tue Nov 11, 2008 2:21 pm UTC
Location: Niels Bohr Institute, Copenhagen.

### Re: Downwind faster than the wind

It is certainly not wrong. Most of it has however been stated before, therfore I will now assault you

Edit:

roflcopter wrote:So as you accelerate you will eventually be going downwind or even slightly past straight downwind and will be working with an ever increasing(in an ideal setup) wind speed which would allow an ever increasing speed of movement.

The downside is that as you go faster, the wind you feel comes more and more from directly ahead. Therefore the speed you can achive is limited by the smallest angle your craft can go to the wind.

Grav
Posts: 61
Joined: Fri Aug 17, 2007 7:45 pm UTC
Contact:

### Re: Downwind faster than the wind

If I took a propellor and simply placed it stationary and parallel to the plane in which the wind is moving, wouldn't the tips of the propellor be traveling (and for a short time... traveling downwind) faster than the wind? Being as the propellor blades have identical angular velocity regardless of the distance from the center, and being that over time, the wind would accelerate the centermost of the blades to have the same linear velocity as the wind, wouldn't that in turn nessecitate that the outer portions of the blade would have a higher linear velocity than the wind?
That's about as witty as something not witty.

Tass
Posts: 1909
Joined: Tue Nov 11, 2008 2:21 pm UTC
Location: Niels Bohr Institute, Copenhagen.

### Re: Downwind faster than the wind

Grav wrote:If I took a propellor and simply placed it stationary and parallel to the plane in which the wind is moving, wouldn't the tips of the propellor be traveling (and for a short time... traveling downwind) faster than the wind? Being as the propellor blades have identical angular velocity regardless of the distance from the center, and being that over time, the wind would accelerate the centermost of the blades to have the same linear velocity as the wind, wouldn't that in turn nessecitate that the outer portions of the blade would have a higher linear velocity than the wind?

Whats the point? The whole car can go faster than the wind.

Grav
Posts: 61
Joined: Fri Aug 17, 2007 7:45 pm UTC
Contact:

### Re: Downwind faster than the wind

Tass wrote:
Grav wrote:If I took a propellor and simply placed it stationary and parallel to the plane in which the wind is moving, wouldn't the tips of the propellor be traveling (and for a short time... traveling downwind) faster than the wind? Being as the propellor blades have identical angular velocity regardless of the distance from the center, and being that over time, the wind would accelerate the centermost of the blades to have the same linear velocity as the wind, wouldn't that in turn nessecitate that the outer portions of the blade would have a higher linear velocity than the wind?

Whats the point? The whole car can go faster than the wind.

I was not including any cars in my design. =p
That's about as witty as something not witty.

Rentsy
Posts: 154
Joined: Tue Dec 02, 2008 4:13 am UTC

Gear it down.