I believe NORAD has the best available tracking software. That might be a bit overkill though, considering the typically zero velocity of fiber optic networks.
The submitter is either an ass, or he's playing a game provoking people to generate additional arguments for the 5th Amendment, perhaps specifically looking to combat the "give us your password or we'll lock you up" crap.
The submission is to full of fail to bother addressing it all, such as complaining that protections for the innocent sometimes make it harder to convict the guilty. Whaaaaaah! Whaaaaah! Whine!
But there's another fundamental reason that no one seems to have mentioned. The government requires a court ordered search warrant before they can intrusively violate the sanctity of your home. But there is something far more sacrosanct than one's home... one's very MIND. I can't think of anything more intrusive than the government wanting to invade your mind to carry out a "search" of your thoughts. There is nothing more sacrosanct than one's mind. Government agents showing up with guns and locking yuo in handcuffs, and screaming at you "Hand over your THOUGHTS and MEMORIES, or we will imprison you by force, if you resist giving us your thoughts and memories we are authorized to use lethal force if necessary to haul you off and imprison you."
if the government grants you immunity, then your answers cannot incriminate you, but since nothing you say will incriminate you, the government can then force you to answer the question or go to jail for contempt of court. (There is actually no literal "right to remain silent"; it's a "right against self-incrimination". So take away the possibility of self-incrimination, and you have to talk.) This is a controversial exception
Yeah. That's bullshit. The government wants to seize, invade, and search your mind, and the government promises not to imprison you if you comply. FUCK THAT.
And if you decline to comply, the government declares it's going to imprison you... and if you resist they can and will use any and all force, up to and including lethal force, to carry out that imprisonment.
When a political scandal hits, partisan hacks appear to try and obfuscate the issue. This "article" is an example... When the administration is found to be unlawfully wiretapping every citizen... well, suddenly we see hacks pop up and say "well, you really didn't need that right anyways, right?".
This is why the homeschooler nuts need to be banned, and we need to do more to ensure toddlers aren't eating lead paint chips. Because seriously, when you can't make it from one to ten without confusing four and five, one or the other is at fault.
if you ever need to find out what it would be like without Amendment X, just crack open a history book.
For a while there I read "Amendment X" as meaning the 10th Amendment, chuckle. That confused me a bit. Anywho, I challenge you or anyone else to crack open a history book and show me how the U.S. would be noticeably different today without the 9th Amendment:
Amendment IX The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
The U.S. Supreme Court is loath to go within a hundred feet of that amendment. It is probably the Bill-of-Rights amendment mentioned by the Supreme Court the fewer times than any other, rivaled perhaps only by the 3rd Amendment. (The 3rd amendment almost never being addressed simply because the government never attempts to quarter soldiers in private homes). The few times the court has mentioned the 9th Amendment they have only done so only to say essentially "we're not going give it any application, not here, not now, not ever".
The quote Justice Antonin Scalia: the Constitution's refusal to 'deny or disparage' other rights is far removed from affirming any one of them, and even farther removed from authorizing judges to identify what they might be, and to enforce the judges' list against laws duly enacted by the people.
In other words, the TRUE text of the 9th Amendment reads as follows: Amendment IX The Bill of Rights is inherently incomplete and obviously other Rights exist, but we only mention that here to troll you. lolz.
if a statement like Beal's conjecture can't be proven, you should be able to prove *that*.
Urk? How did you reach that odd conclusion? "X is unprovable" is itself a mathematical statement, and I see no reason to actively expect it never to fall into the category of unprovable statements.
I would find it rather surprising if there didn't exist a recursively unprovable chain, and by that I mean a chain where all of the following were unprovable: X X1: X is unprovable X2: X1 is unprovable. X3: X2 is unprovable. X(n): X(n-1) is unprovable.
If we want to get meta, it may well be possible to prove that such a chain exists. However it's easy to prove it could only be a non-constructive proof. Any mathematics successfully identifying a specific statement "X" for such a chain would itself constitute a proof of statement X1, in contradiction with the definition of a recursively unprovable chain.
One of the common themes in cart discussions is that different people require wildly different sorts of explanations or analogies for it to "click". Once it does click it's not uncommon for people to feel irritated that "it would have been so much easier if you just said X in the first place". Of course the explainer has no way to know in advance which explanation is going to click for any particular person.
I absolutely agree with you that a force/energy calculation is the gold-standard best possible proof that the cart works. Unfortunately most people can't read force/energy calculations. In most cases throwing a wall of numbers their face is... unhelpful.
Also note that the explanation which did work for you demonstrated that the cart can work, but in many ways (and for many people), it's a completely worthless non-explanation of how it works. For many people it still leaves a very . Since you are a calculations-person, check out the almost magical "how" of wind-energy-collection going on in the following calculation:
The wind is going left at 10 m/s, cart is going 20m/s in the same direction. From the point of view of the cart, the air is going 10 m/s to the right. The kinetic energy of 1 kg of air at 10 m/s is 50 joules. (ke=1/2*mv^2). The cart spends energy to run the prop, accelerating the air faster to the right. The air leaves the prop at 12 m/s rightwards In the frame of the cart). The kinetic energy of the air has increased to 72 joules. Simple enough... the cart spends energy running the prop accelerating the air, and naturally energy is transferred from the cart into the air.
But now look at it from the ground frame. The air is a wind going 10 m/s to the left. 1 kg of air has a kinetic energy of 50 joules. The cart prop is pushing that air rightwards, the resulting in 8 m/s in the ground frame. The kinetic energy of this air, in the ground frame, is now 32 joules. 50 joules - 32 joules = 18 joules of energy vanishing from the air. Where does the energy go? The only place it could go is into the cart, and a careful analysis shows the cart's kinetic energy increasing by the power applied to the prop PLUS the energy lost from the air. The power applied to the prop is then subtracted back out by the drag at the wheels. The net result is the wind energy being teleported into the cart. From the ground frame the air energy went *into* the cart (increasing the cart's kinetic energy). This clearly shows the energy being extracted from the wind. But remember what the car's point of view was.... the cart was spending energy running the prop to pump energy OUT of the cart and INTO the air. The cart saw energy flowing in the opposite direction! Doh!
I have no idea where you got the idea that airplanes need millions of horsepower.
Allow me to recap how we got there, from my point of view. I was trying to get across the idea that the prop can generate greater thrust than the drag at the wheels. Pulling energy from the wheels to drive the prop looks like a perpetual motion design, and your natural gut reaction was to apply conservation laws. Trying to use using a generator to power a motor never gives you more out than you put in. So you mentally had me in the "crackpot zone", or at least in the "potential crackpot" zone. You were actively looking to shoot down everything I said. When I tried to explain that it was "harder" for a prop to push against a faster wind, using an example that it was "hard" for a prop against a 100 MPH wind, you answered that it was trivially easy for a prop to push against 100 MPH air. You presented a graph of a half-million horsepower prop thrusting in 100 MPH air.
I rather naturally took your example and pointed out how it would take twice as much power to get the same thrust in air going twice the speed.
I was trying to get across that the ease/difficulty of generating thrust at the prop was completely relative to the air speed. You were countering/challenging that with a completely non-relative disproporti
You'll have to break out the differential equations if you want to calculate what's going on.
No need for differential equations or even calculus. Once the problem is laid out correctly anyone with minimal algebra and minimal familiarity with force/energy conversions can probably follow it.
(Anyone outside the U.S. can simply pretend I wrote meter and kilogram instead of foot and pound. No need for conversions, everything will turn out fine. I promise, grin.)
Lets assume the cart is going to the right at 40 feet per second, and the wind is going to the right at 30 feet per second. That puts the cart faster than the wind, with the apparent headwind passing over the cart. That apparent headwind is 40 feet per second - 30 feet per second = 10 feet per second.
Now we extract power at the wheels. Lets put a 1 pound drag at the wheels, and that force is exerted against the ground which is passing the wheels at 40 feet per second. Power = force * velocity, so we have power = 1 pound * 40 feet per second. Power extracted from the wheels equals 40 foot-pounds per second.
Now we transfer that 40 foot-pounds per second to drive the propeller. The propeller is pushing against the air, and as a reminder the air is passing the propeller at 10 feet per second. What thrust do we get? Again, power = force * velocity. Rearranging that equation to isolate force we get force = power / velocity. So we have force = 40 foot-pounds per second / 10 feet per second. Our thrust force is 4 pounds. The drag on the cart is one pound, the thrust is 4 pound, the net force is 3 pounds of acceleration. The cart is above windspeed and accelerating.
Of course that calculation is for an imaginary cart, it ignores any sort of friction and assumes everything is 100% efficient. But that's ok.... our imaginary 100% efficient proppeller generated an extremely generous 4 pounds of thrust. Any constructed cart with better than 25% net efficiency will generate more than 1 pound of thrust, sufficient to still yield an accelerating cart.
Q.E.D., using nothing more than the simplest algebra and the most basic power = force * velocity energy equation.
At this point it's extremely easy to go back to the beginning and repeat the calculations replacing the cart speed, windspeed, or wheel drag with any other values of interest. Just don't insert values less than zero unless you have high skill in reanalyzing and reinterpreting everything. (Plugging in zero windspeed or zero wheel drag is good for seeing the cart can't speed up in those conditions, and plugging in zero for the cart's initial speed shows that the cart needs wind-drag or some other push to get started.)
Downwind, below windspeed, you can do it either way. But in this region it also works to hoist a moose on a pole and call it a sail, chuckle.
Downwind, at exactly windspeed, the cart feels dead air. A windmill in dead air collects zero energy to drive the wheels. As you get above windspeed downwind you feel an apparent headwind, but trying to stick a windmill in it is a net drag. The energy of the headwind is your own motion *minus* the true wind. That headwind effectively contains negative-energy as far as wheel drive is concerned.
Downwind faster than the wind only works with the wheels driving a prop.
For an equivalent reason, an upwind cart only works with a windmill driving the wheels. Upwind faster than the wind presents no special issue.
In both directions your windspeed-multiple is capped only by design efficiency, factoring in aerodynamic drag and whatnot. Blackbird gets over 3x downwind and (with a propeller swap and gear change) it gets over 2x upwind.
This is a roadblock to understanding that trips up most people. As long as you look at the cart and you think you see a windmill.... as long as the word "windmill" pops to mind... you aren't going to be able to get a handle on how the cart works. There is no windmill. The propeller is a fan, always a fan, only a fan.
Note that you have completely eliminated the wind from the system.
No, the wind is still blowing. What I have eliminated is the windmill.
I didn't say the wind ceased to exist. I said you eliminated it from the system. The sun exists. But if the cart doesn't have solar panels, the sun obviously isn't a part of the system
If we're talking about a battery-powered machine, and you eliminate the battery wires, and I point out that you have "removed the batteries from the system", I hope you can see that it comes across as a little silly when you object that the batteries still exist.
This is a wind powered cart. If you are having trouble seeing how the cart taps into that energy, I'll happily do my best to explain it. But simply disconnecting the power source very quickly sends things in a very simple and obvious direction. No magic, no free energy, no perpetual motion... a machine which is not connected to a power source simply and inevitably winds down to a halt. A machine which is connected to a power source can run as long as it's connected, it can accelerate within the bounds of available power, it can tapdance and whistle dixie if it wants. Grin.
Check the "Thrust at Constant Power vs. Airspeed" chart here, where the thrust initially increases with airspeed This is presented as a typical case, not a special or corner one.
It is presented as a "typical case" for aircraft, the graph labels show between a quarter-million horse power and a half million horse power, and the intended performance range is obviously in the 100+ MPH region.
I think you'll agree that it's not very surprising that the left side of the graph, that down-left slope going from 50 MPH to 0 MPH, shows an aircraft prop going into an obvious "fail" region outside the intended operation range. A prop designed for low speed efficiency would have a significantly higher thrust at 50 MPH, and the thrust graph would continue to rise as velocity decreased below 50 MPH.
And you mentioned corner cases - that is exactly what we're examining here. We're looking at what happens at zero MPH, which is an extreme corner case. According to the laws of physics for an ideal 100% efficient device we have:
power = force * velocity
If we flip that to isolate force we get:
force = power / velocity
To simplify lets define a constant power input of 1 unit:
force = 1 / velocity
We are examining the extreme corner case where velocity goes to zero, and in that corner case an ideal prop can generate infinite force. Obviously no real machine is 100 percent efficient, no real machine can generate infinite forces. So as we approach zero a prop or other machine can provide increasing force, but we're running into a corner case and at some point we hit a design limit. At some design point the force generated reaches a maximum and anything more gets lost into inefficiencies.
We obviously don't need ideal infinite force for the cart to successfully work at zero air velocity. All we need is for prop thrust to be greater than wheel drag. A prop designed for low speeds can easily generate double, triple, or several more times as much force in low-velocity or zero-velocity air.
Consider a cart going 30 feet per second in a 20 foot per second MPH wind. The car is going 10 feet per second faster than the wind, so there's 10 feet per second of air going through the prop. Lets put one pound of drag on the wheels. Again, power = force * velocity. Power = 1 pound * 30 feet p
Nope. Going downwind-faster-than-the-wind requires the wheels to drive the prop. The easiest way to see this is to consider the cart traveling downwind at exactly windspeed. The cart feels like it's sitting in dead air. A windmill in still air collects zero energy. Nothing to drive the wheels. The math gets worse when traveling downwind faster than windspeed. Above windspeed you feel a headwind which can spin a windmill, but any attempt to stick a windmill in this headwind ends up dragging the cart slower.
You can use windmill to drive the wheels for a cart that goes upwind, and it can even go upwind faster than the wind. In fact an upwind cart can only work with the prop driving the wheels for basically the same reason we couldn't use a windmill to drive the downwind cart.
One side thinks the windmill is a turbine that drives the wheels
I'm the article submitter. I say those people are wrong. They are describing a false or broken design, one which is incapable of going downwind-faster-than-wind. The math states that going downwind-faster-than-wind require wheel powering a propeller. The math also states that going upwind requires a windmill powering the wheels (That's not directly relevant here, but hopefully it's an easier to understand and illuminating mirror image case).
Furthermore, I included in the story a link to the Wikipedia entry on the cart, which states the downwind-windmill idea is wrong.
And I included a link to a physics analysis paper from MIT professor Mark Drela which shows the downwind-windmill idea is wrong
And I included a link to the International Physics Olympiad test with this cart as a sample problem, which includes and answer section explaining the downwind-windmill idea is wrong
And if you like, I can google up a link to the Blackbird builders themselves repeatedly and firmly insisting it's not a windmill cart.
And if you like there are countless videos on line, videos of the large Blackbird as well as videos of small model carts, and a causal visual inspection will easily reveal that propellers on downwind carts always rotate in a fan-like direction, never in a windmill-like direction.
Anywhoo:
For the latter group, I would like to propose a modification
Yep, I'm in the "later group"...
replace the propeller with a generator, and use the power generated to run a linear induction motor which propels the device downwind along a track, which is level, straight and aligned with the wind. You can give the device a push to start it moving, if you like. What happens?
Okey dokey. We strip off the prop and attach the generator directly to the wheels. This is the power we would ordinarily be using to run the prop, but we direct it to a linear induction motor. No prob, simple enough.
Note that you have completely eliminated the wind from the system. The wind was our power source. So the end result is going to be pretty much what you would expect from any cart lacking a power source:
(A) If it's not moving, it simply sits there. It's not going to start moving on it's own. (B) If you give it a shove, it will be ruled by the basic principals of inertia and frictional-style energy losses. It's coasting at the shove-speed, and over time slows to a stop. The only question is how quickly it's going to slow down. That's determined by friction and inefficiencies and any other losses.
Having a generator at the wheels driving an induction motor does not change that, other than potentially contributing additional energy losses which make it slow down faster. In the ideal case the trust at the induction motor will equal the drag at the wheel-generator, for zero net effect on the coasting-slowing cart.
The reason it does work with the propeller is because of the presence of the wind. (Without the wind, the thrust generated at the prop can only be equal to or less than the drag at the wheels, exactly like in your linear accelerator question.) The wind and the propeller are blowing at each other, pushing against each other. The thrust generated at the prop is effectively the combined effect of the energy driving the prop PLUS the effect of the wind.
Note that this additive effect applies even when the cart is going at or above wind speed. Consider a cart going 100 MPH in zero wind. There is going to be a 100 MPH apparent headwind flowing over the cart. The power-driven prop is going to to be very inefficient and it will struggle trying to generate any significant thrust to the rear in a 100 MPH airflow already heading to the rear The prop would have to spin crazy fast and it's going to yield squat thrust. Now consider a cart going 100 MPH, downwind, in a 100MPH wind. The prop now feels like it's sitting
The Blackbird and similar carts are notorious for starting up very slowly. The initial start is from simple wind drag, with the large non-rotating prop acting much like a simple crappy sail increasing the basic wind drag.
Once the prop starts to turn, and while below windspeed, the cart slowly gains speed from a combination of simple wind drag augmented by the wheel-prop-thrust system working at a very low efficiency. I think at low rotation speed the prop blades are like an airplane wing in a stall condition... it can't generate aerodynamic lift when the air is just hitting the flat side of the blade and turbulently swirling over the edges. Anywho.... starting up from a dead stop is crap.
In the Blackbird test runs there's a point, I think in the ballpark of 75% of windspeedish, where it crosses a threshold and the prop gets a better bite on the air. I think at this point the prop blades are escaping the stall condition and they start generating true wing-type aerodynamic lift. The efficiency jumps and the cart starts to accelerate briskly. It then powers through windspeed and aggressively surges to either peak speed or until the drive chain snaps, whichever comes first. They generally run in a windspeed less than 20 MPH, and even with those light winds the peak torque in the driveshaft is comparable to the torque put out by a V8 engine, several hundred footpounds. The conflict between the prop pushing forwards against the wheels actively dragging backwards means that the drive shaft is under several times higher torque and power transfer than a simple car would experience at the same speed. As it picks up speed the prop is able to harvest the wind energy more rapidly from a greater volume of air, so as the speed picks up it starts cranking out pretty massive horsepower.
At the risk of beating a dead analogy horse, the wheel/prop_axle system can be considered reasonable analogous to a keel. The function of a keel is to constrain the available path of motion of the sail when the wind pushes on it. In particular the sail, via the keel, pushes against the water-medium in such a way as to constrain the sail to moving nearly 90-degrees off from the direction of the wind force. Equivalently, the wind force on the prop gets transferred through the keel (the axles and wheels) such that that force presses against the ground-medium in such a way as to constrain the sail to moving nearly 90-degrees off from the direction of the wind force. The cart transfers this force from the prop to the ground along a more complicated path than a ship keel transferring sail force against the water, but the the force transfer is equivalent, and the result is the same. The keel constrains the sail to sideways across the wind, and the cart keep constrains the prop blade to sliding sideways (where that sideways is bent in a circle).
In both cases the keel causes the wind-on-wing-force on the wing to reflect back at the wing in a sideways direction.
Ahh, now I'm looking at the source equations in the International Physics Olympiad and I see I misinterpreted the reference frames of the equations you posted. (You translated the variable "v" into "v_land", which threw me off. Writing it as v_cart would have been much clearer.)
So, trying again.
quoteSo evidently this equation only holds in steady state not in development.
Yeah. They state "the force due to air and the force due to ground must balance", so they are specifically analyzing the cart at steady-state peak speed, where prop force and wheel force sum to zero.
F * v_land = (1-alpha) * F * (v_land - v_wind)
You appear to have mis-copied that one. The equation should read:
F * (v_land - v_wind) = (1-alpha) * F * v_land
put in that magic moment when V_land-V_wind = 0, for another silly result.
V_land-V_wind = 0 puts the cart at windspeed, at which time it is accelerating. Acceleration means that the prop force and wheel force are out of balance. Any such equation will involve two differing F values.
V_land < V_wind. That is where we have not yet exceeded the wind speed.
I inserted a < in there, which I assume you intended but which Slashdot eats unless you type < to get <
Anywho, again you're looking at a case of an accelerating cart involving different wheel and prop forces. Any equation with a single F value is going to be nonsensical.
F * v_land = (1-alpha) * F * (v_land - v_wind)
postitive number = negative number
That's the mis-copied equation again. I'm pretty sure you wanted:
F * (v_land - v_wind) = (1-alpha) * F * v_land
In any case, it's an equation doe a faster-than-wind-cart at peak speed. Therefore v_land > v_wind, and v_land-v_wind > 0. In other words both sides have the same sign as F, and therefore have the same sign as each other. (Unless of course alpha is > 1, which would be a machine with greater than 100% energy loss, chuckle.)
I'm saying that despite the energy argument, the force argument is subtle and completley hidden in the above steady state energy argument.
I'm not sure if this will answer what you want, but some time ago I worked out the complete force and energy calculations for an accelerating cart. If you can follow it you can (hopefully) see where and why the propeller thrust turns out larger than the wheel drag. The short answer is that work = force * distance. The wheels roll a long distance over the ground, in comparison to a shorter distance of air through the prop. The differences in distances can trade off against a difference in forces. A small force at the wheels (pushing against a long distance of ground) can do enough work to generate a large force at the prop (pushing against a short distance of air).
I'm not sure if we fundamentally disagree on the operation of the cart, or if you're quibbling over a reference-frame-dependent inherent ambiguity of "how energy gets into the cart". So lets see if you agree with this:
Rip out the dive shaft. I say we can attach an electric generator to the wheel axle. This generator provides us with a several kilowatt powerline. We then attach that to an electric motor driving the propeller and consuming the several kilowatts of power
If you agree with that, then we're merely discussing a reference frame ambiguity of "how power gets into the cart". From the point of view of an observer nailed to the ground, you're right.... the forwards force of the air on the prop is adding kinetic energy to the cart, and that energy is obtained by the equal-and-opposite force slowing the air (and reducing the air's kinetic energy).
However from the point of view of an observer "nailed to the airmass", energy is entering the cart through the force of the earth applying a torque to rotate the wheels, and that energy is obtained by the equal-and-opposite force slowing down the earth (and reducing earth's kinetic energy).
In my opinion the second version is often an extremely useful way to explain things. It helps nail down for people the crucial direction of the internal energy flow: The wheels are being used to drive the prop to rotate, and that it's the resulting air-vs-prop force pushing the cart forwards. There's nothing fundamentally incorrect about viewing the energy as coming in through the wheels. It's a frame-dependent interpretation.
The propeller never operates as a windmill. The air doesn't move the prop, the prop moves the air.
Agreed, and agreed.
The forces around the prop blades are the wrong way if you think of it as tacking.
I'm not a sailor, but I've seen numerous knowledgeable sailors declaring that a tacking sail can be the equivalent of either a turbine or a propeller, depending upon the particular tack. You're mistaken that a sail tack can only be equated to a turbine. I could be mistaken on the following detail, but I think downwind tacks have the sail operating like a propeller, and upwind tacks have the sail operating like a turbine. I haven't really focused on that aspect though.
All the sailors I've seen have found it acceptable and extremely illuminating to have the cart-prop explained as a sail on downwind tack, with the wheels acting as the keel. Sailors seem to find that to be an extremely intuitive setup extracting energy from the true-wind.
Well, no. I understand "how it works" just fine, wheras you don't. the net force on the propeller from the wind is directed backwards rotating momentum, which, being transmitted to the wheels, is pushing the craft forward
I'm the article submitter. All of those statements are incorrect. I suggest you look at the MIT analysis paper I linked in the article. You'll see he has force of the air on the propeller pushing the cart forwards. In the paper he drew an underwater turbine, but that fulfills the same role as the wheels. The wheel-ground force is a drag, pulling the cart backwards. This is where the torque is generated to power the rotation of the propeller (fan) in the air.
And to reply to your other post:
Direct downwind faster than wind is impossible with a windmill(turbine). Incorrect.
Again, downwind faster than the wind is impossible using a turbine. One reason is that, at the moment you equal windspeed, there is zero apparent wind which means zero torque can be generated by a turbine. If a "turbine" is rotating while sitting in still air, it in fact expends energy pushing the air in a direction, and this expenditure of energy shows up as a drag (negative torque) slowing down the drive shaft.
However the more fundamental reason that downwind-faster-than-the-wind is impossible using a turbine is that at above windspeed you're trying to use the apparent headwind to drive the turbine. The energy content of this apparent headwind is diminished by the existence of the true-wind, whereas the force of the driven prop is augmented by the existence of the true wind. This means that attempting to use a turbine to extract energy from the apparent headwind imposes a drag, with an energy return deficit equal to true wind.
Energy equals force times distance.
Any attempt to extract power from the slow apparent headwind and expend it driving the fast wheels is a losing proposition. Slow apparent headwind means you have a force times a short air distance in that energy formula. You either obtain little energy or a large drag force. Spending the energy at the fast wheels means a force times a long ground distance in the energy formula. For a given energy, you obtain a small drive force over a long distance at the wheels.
An upwind cart uses a turbine to gather energy(torque) to drive the wheels. A downwind faster than wind cart uses the wheels to gather energy(torque) to drive a propeller like a fan.
You're close to getting it, except the propeller is turning like a fan, not a turbine. (Because it's a fan, the cart doesn't notice anything unusual or even interesting as you pass though the apparent "dead air" when you equal windspeed.)
Each blade of the prop is in a constant corkscrew tack, spiraling downwind. The wheels are like the keel, *forcing* the prop-blades to stay on that particular tack. The cart moves forwards forcing the wheels to turn, with the wheels forcing (powering) the prop to rotate. Note that the keel is essentially a drag force.... the wheels experience a large force trying to drag the cart backwards. The existence of the wind ensures that the lift at the prop(sails) is greater than the drag at the wheels(keel). The net force is forwards. And yeah, you nailed it that it all works because attaching to the ground and the air enables us to tap into the energy of the true wind.
I kind hate sailors and the sailing analogy though. For me it ruins all the fun of debating the "energy problem" a physics perspective. The "How the #$%@! does the wind energy get into the cart when you're sitting in dead air" issue, chuckle.
I don't see this described anywhere, but my bet is that you don't travel faster than the wind in the same direction that the wind is traveling
I prominently stated it when I submitted this article: Directly Downwind Faster Than The Wind, Powered Only By The Wind, Steady State
No cheats. No tricks. Just a very simple machine which is connected in the reverse of the way people expect, and which produces a surprising result that seems impossible, but which isn't.
Understanding it is a fun brainbender. However a caution: It's very common for people to think "that can't be right", and try to "correct the miscommunication" by dismissing or reversing a direct statement such as "Directly Downwind" into "not directly downwind".
Caution: It's also a major stumbling block to understanding when people commonly make that sort of reversal "fixing" parts of the explanation that sound wrong. The way it works is very counterintuitive, and until you pull the whole picture together each of the individual parts of the explanation can sound backwards.
The propeller is not a windmill. The prop is a fan. Always a fan, only a fan. The prop pushes the cart forwards. The prop does not drive the wheels. The wheels drive the prop. The wheels don't push the cart forwards. The wheels try to drag it backwards.
If you miss any of those points, or even worse mentally reverse any of them, it can become very difficult to grok the explanation. To avoid redundancy I'll just note that explained in detail elsewhere, but I'm happy to help with any questions or confusion.
the wheels would do the same thing as a keel
Yeah, if you use a sailing analogy the wheels are like the keel, the prop blades are sails on a constant corkscrew tack, and the drag at the wheels(keel) is what forces the the prop(sail) to travel along that tack.
incorrect. The wind can't push the craft forward - the craft goes faster than the wind, so the net force on the craft from the wind is braking it.
It's unclear whether this is merely a language quibble, or you don't yet understand how it works.
The propeller is exerting a rearward force on the air. Newtons Laws: for every action there is an equal and opposite reaction. If a force exists from the prop towards the air, there also exists and equal and opposite force from the air towards the prop. The air *is* exerting a forwards force on the cart, even when the cart is going above windspeed. And assuming we're not getting into some linguistic quibble distinguishing "the air" from "the wind", then "the air" is the same thing as "the wind", and "the wind" is indeed pushing forwards on the propeller. And again, assuming we're not getting into some linguistic quibbling, "the propeller" is a part of "the craft".
So the net force on the craft, from the wind, is a forwards acceleration. Even when the craft is above windspeed. That's true because the prop is turning (and it's turning like a fan, not a windmill).
Slashdot Mirror
Best Software For Tracking Fiber Optic Networks?
I believe NORAD has the best available tracking software. That might be a bit overkill though, considering the typically zero velocity of fiber optic networks.
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The submitter is either an ass, or he's playing a game provoking people to generate additional arguments for the 5th Amendment, perhaps specifically looking to combat the "give us your password or we'll lock you up" crap.
The submission is to full of fail to bother addressing it all, such as complaining that protections for the innocent sometimes make it harder to convict the guilty. Whaaaaaah! Whaaaaah! Whine!
But there's another fundamental reason that no one seems to have mentioned. The government requires a court ordered search warrant before they can intrusively violate the sanctity of your home. But there is something far more sacrosanct than one's home... one's very MIND. I can't think of anything more intrusive than the government wanting to invade your mind to carry out a "search" of your thoughts. There is nothing more sacrosanct than one's mind. Government agents showing up with guns and locking yuo in handcuffs, and screaming at you "Hand over your THOUGHTS and MEMORIES, or we will imprison you by force, if you resist giving us your thoughts and memories we are authorized to use lethal force if necessary to haul you off and imprison you."
if the government grants you immunity, then your answers cannot incriminate you, but since nothing you say will incriminate you, the government can then force you to answer the question or go to jail for contempt of court. (There is actually no literal "right to remain silent"; it's a "right against self-incrimination". So take away the possibility of self-incrimination, and you have to talk.) This is a controversial exception
Yeah. That's bullshit. The government wants to seize, invade, and search your mind, and the government promises not to imprison you if you comply. FUCK THAT.
And if you decline to comply, the government declares it's going to imprison you... and if you resist they can and will use any and all force, up to and including lethal force, to carry out that imprisonment.
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When a political scandal hits, partisan hacks appear to try and obfuscate the issue. This "article" is an example...
When the administration is found to be unlawfully wiretapping every citizen... well, suddenly we see hacks pop up and say "well, you really didn't need that right anyways, right?".
This is why the homeschooler nuts need to be banned, and we need to do more to ensure toddlers aren't eating lead paint chips.
Because seriously, when you can't make it from one to ten without confusing four and five, one or the other is at fault.
It'd be funny if it wasn't so tragic.
Ummm.... yeah. That.
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if you ever need to find out what it would be like without Amendment X, just crack open a history book.
For a while there I read "Amendment X" as meaning the 10th Amendment, chuckle. That confused me a bit. Anywho, I challenge you or anyone else to crack open a history book and show me how the U.S. would be noticeably different today without the 9th Amendment:
Amendment IX
The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
The U.S. Supreme Court is loath to go within a hundred feet of that amendment. It is probably the Bill-of-Rights amendment mentioned by the Supreme Court the fewer times than any other, rivaled perhaps only by the 3rd Amendment. (The 3rd amendment almost never being addressed simply because the government never attempts to quarter soldiers in private homes). The few times the court has mentioned the 9th Amendment they have only done so only to say essentially "we're not going give it any application, not here, not now, not ever".
The quote Justice Antonin Scalia:
the Constitution's refusal to 'deny or disparage' other rights is far removed from affirming any one of them, and even farther removed from authorizing judges to identify what they might be, and to enforce the judges' list against laws duly enacted by the people.
In other words, the TRUE text of the 9th Amendment reads as follows:
Amendment IX
The Bill of Rights is inherently incomplete and obviously other Rights exist, but we only mention that here to troll you. lolz.
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And all the Chicken Littles running around screaming there will be a global economic collapse if RSA isn't Too Big To Factor.
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Give a banker an algorithm, he can rob the world.
Shore? Sure.
Sieve of Eratosthenes? Not so much.
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if a statement like Beal's conjecture can't be proven, you should be able to prove *that*.
Urk? How did you reach that odd conclusion?
"X is unprovable" is itself a mathematical statement, and I see no reason to actively expect it never to fall into the category of unprovable statements.
I would find it rather surprising if there didn't exist a recursively unprovable chain, and by that I mean a chain where all of the following were unprovable:
X
X1: X is unprovable
X2: X1 is unprovable.
X3: X2 is unprovable.
X(n): X(n-1) is unprovable.
If we want to get meta, it may well be possible to prove that such a chain exists. However it's easy to prove it could only be a non-constructive proof. Any mathematics successfully identifying a specific statement "X" for such a chain would itself constitute a proof of statement X1, in contradiction with the definition of a recursively unprovable chain.
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I've solved the physics for ascertaining that no one is pissing your beer before you drink it.
However it only works for spherical beer in a vacuum.
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One of the common themes in cart discussions is that different people require wildly different sorts of explanations or analogies for it to "click". Once it does click it's not uncommon for people to feel irritated that "it would have been so much easier if you just said X in the first place". Of course the explainer has no way to know in advance which explanation is going to click for any particular person.
I absolutely agree with you that a force/energy calculation is the gold-standard best possible proof that the cart works. Unfortunately most people can't read force/energy calculations. In most cases throwing a wall of numbers their face is... unhelpful.
Also note that the explanation which did work for you demonstrated that the cart can work, but in many ways (and for many people), it's a completely worthless non-explanation of how it works. For many people it still leaves a very . Since you are a calculations-person, check out the almost magical "how" of wind-energy-collection going on in the following calculation:
The wind is going left at 10 m/s, cart is going 20m/s in the same direction. From the point of view of the cart, the air is going 10 m/s to the right. The kinetic energy of 1 kg of air at 10 m/s is 50 joules. (ke=1/2*mv^2). The cart spends energy to run the prop, accelerating the air faster to the right. The air leaves the prop at 12 m/s rightwards In the frame of the cart). The kinetic energy of the air has increased to 72 joules. Simple enough... the cart spends energy running the prop accelerating the air, and naturally energy is transferred from the cart into the air.
But now look at it from the ground frame. The air is a wind going 10 m/s to the left. 1 kg of air has a kinetic energy of 50 joules. The cart prop is pushing that air rightwards, the resulting in 8 m/s in the ground frame. The kinetic energy of this air, in the ground frame, is now 32 joules. 50 joules - 32 joules = 18 joules of energy vanishing from the air. Where does the energy go? The only place it could go is into the cart, and a careful analysis shows the cart's kinetic energy increasing by the power applied to the prop PLUS the energy lost from the air. The power applied to the prop is then subtracted back out by the drag at the wheels. The net result is the wind energy being teleported into the cart. From the ground frame the air energy went *into* the cart (increasing the cart's kinetic energy). This clearly shows the energy being extracted from the wind. But remember what the car's point of view was.... the cart was spending energy running the prop to pump energy OUT of the cart and INTO the air. The cart saw energy flowing in the opposite direction! Doh!
I have no idea where you got the idea that airplanes need millions of horsepower.
Allow me to recap how we got there, from my point of view. I was trying to get across the idea that the prop can generate greater thrust than the drag at the wheels. Pulling energy from the wheels to drive the prop looks like a perpetual motion design, and your natural gut reaction was to apply conservation laws. Trying to use using a generator to power a motor never gives you more out than you put in. So you mentally had me in the "crackpot zone", or at least in the "potential crackpot" zone. You were actively looking to shoot down everything I said. When I tried to explain that it was "harder" for a prop to push against a faster wind, using an example that it was "hard" for a prop against a 100 MPH wind, you answered that it was trivially easy for a prop to push against 100 MPH air. You presented a graph of a half-million horsepower prop thrusting in 100 MPH air.
I rather naturally took your example and pointed out how it would take twice as much power to get the same thrust in air going twice the speed.
I was trying to get across that the ease/difficulty of generating thrust at the prop was completely relative to the air speed. You were countering/challenging that with a completely non-relative disproporti
You'll have to break out the differential equations if you want to calculate what's going on.
No need for differential equations or even calculus. Once the problem is laid out correctly anyone with minimal algebra and minimal familiarity with force/energy conversions can probably follow it.
(Anyone outside the U.S. can simply pretend I wrote meter and kilogram instead of foot and pound. No need for conversions, everything will turn out fine. I promise, grin.)
Lets assume the cart is going to the right at 40 feet per second, and the wind is going to the right at 30 feet per second. That puts the cart faster than the wind, with the apparent headwind passing over the cart. That apparent headwind is 40 feet per second - 30 feet per second = 10 feet per second.
Now we extract power at the wheels. Lets put a 1 pound drag at the wheels, and that force is exerted against the ground which is passing the wheels at 40 feet per second. Power = force * velocity, so we have power = 1 pound * 40 feet per second. Power extracted from the wheels equals 40 foot-pounds per second.
Now we transfer that 40 foot-pounds per second to drive the propeller. The propeller is pushing against the air, and as a reminder the air is passing the propeller at 10 feet per second. What thrust do we get? Again, power = force * velocity. Rearranging that equation to isolate force we get force = power / velocity. So we have force = 40 foot-pounds per second / 10 feet per second. Our thrust force is 4 pounds. The drag on the cart is one pound, the thrust is 4 pound, the net force is 3 pounds of acceleration. The cart is above windspeed and accelerating.
Of course that calculation is for an imaginary cart, it ignores any sort of friction and assumes everything is 100% efficient. But that's ok.... our imaginary 100% efficient proppeller generated an extremely generous 4 pounds of thrust. Any constructed cart with better than 25% net efficiency will generate more than 1 pound of thrust, sufficient to still yield an accelerating cart.
Q.E.D., using nothing more than the simplest algebra and the most basic power = force * velocity energy equation.
At this point it's extremely easy to go back to the beginning and repeat the calculations replacing the cart speed, windspeed, or wheel drag with any other values of interest. Just don't insert values less than zero unless you have high skill in reanalyzing and reinterpreting everything. (Plugging in zero windspeed or zero wheel drag is good for seeing the cart can't speed up in those conditions, and plugging in zero for the cart's initial speed shows that the cart needs wind-drag or some other push to get started.)
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tristes_tigres decided to be obtuse and insist the vehicle was wheel driven
Update:
tristes_tigres finally decided to become acute while observing the prop in a cart video. lol
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I wonder if a mill driven version is feasible
Downwind, below windspeed, you can do it either way. But in this region it also works to hoist a moose on a pole and call it a sail, chuckle.
Downwind, at exactly windspeed, the cart feels dead air. A windmill in dead air collects zero energy to drive the wheels. As you get above windspeed downwind you feel an apparent headwind, but trying to stick a windmill in it is a net drag. The energy of the headwind is your own motion *minus* the true wind. That headwind effectively contains negative-energy as far as wheel drive is concerned.
Downwind faster than the wind only works with the wheels driving a prop.
For an equivalent reason, an upwind cart only works with a windmill driving the wheels. Upwind faster than the wind presents no special issue.
In both directions your windspeed-multiple is capped only by design efficiency, factoring in aerodynamic drag and whatnot. Blackbird gets over 3x downwind and (with a propeller swap and gear change) it gets over 2x upwind.
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What I have eliminated is the windmill.
IMPORTANT: There is no windmill.
This is a roadblock to understanding that trips up most people. As long as you look at the cart and you think you see a windmill.... as long as the word "windmill" pops to mind... you aren't going to be able to get a handle on how the cart works. There is no windmill. The propeller is a fan, always a fan, only a fan.
Note that you have completely eliminated the wind from the system.
No, the wind is still blowing. What I have eliminated is the windmill.
I didn't say the wind ceased to exist. I said you eliminated it from the system. The sun exists. But if the cart doesn't have solar panels, the sun obviously isn't a part of the system
If we're talking about a battery-powered machine, and you eliminate the battery wires, and I point out that you have "removed the batteries from the system", I hope you can see that it comes across as a little silly when you object that the batteries still exist.
This is a wind powered cart. If you are having trouble seeing how the cart taps into that energy, I'll happily do my best to explain it. But simply disconnecting the power source very quickly sends things in a very simple and obvious direction. No magic, no free energy, no perpetual motion... a machine which is not connected to a power source simply and inevitably winds down to a halt. A machine which is connected to a power source can run as long as it's connected, it can accelerate within the bounds of available power, it can tapdance and whistle dixie if it wants. Grin.
Check the "Thrust at Constant Power vs. Airspeed" chart here, where the thrust initially increases with airspeed This is presented as a typical case, not a special or corner one.
It is presented as a "typical case" for aircraft, the graph labels show between a quarter-million horse power and a half million horse power, and the intended performance range is obviously in the 100+ MPH region.
I think you'll agree that it's not very surprising that the left side of the graph, that down-left slope going from 50 MPH to 0 MPH, shows an aircraft prop going into an obvious "fail" region outside the intended operation range. A prop designed for low speed efficiency would have a significantly higher thrust at 50 MPH, and the thrust graph would continue to rise as velocity decreased below 50 MPH.
And you mentioned corner cases - that is exactly what we're examining here. We're looking at what happens at zero MPH, which is an extreme corner case. According to the laws of physics for an ideal 100% efficient device we have:
power = force * velocity
If we flip that to isolate force we get:
force = power / velocity
To simplify lets define a constant power input of 1 unit:
force = 1 / velocity
We are examining the extreme corner case where velocity goes to zero, and in that corner case an ideal prop can generate infinite force. Obviously no real machine is 100 percent efficient, no real machine can generate infinite forces. So as we approach zero a prop or other machine can provide increasing force, but we're running into a corner case and at some point we hit a design limit. At some design point the force generated reaches a maximum and anything more gets lost into inefficiencies.
We obviously don't need ideal infinite force for the cart to successfully work at zero air velocity. All we need is for prop thrust to be greater than wheel drag. A prop designed for low speeds can easily generate double, triple, or several more times as much force in low-velocity or zero-velocity air.
Consider a cart going 30 feet per second in a 20 foot per second MPH wind. The car is going 10 feet per second faster than the wind, so there's 10 feet per second of air going through the prop. Lets put one pound of drag on the wheels. Again, power = force * velocity. Power = 1 pound * 30 feet p
In this case, it's wheels driving a propeller
Right...
but I think the other way could work too.
Nope. Going downwind-faster-than-the-wind requires the wheels to drive the prop. The easiest way to see this is to consider the cart traveling downwind at exactly windspeed. The cart feels like it's sitting in dead air. A windmill in still air collects zero energy. Nothing to drive the wheels. The math gets worse when traveling downwind faster than windspeed. Above windspeed you feel a headwind which can spin a windmill, but any attempt to stick a windmill in this headwind ends up dragging the cart slower.
You can use windmill to drive the wheels for a cart that goes upwind, and it can even go upwind faster than the wind. In fact an upwind cart can only work with the prop driving the wheels for basically the same reason we couldn't use a windmill to drive the downwind cart.
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One side thinks the windmill is a turbine that drives the wheels
I'm the article submitter. I say those people are wrong. They are describing a false or broken design, one which is incapable of going downwind-faster-than-wind. The math states that going downwind-faster-than-wind require wheel powering a propeller. The math also states that going upwind requires a windmill powering the wheels (That's not directly relevant here, but hopefully it's an easier to understand and illuminating mirror image case).
Furthermore, I included in the story a link to the Wikipedia entry on the cart, which states the downwind-windmill idea is wrong.
And I included a link to a physics analysis paper from MIT professor Mark Drela which shows the downwind-windmill idea is wrong
And I included a link to the International Physics Olympiad test with this cart as a sample problem, which includes and answer section explaining the downwind-windmill idea is wrong
And if you like, I can google up a link to the Blackbird builders themselves repeatedly and firmly insisting it's not a windmill cart.
And if you like there are countless videos on line, videos of the large Blackbird as well as videos of small model carts, and a causal visual inspection will easily reveal that propellers on downwind carts always rotate in a fan-like direction, never in a windmill-like direction.
Anywhoo:
For the latter group, I would like to propose a modification
Yep, I'm in the "later group"...
replace the propeller with a generator, and use the power generated to run a linear induction motor which propels the device downwind along a track, which is level, straight and aligned with the wind. You can give the device a push to start it moving, if you like. What happens?
Okey dokey. We strip off the prop and attach the generator directly to the wheels. This is the power we would ordinarily be using to run the prop, but we direct it to a linear induction motor. No prob, simple enough.
Note that you have completely eliminated the wind from the system. The wind was our power source. So the end result is going to be pretty much what you would expect from any cart lacking a power source:
(A) If it's not moving, it simply sits there. It's not going to start moving on it's own.
(B) If you give it a shove, it will be ruled by the basic principals of inertia and frictional-style energy losses. It's coasting at the shove-speed, and over time slows to a stop. The only question is how quickly it's going to slow down. That's determined by friction and inefficiencies and any other losses.
Having a generator at the wheels driving an induction motor does not change that, other than potentially contributing additional energy losses which make it slow down faster. In the ideal case the trust at the induction motor will equal the drag at the wheel-generator, for zero net effect on the coasting-slowing cart.
The reason it does work with the propeller is because of the presence of the wind. (Without the wind, the thrust generated at the prop can only be equal to or less than the drag at the wheels, exactly like in your linear accelerator question.) The wind and the propeller are blowing at each other, pushing against each other. The thrust generated at the prop is effectively the combined effect of the energy driving the prop PLUS the effect of the wind.
Note that this additive effect applies even when the cart is going at or above wind speed. Consider a cart going 100 MPH in zero wind. There is going to be a 100 MPH apparent headwind flowing over the cart. The power-driven prop is going to to be very inefficient and it will struggle trying to generate any significant thrust to the rear in a 100 MPH airflow already heading to the rear The prop would have to spin crazy fast and it's going to yield squat thrust. Now consider a cart going 100 MPH, downwind, in a 100MPH wind. The prop now feels like it's sitting
What they did not do was crash off the roof of a building, because that would be stupid.
Yeah. Because on Mythbusters they would never do anything stupid. lol
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The Blackbird and similar carts are notorious for starting up very slowly. The initial start is from simple wind drag, with the large non-rotating prop acting much like a simple crappy sail increasing the basic wind drag.
Once the prop starts to turn, and while below windspeed, the cart slowly gains speed from a combination of simple wind drag augmented by the wheel-prop-thrust system working at a very low efficiency. I think at low rotation speed the prop blades are like an airplane wing in a stall condition... it can't generate aerodynamic lift when the air is just hitting the flat side of the blade and turbulently swirling over the edges. Anywho.... starting up from a dead stop is crap.
In the Blackbird test runs there's a point, I think in the ballpark of 75% of windspeedish, where it crosses a threshold and the prop gets a better bite on the air. I think at this point the prop blades are escaping the stall condition and they start generating true wing-type aerodynamic lift. The efficiency jumps and the cart starts to accelerate briskly. It then powers through windspeed and aggressively surges to either peak speed or until the drive chain snaps, whichever comes first. They generally run in a windspeed less than 20 MPH, and even with those light winds the peak torque in the driveshaft is comparable to the torque put out by a V8 engine, several hundred footpounds. The conflict between the prop pushing forwards against the wheels actively dragging backwards means that the drive shaft is under several times higher torque and power transfer than a simple car would experience at the same speed. As it picks up speed the prop is able to harvest the wind energy more rapidly from a greater volume of air, so as the speed picks up it starts cranking out pretty massive horsepower.
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At the risk of beating a dead analogy horse, the wheel/prop_axle system can be considered reasonable analogous to a keel. The function of a keel is to constrain the available path of motion of the sail when the wind pushes on it. In particular the sail, via the keel, pushes against the water-medium in such a way as to constrain the sail to moving nearly 90-degrees off from the direction of the wind force. Equivalently, the wind force on the prop gets transferred through the keel (the axles and wheels) such that that force presses against the ground-medium in such a way as to constrain the sail to moving nearly 90-degrees off from the direction of the wind force. The cart transfers this force from the prop to the ground along a more complicated path than a ship keel transferring sail force against the water, but the the force transfer is equivalent, and the result is the same. The keel constrains the sail to sideways across the wind, and the cart keep constrains the prop blade to sliding sideways (where that sideways is bent in a circle).
In both cases the keel causes the wind-on-wing-force on the wing to reflect back at the wing in a sideways direction.
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Ahh, now I'm looking at the source equations in the International Physics Olympiad and I see I misinterpreted the reference frames of the equations you posted. (You translated the variable "v" into "v_land", which threw me off. Writing it as v_cart would have been much clearer.)
So, trying again.
quoteSo evidently this equation only holds in steady state not in development.
Yeah. They state "the force due to air and the force due to ground must balance", so they are specifically analyzing the cart at steady-state peak speed, where prop force and wheel force sum to zero.
F * v_land = (1-alpha) * F * (v_land - v_wind)
You appear to have mis-copied that one. The equation should read:
F * (v_land - v_wind) = (1-alpha) * F * v_land
put in that magic moment when V_land-V_wind = 0, for another silly result.
V_land-V_wind = 0 puts the cart at windspeed, at which time it is accelerating. Acceleration means that the prop force and wheel force are out of balance. Any such equation will involve two differing F values.
V_land < V_wind. That is where we have not yet exceeded the wind speed.
I inserted a < in there, which I assume you intended but which Slashdot eats unless you type < to get <
Anywho, again you're looking at a case of an accelerating cart involving different wheel and prop forces. Any equation with a single F value is going to be nonsensical.
F * v_land = (1-alpha) * F * (v_land - v_wind)
postitive number = negative number
That's the mis-copied equation again. I'm pretty sure you wanted:
F * (v_land - v_wind) = (1-alpha) * F * v_land
In any case, it's an equation doe a faster-than-wind-cart at peak speed. Therefore v_land > v_wind, and v_land-v_wind > 0. In other words both sides have the same sign as F, and therefore have the same sign as each other. (Unless of course alpha is > 1, which would be a machine with greater than 100% energy loss, chuckle.)
I'm saying that despite the energy argument, the force argument is subtle and completley hidden in the above steady state energy argument.
I'm not sure if this will answer what you want, but some time ago I worked out the complete force and energy calculations for an accelerating cart. If you can follow it you can (hopefully) see where and why the propeller thrust turns out larger than the wheel drag. The short answer is that work = force * distance. The wheels roll a long distance over the ground, in comparison to a shorter distance of air through the prop. The differences in distances can trade off against a difference in forces. A small force at the wheels (pushing against a long distance of ground) can do enough work to generate a large force at the prop (pushing against a short distance of air).
http://talkrational.org/showpost.php?p=1278991&postcount=311
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I'm not sure if we fundamentally disagree on the operation of the cart, or if you're quibbling over a reference-frame-dependent inherent ambiguity of "how energy gets into the cart". So lets see if you agree with this:
Rip out the dive shaft. I say we can attach an electric generator to the wheel axle. This generator provides us with a several kilowatt powerline. We then attach that to an electric motor driving the propeller and consuming the several kilowatts of power
If you agree with that, then we're merely discussing a reference frame ambiguity of "how power gets into the cart". From the point of view of an observer nailed to the ground, you're right.... the forwards force of the air on the prop is adding kinetic energy to the cart, and that energy is obtained by the equal-and-opposite force slowing the air (and reducing the air's kinetic energy).
However from the point of view of an observer "nailed to the airmass", energy is entering the cart through the force of the earth applying a torque to rotate the wheels, and that energy is obtained by the equal-and-opposite force slowing down the earth (and reducing earth's kinetic energy).
In my opinion the second version is often an extremely useful way to explain things. It helps nail down for people the crucial direction of the internal energy flow: The wheels are being used to drive the prop to rotate, and that it's the resulting air-vs-prop force pushing the cart forwards. There's nothing fundamentally incorrect about viewing the energy as coming in through the wheels. It's a frame-dependent interpretation.
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The propeller never operates as a windmill.
The air doesn't move the prop, the prop moves the air.
Agreed, and agreed.
The forces around the prop blades are the wrong way if you think of it as tacking.
I'm not a sailor, but I've seen numerous knowledgeable sailors declaring that a tacking sail can be the equivalent of either a turbine or a propeller, depending upon the particular tack. You're mistaken that a sail tack can only be equated to a turbine. I could be mistaken on the following detail, but I think downwind tacks have the sail operating like a propeller, and upwind tacks have the sail operating like a turbine. I haven't really focused on that aspect though.
All the sailors I've seen have found it acceptable and extremely illuminating to have the cart-prop explained as a sail on downwind tack, with the wheels acting as the keel. Sailors seem to find that to be an extremely intuitive setup extracting energy from the true-wind.
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Well, no. I understand "how it works" just fine, wheras you don't.
the net force on the propeller from the wind is directed backwards
rotating momentum, which, being transmitted to the wheels, is pushing the craft forward
I'm the article submitter. All of those statements are incorrect. I suggest you look at the MIT analysis paper I linked in the article. You'll see he has force of the air on the propeller pushing the cart forwards. In the paper he drew an underwater turbine, but that fulfills the same role as the wheels. The wheel-ground force is a drag, pulling the cart backwards. This is where the torque is generated to power the rotation of the propeller (fan) in the air.
And to reply to your other post:
Direct downwind faster than wind is impossible with a windmill(turbine).
Incorrect.
Again, downwind faster than the wind is impossible using a turbine. One reason is that, at the moment you equal windspeed, there is zero apparent wind which means zero torque can be generated by a turbine. If a "turbine" is rotating while sitting in still air, it in fact expends energy pushing the air in a direction, and this expenditure of energy shows up as a drag (negative torque) slowing down the drive shaft.
However the more fundamental reason that downwind-faster-than-the-wind is impossible using a turbine is that at above windspeed you're trying to use the apparent headwind to drive the turbine. The energy content of this apparent headwind is diminished by the existence of the true-wind, whereas the force of the driven prop is augmented by the existence of the true wind. This means that attempting to use a turbine to extract energy from the apparent headwind imposes a drag, with an energy return deficit equal to true wind.
Energy equals force times distance.
Any attempt to extract power from the slow apparent headwind and expend it driving the fast wheels is a losing proposition. Slow apparent headwind means you have a force times a short air distance in that energy formula. You either obtain little energy or a large drag force. Spending the energy at the fast wheels means a force times a long ground distance in the energy formula. For a given energy, you obtain a small drive force over a long distance at the wheels.
An upwind cart uses a turbine to gather energy(torque) to drive the wheels. A downwind faster than wind cart uses the wheels to gather energy(torque) to drive a propeller like a fan.
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You're close to getting it, except the propeller is turning like a fan, not a turbine. (Because it's a fan, the cart doesn't notice anything unusual or even interesting as you pass though the apparent "dead air" when you equal windspeed.)
Each blade of the prop is in a constant corkscrew tack, spiraling downwind. The wheels are like the keel, *forcing* the prop-blades to stay on that particular tack. The cart moves forwards forcing the wheels to turn, with the wheels forcing (powering) the prop to rotate. Note that the keel is essentially a drag force.... the wheels experience a large force trying to drag the cart backwards. The existence of the wind ensures that the lift at the prop(sails) is greater than the drag at the wheels(keel). The net force is forwards. And yeah, you nailed it that it all works because attaching to the ground and the air enables us to tap into the energy of the true wind.
I kind hate sailors and the sailing analogy though. For me it ruins all the fun of debating the "energy problem" a physics perspective. The "How the #$%@! does the wind energy get into the cart when you're sitting in dead air" issue, chuckle.
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I don't see this described anywhere, but my bet is that you don't travel faster than the wind in the same direction that the wind is traveling
I prominently stated it when I submitted this article:
Directly Downwind Faster Than The Wind, Powered Only By The Wind, Steady State
No cheats. No tricks. Just a very simple machine which is connected in the reverse of the way people expect, and which produces a surprising result that seems impossible, but which isn't.
Understanding it is a fun brainbender. However a caution: It's very common for people to think "that can't be right", and try to "correct the miscommunication" by dismissing or reversing a direct statement such as "Directly Downwind" into "not directly downwind".
Caution: It's also a major stumbling block to understanding when people commonly make that sort of reversal "fixing" parts of the explanation that sound wrong. The way it works is very counterintuitive, and until you pull the whole picture together each of the individual parts of the explanation can sound backwards.
The propeller is not a windmill. The prop is a fan. Always a fan, only a fan.
The prop pushes the cart forwards.
The prop does not drive the wheels. The wheels drive the prop.
The wheels don't push the cart forwards. The wheels try to drag it backwards.
If you miss any of those points, or even worse mentally reverse any of them, it can become very difficult to grok the explanation. To avoid redundancy I'll just note that explained in detail elsewhere, but I'm happy to help with any questions or confusion.
the wheels would do the same thing as a keel
Yeah, if you use a sailing analogy the wheels are like the keel, the prop blades are sails on a constant corkscrew tack, and the drag at the wheels(keel) is what forces the the prop(sail) to travel along that tack.
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incorrect. The wind can't push the craft forward - the craft goes faster than the wind, so the net force on the craft from the wind is braking it.
It's unclear whether this is merely a language quibble, or you don't yet understand how it works.
The propeller is exerting a rearward force on the air. Newtons Laws: for every action there is an equal and opposite reaction. If a force exists from the prop towards the air, there also exists and equal and opposite force from the air towards the prop. The air *is* exerting a forwards force on the cart, even when the cart is going above windspeed. And assuming we're not getting into some linguistic quibble distinguishing "the air" from "the wind", then "the air" is the same thing as "the wind", and "the wind" is indeed pushing forwards on the propeller. And again, assuming we're not getting into some linguistic quibbling, "the propeller" is a part of "the craft".
So the net force on the craft, from the wind, is a forwards acceleration. Even when the craft is above windspeed.
That's true because the prop is turning (and it's turning like a fan, not a windmill).
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