Doh! I know exactly what happened. That part was small and blurry, and in my initial scan over the graph, before I sorted out what the graph wa showing, it looked like "kp". A corner of my brain thought WTF is "kp", and I kept scanning elsewhere for information. I saw the speeds across the bottom and the thrusts on the left and I recognized the shape of the graph, then saw the HP vs MPH title at the top. I realized the different color lines had to be different engine inputs and I glanced back at that top-right box to confirm it.... that it was listing different HP engine inputs.... and that "k" from "kp" was still lingering in my brain. chuckle. So the blurry "h" was read twice, once as "k" and once as "h". The 250khp to 500khp power figures did strike me as unreasonably large, but I wasn't going to doubt the graph and my attention was absorbed on other issues. Sso without further consideration I just mentally filed it away as presumptively plausible values for a top end (?military?) engine.

Ohhhh noooooo! You didn't...... cry cry cry. LoL.
I follow your reasoning, and it is a kinda cool point, but oh jezus I wish you didn't make that analogy. The prop is NOT spinning as a turbine, and I know that you know that it's not spinning as a turbine, but someone is going to read what you wrote and think that one or both of us said it's a turbine. Newbies already have a hard time wrapping their heads around the idea that the prop is a fan. Any whiff of describing it as a turbine feeds badly into the exact "contradictory explanations" that set off alarm bells for you.

I wish. You and I went to significantly above average highschools. The majority of U.S. highschool graduates only have one year of science, and it's generally something very generic like "Earth science" or something. It's only in the last few years that most highschools have moved to a two year science requirement, and even then, what percentage are going to include force-energy physics? I think the most common is a year of Bio, and even there most schools avoid or actively deny Evolution in that class :/

What happened there is an entirely arbitrary and semi-self-contradictory cornercase crawling out of the simplifying assumptions. They started with a model of an ideal (frictionless) cart, and then to model a "real" cart they lumped together all losses... including rolling friction.... into one term alpha. They then set alpha to total energy loss... and they were still modeling that alpha on an ideal frictionless cart. They also silently and arbitrarily assumed wind drag *wasn't* zero, despite the opposite parallel assumption of zero rolling resistance. chuckle.

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They say the only computer that can't be hacked is one that unplugged... but when your adversary is (apparently) a U.S. or Israeli Intelligence Agency, even that's not going to save you.

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The HTML code for extracapslock is <B>, like this:
"the <B>WORST WORST WORST</B> idea ever."

The HTML code for doubleextracapslock is <B><BLINK>, but most browsers don't support it because only fucktards use doubleextracapslock.

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In related news, an oil refinery did not explode today. Police and rescue workers report recovering zero dead bodies thus far from the fully intact structure. It is feared that the final death toll may rise as high as zero. We have no reporters live on the scene, so stay tuned for more breaking coverage as it doesn't happen.

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That's great in theory, but evolved monkeys are generally in short supply. Companies usually have to hire the regular kind.

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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."

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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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.

Ummm.... yeah. That.

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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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Shore? Sure.

Sieve of Eratosthenes? Not so much.

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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!

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 disproportionate example calling it "easy" to push against 100 MPH air.... and the gross million horsepower number was deliberately highlighting how the objection had wandered off in a flawed/silly direction.

Yeah, although the interpretation "efficiency" be context-dependent, depending on what we are trying to obtain. Prop power efficiency breaks down at low speed, but to get the cart to work what we actually desire at the prop force, greater force than the drag at the wheels. Props are more efficient at converting power into force at low (or zero) airspeed. Perhaps it would be better wording to say the prop is "more effective" at producing force under those conditions.

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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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