Does Betteridge's Law apply to this question?
May 29, 2021 11:44 AM Subscribe
Everybody knows that switching doors doubles your chance of a win. Everybody knows that the airplane will take off from the treadmill. But can a wind-driven surface craft run directly downwind faster than the wind? (Veritasium, YouTube, 22 minutes)
I’m interested in the seeming paradox that I’ve heard discussed on Car Talk a couple of times related to “drafting” behind a truck on the freeway.
A car following right behind a truck will use less power to maintain its speed and thus enjoys improved gas mileage. You might think this would necessarily increase the power required for the truck to maintain its speed, but it doesn’t.
posted by chrchr at 12:17 PM on May 29, 2021
A car following right behind a truck will use less power to maintain its speed and thus enjoys improved gas mileage. You might think this would necessarily increase the power required for the truck to maintain its speed, but it doesn’t.
posted by chrchr at 12:17 PM on May 29, 2021
You might think this would necessarily increase the power required for the truck to maintain its speed, but it doesn’t.
Why would somebody think this ?
posted by Pendragon at 12:39 PM on May 29, 2021 [1 favorite]
Why would somebody think this ?
posted by Pendragon at 12:39 PM on May 29, 2021 [1 favorite]
I would think it actually decreased the aerodynamic drag on the truck.
posted by aubilenon at 12:47 PM on May 29, 2021
posted by aubilenon at 12:47 PM on May 29, 2021
Why would somebody think this ?
Analogy to a tow rope. If the truck is pulling me forward, I must be extracting energy from the truck. The idea that I'm extracting energy from the turbulence which is always in the truck's wake is counterintuitive; it's surprising that so much energy is being stored invisibly in the air, in the wake of every vehicle.
posted by justsomebodythatyouusedtoknow at 12:52 PM on May 29, 2021 [4 favorites]
Analogy to a tow rope. If the truck is pulling me forward, I must be extracting energy from the truck. The idea that I'm extracting energy from the turbulence which is always in the truck's wake is counterintuitive; it's surprising that so much energy is being stored invisibly in the air, in the wake of every vehicle.
posted by justsomebodythatyouusedtoknow at 12:52 PM on May 29, 2021 [4 favorites]
Why would somebody think this ?
It seems reasonable that a truck which is pulling another vehicle along in its wake would consume fuel more rapidly than a truck which is pulling only a turbulent low-pressure air system. Certainly towing another vehicle on a hitch costs more fuel that towing the empty hitch.
But in the case of highway drafting, both the truck and the car have their engines running: the truck isn’t doing all, or even necessarily most, of the work of pulling the car along in its wake. In that case it’s possible that reducing the size of the turbulent region (by putting a car in it) would reduce the power needed by both vehicles.
posted by fantabulous timewaster at 12:54 PM on May 29, 2021
It seems reasonable that a truck which is pulling another vehicle along in its wake would consume fuel more rapidly than a truck which is pulling only a turbulent low-pressure air system. Certainly towing another vehicle on a hitch costs more fuel that towing the empty hitch.
But in the case of highway drafting, both the truck and the car have their engines running: the truck isn’t doing all, or even necessarily most, of the work of pulling the car along in its wake. In that case it’s possible that reducing the size of the turbulent region (by putting a car in it) would reduce the power needed by both vehicles.
posted by fantabulous timewaster at 12:54 PM on May 29, 2021
it's surprising that so much energy is being stored invisibly in the air, in the wake of every vehicle.
Indeed. (Just Have a Think, YouTube, 12 minutes)
posted by flabdablet at 12:58 PM on May 29, 2021 [3 favorites]
Indeed. (Just Have a Think, YouTube, 12 minutes)
posted by flabdablet at 12:58 PM on May 29, 2021 [3 favorites]
(NB: this comment is unrelated to the truck drafting business.) For me the thought exercise that helps for thinking about the vehicle from the video is to imagine a make-believe alternative version of the vehicle that's very, very long.
Instead of a propeller, it has a "sail on a rail". There's a long rail that goes from the nose to the tail, and then there's a little cart on the "nose-to-tail sail rail" that has a big square sail attached to it. Nothing fancy --- you can just imagine a big board, like a protester's sign.
The cart has got a chain drive that's attached to the vehicle's wheels (not the cart's wheels) in such a way that when you roll the whole vehicle forward, the sail moves backward along the rail. It works the other way, too --- you could imagine a giant pinching the sail between their finger and their thumb, and when they push the sail ahead a bit, the rest of the vehicle zips along underneath the sail even faster. The chain drive is just set up with that kind of gearing.
(Hint: the giant is the wind. But to elaborate...)
Now we set the thing out in the breeze. The wind pushes on the sail, and that sets the whole vehicle rolling a bit. But the chain drive causes the rest of the vehicle to roll ahead a little further than the sail goes. After enough breeze, the sail matches the speed of the wind --- that's as fast as it can go --- but the part underneath the sail is scooting ahead even faster!
Now eventually our vehicle's going to run out of rail for the sail. That's why the propeller attached to the wheels is a handy alternative! As it slices through the air, the angled pitch of the propeller means that if we take any one line parallel to the vehicle's direction of motion, we'll see that the rear surface of the propeller rushes backward along the line, relative to the vehicle. It's doing the same thing the sail-on-a-rail did!
(Now, it might be a little more complicated than this: wind doesn't stubbornly go in a straight line when it meets an angled surface, for example. I'd like to know whether this thought experiment reflects a useful intuition, or if it's wrong in ways I can learn from. A video that shows whether the rear surface of the propeller really does what I've said it does --- or not --- would be really helpful!)
posted by tss at 1:01 PM on May 29, 2021
Instead of a propeller, it has a "sail on a rail". There's a long rail that goes from the nose to the tail, and then there's a little cart on the "nose-to-tail sail rail" that has a big square sail attached to it. Nothing fancy --- you can just imagine a big board, like a protester's sign.
The cart has got a chain drive that's attached to the vehicle's wheels (not the cart's wheels) in such a way that when you roll the whole vehicle forward, the sail moves backward along the rail. It works the other way, too --- you could imagine a giant pinching the sail between their finger and their thumb, and when they push the sail ahead a bit, the rest of the vehicle zips along underneath the sail even faster. The chain drive is just set up with that kind of gearing.
(Hint: the giant is the wind. But to elaborate...)
Now we set the thing out in the breeze. The wind pushes on the sail, and that sets the whole vehicle rolling a bit. But the chain drive causes the rest of the vehicle to roll ahead a little further than the sail goes. After enough breeze, the sail matches the speed of the wind --- that's as fast as it can go --- but the part underneath the sail is scooting ahead even faster!
Now eventually our vehicle's going to run out of rail for the sail. That's why the propeller attached to the wheels is a handy alternative! As it slices through the air, the angled pitch of the propeller means that if we take any one line parallel to the vehicle's direction of motion, we'll see that the rear surface of the propeller rushes backward along the line, relative to the vehicle. It's doing the same thing the sail-on-a-rail did!
(Now, it might be a little more complicated than this: wind doesn't stubbornly go in a straight line when it meets an angled surface, for example. I'd like to know whether this thought experiment reflects a useful intuition, or if it's wrong in ways I can learn from. A video that shows whether the rear surface of the propeller really does what I've said it does --- or not --- would be really helpful!)
posted by tss at 1:01 PM on May 29, 2021
aubilenon: "I would think it actually decreased the aerodynamic drag on the truck."
In fact, this is (or can be) true. When vehicle A has vehicle B drafting off it, vehicle A can see a tiny decrease in aerodynamic drag because some of the air flows around both vehicles, rather than getting sucked into vehicle A's wake and creating turbulence.
posted by adamrice at 1:03 PM on May 29, 2021 [2 favorites]
In fact, this is (or can be) true. When vehicle A has vehicle B drafting off it, vehicle A can see a tiny decrease in aerodynamic drag because some of the air flows around both vehicles, rather than getting sucked into vehicle A's wake and creating turbulence.
posted by adamrice at 1:03 PM on May 29, 2021 [2 favorites]
I've also had my mind blown by the idea of sailing upriver with no wind and only a sail for power.
posted by clawsoon at 1:03 PM on May 29, 2021 [2 favorites]
posted by clawsoon at 1:03 PM on May 29, 2021 [2 favorites]
Looking just at the first few seconds, if you have to build a propeller to do it then I'm going to guess that the answer is: technically yes, but once you start adding moving parts you subtly change the nature of the question.
posted by JHarris at 1:38 PM on May 29, 2021
posted by JHarris at 1:38 PM on May 29, 2021
The propeller changes the problem less than you’re expecting. If you want a two-minute explanation, watch from 6:45 to 8:45, when they explain how outrunning the wind on a sailboat works, and then connect the sailboat to the prop.
posted by fantabulous timewaster at 2:46 PM on May 29, 2021
posted by fantabulous timewaster at 2:46 PM on May 29, 2021
That Ask thread linked above also had a cool visualization involving gears similar to tss's comment.
posted by RobotVoodooPower at 2:59 PM on May 29, 2021 [2 favorites]
posted by RobotVoodooPower at 2:59 PM on May 29, 2021 [2 favorites]
And linked from a video that's linked from that visualization: a little ruler-powered cart that goes faster than the ruler that's pushing it.
posted by flabdablet at 3:22 PM on May 29, 2021 [8 favorites]
posted by flabdablet at 3:22 PM on May 29, 2021 [8 favorites]
Next in that series: the analog of the boat that sails upstream against the current in still air.
posted by flabdablet at 3:27 PM on May 29, 2021 [2 favorites]
posted by flabdablet at 3:27 PM on May 29, 2021 [2 favorites]
I know that vessels can tack downwind with a net downwind velocity faster than the wind that propels them. A pair of such vessels tacking in opposite directions could tow a third vessel directly downwind, which would consequently move faster than the wind propelling the leading vessels. Intuitively, one should be able to construct a single vessel that incorporates sails which perform the same task as the two leading sailboats in our thought experiment, and would by itself move downwind at a speed greater than the wind.
posted by Joe in Australia at 4:10 PM on May 29, 2021 [1 favorite]
posted by Joe in Australia at 4:10 PM on May 29, 2021 [1 favorite]
Intuitively, one should be able to construct a single vessel that incorporates sails which perform the same task as the two leading sailboats in our thought experiment, and would by itself move downwind at a speed greater than the wind.
That's one of the explanations in the video. You can imagine the two blades of the propellor like two sailboats at a continuous tack against the wind.
posted by Popular Ethics at 5:44 PM on May 29, 2021 [2 favorites]
That's one of the explanations in the video. You can imagine the two blades of the propellor like two sailboats at a continuous tack against the wind.
posted by Popular Ethics at 5:44 PM on May 29, 2021 [2 favorites]
Does Betteridge's Law apply to this question?On behalf of Star Trek computers everywhere, thanks a lot, jerk.
posted by gelfin at 6:05 PM on May 29, 2021 [8 favorites]
Here's how I'm thinking about it after watching the video: it's getting motive power from the difference between wind speed and ground speed. The wind pushes it up to wind speed, and the wheels on the ground then turn the propellar that pull it faster. The wind is pushing and making it cost basically zero propulsion to move at wind speed, even syphoning some power to turn a gear, and that gear then provides additional propulsion. If the wind stops there's nothing pushing it forward, and therefore nothing turning the wheels, and therefore nothing turning the propellar. It's that wind vs ground speed difference that makes it work.
posted by PennD at 6:18 PM on May 29, 2021 [2 favorites]
posted by PennD at 6:18 PM on May 29, 2021 [2 favorites]
Humans just don't understand invisible fluids. The pandemic also showed us this.
Everyone needs to go back to flying kites and riding bikes to understand
posted by eustatic at 7:09 PM on May 29, 2021 [3 favorites]
Everyone needs to go back to flying kites and riding bikes to understand
posted by eustatic at 7:09 PM on May 29, 2021 [3 favorites]
I thought I understood it midway through the video with the sails on a cylindrical world analogy. I mean, I have to press the "I believe" button a bit there - I know sailboats go faster than the wind in a straight line on a broad reach, but the directly-downwind component being faster than the wind? Not what I would guess but... ok, that doesn't seem to be controversial.
But that's NOT how it works, so I don't know why he even brought it up. I don't think he did a very good job of explaining how it DOES work, because I'm still guessing. Wind pushing the car downwind against the sail (propeller) makes the wheels turn, which is chain driven to the wheels to spin faster than the wind would spin it? So you have wind force PLUS propeller force, which would have to be more than wind force alone. (?)
But now you're doing work with the wheels, which should slow down the car. But the net of the propeller propulsion minus the wheel drag is still positive? I would say [citation needed], but I guess I've just seen it.
posted by ctmf at 8:28 PM on May 29, 2021
But that's NOT how it works, so I don't know why he even brought it up. I don't think he did a very good job of explaining how it DOES work, because I'm still guessing. Wind pushing the car downwind against the sail (propeller) makes the wheels turn, which is chain driven to the wheels to spin faster than the wind would spin it? So you have wind force PLUS propeller force, which would have to be more than wind force alone. (?)
But now you're doing work with the wheels, which should slow down the car. But the net of the propeller propulsion minus the wheel drag is still positive? I would say [citation needed], but I guess I've just seen it.
posted by ctmf at 8:28 PM on May 29, 2021
It's that wind vs ground speed difference that makes it work.
Same as a tacking sailboat. Without the keel to react against the stationary water, you just go downwind at the speed of the wind.
posted by Popular Ethics at 8:35 PM on May 29, 2021 [1 favorite]
Same as a tacking sailboat. Without the keel to react against the stationary water, you just go downwind at the speed of the wind.
posted by Popular Ethics at 8:35 PM on May 29, 2021 [1 favorite]
I'm reminded of the infamous "airplane on a treadmill" episode of Mythbusters, which people argue about to this day (even though that's a comparatively obvious effect, relative to this one). The bottom line here is that Internet commenters should not, as a rule, be trusted to have good intuitions about how gasses interact with objects in physical systems particularly when there is either a transfer of energy or vehicular thrust involved.
posted by belarius at 8:39 PM on May 29, 2021 [1 favorite]
posted by belarius at 8:39 PM on May 29, 2021 [1 favorite]
This is fun. My mind is not around it fully. But it seems like one way to think of it is that you stop running downwind relative to stationary ground and start running upground relative to stationary wind. Are there any kind of prop or hydrofoil setups that might be able to work like this?
posted by dsword at 9:04 PM on May 29, 2021
posted by dsword at 9:04 PM on May 29, 2021
I don't get it yet but this is so cool to think about. I'm stuck because, making the propeller spin while the vehicle is at windspeed seems to be an "inertial disequilibrium", in that it cannot possibly remain at that speed; something has to give. But then, how did the system progress to that critical moment? Evidently it does reach that state.
Maybe a numerical computer simulation could show exactly all the things that are happening over the process, starting from standstill to final speed.
posted by polymodus at 11:39 PM on May 29, 2021
Maybe a numerical computer simulation could show exactly all the things that are happening over the process, starting from standstill to final speed.
posted by polymodus at 11:39 PM on May 29, 2021
I'm stuck because, making the propeller spin while the vehicle is at windspeed seems to be an "inertial disequilibrium", in that it cannot possibly remain at that speed; something has to give.
Consider the cart as a black box; ignore all its internal organization.
Now consider the work done on the cart by the wind, and the work done by the cart in overcoming various kinds of friction including drag.
As long as the rate at which work is done on the cart is greater than the rate at which work is done by the cart - that is, as long as the applied power is greater than the loss power - then the cart will accelerate. There's your inertial disequilibrium, and it's fine.
The reason that this propellor cart is counter-intuitive is that we instinctively see the case of a cart running freely downwind, moving at the same groundspeed as the wind on frictionless wheels, as a limiting case. But that's not so much a limiting case as a special case, a case where power applied to and power lost by the cart - power related to drag in both cases - are both reduced to zero as the cart's airspeed also drops to zero.
But there are ways to achieve an equilibrium between power applied by the wind and power lost to drag where both of those numbers remain nonzero at equilibrium, and this cart demonstrates one of them. In all such cases there will necessarily be nonzero forces appearing between cart and ground at equilibrium.
I note in passing that even in the frictionless-wheels special case, at equilibrium cart speed the tops of the wheels are running downwind at twice the windspeed.
posted by flabdablet at 3:48 AM on May 30, 2021 [2 favorites]
Consider the cart as a black box; ignore all its internal organization.
Now consider the work done on the cart by the wind, and the work done by the cart in overcoming various kinds of friction including drag.
As long as the rate at which work is done on the cart is greater than the rate at which work is done by the cart - that is, as long as the applied power is greater than the loss power - then the cart will accelerate. There's your inertial disequilibrium, and it's fine.
The reason that this propellor cart is counter-intuitive is that we instinctively see the case of a cart running freely downwind, moving at the same groundspeed as the wind on frictionless wheels, as a limiting case. But that's not so much a limiting case as a special case, a case where power applied to and power lost by the cart - power related to drag in both cases - are both reduced to zero as the cart's airspeed also drops to zero.
But there are ways to achieve an equilibrium between power applied by the wind and power lost to drag where both of those numbers remain nonzero at equilibrium, and this cart demonstrates one of them. In all such cases there will necessarily be nonzero forces appearing between cart and ground at equilibrium.
I note in passing that even in the frictionless-wheels special case, at equilibrium cart speed the tops of the wheels are running downwind at twice the windspeed.
posted by flabdablet at 3:48 AM on May 30, 2021 [2 favorites]
Another way to think about what this cart is doing is that it's continuously constructing a large sail behind and around itself that's made of air, upon which the full force of the prevailing wind can bear.
That huge gaseous sail is not travelling with the cart; it's being continuously constructed by the cart and also continuously destroyed by wind at its edges. This is how it can offer resistance to the wind behind it in order to pick up energy from it and couple that to the cart, while not itself losing that energy to drag.
And in fact there will probably be a range of cart speeds in which there exists a positive feedback between the groundspeed of the cart and the size of the gas sail it builds and therefore the amount of power that the gas sail couples to the cart. This will be why all those people were yelling at Derek to slow the thing down near the end of his run.
posted by flabdablet at 5:09 AM on May 30, 2021 [2 favorites]
That huge gaseous sail is not travelling with the cart; it's being continuously constructed by the cart and also continuously destroyed by wind at its edges. This is how it can offer resistance to the wind behind it in order to pick up energy from it and couple that to the cart, while not itself losing that energy to drag.
And in fact there will probably be a range of cart speeds in which there exists a positive feedback between the groundspeed of the cart and the size of the gas sail it builds and therefore the amount of power that the gas sail couples to the cart. This will be why all those people were yelling at Derek to slow the thing down near the end of his run.
posted by flabdablet at 5:09 AM on May 30, 2021 [2 favorites]
It makes some sense to me at least in a thermodynamic sense. The cross section of the props is the area you have to collect energy from the wind. And I think that once it gets moving a bit the props work as a fan that creates a big mass of air moving backwards relative to the vehicle that the wind can push against (which then makes the props push harder). So it doesn't seem like perpetual motion to me, just really cool counter-intuitive physics.
Fortunately that's as far as my physics knowledge extends and I have no way of calculating anything close to the actual numbers involved so I can't disprove any of this to myself.
posted by VTX at 7:03 AM on May 30, 2021
Fortunately that's as far as my physics knowledge extends and I have no way of calculating anything close to the actual numbers involved so I can't disprove any of this to myself.
posted by VTX at 7:03 AM on May 30, 2021
This is fascinating and surprising. (Which doesn't mean it isn't real. I've written several homework questions about tippe tops and still find their existance hard to fully accept.) Neat!
The explanation given in the video, as I understand it - the wind pushes on the car frame, which drives the wheels, which are linked to the propeller, which makes it go faster - sounds like nonsense. Once you're traveling faster than the wind, the wind isn't pushing on the car frame in the right direction at all. It's not impossible I just misunderstood the explanation, but if so, it could have been much clearer.
My naive guess is that what's actually happens involves the interaction of the wind with the air flow behind the propeller; the vessel is essentially slowing down a large volume of the wind behind it and using a bit of that lost energy to drive itself forward. Which is weird. But, using a stationary windmill to power an electric car that travels faster than the wind doesn't seem at all weird, which isn't fundamentally that different.
I'd love to see someone actually try to simulate what's happening in detail. It's a hard problem, but not that hard compared to what aerospace grad students do every day. The natural skeptic in me also wants to see someone check for batteries and electric motors in the car. Not because this is impossible. Just because the people who built it can't seem to explain it in a way that I understand, which always makes me suspicious. But, lots of people invent things they don't really understand.
posted by eotvos at 8:10 AM on May 30, 2021
The explanation given in the video, as I understand it - the wind pushes on the car frame, which drives the wheels, which are linked to the propeller, which makes it go faster - sounds like nonsense. Once you're traveling faster than the wind, the wind isn't pushing on the car frame in the right direction at all. It's not impossible I just misunderstood the explanation, but if so, it could have been much clearer.
My naive guess is that what's actually happens involves the interaction of the wind with the air flow behind the propeller; the vessel is essentially slowing down a large volume of the wind behind it and using a bit of that lost energy to drive itself forward. Which is weird. But, using a stationary windmill to power an electric car that travels faster than the wind doesn't seem at all weird, which isn't fundamentally that different.
I'd love to see someone actually try to simulate what's happening in detail. It's a hard problem, but not that hard compared to what aerospace grad students do every day. The natural skeptic in me also wants to see someone check for batteries and electric motors in the car. Not because this is impossible. Just because the people who built it can't seem to explain it in a way that I understand, which always makes me suspicious. But, lots of people invent things they don't really understand.
posted by eotvos at 8:10 AM on May 30, 2021
I realized after posting the above that I hadn't actually seen the last 3 minutes of the video, which does go into an explanation that is pretty close to my half-assed one and makes sense. (I got interrupted yesterday while watching it.) I don't know why they left in the long and bad explanation at the start, but I withdraw much of my criticism.
posted by eotvos at 8:19 AM on May 30, 2021
posted by eotvos at 8:19 AM on May 30, 2021
Once you're traveling faster than the wind, the wind isn't pushing on the car frame in the right direction at all.
....but you have a bunch of momentum driving a propellor pushing against the wind.
posted by pompomtom at 8:20 AM on May 30, 2021
....but you have a bunch of momentum driving a propellor pushing against the wind.
posted by pompomtom at 8:20 AM on May 30, 2021
...except it's not just momentum; it's leverage as well.
Have another look at the ruler-powered cart I linked upthread, and wrap your head around the geometry of that. Now substitute a prop screwing its way down a windstream for the rolling contact between the ruler and the top of the big wheel on that cart.
posted by flabdablet at 8:43 AM on May 30, 2021
Have another look at the ruler-powered cart I linked upthread, and wrap your head around the geometry of that. Now substitute a prop screwing its way down a windstream for the rolling contact between the ruler and the top of the big wheel on that cart.
posted by flabdablet at 8:43 AM on May 30, 2021
It's like the ruler-powered cart, but with a variable mechanical advantage (adjustable prop pitch). That will give them a wider speed range where they can keep the prop out of aerodynamic stall.
posted by mscibing at 10:30 AM on May 30, 2021 [1 favorite]
posted by mscibing at 10:30 AM on May 30, 2021 [1 favorite]
Once you're traveling faster than the wind, the wind isn't pushing on the car frame in the right direction at all.
The propeller is making a fast, high-pressure, backwards-moving column of air behind it, and the wind is pushing on that.
If the propeller is designed well and moving at the right speed (which it will be given all the aerodynamic engineers who worked on this project), the wind will be hardly pushing on it at all from the front. The propeller will be slicing throw the wind with very little air resistance. Instead, the propeller will be pulling the wind in, making it go even faster, and pushing that even faster wind out the back. The faster wind coming out the back of the propeller will push on the slower surrounding wind coming from behind.
And since the propeller is driven by the wheels, not directly by the wind...
posted by clawsoon at 11:02 AM on May 30, 2021
The propeller is making a fast, high-pressure, backwards-moving column of air behind it, and the wind is pushing on that.
If the propeller is designed well and moving at the right speed (which it will be given all the aerodynamic engineers who worked on this project), the wind will be hardly pushing on it at all from the front. The propeller will be slicing throw the wind with very little air resistance. Instead, the propeller will be pulling the wind in, making it go even faster, and pushing that even faster wind out the back. The faster wind coming out the back of the propeller will push on the slower surrounding wind coming from behind.
And since the propeller is driven by the wheels, not directly by the wind...
posted by clawsoon at 11:02 AM on May 30, 2021
a variable mechanical advantage (adjustable prop pitch)
And that explains why Derek gets contradictory instructions about how to slow the cart down if it starts to run away on him.
Altering the pitch adjustment to reduce the angle of attack would reduce the amount of wheel speed that gets translated into propellor thrust, which would probably slow the cart down OK in a light wind; but it could also tend to make the prop spin faster, which you maybe don't want if the issue is that the machine is trying to shake itself to pieces.
To slow down in a heavier wind you'd want as much wind energy as possible to be wasted as propellor drag, which you can maximize by increasing the angle of attack until the propeller blades go into stall, which you'd do by pushing the pitch control the other way.
posted by flabdablet at 11:11 AM on May 30, 2021 [1 favorite]
And that explains why Derek gets contradictory instructions about how to slow the cart down if it starts to run away on him.
Altering the pitch adjustment to reduce the angle of attack would reduce the amount of wheel speed that gets translated into propellor thrust, which would probably slow the cart down OK in a light wind; but it could also tend to make the prop spin faster, which you maybe don't want if the issue is that the machine is trying to shake itself to pieces.
To slow down in a heavier wind you'd want as much wind energy as possible to be wasted as propellor drag, which you can maximize by increasing the angle of attack until the propeller blades go into stall, which you'd do by pushing the pitch control the other way.
posted by flabdablet at 11:11 AM on May 30, 2021 [1 favorite]
The propeller is making a fast, high-pressure, backwards-moving column of air behind it
I'm actually in some doubt about that.
From the point of view of the cart and driver there will certainly be a roaring headwind, and that's the source of the drag forces that ultimately limit the cart's top speed.
But by analogy with the faster-than-ruler model cart, where the contact point with the ruler runs ahead of the ruler speed, I'd expect the prop to be essentially screwing its way downwind through the column of air that's pushing on it from behind. Following from that, I'd expect that backward movement of the air behind the prop, as measured relative to the bulk speed of the wind across the landscape, would be quite slight and more reflective of prop losses than anything else.
posted by flabdablet at 11:27 AM on May 30, 2021
I'm actually in some doubt about that.
From the point of view of the cart and driver there will certainly be a roaring headwind, and that's the source of the drag forces that ultimately limit the cart's top speed.
But by analogy with the faster-than-ruler model cart, where the contact point with the ruler runs ahead of the ruler speed, I'd expect the prop to be essentially screwing its way downwind through the column of air that's pushing on it from behind. Following from that, I'd expect that backward movement of the air behind the prop, as measured relative to the bulk speed of the wind across the landscape, would be quite slight and more reflective of prop losses than anything else.
posted by flabdablet at 11:27 AM on May 30, 2021
flabdablet: Following from that, I'd expect that backward movement of the air behind the prop, as measured relative to the bulk speed of the wind across the landscape, would be quite slight and more reflective of prop losses than anything else.
I don't know about the relative sizes of the effects, but I do know that force=mass*acceleration applies here (minus losses due to turbulence and whatnot). The force that the propeller has available to push the cart forward comes from accelerating the mass of air backwards.
I think "screwing its way downwind" would be a better analogy if the air was able to transmit the propeller's force to the ground. Since air is a thin fluid it's not able to do that, so the air has to be accelerated backward to extract forward force from it.
I'm not sure how large the numbers would be, though, and you might be right that "fast" is an overstatement.
posted by clawsoon at 4:32 PM on May 30, 2021
I don't know about the relative sizes of the effects, but I do know that force=mass*acceleration applies here (minus losses due to turbulence and whatnot). The force that the propeller has available to push the cart forward comes from accelerating the mass of air backwards.
I think "screwing its way downwind" would be a better analogy if the air was able to transmit the propeller's force to the ground. Since air is a thin fluid it's not able to do that, so the air has to be accelerated backward to extract forward force from it.
I'm not sure how large the numbers would be, though, and you might be right that "fast" is an overstatement.
posted by clawsoon at 4:32 PM on May 30, 2021
I think "screwing its way downwind" would be a better analogy if the air was able to transmit the propeller's force to the ground.
That's exactly what the drivetrain between the prop and the wheels allows it to do.
The force that the propeller has available to push the cart forward comes from accelerating the mass of air backwards.
At equilibrium speed there is zero net force on the cart. There's a balance of forces acting backward against forces acting forward.
Acting backward there's direct drag on the frame from the headwind the cart experiences by virtue of moving faster than the driving wind, plus indirect drag from the prop translated via the drivetrain, plus friction losses in the drivetrain; these last two forces act at the rolling point of contact between wheels and ground. Acting forward there's the pressure of the air column that the prop is cutting through, maintained by the wind from behind.
That forward-acting force acts on the blades of the prop, which it's able to do despite the fact that the prop as a whole is running ahead of the wind that's applying that force, due to drive geometry analogous to what allows the big wheel on the ruler-driven cart to roll forward along the ruler that's pushing it. At the blades, the balancing force acting in opposition to wind pressure from behind is lift from the motion of the prop.
All that's required for this situation to be sustainable is that there is a column of air for the prop to sit inside that's moving with respect to the ground that the prop's motion is controlled by via the drivetrain.
posted by flabdablet at 9:57 PM on May 30, 2021 [1 favorite]
That's exactly what the drivetrain between the prop and the wheels allows it to do.
The force that the propeller has available to push the cart forward comes from accelerating the mass of air backwards.
At equilibrium speed there is zero net force on the cart. There's a balance of forces acting backward against forces acting forward.
Acting backward there's direct drag on the frame from the headwind the cart experiences by virtue of moving faster than the driving wind, plus indirect drag from the prop translated via the drivetrain, plus friction losses in the drivetrain; these last two forces act at the rolling point of contact between wheels and ground. Acting forward there's the pressure of the air column that the prop is cutting through, maintained by the wind from behind.
That forward-acting force acts on the blades of the prop, which it's able to do despite the fact that the prop as a whole is running ahead of the wind that's applying that force, due to drive geometry analogous to what allows the big wheel on the ruler-driven cart to roll forward along the ruler that's pushing it. At the blades, the balancing force acting in opposition to wind pressure from behind is lift from the motion of the prop.
All that's required for this situation to be sustainable is that there is a column of air for the prop to sit inside that's moving with respect to the ground that the prop's motion is controlled by via the drivetrain.
posted by flabdablet at 9:57 PM on May 30, 2021 [1 favorite]
Another variant of this problem to consider: Is it possible to make a rotor-powered car drive into the wind?
Imagine a car with a free-spinning rotor fan, sitting in the wind with its handbrake on prevent its wheels from rolling. The wind imparts quite a bit of force on the car, but nowhere near enough to defeat the brakes, so it just sits there with its rotor rotating, dissipating energy as friction heat in the fan bearings. All of that energy is just there, going to waste, so why not use it?
Now attach a gearbox between the fan and the wheels, like a bicycle set on a very low gear, so you can pedal easily when going up steep hills. This turns a little effort into a lot of torque, which can be translated into a very large force if you don't mind going very slowly. In this example, the resulting torque can be made larger than the force of the wind on the car that's trying to rotate the wheels, just by picking a low enough gear. So, release the now unnecessary handbrake, and the car will now creep very slowly against the wind.
While this car doesn't work in the same way as the one in the main link, they both derive useful motive power while driving into an effective headwind.
posted by Eleven at 8:09 AM on June 1, 2021
Imagine a car with a free-spinning rotor fan, sitting in the wind with its handbrake on prevent its wheels from rolling. The wind imparts quite a bit of force on the car, but nowhere near enough to defeat the brakes, so it just sits there with its rotor rotating, dissipating energy as friction heat in the fan bearings. All of that energy is just there, going to waste, so why not use it?
Now attach a gearbox between the fan and the wheels, like a bicycle set on a very low gear, so you can pedal easily when going up steep hills. This turns a little effort into a lot of torque, which can be translated into a very large force if you don't mind going very slowly. In this example, the resulting torque can be made larger than the force of the wind on the car that's trying to rotate the wheels, just by picking a low enough gear. So, release the now unnecessary handbrake, and the car will now creep very slowly against the wind.
While this car doesn't work in the same way as the one in the main link, they both derive useful motive power while driving into an effective headwind.
posted by Eleven at 8:09 AM on June 1, 2021
In fact the very same craft has also set records for speed directly upwind (see aubilenon's earlier "what looks like the exact same vehicle" link).
posted by flabdablet at 11:34 AM on June 1, 2021
posted by flabdablet at 11:34 AM on June 1, 2021
That's exactly what the drivetrain between the prop and the wheels allows it to do.
When I said "transmit the propeller's force to the ground", I was thinking of the forward/lift force on the cart. The force between the wheels and the ground will all be in the backwards/drag direction, since it's the wheels driving the propeller.
The lift force gets transmitted to the air by the propeller; the drag force on the propeller gets transmitted to the ground by the wheels. Overall, the cart pushes the air back relative to itself and pulls the earth (a very tiny bit) forward.
At the blades, the balancing force acting in opposition to wind pressure from behind is lift from the motion of the prop.
And lift works* by accelerating air in the direction opposite the lift force, no? The air always comes faster out the back of a propeller than it came in the front, right?
*From one perspective; there are exactly equivalent perspectives involving pressure which are expressed in different ways, of course.
posted by clawsoon at 8:09 PM on June 1, 2021
When I said "transmit the propeller's force to the ground", I was thinking of the forward/lift force on the cart. The force between the wheels and the ground will all be in the backwards/drag direction, since it's the wheels driving the propeller.
The lift force gets transmitted to the air by the propeller; the drag force on the propeller gets transmitted to the ground by the wheels. Overall, the cart pushes the air back relative to itself and pulls the earth (a very tiny bit) forward.
At the blades, the balancing force acting in opposition to wind pressure from behind is lift from the motion of the prop.
And lift works* by accelerating air in the direction opposite the lift force, no? The air always comes faster out the back of a propeller than it came in the front, right?
*From one perspective; there are exactly equivalent perspectives involving pressure which are expressed in different ways, of course.
posted by clawsoon at 8:09 PM on June 1, 2021
The air always comes faster out the back of a propeller than it came in the front, right?
Depends how far from the blades you measure it.
Anyway, in this case it's the existence of the lift force itself that matters, as seen by the prop blades; not so much what that force is doing to the air. Yes, relative to the cart there will be a jet of air behind the prop that's moving backward faster than the headwind the rest of the cart is seeing; but relative to the ground I would expect that jet to remain moving forward, and furthermore moving forward not much slower than the bulk of the wind.
If there were some kind of imaginary boundary around the cylindrical slug of air that the prop moves through, and some kind of magic that stopped any air molecule moving either inward or outward through that boundary, and the prop blades were perfect and generated only lift and no drag, and the wheels and drivetrain were all frictionless, and the cart frame was also perfect and generated no drag: then keeping the cart moving at a constant speed would require no power to be extracted from the wind, the prop would be connecting to the driving air in pretty much exactly the same way as the rolling contact at the top of the ruler cart connects to the ruler, the entire air column it's screwing through would keep moving at exactly the same speed as the bulk wind blowing across the landscape, and the cart's equilibrium groundspeed would be a fixed multiple of that bulk wind's groundspeed as set by the pitch of the prop and the gearing in the drivetrain, just as the ruler cart's groundspeed is a fixed multiple of the driving ruler's groundspeed as set by its own gearing.
In other words, under these absolutely ideal and unrealistic conditions there would not be a fast backward jet coming off the back of the prop except as seen from the cart; from the cart, the jet coming off the back of the prop would appear to be moving at the difference between cart and wind groundspeeds.
The extent to which the air's behaviour departs from this spherical-cow-of-uniform density ideal picture is reflective of various real-world frictional and drag and turbulence losses in the system, not fundamental to the operation of the drive.
posted by flabdablet at 8:28 PM on June 1, 2021
Depends how far from the blades you measure it.
Anyway, in this case it's the existence of the lift force itself that matters, as seen by the prop blades; not so much what that force is doing to the air. Yes, relative to the cart there will be a jet of air behind the prop that's moving backward faster than the headwind the rest of the cart is seeing; but relative to the ground I would expect that jet to remain moving forward, and furthermore moving forward not much slower than the bulk of the wind.
If there were some kind of imaginary boundary around the cylindrical slug of air that the prop moves through, and some kind of magic that stopped any air molecule moving either inward or outward through that boundary, and the prop blades were perfect and generated only lift and no drag, and the wheels and drivetrain were all frictionless, and the cart frame was also perfect and generated no drag: then keeping the cart moving at a constant speed would require no power to be extracted from the wind, the prop would be connecting to the driving air in pretty much exactly the same way as the rolling contact at the top of the ruler cart connects to the ruler, the entire air column it's screwing through would keep moving at exactly the same speed as the bulk wind blowing across the landscape, and the cart's equilibrium groundspeed would be a fixed multiple of that bulk wind's groundspeed as set by the pitch of the prop and the gearing in the drivetrain, just as the ruler cart's groundspeed is a fixed multiple of the driving ruler's groundspeed as set by its own gearing.
In other words, under these absolutely ideal and unrealistic conditions there would not be a fast backward jet coming off the back of the prop except as seen from the cart; from the cart, the jet coming off the back of the prop would appear to be moving at the difference between cart and wind groundspeeds.
The extent to which the air's behaviour departs from this spherical-cow-of-uniform density ideal picture is reflective of various real-world frictional and drag and turbulence losses in the system, not fundamental to the operation of the drive.
posted by flabdablet at 8:28 PM on June 1, 2021
from the cart, the jet coming off the back of the prop would appear to be moving at the difference between cart and wind groundspeeds
i.e. the same speed as the headwind as seen from the cart.
posted by flabdablet at 8:36 PM on June 1, 2021
i.e. the same speed as the headwind as seen from the cart.
posted by flabdablet at 8:36 PM on June 1, 2021
and the cart's equilibrium groundspeed would be a fixed multiple of that bulk wind's groundspeed as set by the pitch of the prop and the gearing in the drivetrain
Something feels wrong about this. I'm not an expert by any means, but it feels like what you're describing would only be applicable to a flat-bladed propeller moving through air with no compressibility, one which only creates lift by putting more air behind it than in front of it, like the screw of a grain auger. It feels off somehow for a propeller blade which creates lift by making the air traverse the top of its airfoil surface faster than the bottom surface, resulting in downwash. (Or... would you call it "backwash" in this case? Sounds mildly disgusting.)
It feels like - in the absence of all the forces you've absented, plus absenting sound barriers and whatnot - the propeller could keep accelerating the cart forward as long as it was able to create a low-pressure zone in front of it, as long as it was able to keep pulling air from ahead of it into it. And I think (I think?) it could keep doing that no matter how fast it was travelling forward as long as it was able to spin faster and faster, since the low-pressure zone it creates in front of it extends (theoretically) to infinity, or at least moves forward at the speed of sound. I think that the lift equation agrees with me:
lift = coefficient_of_lift * density_of_air * velocity^2 * wing_area / 2
Since all of those things except velocity are fixed in our spherical cow example, I think lift keeps going up and up as the cart goes faster.
Or... is it that the apparent angle of attack goes lower and lower and eventually the coefficient of lift becomes zero? The blade ends up acting just like a grain auger, just with a few extra degrees of available lift because of its airfoil shape? (But wouldn't a propeller which has no limit on its rotational speed always be able to raise its apparent angle of attack above its zero-lift angle of attack just by going faster?)
I could be completely wrong about all of this.
If you have more ambition than I do, you could read through Mark Drela's analysis (PDF) and figure out the equations there.
posted by clawsoon at 9:13 PM on June 1, 2021
Something feels wrong about this. I'm not an expert by any means, but it feels like what you're describing would only be applicable to a flat-bladed propeller moving through air with no compressibility, one which only creates lift by putting more air behind it than in front of it, like the screw of a grain auger. It feels off somehow for a propeller blade which creates lift by making the air traverse the top of its airfoil surface faster than the bottom surface, resulting in downwash. (Or... would you call it "backwash" in this case? Sounds mildly disgusting.)
It feels like - in the absence of all the forces you've absented, plus absenting sound barriers and whatnot - the propeller could keep accelerating the cart forward as long as it was able to create a low-pressure zone in front of it, as long as it was able to keep pulling air from ahead of it into it. And I think (I think?) it could keep doing that no matter how fast it was travelling forward as long as it was able to spin faster and faster, since the low-pressure zone it creates in front of it extends (theoretically) to infinity, or at least moves forward at the speed of sound. I think that the lift equation agrees with me:
lift = coefficient_of_lift * density_of_air * velocity^2 * wing_area / 2
Since all of those things except velocity are fixed in our spherical cow example, I think lift keeps going up and up as the cart goes faster.
Or... is it that the apparent angle of attack goes lower and lower and eventually the coefficient of lift becomes zero? The blade ends up acting just like a grain auger, just with a few extra degrees of available lift because of its airfoil shape? (But wouldn't a propeller which has no limit on its rotational speed always be able to raise its apparent angle of attack above its zero-lift angle of attack just by going faster?)
I could be completely wrong about all of this.
If you have more ambition than I do, you could read through Mark Drela's analysis (PDF) and figure out the equations there.
posted by clawsoon at 9:13 PM on June 1, 2021
A back-of-the-envelope calculation for faster-than-a-grain-auger-in-jello propellers:
Mustang P-51B specs: 11 ft 2 in diameter propeller, 3000 RPM = tip speed of ~534 meters per second. If it's at a slicing-through-jello angle of 1:6 (about 9 degrees), that gives a maximum airspeed in level flight of 89 meters per second. Actual maximum airspeed in level flight was ~198 meters per second.
To get the slicing-through-jello numbers to line up with the actual airspeed, you'd have to have an angle of attack of about 20 degrees, which is well into airfoil stall territory for pretty much all airfoils.
Unless I've done my math wrong or made some wrong assumptions - and both are entirely possible - I think that's a real-world example of a propeller-driven craft going faster in level flight than you'd expect it to be able to go if it was simply slicing through the air.
But, again, I could be wrong about all of this.
posted by clawsoon at 10:18 PM on June 1, 2021
Mustang P-51B specs: 11 ft 2 in diameter propeller, 3000 RPM = tip speed of ~534 meters per second. If it's at a slicing-through-jello angle of 1:6 (about 9 degrees), that gives a maximum airspeed in level flight of 89 meters per second. Actual maximum airspeed in level flight was ~198 meters per second.
To get the slicing-through-jello numbers to line up with the actual airspeed, you'd have to have an angle of attack of about 20 degrees, which is well into airfoil stall territory for pretty much all airfoils.
Unless I've done my math wrong or made some wrong assumptions - and both are entirely possible - I think that's a real-world example of a propeller-driven craft going faster in level flight than you'd expect it to be able to go if it was simply slicing through the air.
But, again, I could be wrong about all of this.
posted by clawsoon at 10:18 PM on June 1, 2021
I think lift keeps going up and up as the cart goes faster
Yeah, it would. The point is that there's no energy available to make the cart go faster. Over-unity free energy machines are Not A Thing, not even in spherical cow country.
There's a particular speed at which the amount of force acting forward due to lift generated by the prop plus the amount of force acting forward due to wind pressure behind the prop exactly matches the amount of force acting backward at the contact point between wheel and ground. That equilibrium speed is going to be set by the ratio between contact point force and prop lift, and that ratio is going to set mainly by the prop pitch and drivetrain gearing though there will be a speed-dependent factor in there as well because of the velocity squared term in the lift equation.
A spherical cow cart could achieve any multiple of wind speed you cared to set it for, because that multiple increases without limit as prop lift to wheel force ratio approaches 1 from below. Real-world carts, not so much; there's a velocity-squared term in the drag equation too.
posted by flabdablet at 8:25 AM on June 2, 2021
Yeah, it would. The point is that there's no energy available to make the cart go faster. Over-unity free energy machines are Not A Thing, not even in spherical cow country.
There's a particular speed at which the amount of force acting forward due to lift generated by the prop plus the amount of force acting forward due to wind pressure behind the prop exactly matches the amount of force acting backward at the contact point between wheel and ground. That equilibrium speed is going to be set by the ratio between contact point force and prop lift, and that ratio is going to set mainly by the prop pitch and drivetrain gearing though there will be a speed-dependent factor in there as well because of the velocity squared term in the lift equation.
A spherical cow cart could achieve any multiple of wind speed you cared to set it for, because that multiple increases without limit as prop lift to wheel force ratio approaches 1 from below. Real-world carts, not so much; there's a velocity-squared term in the drag equation too.
posted by flabdablet at 8:25 AM on June 2, 2021
The point is that there's no energy available to make the cart go faster. Over-unity free energy machines are Not A Thing, not even in spherical cow country.
As long as the wind and the ground have different relative speeds, though, there's energy available to extract, isn't there?
Even if all you're working with is two columns of air moving at ~50mph relative to each other, that's enough [really interesting lecture, worth a watch if you haven't seen it already] to get a glider over 500mph. And the limit they hit there isn't a spherical cow limit, it's the practical matter of transonic airflow over the airfoil dramatically increasing drag.
and that ratio is going to set mainly by the prop pitch and drivetrain gearing
I think this is where I disagree (or maybe not, if I'm misunderstanding you): As I understand it, that ratio is mainly going to be set by the lift-to-drag ratio of the craft as a whole, rather than by pitch and gearing. They've set the pitch and gearing to always accelerate up to the limit of drag, not up to a pitch+gearing limit.
Real-world carts, not so much; there's a velocity-squared term in the drag equation too.
On this we entirely agree. :-)
posted by clawsoon at 9:21 AM on June 2, 2021
As long as the wind and the ground have different relative speeds, though, there's energy available to extract, isn't there?
Even if all you're working with is two columns of air moving at ~50mph relative to each other, that's enough [really interesting lecture, worth a watch if you haven't seen it already] to get a glider over 500mph. And the limit they hit there isn't a spherical cow limit, it's the practical matter of transonic airflow over the airfoil dramatically increasing drag.
and that ratio is going to set mainly by the prop pitch and drivetrain gearing
I think this is where I disagree (or maybe not, if I'm misunderstanding you): As I understand it, that ratio is mainly going to be set by the lift-to-drag ratio of the craft as a whole, rather than by pitch and gearing. They've set the pitch and gearing to always accelerate up to the limit of drag, not up to a pitch+gearing limit.
Real-world carts, not so much; there's a velocity-squared term in the drag equation too.
On this we entirely agree. :-)
posted by clawsoon at 9:21 AM on June 2, 2021
They've set the pitch and gearing to always accelerate up to the limit of drag
Yeah, but they don't have a spherical cow doing the driving.
Also I'm pretty sure the real cart has a variable pitch control to allow the pilot to tune performance to the wind conditions.
I've been trying to work out what happens to the air around the cart when it's running at speed, and to a first approximation I think the model I like best so far is that of the cart as being at the centre of a pressure anomaly that propagates downwind.
Rather than any kind of well formed jet coming off the back of the prop I think there's probably a zone of below-ambient pressure in front of the prop and a zone of above-ambient pressure behind it, with the pressures trailing off toward ambient the further from the prop you get and a big step change right at the prop itself.
So the cart is both maintaining and riding what amounts to a soliton moving downwind, continuously harvesting a little extra energy from the nonzero speed of the ground relative to its propagation medium that offsets losses and keeps the whole thing in shape.
posted by flabdablet at 9:47 AM on June 2, 2021 [1 favorite]
Yeah, but they don't have a spherical cow doing the driving.
Also I'm pretty sure the real cart has a variable pitch control to allow the pilot to tune performance to the wind conditions.
I've been trying to work out what happens to the air around the cart when it's running at speed, and to a first approximation I think the model I like best so far is that of the cart as being at the centre of a pressure anomaly that propagates downwind.
Rather than any kind of well formed jet coming off the back of the prop I think there's probably a zone of below-ambient pressure in front of the prop and a zone of above-ambient pressure behind it, with the pressures trailing off toward ambient the further from the prop you get and a big step change right at the prop itself.
So the cart is both maintaining and riding what amounts to a soliton moving downwind, continuously harvesting a little extra energy from the nonzero speed of the ground relative to its propagation medium that offsets losses and keeps the whole thing in shape.
posted by flabdablet at 9:47 AM on June 2, 2021 [1 favorite]
Well I guess that means we're one step closer to faster than light travel powered by light!
Uh, would you believe one half step closer?
posted by aubilenon at 1:21 PM on June 2, 2021
Uh, would you believe one half step closer?
posted by aubilenon at 1:21 PM on June 2, 2021
I decided to email Mark Drela on the off chance that he'd respond to an Internet rando, and lo-and-behold he answered! (And said it was okay to post his answer.)
My question :
posted by clawsoon at 2:57 PM on June 2, 2021 [1 favorite]
My question :
As total drag (aerodynamic and mechanical) on the [Blackbird] approaches zero, which would happen?His answer:
1. The craft would accelerate to higher and higher speeds, limited by drag. As drag went down, top speed would go up, with no theoretical limit.
2. The craft would reach a speed limit set by propeller pitch and drivetrain gearing ratio. It would not go faster than that pitch+gearing limit, no matter how low drag got.
If there is no drag, there is no theoretical speed limit to DDWFTTW [dead downwind faster than the wind]. It’s no different than applying thrust to an object which has no drag — it will keep accelerating without limit.So I guess our spherical cow needs to not only be frictionless and dragless but also infinitely strong. Given all that, though, it has no speed limit.
In reality there is drag of course, and there are also structural limits.
For fixed gearing the wheel rpm and prop rpm will be proportional to the ground speed, so at some point something will blow up from the centrifugal loads.
posted by clawsoon at 2:57 PM on June 2, 2021 [1 favorite]
Have you ever met a spherical cow of uniform density who isn't infinitely strong?
I rest my case.
posted by flabdablet at 5:13 AM on June 3, 2021 [5 favorites]
I rest my case.
posted by flabdablet at 5:13 AM on June 3, 2021 [5 favorites]
Thinking back through what I used to know about propellers and airfoils, I think you were right to criticize my image of a fast-moving column of air moving back from the propeller. The basic equation (minus losses to turbulence) is still correct: The forward force on the cart is equal to the mass of air being accelerated backward by the propeller, times the amount it is being accelerated. So far I haven't been able to find enough information to calculate those numbers for the Blackbird given what I understand, though, and I'm not smart enough to calculate it given what I don't understand. And I'm definitely not smart enough to figure out how far back that faster moving air would penetrate into the surrounding air before its energy was dissipated.
Random things I remember: The air coming off the back of the propeller will mostly be moving back, but because of propeller drag it'll also have some swirl to it in the direction of propeller rotation. I think that there'll also be trailing vortices coming off the tips of the propeller. For maximum efficiency, the blades of the propeller will have to have a much higher angle of attack near the center than the tips, since the center is moving slower and will have a lowered effective angle of attack with respect to the incoming air than the tips.
One interesting thing that came to mind while thinking about airfoils was how a flat-bottomed airfoil like the widely-used Clark Y has its highest lift-to-drag ratio at the angle where its bottom surface is parallel to the air it's cutting through. That's one reason that the screw analogy felt intuitively not-quite-right to me. You're getting the most thrust for your drag when the bottom of the airfoil is slicing flat through the air and affecting it as little as possible. At that angle it's the top surface of the airfoil doing almost all of the work by creating a low-pressure, high-speed airflow stuck to its surface.
posted by clawsoon at 6:54 AM on June 3, 2021
Random things I remember: The air coming off the back of the propeller will mostly be moving back, but because of propeller drag it'll also have some swirl to it in the direction of propeller rotation. I think that there'll also be trailing vortices coming off the tips of the propeller. For maximum efficiency, the blades of the propeller will have to have a much higher angle of attack near the center than the tips, since the center is moving slower and will have a lowered effective angle of attack with respect to the incoming air than the tips.
One interesting thing that came to mind while thinking about airfoils was how a flat-bottomed airfoil like the widely-used Clark Y has its highest lift-to-drag ratio at the angle where its bottom surface is parallel to the air it's cutting through. That's one reason that the screw analogy felt intuitively not-quite-right to me. You're getting the most thrust for your drag when the bottom of the airfoil is slicing flat through the air and affecting it as little as possible. At that angle it's the top surface of the airfoil doing almost all of the work by creating a low-pressure, high-speed airflow stuck to its surface.
posted by clawsoon at 6:54 AM on June 3, 2021
Clark Y
Fair point, but if you were to trace the tips of that propeller relative to the ground you'd find them moving in helical paths all the same. A screw's a screw regardless of the details of its thread profile.
The forward force on the cart is equal to the mass of air being accelerated backward by the propeller, times the amount it is being accelerated.
Sure. And as the soliton propagates downwind, the prop is accelerating a certain mass of air backward per second, thereby creating the step increase in pressure from front to back that translates to the forward lift force applied to the blades.
If we zoom out and consider everything that's moving downwind, we see a cart and its prop at the centre, a low-pressure region in front of the prop, and a high-pressure region behind the prop. Those pressure regions are attached to the prop and they move downwind at the same speed that the cart does. Any given set of air molecules inside those regions, however, does not move downwind at cart speed; only the pressure wavefront does.
There's a whole class of phenomenon - vortex rings - that involves a broadly similar kind of pressure anomaly that can be made to move through bulk air for quite some distance at essentially arbitrary speed while retaining its own integrity to some extent. For a vortex ring, the energy required for that integrity maintenance is all supplied up-front at point of creation; for the prop cart it's continuously extracted from the energy of the wind with respect to the ground.
Because there are losses involved in moving a cart like this, the particular portion of the wind that supplies the energy to overcome those losses will get some of its uniform, low-entropy motion converted to eddies and micro-eddies and nano-eddies and noise and ultimately heat, just as happens with wind turbines fixed to the landscape. The difference is that in the fixed wind turbine's case most of that stuff happens downwind of the turbine, creating a wind shadow; with the prop cart it happens mostly upwind, creating a wake.
posted by flabdablet at 7:31 AM on June 3, 2021
Fair point, but if you were to trace the tips of that propeller relative to the ground you'd find them moving in helical paths all the same. A screw's a screw regardless of the details of its thread profile.
The forward force on the cart is equal to the mass of air being accelerated backward by the propeller, times the amount it is being accelerated.
Sure. And as the soliton propagates downwind, the prop is accelerating a certain mass of air backward per second, thereby creating the step increase in pressure from front to back that translates to the forward lift force applied to the blades.
If we zoom out and consider everything that's moving downwind, we see a cart and its prop at the centre, a low-pressure region in front of the prop, and a high-pressure region behind the prop. Those pressure regions are attached to the prop and they move downwind at the same speed that the cart does. Any given set of air molecules inside those regions, however, does not move downwind at cart speed; only the pressure wavefront does.
There's a whole class of phenomenon - vortex rings - that involves a broadly similar kind of pressure anomaly that can be made to move through bulk air for quite some distance at essentially arbitrary speed while retaining its own integrity to some extent. For a vortex ring, the energy required for that integrity maintenance is all supplied up-front at point of creation; for the prop cart it's continuously extracted from the energy of the wind with respect to the ground.
Because there are losses involved in moving a cart like this, the particular portion of the wind that supplies the energy to overcome those losses will get some of its uniform, low-entropy motion converted to eddies and micro-eddies and nano-eddies and noise and ultimately heat, just as happens with wind turbines fixed to the landscape. The difference is that in the fixed wind turbine's case most of that stuff happens downwind of the turbine, creating a wind shadow; with the prop cart it happens mostly upwind, creating a wake.
posted by flabdablet at 7:31 AM on June 3, 2021
A screw's a screw regardless of the details of its thread profile.
So I guess from that perspective the craft accelerates (without limit in the case of no drag) because the "screw" keeps going faster and faster? I guess I can see how that makes sense. It's not so much that the thread pitch is the physical shape of the airfoil, but rather the "screw pitch" is the downwash angle of the air coming off the trailing edge of the airfoil? (Or related to the downwash angle somehow or another?)
Any given set of air molecules inside those regions, however, does not move downwind at cart speed; only the pressure wavefront does.
That makes sense. In the region of the propeller itself, would some set of air molecules be moving backward relative to the wind speed, being forced by the propeller from the low pressure zone into the high pressure zone in order to maintain the high pressure? That's how I picture it.
The rest of what you said makes sense to me, at least as far as I understand it. :-)
posted by clawsoon at 8:11 AM on June 3, 2021
So I guess from that perspective the craft accelerates (without limit in the case of no drag) because the "screw" keeps going faster and faster? I guess I can see how that makes sense. It's not so much that the thread pitch is the physical shape of the airfoil, but rather the "screw pitch" is the downwash angle of the air coming off the trailing edge of the airfoil? (Or related to the downwash angle somehow or another?)
Any given set of air molecules inside those regions, however, does not move downwind at cart speed; only the pressure wavefront does.
That makes sense. In the region of the propeller itself, would some set of air molecules be moving backward relative to the wind speed, being forced by the propeller from the low pressure zone into the high pressure zone in order to maintain the high pressure? That's how I picture it.
The rest of what you said makes sense to me, at least as far as I understand it. :-)
posted by clawsoon at 8:11 AM on June 3, 2021
would some set of air molecules be moving backward relative to the wind speed, being forced by the propeller from the low pressure zone into the high pressure zone in order to maintain the high pressure?
Way I see it, yes. In the low pressure zone in front of the prop, air molecules are spreading out as the prop gobbles victims from the back of the LP zone and shoves them through into the front of the high pressure zone; the displaced molecules then spread out again and return to ambient pressure as the front of the HP zone disappears downwind with the cart.
If you like, the prop is borrowing some airspeed to push the cart with.
posted by flabdablet at 9:07 AM on June 3, 2021
Way I see it, yes. In the low pressure zone in front of the prop, air molecules are spreading out as the prop gobbles victims from the back of the LP zone and shoves them through into the front of the high pressure zone; the displaced molecules then spread out again and return to ambient pressure as the front of the HP zone disappears downwind with the cart.
If you like, the prop is borrowing some airspeed to push the cart with.
posted by flabdablet at 9:07 AM on June 3, 2021
And do I remember correctly that some of the molecules in the high-pressure zone are trying very hard to get around the propeller blades and move upstream to the low-pressure zone, as air molecules usually do, which is how some of the energy-consuming vortices are generated?
posted by clawsoon at 10:51 AM on June 3, 2021
posted by clawsoon at 10:51 AM on June 3, 2021
I'd expect a vortex ring to persist around the outside of the prop. On the inside of the ring there'd be a band of air moving even faster downwind than the cart, slipping forward past the edge of the prop to try to get back into the low pressure zone; the outside of the ring would be rolling through the ambient wind. The inside edge would probably get a bit tangled up in tip vortices off the prop blades.
But this is all guesswork. The only way to be sure would be to mount a smoke generator near the prop and a high speed cam on the cart.
posted by flabdablet at 12:48 PM on June 3, 2021 [1 favorite]
But this is all guesswork. The only way to be sure would be to mount a smoke generator near the prop and a high speed cam on the cart.
posted by flabdablet at 12:48 PM on June 3, 2021 [1 favorite]
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