I'm going to go over the engineering concept you need to make this work
July 1, 2021 2:42 PM   Subscribe

A month ago (previously), Youtuber Veritasium sailed Blackbird (previouslier) directly downwind faster than the wind. Afterwards, a physics professor bet him $10,000 that it didn't happen. Neil deGrasse Tyson and Bill Nye weighed in. Veritasium asked Xyla Foxlin to design and build a working model to win the bet. Foxlin (who surprisingly never seems to have been featured on Metafilter) has also built a cedar-strip canoe, built some flame throwing greeting cards, and sent her Miss America crown to the edge of space.
posted by clawsoon (149 comments total) 55 users marked this as a favorite
 
Thanks for posting, this was excellent science fun.
And building a kayak out of fiberglass with LEDS !!!
posted by winesong at 3:16 PM on July 1 [5 favorites]


The description of the "design and build" video contains a parts list and models for 3D printing if you want to build a working version of it for yourself. In that video, Foxlin goes over the three models she built that didn't work; it turns out that getting the engineering exactly right to go directly downwind faster than the wind isn't trivial.
posted by clawsoon at 3:18 PM on July 1 [1 favorite]


Engineering with Rosie has the most accurate explanation I've seen so far on Youtube. She worked with the designer of Blackbird to make sure that she was getting everything right. She walks through the basic aerodynamics involved in detail.
posted by clawsoon at 3:45 PM on July 1 [12 favorites]


it turns out that getting the engineering exactly right to go directly downwind faster than the wind isn't trivial.

No doubt. I'm surprised Blackbird was able to do it, as it looks dodgy as hell.
posted by 2N2222 at 3:46 PM on July 1


he showed the demo from the video flabdablet linked in the previous thread but didn't do a great job of introducing it (what do you think will happen?) or explaining how it is related.
posted by onya at 3:46 PM on July 1 [1 favorite]


So, dude wins a 10k bet and still has to accept a sponsor for this video?
posted by pwnguin at 4:24 PM on July 1 [1 favorite]


This is wonderful!

I'm feeling a little sorry for the professor, though; with his salary a $10,000 hit could be a pretty big one to take, and he did play the devlishly difficult role of loyal oppositional friendship exquisitely well.

I'm not making any promises, but if he has a Patreon page, I might have to come up with something for him.
posted by jamjam at 4:28 PM on July 1


I'm feeling a little sorry for the professor, though; with his salary a $10,000 hit could be a pretty big one to take

It's not football coach level comp, but I think that professor will be okay.
posted by pwnguin at 4:34 PM on July 1 [10 favorites]


If one didn't feel like watching a bunch of youtube videos but still wanted an explanation of whether / how this works, what would one do?
posted by signal at 4:36 PM on July 1 [6 favorites]


What if it were a plane on a treadmill?
posted by geoff. at 4:37 PM on July 1 [8 favorites]


signal: If one didn't feel like watching a bunch of youtube videos but still wanted an explanation of whether / how this works, what would one do?

Maybe reading all three pages of this forum thread from a decade ago involving one of the builders of Blackbird would be helpful?

Edit: Especially the second page.
posted by clawsoon at 4:40 PM on July 1 [4 favorites]


They said "no tacking" but if they're changing the pitch of the propellers to achieve greater than the downwind speed isn't that effectively the same as tacking?
posted by geoff. at 4:46 PM on July 1 [4 favorites]


Also, Engineering with Rosie (a great channel) has an article on medium that lays out her analysis, the same one as her video.
posted by phliar at 4:49 PM on July 1 [6 favorites]


winesong: And building a kayak out of fiberglass with LEDS!!!

Some fish has been waiting their whole life for that psychedelic experience.
posted by clawsoon at 4:51 PM on July 1 [4 favorites]


Looking back through my emails (I'm someone who never deletes them), I see that I've been trying to fully wrap my head around this since I first heard about it in 2011.

I have had (and heard) so many wrong and/or inaccurate intuitions in the past decade that I no longer trust myself and only fully accept an explanation if it comes from one of the very few people (basically only MIT aero prof Mark Drela and Blackbird designer Rick Cavallaro) who I've figured out actually know what they're talking about. The fact that Cavallaro gave Engineering by Rosie direct help to understand and explain this (and is participating actively in the comments on her video) gives me extra confidence in what she's saying.

The only remaining problem is that I don't always understand what they're talking about, lol...
posted by clawsoon at 5:27 PM on July 1 [5 favorites]


I think this video (50s youtube video) linked from clawsoon's thread is perhaps the most useful intuition builder: forget wind and propellors and fluid dynamics, and consider a completely rigid scenario of a moving cable or chain. Could you use a moving cable and the ground to propel yourself faster than the cable? (Yes, with the right gearing as shown in the video).
posted by Pyry at 6:05 PM on July 1 [15 favorites]


They said "no tacking" but if they're changing the pitch of the propellers to achieve greater than the downwind speed isn't that effectively the same as tacking?

Merriam Webster’s definition of “tack”: to change the direction of (a sailing ship) when sailing close-hauled by turning the bow to the wind and shifting the sails so as to fall off on the other side at about the same angle as before

As long as the Blackbird is heading straight downwind and not zig-zagging, it’s not tacking.
posted by ejs at 7:20 PM on July 1 [3 favorites]


> completely rigid scenario of a moving cable or chain. Could you use a moving cable and the ground to propel yourself faster than the cable?

As soon as the vehicle was moving faster than the cable, the cable would no longer be pulling it (assuming no elasticity). Without that pull, friction would immediately start to slow the vehicle.

I'd be more convinced of this if the streamer were set at the same height as the maximum height of the propeller. My thought is that as soon as the vehicle reaches and possibly surpasses the wind speed, the propeller should begin to slow as there is nothing left to power it.

I admit to not watching all the videos and reading all the links. Perhaps my objection is covered in one of those sources.
posted by DarkForest at 7:52 PM on July 1


DarkForest: My thought is that as soon as the vehicle reaches and possibly surpasses the wind speed, the propeller should begin to slow as there is nothing left to power it.

The first thing to understand is that the wind is not driving the propeller. The wheels are driving the propeller. The propeller is turning in the direction opposite what it would if the wind were driving it.

The record is 2.8 times the speed of the wind, so well past doubt about whether the effect is real. This is definitely one to approach with "why are my intuitions about this wrong, and how does it actually work?" instead of "my intuition has convinced me that this can't possibly work."
posted by clawsoon at 7:58 PM on July 1 [22 favorites]


DarkForest, both of those objections are addressed in the first YouTube link. The original Blackbird has been done with streamers at blade-level.

As to the cable idea: you wear rollerblades and grab onto the cable, which accelerates you up to speed. Now you're exactly at cable speed. Next, all you need to do is hook up something to siphon a little bit of the energy coming through your skates to let you crawl up the cable. Now you're moving faster than the cable.

In the Veritasium video, he does it with a long plank and some unequal-sized wheels, like the video Pyry linked but bigger. The top (big) wheel pushes against the bottom of the plank and the small (fast) wheels on the ground provide the motive force for the pushing wheel, and the ratio means that you end up doing more force against the moving plank than you get from the ground, and the wheeled contraption moves forward along the plank, faster than the plank.

They said "no tacking" but if they're changing the pitch of the propellers to achieve greater than the downwind speed isn't that effectively the same as tacking?

The models don't have variable pitch at all, so you don't need it, it just helps. I think the variable pitch is just to adjust between the two modes- slower than the wind vs faster than the wind. If it was like tacking, you'd have to keep adjusting the pitch back and forth to keep moving, but they aren't doing that.
posted by BungaDunga at 8:08 PM on July 1 [3 favorites]


Also: I'm so excited to see this thing get the 2020-era YouTuber treatment. I remember the grainy blurry treadmill video and seeing someone do it in crystal clear 1080p is sort of mindboggling (and much more convincing!)
posted by BungaDunga at 8:13 PM on July 1 [2 favorites]


I suppose I'll have to watch all the videos etc. (though I loathe long videos) to raise more substantive objections, but it looks just like another perpetual motion machine to me. Why does it even need wind to start it? Why not just push it with something to start it? Why does it ever stop?

> siphon a little bit of the energy coming through your skates to let you crawl up the cable

I don't like the cable analogy because we can direct as much energy as we want through the cable to mantian speed. The skater can climb up the cable only by pulling more energy from it, requiring the cable to exert more force to maintain its speed.

But the wind is not a cable and the amount of force it supplies is dependent on the cross section of the vehicle and the relative wind speed. This force is greatest at rest, and least when the vehicle is travelling at wind speed. The force to drive the propeller comes from the wheels, which means the wheels have to resist turning by a related amount depending on gearing. I don't see how that can be anything but net zero at best. But perhaps enlightenment awaits me in watching all the videos.
posted by DarkForest at 9:03 PM on July 1


I hadn't heard about Blackbird before the last previous about the Veritasium video. It did seem improbable at first, but became clearer as it went. A stationary windmill could clearly propel a light car very vast, just balancing energy, and the exact same windmill in still air moving over the ground makes the same amount of energy. So what's different about a moving windmill geared to the ground? It's just relative motion that creates power.
posted by netowl at 9:07 PM on July 1 [1 favorite]


> exact same windmill in still air moving over the ground makes the same amount of energy

But it takes at least as much energy to keep it moving through the air as it can generate.
posted by DarkForest at 9:16 PM on July 1


DarkForest: But it takes at least as much energy to keep it moving through the air as it can generate.

The energy it needs to move through the air is the energy needed to overcome drag. Why would you expect the drag on the craft to always be equal to the thrust that the propeller is generating?
posted by clawsoon at 9:25 PM on July 1 [4 favorites]


This moment in the second Veritasium video, which is essentially the same demonstration also shown in the video that Pyry linked above, is where my intuition clicked into gear (pun intended); I thought I more or less understood it by that point, but as soon as he brought out the little wheeled vehicle thing and the board I literally said out loud "Oooh, of course." It's amazing how much just the right simplified model can help build intuition.
posted by biogeo at 9:37 PM on July 1 [8 favorites]


So, dude wins a 10k bet and still has to accept a sponsor for this video?

He's using the $10k to offer three prizes awarded to the best short science communication videos explaining a complex or counterintuitive concept. I'll admit I'm tempted to give it a go. If anyone has any thoughts on some complex or counterinuitive neurobiology-related topic they'd like an expert to try explaining to a lay audience in a minute or less, please memail me!
posted by biogeo at 9:42 PM on July 1 [11 favorites]


>> exact same windmill in still air moving over the ground makes the same amount of energy

>But it takes at least as much energy to keep it moving through the air as it can generate.

I probably should have said power, but that's exactly right: whatever is pulling must exert that much power (plus losses), since there's no energy in the air/ground system to help. But say a slight tailwind shows up... now it can make the same power with less power pulling it, because the wind is helping. It should help with the same amount of power a stationary windmill makes in the same breeze.

The pulled windmill is certainly going faster than the air, but still makes power when a forward breeze shows up. So, just gear the pulling part and the windmill together. That's Blackbird.
posted by netowl at 9:59 PM on July 1


clawsoon: Why would you expect the drag on the craft to always be equal to the thrust that the propeller is generating?

Otherwise, its magic free energy. Or so it seems to me.

If the wheels are driving the propeller, then the wheels will require force to rotate. Can the propeller provide enough force to overcome that and accelerate the vehicle, or realistically even maintain speed? I don't see how it can. Where does the energy come from?

biogeo: the problem with that moment of the video is just the same as what i said about the cable argument above. That's just a matter of gearing and you can get whatever speed you want by altering the gear ratio and providing sufficient energy by moving the board.
posted by DarkForest at 10:01 PM on July 1


it looks just like another perpetual motion machine to me.

It probably looked like that to the physics professor, the astrophysicist and the Science Guy on the losing side of the bet as well.

Why does it even need wind to start it?

Because perpetual motion is not a thing.

Why not just push it with something to start it?

Because then you'd be powering downwind faster than the wind, not sailing downwind faster than the wind.

Why does it ever stop?

Because the wind does, or because the driver applies the brakes and/or feathers the prop.

This bet is essentially a cautionary tale about Engineers' Disease. It's really easy for somebody with more expertise in a technical field than the general run of humanity to come to believe that their expertise extends much further than it does.

It's also really easy for somebody highly qualified in Physics, the Queen of Sciences, to come to believe that nobody similarly qualified in a "lesser" discipline (mere aerodynamics! Pfft!) could possibly know anything they don't. Also fun watching the astrophysicist and the Science Guy jump on the wrong train for much the same reason.

That whole business where they all notice a denominator going to zero in and then proceed to claim that the equation concerned must be wrong because its limiting case would imply infinite forces somehow equivalent to a nuclear bomb going off behind the driver was pretty funny, as was Derek's subsequent demolition of that line of reasoning with the analogous case of the zero-length lever arm. I was actually quite surprised to see a professor of physics conflating infinite force with infinite energy in such a slipshod fashion.

To be fair, though, it really is quite rare to find a genuine instance of And Yet It Moves rise gasping to the surface of the customary tar pit of cranks and frauds. And the Prof did accept he'd been wrong and paid up, which good on him for doing that.

If the wheels are driving the propeller, then the wheels will require force to rotate. Can the propeller provide enough force to overcome that and accelerate the vehicle, or realistically even maintain speed? ... That's just a matter of gearing and you can get whatever speed you want by altering the gear ratio and providing sufficient energy ...

There you go: you've provided two nice solid dots. Your job now is to connect them despite your intuition howling at you that you're not allowed to. Some of the discussion under (previously) might help you.

It's OK. Your intuition will retrain, and expand to your benefit.

This was a good post! Thanks, clawsoon.
posted by flabdablet at 10:10 PM on July 1 [24 favorites]


I don't understand the impulse to make a large bet on something like this. If you have legitimate questions about others' methods (theoretical or experimental), raise them. Proposing a bet either implies the other person is acting is bad faith or attempts to embarrass them for making a good-faith mistake. Neither is great. Being willing to bet about this sort of thing doesn't make you right. It makes you arrogant. I'm glad I'm not that prof's student.
posted by samw at 10:19 PM on July 1 [1 favorite]


I think I might just barely understand this: it doesn't count as tacking because changing the angle of the propellor blades doesn't change the direction the propellor itself is moving, which is straight forward and around in a circle, the propellor being like two ships attached at the keel and locked to an imaginary rope guiding their path as they rotate around a cylindrical axle. There might be something akin to tacking if instead the propellor were mounted on some globular thing instead and allowed to wobble?

I'm neither a sailor nor aeronautics engineer though so I have no idea how that jibes with reality. In fact thinking about it gave my brain quite a beating.
posted by mcrandello at 10:21 PM on July 1


Wow. I clearly remember spending a few hours thinking about this 10 years ago. At the time I decided that the easiest way to understand it was to consider some of the wind energy that would otherwise be lost to drag and friction as being captured to propel the cart.

I don't understand the impulse to make a large bet on something like this.

Most likely they had decided beforehand that regardless of the result it would go to a good cause.
posted by mr_roboto at 10:22 PM on July 1


Being willing to bet about this sort of thing doesn't make you right. It makes you arrogant.

$10k strikes me as a completely reasonable price for anti-arrogance tuition. It's win-win!

it doesn't count as tacking because changing the angle of the propellor blades doesn't change the direction the propellor itself is moving

The whole "changing direction" thing with tacking is a bit of a red herring. Tacking lets you sail directly upwind on average by changing direction, but getting some component of your velocity to point upwind doesn't require tacking, just setting the sail at the correct angle. In other words, the interesting part is the upwindness of each leg of a tack, not the zigzag shape of the tacking manoeuvre as a whole.

The right place to look for the analogy between a tacking sailboat and a propellor-driven ground cart is not between the propellor and the sail, but between the propellor blade and the sail. The fact that they're rotating means that the blades change direction continuously while maintaining a consistent angle to the wind.
posted by flabdablet at 10:30 PM on July 1 [12 favorites]


it's a lever, right? objections to it being free energy or perpetual motion would be like saying multiplying force via a lever is creating free energy, so therefore levers are impossible.
posted by wibari at 10:37 PM on July 1 [9 favorites]


DarkForest: Where does the energy come from?

There is energy available to be harvested in the different velocities of the air and the ground. These craft are cleverly designed to extract that energy. The increase in kinetic of the craft is drawn from a decrease in the kinetic energy of the air relative to the ground; the air goes more slowly relative to the ground after the craft has passed through it.

That probably doesn't clarify things for you at this point, but it is the answer to your question.

The great difficulty that we have understanding interactions with air other than being pushed along by drag explains, I think, why it seems so counter-intuitive that an ice boat could travel 6-7 times wind speed, or that a very efficient sailboat could sail upriver with no wind, or that a 50mph wind and 0mph still air could accelerate a glider to 500+mph. I know I've spent years myself trying to wrap my head around all of these things.
posted by clawsoon at 10:38 PM on July 1 [13 favorites]


The best explanation I remember reading back in the day was to consider the path of one of the propeller blades as the car moves. It's going around in a helix, as if it was sailing around a long cylinder whose centerline was above the car. And for something traveling in that direction, along that path, it's the same as sailing across the wind. I think I even saw an animated gif diagram, but I can't find it now.
posted by spacewrench at 10:41 PM on July 1 [5 favorites]


mcrandello: the propellor being like two ships attached at the keel and locked to an imaginary rope guiding their path as they rotate around a cylindrical axle

IIRC, you have come upon exactly the intuition which inspired some of the first people who thought of this.
posted by clawsoon at 10:42 PM on July 1 [2 favorites]


spacewrench, clawsoon- yeah, I was trying to describe exactly that same animation, which I think was somewhere in the middle of the video from the [previously] link. Seeing that was like a nearly-aha moment for me, if that makes any sense...

flabdablet - thanks, I was kind of thinking of the hub section of the half of a two bladed propellor as the body of some misshappen ship. I don't fully get it but it sounds like I have a new hobby now, and maybe an idea for a zoetrope.
posted by mcrandello at 11:15 PM on July 1


Tacking lets you sail directly upwind on average by changing direction, but getting some component of your velocity to point upwind doesn't require tacking, just setting the sail at the correct angle. In other words, the interesting part is the upwindness of each leg of a tack, not the zigzag shape of the tacking manoeuvre as a whole.

My own intuitions have still got "tacking" and "upwind" so firmly entangled that I'd lost track of the vital point here, which is that setting a good enough sail at just the right angle can also make a good enough boat sail across-and-downwind in such a way that not only the boat's overall velocity but the downwind component of it alone is faster than the windspeed.

Which means that you can use tacking to make such a boat sail a zigzag course that runs directly downwind on average, faster than the windspeed. Getting from there to Blackbird is essentially just stepwise use-case adaptation.

Intuitions based on the behaviours of drag-dominated sails are simply not applicable to these cases and actively impede understanding them.

For what it's worth, Blackbird has also set records for the speed of a wind-powered craft running directly upwind.
posted by flabdablet at 11:21 PM on July 1 [5 favorites]


I don't think Prof. Kusenko was wrong or a jerk for proposing a bet on this, and in fact despite the fact that he was wrong about the Blackbird, I think he comes off pretty well here. Science has a long history of friendly bets being made, and there's also a long history of cranks and fraudsters claiming to have invented free energy devices, and one of the best ways to separate the cranks from the fraudsters is to ask them to put some of their own money on the line: cranks will do it every time, fraudsters never will. A friendly bet helps establish that everyone is acting in good faith, and while $10,000 is a lot of money, Kusenko can obviously afford it. And as the money is going to support science communication, I imagine he's probably still happy knowing it's going to a good cause. Had he been correct that there was an error in the Veritasium video, he would have been able to reach literally millions of people to help them understand something about physics. As it turned out, he still gets to help reach millions of people with a video helping them to understand something (different than he expected!) about physics, and also help fund more people becoming science communicators.

Although this definitely isn't a free energy device, it really, really feels like one. And I also don't think this is a clear case of "physicist's disease" making him think he's an expert in something that he's not. The reason this thing works is really subtle, and as the videos from Engineering with Rosie make clear, even engineers who directly specialize in the aerodynamics of wind turbines find it surprising and counterintuitive. Hell, even the rigid body toy model version feels a little bit like black magic when you watch it zip along faster than it's being pushed, at least to me, even though in that case it's totally obvious what's going on. I think that's what makes this such an interesting problem, what makes it worth Kusenko wagering $10 grand on and bringing in two famous science communicators to discuss it. Although the physics is not actually that complicated in one sense, it's still really, really hard to explain what's going on, because the intuitions of even well-trained people are not tuned to this type of problem.

This is a bit like the airplane-on-a-treadmill problem, except way more subtle. In that case, people are led astray by an unrecognized assumption that a plane is pushing against the ground during takeoff, instead of the reality that it's pushing against the air. Even when this is explained to them, some people refuse to let go of this assumption and persist in arguing that the plane can't take off. In this case, there's many more layers of assumptions, some of which are really hard to identify, all of which need to be identified and corrected, and have those corrections accepted, for understanding to follow. In the end, while the plane-on-a-treadmill is pushing against the air and not the ground to accelerate, the Blackbird accelerates only because it is being pushed by both the air and the ground, at different speeds.
posted by biogeo at 12:21 AM on July 2 [12 favorites]


clawsoon: or that a very efficient sailboat could sail upriver with no wind

Now I want to see Blackbird fitted to a rowing shell, with the wheels replaced by an underwater turbine.
posted by Popular Ethics at 1:20 AM on July 2 [2 favorites]


The top (big) wheel pushes against the bottom of the plank and the small (fast) wheels on the ground provide the motive force for the pushing wheel, and the ratio means that you end up doing more force against the moving plank than you get from the ground, and the wheeled contraption moves forward along the plank, faster than the plank.

Quite so.

And if that rolling cart makes sense to you but Blackbird still doesn't, here is a little set of stepping stones:

1. The rolling contact between the top of the big wheel and the plank that's applying motive force to it is equivalent to a rack and pinion gear.

2. A rack and pinion gear is an arrangement for converting between linear motion and rotary motion. The geometry of that arrangement makes the rotary motion happen around an axis that's at 90° to the direction of linear motion.

3. A rack and worm screw is also an arrangement for converting between linear motion and rotary motion. The geometry of that arrangement makes the rotary motion happen around an axis that's parallel to the direction of linear motion. And although most worm drives have the rotary motion as input and the linear motion as output, given a sufficiently coarse thread it's completely practicable to have motion transfer work both ways.

4. A pair of meshing bevel gears can be used to change the axis of any rotary motion by any angle you like, including 90°, and the tooth count ratio between those gears can also transform the rotation speed and torque of those motions any way you like (provided only that the product of rotation speed and torque is the same for both sides of the transform, less losses).

5. Therefore, in theory it should be possible to substitute a worm drive and a set of bevel gears for any rack and pinion, including the effective one at the top of the rolling cart, provided that (a) you can build them with low enough frictional losses and (b) you get the thread pitch and gear ratios right.

6. A propeller, aka an airscrew, is in many ways functionally equivalent to a somewhat lossy worm drive, where the "rack" component is the air through which the airscrew is moving.

7. Blackbird is functionally equivalent to the rolling cart, except that the motive force is supplied by the surrounding air rather than a plank in rolling contact at the top, and it moves faster than its motivator does for the same reason the rolling cart does: leverage/gearing.
posted by flabdablet at 3:45 AM on July 2 [5 favorites]


My own intuitions have still got "tacking" and "upwind" so firmly entangled that I'd lost track of the vital point here, which is that setting a good enough sail at just the right angle can also make a good enough boat sail across-and-downwind in such a way that not only the boat's overall velocity but the downwind component of it alone is faster than the windspeed.

This is how I explain it to myself; it's a down-wind tack with fewer steps. Down-wind tacking is very much a thing, though usually considered fairly dangerous.
posted by bonehead at 5:03 AM on July 2 [2 favorites]


The wind gets the craft moving, the movement of the craft rotates the wheels, the rotation of the wheels spins the propeller, the spinning propeller imparts thrust that increases the craft's speed to higher than the wind. Without wind to make the wheels go round even a little, the craft stops.

Did I get that right?
posted by dazed_one at 5:13 AM on July 2 [2 favorites]


I wonder if there are design changes that could be used for a spacecraft, for it to take advantage of the solar wind in a similar way. Instead of using wheels to drive a propeller, perhaps the flow of charged ions over the craft could be turned into electricity, to do work such as generating thrust.
posted by They sucked his brains out! at 5:35 AM on July 2


Now I want to see Blackbird fitted to a rowing shell, with the wheels replaced by an underwater turbine.

The effect depends on two different media with a difference in relative motion between them. It's air/ground in the case of Blackbird.

A boat with a turbine in water alone won't do it because there's nothing to push against. A boat with a sail and a keel, however, can experience the same effect, with the sails acting as the propeller does, with the keel functioning as the wheels. The boat also has to do it as a zig-zag or tack down-wind. Humanity has been using a very similar force balance trick for a long time, but Blackbird is a really novel application of the same principle.
posted by bonehead at 5:52 AM on July 2


I wonder if there are design changes that could be used for a spacecraft

The effect needs two things moving at different speeds to push against to work. Solar wind is only one, so interstellar space travel is likely out. However, within a gravity field, like in a solar system or even around a planet, that might well provide opportunities.
posted by bonehead at 5:55 AM on July 2 [1 favorite]


A boat with a turbine in water alone won't do it because there's nothing to push against.

Sure there is. There's water for the turbine to react on, there's air for the prop to react on, there's the flat air/water interface to provide stability, and there's relative motion between air and water to extract kinetic energy from.

Going from the geared rolling cart to the Blackbird mainly involves transforming the rolling contact at the top of the cart to an equivalent airscrew. I can see no reason why you couldn't apply the very same transformation to the rolling contact at the bottom. In fact, with suitable blade pitches the coupling between the airscrew and the water screw might even be able to be as simple as a single shaft.
posted by flabdablet at 5:57 AM on July 2 [1 favorite]


The useful thing for me is that I have so little intuitive understanding of physics that I didn't realize I was supposed to find it improbable in the first place.
posted by eponym at 5:58 AM on July 2 [9 favorites]


Xyla switched, after version 1 of her model (which briefly appears in her video), from using the rear wheels (as Blackbird has it) to using the front wheels to be the propeller-drivers. I didn't find the reason for this mentioned anywhere: is it just because Blackbird's chain transmission was improbable to replicate at the smaller scale, whereas shaft transmission was workable? Or was there some inherent stability issue that doesn't get mentioned? (Blackbird's L-shape looks somehow unbalanced, and in Derek's video it does appear dangerously shaky at times...)

Great creator-energy in her other videos too, tftl clawsoon.
posted by progosk at 6:12 AM on July 2 [2 favorites]


A boat with a turbine connected to a prop should work sure, that's essentially a fancy sailboat. A boat with only a turbine would not. Sorry if I misread the question, but I thought the turbine-only question was the one being asked.
posted by bonehead at 6:15 AM on July 2 [2 favorites]


flabdablet: setting a good enough sail at just the right angle can also make a good enough boat sail across-and-downwind in such a way that not only the boat's overall velocity but the downwind component of it alone is faster than the windspeed.

I believe that velocity made good is the sailing term you're looking for.
posted by clawsoon at 6:19 AM on July 2 [2 favorites]


The math of a boat with a turbine in the water and a propeller in the air is, in fact, exactly what Drela analysed (PDF) first, and he replaced the turbine with wheels in the equations as a limiting/simplifying assumption.
posted by clawsoon at 6:22 AM on July 2 [1 favorite]


It would be great if this stuff inspires some people to do more testing with more controls, variations on the experiment, different environments (wind tunnels? really long treadmills?), and more instrumentation to get more insight into what is happening and how exactly it all works.
posted by thefool at 6:34 AM on July 2


Great work guys, we found a physics glitch and now they're going to have to reboot the simulation to patch it out. Nice knowing you all. I hope humans evolve again next ti
posted by EndsOfInvention at 6:36 AM on July 2 [10 favorites]


It has been mentioned a few times in discussions about how this would apply to boats. My immediate guess is that the hard part there is having an efficient enough driver (i.e. connection between boat and water -- a regenerative impeller is likely not as efficient as the wheels on the Blackbird and the models??), plus much more drag in the water?
posted by thefool at 6:36 AM on July 2 [1 favorite]


Sure there is. There's water for the turbine to react on, there's air for the prop to react on

I believe that when bonehead said "turbine alone" they meant no propeller (or sail), i.e. a case where there's nothing pushing on the air.
posted by clawsoon at 6:40 AM on July 2


There's also a lot more drag on the hull in the water, so you want a sailboat amplified by a turbine underwater driving an air fan.
posted by k3ninho at 6:44 AM on July 2


But if pushing water around is an option, a boom in front and behind could create a standing pool of non-draggy water around the hull with a shear envelope between the boat-water and the seas it's riding.
posted by k3ninho at 6:50 AM on July 2


progosk: Xyla switched, after version 1 of her model from using the rear wheels (as Blackbird has it) to using the front wheels to be the propeller-drivers.

My guess is that it's just simpler to build (and as she said she made the gear transmission 1:1 for simplicity of design and analysis) and more reliable and stable (the axle is the main structural member now), at the cost of the propeller tilting up a bit and not facing directly backwards. It's also only one gear transmission, so less overall gear transmission loss.
posted by thefool at 6:55 AM on July 2 [3 favorites]


thefool: plus much more drag in the water?

You want as little drag in the water as possible. The ideal would probably be a foiling boat (e.g. something like a Moth or the last couple of generations of America's Cup boats) because of the dramatic reduction in drag that foiling gives. What you do want under water is a turbine which is transforming its movement through the water into rotational power as efficiently as possible.

Hmm... maybe a good starting point would be one of the craft designed to set human-powered boating records.
posted by clawsoon at 7:02 AM on July 2


> The effect needs two things moving at different speeds to push against to work. Solar wind is only one, so interstellar space travel is likely out. However, within a gravity field, like in a solar system or even around a planet, that might well provide opportunities.

Not quite technically correct - the photons emitted from the sun (i.e. light) and the charged particles emitted from the sun (the solar wind) are two different things. Solar sail ideas tend not to actually use the solar wind, just reflected sunlight, to push them along. This is because the charged particles emitted from the sun are so sparse, the pressure of sunlight is about 1000 times greater than the pressure of solar wind particles at the distance Earth is from the sun.

That said, there's also a proposed idea for making an "electric solar sail" which does use the solar wind particles, operating off the principle that you don't have to actually make direct contact with the particles, just deflect them with an electromagnetic field, so you could have a much sparser and much wider "net" of charged wires and use that to push yourself along.

Unlike light which just shoots straight outward, the solar wind itself is a turbulent plasma that carries the sun's magnetic field with it - it's a little wiggly. So the direction you'd get pushed by the solar wind and by sunlight are actually slightly different. So it's possible you could pull some counterintuitive tricks with that, but the margins would be pretty tiny.

Then again orbital mechanics are themselves counterintuitive - if you're accelerating yourself forward in a circular orbit, what you actually end up doing is pushing your orbit out into an ellipse to the side. And the speed of light is a lot harder limit than the speed of wind, so I'm not sure how far you can draw the analogy. Space is already weird.
posted by Zalzidrax at 7:10 AM on July 2 [3 favorites]


Zalzidrax: Then again orbital mechanics are themselves counterintuitive... And the speed of light is a lot harder limit than the speed of wind... Space is already weird.

I was thinking last night that downwind faster than the wind breaks our intuitions something like relativity did for Newtonian physicists, and something like Newtonian physics did for the folk physics that came before it.
posted by clawsoon at 7:38 AM on July 2


One of the ways intuition trips up on this thing is that people tend to leap to the conclusion that if a machine is claimed to sail downwind faster than the wind then it must logically be an "over-unity" device and therefore impossible.

But the term "over-unity" is properly applied only to machines that provide more energy than they consume. Such machines are impossible, but that's not what Blackbird is. The only thing that's over-unity about Blackbird is its speed with respect to the driving wind. It can't magically extract more energy from the wind than is there for the taking.

What it can do is extract that energy in ways that don't fit within the intuitive frameworks of people whose personal experience with wind forces is dominated by the drag force that wind exerts on human bodies, a force that disappears when body speed matches wind speed.

Blackbird is not capable of arbitrary acceleration any more than a sailboat is. The prop has a variable pitch, controllable by the driver. For any given prop pitch there's a maximum ratio between vehicle speed and windspeed, because that's how leverage works; and for any given windspeed there's an optimal prop pitch that minimizes the amount of energy lost to drag and assorted drivetrain inefficiencies.

Blackbird is not so much a physics glitch as a physicist glitcher.

This, on the other hand...
posted by flabdablet at 7:42 AM on July 2 [11 favorites]


flabdablet: For any given prop pitch there's a maximum ratio between vehicle speed and windspeed, because that's how leverage works

I'm gonna ask Mark Drela about that, maybe after the long weekend, because an earlier response from him about infinite acceleration in conditions of zero drag suggested that that's not correct.

...but it could also be that I misunderstood him or wasn't clear enough in my first question and that you're correct.

Until then, there is this clue from the forum thread I've linked a couple of times:
If the cart is moving at twice the windspeed, then the wheels will actually generate twice as much energy as the prop would require (if it were 100% efficient), since the force is the same and the wheels move twice as far along the ground as the prop does through the air. If the cart is moving at triple the wind speed, then the wheels generate 150% of the energy the prop requires, again ignoring losses.
I think(?) they might mean power instead of energy, but I'm not entirely sure.
posted by clawsoon at 7:54 AM on July 2


...this suspicion is also why I'm not quite sure about the value of the geared-cart-driven-by-a-ruler models for explaining exactly what's going on. They're good for breaking intuitions about slower movement producing faster movement, but I'm not sure if they're truly capturing the thrust dynamics in these craft.

And when I say "I'm not sure", I really mean it, lol...
posted by clawsoon at 7:58 AM on July 2 [1 favorite]


Dang, even after sleeping on it my brain just refuses to accept it. I keep going back to Rosie's excellent analysis to bludgeon my intuition into line. (Can't argue with math.)

I guess this is what it felt like to be a physicist around 1900 when those punks were talking about all that quantum shit.

(I'm a former math professor and current pilot.)
posted by phliar at 8:28 AM on July 2 [1 favorite]


Lecture from Rick Cavallaro which I'm just starting to watch.
posted by clawsoon at 8:36 AM on July 2


Trying to research this online, I learned of hydrofoil sailboats, which are amazing —and somewhat relevant to the topic at hand. From there I came across hydrofoil surfboards which blow my mind way more than the propeller car thing (and are somewhat less relevant).
posted by thedward at 8:43 AM on July 2 [1 favorite]


I saw someone using one of those things on a nearby lake a few months before the 'rona, Thedward.

At first glance I thought they were testing some sort of hovercraft and just flying above water in case they crashed. It was a pretty magical moment, and learning what they were actually doing was almost as cool.
posted by FallibleHuman at 8:57 AM on July 2


Cool post.

But, Foxlin was drilling into a piece that she was holding in her bare hand, with the drill bit passing between her fingers. This is a really terrible idea, isn't it? Something that shouldn't be in a science explainer video that kids will watch?
posted by paper chromatographologist at 9:04 AM on July 2 [1 favorite]


hydrofoil surfboards which blow my mind

Yeah, those things are just crazy efficient.
posted by flabdablet at 9:15 AM on July 2


If you're a sailor, the Rick Cavallaro lecture I linked above is pretty good, though he does get interrupted a lot by yacht club member questions.

The yo-yo demo at 37:30 is nicely counterintuitive even if you're not a sailor. I got it wrong myself, which shows how much I know. And when he explained the effect that changing the yo-yo's axle diameter would have, I realized that I would've gotten that exactly backwards, too.
posted by clawsoon at 9:26 AM on July 2 [1 favorite]


I found the gear cars to get more unintuitive the more I thought about them, until I stopped thinking of gear systems as being a one-way transmission of motion (gear A moves B moves C and so on) and as a system of constraints. The problem is that if you write out the constraints as equations, they have a loop in them*: you can't solve them one at a time from either end, and attempting to do so usually leads to making hidden assumptions that break down.

I think this is one of the reasons the propellor cart trips people up: you really want to start with either the propellor or the wheels, and then reason about how everything else moves in relation to that. But you can't, because they're coupled together in a way that has to be considered jointly.

*If you've taken linear algebra, then a system that you can solve in the 'intuitive' way has a matrix that's diagonal or triangular: you can completely determine one constraint, then use that to completely determine another, and so on.
posted by Pyry at 9:28 AM on July 2 [1 favorite]


This , on the other hand...

Sadly, that one's actually a hoax -- don't even need any complicated arguments about tacking against the wind, you can clearly see they changed out the wheels for a skateboard, probably one with electric motors and a battery.
posted by pwnguin at 9:33 AM on July 2 [1 favorite]


The yo-yo demo at 37:30 is nicely counterintuitive even if you're not a sailor.

And when he converted the demo to a model of a paddle wheel, I got it wrong again!

...but that paddle wheel going downstream twice as fast as the river would make a really cool live demo.
posted by clawsoon at 9:42 AM on July 2


If the cart is moving at twice the windspeed, then the wheels will actually generate twice as much energy as the prop would require (if it were 100% efficient), since the force is the same and the wheels move twice as far along the ground as the prop does through the air. If the cart is moving at triple the wind speed, then the wheels generate 150% of the energy the prop requires, again ignoring losses.

Not right, because it switches reference frames halfway through a sentence. Either with respect to the ground or with respect to the wind, the wheels move at the same speed as the prop; they have to because they're parts of the same rigid assembly. And if you're going to compare input and output energies based on force and motion, you need to pick a consistent reference frame from which to judge the motion.

Clearly, if there are no losses then all of the energy transferred into the driveline by the wheels has to be supplied to the prop. For the wheels to be generating more energy than the prop consumes means that the system is not lossless. So if you're doing a loss-ignoring calculation and get energy results like 200% or 150%, you've simply made an error.

For any constant speed, the net force on the cart is zero, which - given that we're assuming no losses - means that the forward force exerted on the cart by prop thrust exactly cancels the backward force exerted on the cart at the driving wheels. It also necessarily means that the net power being consumed by the cart is zero; exactly 100% of the power transferred into the cart via the wheels is coming out again via the prop.

No losses, for a prop, means that the prop is acting as a perfect airscrew: the product of shaft torque and rotation rate is exactly equal to the product of thrust force and airspeed, and you can get any ratio you want between airspeed and rotation rate by setting the pitch of the airscrew.

No losses, for a shaft attached to a set of drive wheels via a gear train, means that the product of shaft torque and rotation rate is the same as the product of ground force and groundspeed. Again, you can get any ratio you want between rotation rate and groundspeed by setting the wheel diameter and the gear ratio.

Link those lossless assemblies together and you can define any ratio you want between the airspeed of the prop and the groundspeed of the wheels. And you'll find that when the cart achieves that ratio, and only then, the backward force on the driving wheels is equal to the thrust force from the prop so that your lossless model actually works.

As Pyry says, the lossless model defines a system of constraints on the motion of the cart with respect to the ground and the wind.
posted by flabdablet at 10:13 AM on July 2


So if you're doing a loss-ignoring calculation and get energy results like 200% or 150%, you've simply made an error.

Note that it doesn't say that the wheels are generating 150% of the energy (power?) that the prop consumes. It says that the wheels are generating 150% of the energy that the prop requires, which is a different thing.
posted by clawsoon at 10:20 AM on July 2


Different how? If the wheels are generating more energy than the prop requires, and the model is lossless, what do you suppose they're doing with the extra energy?
posted by flabdablet at 10:23 AM on July 2


Accelerating, I'd think.
posted by clawsoon at 10:24 AM on July 2


...but I could be wrong, as always. I do hope to get an answer back from Drela.
posted by clawsoon at 10:25 AM on July 2


Given that the only way that the machine can accelerate is by inducing the prop to generate thrust, I don't think that works.
posted by flabdablet at 10:26 AM on July 2


flabdablet, I took a long shower and did some visualizing and math that I hadn't bothered to do so far, and I think I see more of what you're saying about the screw pitch limiting cart velocity. Does this math look right?

propeller_pitch: defined for convenience as the ratio between the distance that the propeller screws forward through a block of jello-like air and the distance the cart moves over the ground. If the cart moving forward 1 meter would cause the propeller to screw forward 0.1 meters, that's a 0.1 (or 10%) propeller_pitch for the purpose of these calculations.

propeller_speed_relative_to_wind = cart_ground_speed * propeller_pitch

propeller_speed_relative_to_ground = wind_speed + propeller_speed_relative_to_wind

propeller_speed_relative_to_ground = wind_speed + (cart_ground_speed * propeller_pitch)

Steady state/limiting speed when the wind speed plus the propeller speed through the jello-air is equal to the cart speed:

propeller_speed_relative_to_ground = cart_ground_speed

Substituting full equation for propeller_speed_relative_to_ground:

wind_speed + (cart_ground_speed * propeller_pitch) = cart_ground_speed

We can solve this for cart_ground_speed with some rearranging:

cart_ground_speed = wind_speed / (1 - propeller_pitch)

So if the propeller pitch is 10%, we will max out at 1.111... times the speed of the wind.

However, things get interesting when propeller_pitch = 1 (cart ground speed goes infinite), and they get downright weird when propeller_pitch > 1 (cart_ground_speed goes negative).

Did I do my math wrong, or does that mean that a pitch of 1 is our limit, and arbitrarily large velocity (ignoring losses) is achieved by approaching a pitch of 1? That does seem to match some of what was said in the physicsforum discussion I've been linking to, though I'll admit I don't understand all of it.
posted by clawsoon at 11:08 AM on July 2


(And apologies if you've already done this math in a previous post and I glossed over it.)
posted by clawsoon at 11:19 AM on July 2


...and if I get an answer back from Prof. Drela saying that this is correct, I'll take back all the things I said about the ruler-propelled carts not being a good way to explain what's going on. And I'll apologize for arguing with you so much about this, flabdablet. :-)
posted by clawsoon at 11:25 AM on July 2


things get interesting when propeller_pitch = 1 (cart ground speed goes infinite), and they get downright weird when propeller_pitch > 1 (cart_ground_speed goes negative).

In effect, your propeller_pitch value is equivalent to the ratio between the yoyo's wheel and hub diameters in the lecture you linked to. As that ratio approaches 1 from below, the point at which the thread pulls on the bottom of the hub gets closer to the point of rolling contact on the table, and the ratio between the tug-point-to-tabletop and axle-to-tabletop lever arms rises without limit.

So yes, as propeller_pitch approaches 1 from below the ratio of your model cart's ground and jello speeds would increase without limit, but so would the thrust forces that the ground applies to the wheels and the prop applies to the jello.

Propeller_pitch > 1 is equivalent to a yoyo hub that's bigger than the wheels (you'd need a slot in the tabletop for the hub to descend into to make this work in practice), which makes the yoyo run away from the pulling thread; this is what you'd want for a cart that sails dead upwind.
posted by flabdablet at 11:50 AM on July 2 [1 favorite]


I'll apologize for arguing with you so much about this

Have we been arguing? I thought we'd been cross-checking various aspects of assorted conceptual models in the mutual pursuit of understanding.
posted by flabdablet at 11:58 AM on July 2 [5 favorites]


lol, fair point about arguing. :-) In these discussions there are always places where I feel like I'm saying things more confidently (and maybe it comes across confrontationally because that's how online comments are often read?) than I actually know.

The yo-yo example clicks in very nicely with propeller_pitch, exactly as you're describing, now that I've finally done the math.
posted by clawsoon at 12:23 PM on July 2


...and that equation makes sense of the fact that Cavallaro recommended a pitch of ~0.7 (no-drag max ~3.3 times the speed of wind) and Xyla Foxlin found that a pitch of 0.47 (no-drag max ~1.9 times the speed of wind) worked best for her model.
posted by clawsoon at 12:32 PM on July 2 [1 favorite]


Cavallaro discussing vehicle design speed, which is all about setting these ratios to minimize losses.
posted by flabdablet at 12:44 PM on July 2 [1 favorite]


It would be much easier if people who try to explain this to me would just talk about the actual vehicle, the Blackbird, and avoid all kinds of weird metaphors. They are all like, "think of the Earth as a cylinder ..." "it's almost like a lever, so let's talk about a lever instead ...", "consider two sailing ships joined at the keel ..."

Maybe it's not so difficult after all, but you make it sound incomprehensible.
posted by Termite at 12:56 PM on July 2 [1 favorite]


Maybe it's not so difficult after all, but you make it sound incomprehensible.

From Cavallaro:
"There's a dozen ways to explain how this can be done. Eleven of them sound like complete nonsense to most people, but it's always a different eleven. When I get to the one that clicks for somebody, they say, 'Why didn't you start with that one?'"
posted by clawsoon at 1:01 PM on July 2 [9 favorites]


Termite: It would be much easier if people who try to explain this to me would just talk about the actual vehicle, the Blackbird, and avoid all kinds of weird metaphors.

I think the reason that people go into all the alternate explanations is because when you explain directly how the cart works people think that conservation of energy is being violated and that you're describing a free-energy perpetual motion machine. All of the extra explanations are to show why it doesn't violate any physical laws.

Here's an attempt at a straightforward description: The wheels are attached to the propeller by a chain. The chain has a ratchet so that it only transmits force one way: From the wheels to the propeller. When the craft is standing still in the wind, the wind pushes on the propeller using plain old drag, which slowly (very slowly) makes the cart start moving forward. When the cart starts moving forward, it turns the wheels. Since the wheels drive the propeller, that makes the propeller start turning. The turning propeller generates thrust backward which pushes the cart forward. As the cart goes faster, the wheels turn faster, which turns the propeller faster, which generates more thrust. With a correct ratio between cart speed and propeller pitch, and low enough drag on the propeller and the cart, the cart can go directly downwind faster than the wind. The current record is 2.8 times the speed of the wind.

Did that help at all?

Does it give you any sort of feeling that conservation of energy is being violated and someone is trying to pull the wool over your eyes?

Side note: I wonder if we make mistakes about conservation energy because the classic examples of no-free-energy always involve something slowing down. Energy is extracted from a rolling ball by friction, so it slows down and then stops. You can't make your truck go faster than itself by attaching an alternator to the wheels and feeding the electricity back to an electric motor; the truck will always go slower when you add more energy conversions. We come to associate "conservation of energy" with "conservation of velocity" and are immediately suspicious if something being pushed goes faster than what's pushing it.
posted by clawsoon at 1:18 PM on July 2 [3 favorites]


It would be much easier if people who try to explain this to me would just talk about the actual vehicle, the Blackbird, and avoid all kinds of weird metaphors.

Okay then, here's the thumbnail sketch.

What we have is a cart, with a propellor chain-driven off the wheels. The drive train establishes a fixed ratio between the speed that the cart runs along the ground and the rotation rate of the propellor. The driver can vary the pitch of the propellor blades, making it possible to trade off the amount of thrust that the propellor delivers against the amount of power that the wheels have to pick up from the ground in order to generate that thrust. The propellor works just like the one on an aeroplane, acting to push the cart through the air.

The reason that this isn't an idiot perpetual-motion nonsense machine is that there is more power available to the driving wheels than is required to drive the prop. And the reason for that is that there is a prevailing wind blowing in the same direction that the cart is going, and that wind makes the cart's airspeed lower than its groundspeed.

Although the cart is running downwind faster than the wind, and therefore running into an apparent headwind, that apparent headwind is slower than the cart's groundspeed. And as it turns out, that difference means that there's enough power extractable from the wheels to overcome the headwind with prop thrust, even though a fair bit of the extracted power gets lost to various drags and inefficiencies.

Does that help?
posted by flabdablet at 1:19 PM on July 2 [6 favorites]


One further point: any given drive train gearing and propellor pitch establishes a ratio of groundspeed to wind speed at which the power extracted from the wheels would be exactly enough to overcome the apparent headwind using propellor thrust if there were no drag losses on the cart frame or propellor blades and no losses in the drivetrain.

Pitching the propellor more coarsely (which the driver can do on-the-fly) raises that ratio, but it also makes the drive less efficient; there always are losses, and the more thrust the prop is made to deliver, the worse they get. For any given windspeed, then, there's a propellor pitch setting that maximizes the cart's speed. So the cart can't travel arbitrarily faster downwind than the wind.

In fact there's a particular propellor pitch at which the theoretical ratio between cart speed and wind speed would become infinite, but in practice the prop efficiency at that pitch is so poor that choosing it just makes the cart come to a dead stop instead.

Pitching the propellor even more coarsely than that reverses the power transfer through the drive train, the prop begins to work as a turbine and deliver power to the wheels instead of extracting it from them, and the cart starts running backwards - directly upwind.

The explanatory presentation from the cart's designer that clawsoon linked above is well worth watching, as are both the (considerably shorter) Veritasium videos, if you're interested in understanding how the cart actually works.
posted by flabdablet at 1:40 PM on July 2 [1 favorite]


Here's an article she wrote a few years ago, it's powerful.
posted by mareli at 1:42 PM on July 2 [8 favorites]


Thanks for that link, mareli. I wish I would've seen it in time to include it in the post. Almost feels like it deserves an FPP of its own.
posted by clawsoon at 1:52 PM on July 2 [2 favorites]


I'm a coach of a high school robotics team. That post is deeply disappointing (but important) to read. I'm glad the experience didn't push Foxlin to abandon engineering (I'm sure it would and does many other women).
posted by Popular Ethics at 2:05 PM on July 2


Would and does and has. I've seen it happen.
posted by flabdablet at 2:09 PM on July 2 [1 favorite]


I liked the example from the talk of pulling on the telephone pole, that made the yo-yo situation much clearer to me.
posted by fleacircus at 3:07 PM on July 2


Flame
throwing
greeting cards.

This is just to say...
posted by clavdivs at 9:19 PM on July 2


Thanks to this post I now am subscribed to Xyla Foxlin's excellent YouTube channel. I love maker channels!
posted by Pendragon at 5:06 AM on July 3 [3 favorites]


this thread rules
posted by lazaruslong at 7:44 AM on July 3 [2 favorites]


Clawsoon is right, Mareli; that does deserve a post of its own.
posted by jamjam at 1:05 PM on July 3 [1 favorite]


I paused the video halfway through so I can think through this, and even going back to first principles there are some things that are not obvious and not covered in intro physics, since traditionally stuff about wind or fluids is done in specialized courses (which I didn't take).

Here's my problem: consider the simple case of an ideal object on a frictionless surface, sitting in constant wind. Then the object's acceleration is actually nonlinear, given by:

Net force = k (w - v) = m a, where
k = some wind interaction constant (that is proportional to surface area, etc.),
w = wind velocity
v, m, a = velocity, mass, and acceleration of the object.

But since v(t), a(t), x(t) are functions of time, that leads to a differential equation of the form
kw - kx' = mx''
And the solution is.. what!? I have no idea what that is.
posted by polymodus at 5:01 PM on July 4


So I fixed the variable names to get what I think is the solution for an ideal object floating in the wind, and looking at the terms, it seem from initial position the object never actually even reaches wind velocity, only asymptotically. There's a discontinuity there. That's interesting and nonobvious (and somewhat counter to intuition as well).
posted by polymodus at 5:23 PM on July 4


Polymodus, does my calculation above for the simple case of limiting velocity with the propeller's screwing forward through the wind also factored in make sense to you? I'm hoping it makes sense to someone other than just me, because I've just spent some money on some Meccano bits to make an analog of Blackbird where the propeller is represented by a screw and the air is represented by a nut and that equation is supposed to describe what will happen... :-)

I assume you've already read through Drela's analysis (PDF), which mostly went over my head. Have you had a chance to look at the real-world acceleration data in the various (PDF) reports (PDF) from the NALSA page?

FWIW, once you add in the gearing of the propeller screwing its way through the wind (if my equation above is correct), the vehicle speed ratio of the cart goes toward infinity as the gearing of the entire vehicle approaches 1. (It goes toward negative infinity as it approaches 1 from above.) I called that gearing "propeller pitch" above, but that was a bad choice, since that term is already used for something else. I've started calling it "cart_pitch" instead (as I talk to myself all night about it, lol). The terms I've been using for my equation today:

cart_speed = wind_speed / (1 - cart_pitch)

vehicle_speed_ratio = 1 / (1 - cart_pitch)

This is for zero losses of any kind; a spherical cow of a Blackbird.

I think I've figured out what that equation means, and what the divide-by-zero that shows up in it means, too.

- When cart_pitch is less than 1, it means that the wheels have a mechanical advantage over the propeller. Thus, the wheels will force the propeller to turn in the direction opposite to what it would turn if the wind were turning it. If cart_pitch is between 0 and 1, the cart will go downwind faster than the wind. If cart_pitch is less that 0, the cart will go downwind slower than the wind.

- When cart_pitch is greater than 1, it means that the propeller has a mechanical advantage over the wheels. Thus, the propeller will force the wheels to turn in the direction opposite to what they would turn if they were rolling with the wind. If cart_pitch is between 1 and 2, the cart will go upwind faster than the wind. If cart_pitch is greater than 2, the cart will go upwind slower than the wind.

- When cart_pitch equals 1, it means that the propeller and wheels have equal mechanical advantage. They are stuck pushing each other with no winner, and the cart stands still. We have divided by zero in the real world.

- When cart_pitch is very close to 1, the vehicle speed ratio gets very large. However, the law of conservation of energy means that the torque goes down as speed goes up. At some point, the torque gets tiny and is unable to overcome to losses in a real-world system. This is true even if the system is moving very slowly and we don't have to worry about all the "drag goes up with the square of velocity" stuff. It's that tradeoff between speed and torque as we increase which stops us from going to infinity in the real world.
posted by clawsoon at 5:40 PM on July 4 [1 favorite]


polymodus: Here's my problem: consider the simple case of an ideal object on a frictionless surface, sitting in constant wind. Then the object's acceleration is actually nonlinear, given by:
Net force = k (w - v) = m a, where
k = some wind interaction constant (that is proportional to surface area, etc.),


If it helps (or complicates things), it sounds like you're describing purely drag-based acceleration, in which case k(w-v) will vary with (w-v)2, as per ye olde drag equation.

Once the propeller starts turning and you get into lift-based acceleration, you gotta start drawing vectors everywhere...
posted by clawsoon at 7:18 PM on July 4


The reason you gotta start drawing vectors: Drag acts parallel to the flow of the air over the object, but lift acts perpendicular to the flow of air over the object.

For an airfoil shape, the force of lift will be anywhere from about 10 to 80 times the force of drag. The combined vectors produce a force which is almost perpendicular to the flow. Not quite perpendicular, though, because of drag; it'll be anywhere from 5 to 15 degrees back of perpendicular.

If you move your object through the air in a direction perpendicular to the flow of the air - like a propeller does - the perpendicular force of lift and the perpendicular travel through the air combine to produce an anti-parallel force, i.e. forward. Hence the forward thrust of a propeller.

...well, almost. You've still got a drag vector acting at 90 degrees to the lift vector with 1% to 10% of its force. And if there's a wind, it will change the effective angle of your attempt at perpendicular motion into an angled motion through the air. And if you're moving through the air, that'll change your effective angle yet again...
posted by clawsoon at 3:31 AM on July 5


(This is one of those times when explanations would be much easier if we were standing in front of a chalkboard together. Or even on the beach drawing with a stick in the sand...)
posted by clawsoon at 3:40 AM on July 5


Also worth having a good think about what "ignoring losses" actually implies. If it implies that the prop doesn't interact with the air even slightly then there's trouble because, ignoring losses, even a simple wheeled cart with no complicated drive train at all can maintain any completely arbitrary velocity regardless of wind speed.

But if "ignoring losses" means that the prop blades generate only lift forces and therefore act like a perfect, frictionless airscrew, then a Blackbird-style drive train sets up a purely geometrical relationship between the speed at which the air moves over the ground, the speed at which the prop screws through air, and the speed at which the wheels roll over the ground. That's the analogue of the telegraph pole and yo-yo and assorted ruler-rolling cart models (and clawsoon's hopefully-soon-to-exist screw model as well). In other words, under completely ideal conditions the cart is constrained by geometry to move at a multiple of the windspeed defined by the drive train; and since there are no drag or frictional losses assumed, it's pointless to analyze forces or power transfers under these conditions because there aren't any.

But losses always do exist, and that's what makes this cart so demanding of explanation. The idea of picking up power from the wheels and dumping it into the prop to make the cart go faster has such a strong stink of over-unity generator-powering-motor-spinning-generator as to raise huge red flags immediately.

So it's necessary to think about power transfers and losses to understand how Blackbird manages not to be an over-unity bullshit machine.

If object A is moving relative to object B, and also exerts a force on object B, then as judged from B, A is transferring to B an amount of power equal to the relative velocity multiplied by the relative force.

The ground exerts a backward force ground_force on the cart's drive wheels, and is also moving backward at ground_speed with respect to the cart; therefore as judged from the cart there is (ground_power = ground_force × ground_speed) power being transferred to the cart at the wheels.

The air exerts a forward force thrust_force on the cart's prop, while also moving backward at (ground_speed - wind_speed) with respect to the cart (because that's what props do); therefore as judged from the cart there is (thrust_power = thrust_force × (ground_speed - wind_speed)) power being transferred from the cart at the prop.

To allow for losses and avoid over-unity bullshit, all we need is

thrust_power < ground_power

Expanding and rearranging:

thrust_force × (ground_speed - wind_speed) < ground_force × ground_speed
thrust_force × ground_speed - thrust_force × wind_speed < ground_force × ground_speed
thrust_force × ground_speed - ground_force × ground_speed < thrust_force × wind_speed
(thrust_force - ground_force) × ground_speed < thrust_force × wind_speed
ground_speed / wind_speed < thrust_force / (thrust_force - ground_force)

Note that the relationship between thrust_force and ground_force is defined entirely by wheel, prop and drive train geometry, which we can easily manipulate to make thrust_force exceed ground_force and the right hand side therefore exceed 1. Which means we don't need over-unity magic to make the left hand side exceed 1 as well, just careful minimization of losses so that the amount of < that's actually required isn't too dramatic.
posted by flabdablet at 7:01 AM on July 5 [1 favorite]


consider the simple case of an ideal object on a frictionless surface, sitting in constant wind

Consider it all you like, but that's not what Blackbird is. Blackbird is strongly coupled to both the wind and the surface.
posted by flabdablet at 7:20 AM on July 5 [1 favorite]


I realized that I made a major mistake here which I think is tied to the mistake nearly everyone makes with Blackbird:

You can't make your truck go faster than itself by attaching an alternator to the wheels and feeding the electricity back to an electric motor

This implies a "law of conservation of velocity", which does not exist. You can make your truck go faster with the right choice of alternator and electric motor, if you set them up to effectively increase your gearing. What the law of conservation of energy will impose on you in that case, though, is that the torque available from your wheels will go down, just as it would with any change in gearing which increases your speed.

I think that might be the next challenge for someone to blow people's minds and start a million Internet arguments: Make a truck go faster by using a clever combination of alternator and electric motor in order to increase its effective gearing.

Fuel efficiency will go down - you don't get free energy - but it should be possible to make speed go up.
posted by clawsoon at 8:09 AM on July 5


If you're not going to stipulate that your increased speed must be had at the same engine power output then you might as well just press harder on the accelerator, no?

You can make your truck go faster with the right choice of alternator and electric motor, if you set them up to effectively increase your gearing. What the law of conservation of energy will impose on you in that case, though, is that the torque available from your wheels will go down, just as it would with any change in gearing which increases your speed.

Pretty sure any involvement of a ground wheel in the connection between your engine and your alternator is going to bollix up the "gearing" and turn any wheels->alternator->motor->wheels pathway into nothing more than an overcomplicated brake.

If you don't involve a ground wheel, and just connect the engine directly to the alternator, then what you've made is a completely ordinary series hybrid drive and that's not going to blow many minds.
posted by flabdablet at 9:22 AM on July 5


You're no doubt correct, flabdablet. Although... how is connecting an alternator to the wheels any different from connecting it directly to the engine, other than the gearing that's in between?
posted by clawsoon at 10:22 AM on July 5


No connection from engine to wheels means the ground speed isn't putting a constraint on the way engine power factors out into force and speed.

Once you've forced a particular factoring by making a mechanical connection from engine to wheels, the only thing you can do by adding additional items that function as if geared to the wheels is make their internals move.

If those internals effectively amount to a gear train whose input and output forces are different, then that means their input and output speeds are necessarily also different. So if you hook up such a gear train to the same set of drive wheels at both ends, it will just lock up.

If you separate driving wheels from driven wheels, but they're both the same diameter and they're both running on the same ground, you still get a lockup. And if you play with the drive and driven wheel diameters to compensate for that, then all you're doing is returning the gear train's effective gear ratio back to 1:1 and you might as well not have bothered.
posted by flabdablet at 11:22 AM on July 5


Ah, so hybrid drive where the engine doesn't drive the wheels directly. I think I was mixing together a simple engine->alternator->motor hybrid in my mind with something like this or this (where the electric power is provided by batteries and the motor output is mixed into the engine output) to produce a monster.
posted by clawsoon at 11:45 AM on July 5


Is this interpretation correct?

Imagine we just use a regular sail across the wind to get up to wind speed. Once we get up to speed, take down the sail and engage a heat pump to run off the wheels. Use the heat pump to run a steam engine to further propel the wheels. So long as the energy the heat pump can extract from the air is greater than the energy needed to run the heat pump, the car will accelerate.

The heat pump isn't creating energy, it is moving energy around. It is perfectly reasonable for a heat pump to extract more energy from the environment than is used to run it. In fact this is why they are used to heat homes rather than use the energy directly.

In this case the heat pump is the Bernoulli's Principle of the propeller blade.
posted by lowtide at 1:09 PM on July 5


I feel like it should be noted explicitly that the fan is not fixed pitch, which means the effective gear ratio can be changed. That's how it can first use the relative wind to drive the wheels and then switch to driving the fan from the wheels.
posted by wierdo at 1:19 PM on July 5 [1 favorite]


lowtide: Once we get up to speed, take down the sail and engage a heat pump to run off the wheels. Use the heat pump to run a steam engine to further propel the wheels. So long as the energy the heat pump can extract from the air is greater than the energy needed to run the heat pump, the car will accelerate.

The heat pump isn't creating energy, it is moving energy around. It is perfectly reasonable for a heat pump to extract more energy from the environment than is used to run it.


If I'm understanding your description correctly, that will only work if you have two temperatures to put the different parts of the heat pump in. And if you have that, you don't need the sail in the first place, since the heat pump by itself could power the wheels.

If you're thinking of using the heat pump like a battery, where you "charge it up" while using the sail, and then when you put away the sail you deplete the heat difference to accelerate past wind speed, you'd generally be accused of cheating in this particular exercise. :-) You'll also run out of energy to extract at some point, when your accumulated heat has depleted.

Blackbird has the ability to start at 1.4 times wind speed and go up from there to 2.8 times wind speed; it doesn't need to store up any energy while it's at less than 1 time wind speed.
posted by clawsoon at 1:38 PM on July 5 [1 favorite]


the fan is not fixed pitch, which means the effective gear ratio can be changed. That's how it can first use the relative wind to drive the wheels and then switch to driving the fan from the wheels.

The variable pitch control is a fairly late addition to the design. The first working version of Blackbird didn't have it.

There isn't really a "switch" to driving the prop from the wheels; the prop is always driven from the wheels. With a fixed pitch, it just works inefficiently until the cart's speed climbs to the extent that prop thrust and wheel resistance get quite close to matching; that's the point at which the drive train geometry has the prop working as close as it's going to get to a perfect airscrew.

Making the pitch variable and driver-controlled allows the driver to find that efficiency sweet spot at a relatively low groundspeed-to-windspeed ratio, then keep the machine working as efficiently as it can while gradually increasing that ratio. But all that does is shorten the runup to full speed; the machine can still start from rest and accelerate to 3x windspeed even if the pitch stays set for 3x windspeed for the whole run.
posted by flabdablet at 2:11 PM on July 5


take down the sail and engage a heat pump to run off the wheels. Use the heat pump to run a steam engine to further propel the wheels.

The presentation that clawsoon linked above includes a section analyzing the behaviour of a conceptual model where the driving wheels run a generator that makes electricity to power a motor driving the prop, and where the whole affair is started off by dragging it behind a car, which is essentially a simpler way to achieve the heat pump running a steam engine idea started off by sails idea.

Using a generator to run a motor would certainly be less inefficient than using a heat pump to run a steam engine.

The reciprocal of a heat pump's best theoretical coefficient of performance for a given mechanical power input and a given heat power output at a given temperature difference is the corresponding heat engine's best theoretical efficiency for converting the same quantity of heat power input at the same given temperature difference back to mechanical power. So if you had a perfect heat pump with perfect thermal coupling to a perfect heat engine, you could in theory extract all of and exactly the heat pump's input power at the output of the heat engine.

In practice, heat pumps and heat engines fall horrendously short of these maximum efficiencies compared to electric motors and generators, which are themselves not quite as good as a low-loss direct mechanical drive such as the bicycle chain that Blackbird uses. The overwhelming majority of the power lost between Blackbird's wheels and prop is drag losses inside the prop itself.
posted by flabdablet at 2:28 PM on July 5


hybrid drive where the engine doesn't drive the wheels directly

as has been used in diesel-electric locomotives for many decades.
posted by flabdablet at 2:57 PM on July 5 [2 favorites]


flabdablet: There isn't really a "switch" to driving the prop from the wheels; the prop is always driven from the wheels.

I could be wrong, but I believe that the "switch" is the change in pitch or gearing which gives the propeller a mechanical advantage over the wheels instead of the other way around, at which point Blackbird starts travelling upwind. (Well... it would work that way if the chain were fixed instead of being ratcheted. To get the upwind record, they did have to physically flip the ratchet direction over, though I believe that in theory it's not necessary.)
posted by clawsoon at 3:10 PM on July 5


Fair point, but that's a switch that doesn't occur anywhere between starting from a standstill and achieving maximum speed on a downwind run, as wierdo seemed to be implying that it did. In no part of a downwind run does the prop ever drive the wheels.
posted by flabdablet at 4:56 PM on July 5 [1 favorite]


In no part of a downwind run does the prop ever drive the wheels.

True.

I haven't quite figured out if it could. I think so, maybe? If you started with the front of the blades pointing back (cart_pitch<0) I believe that the propeller could drive the wheels up until the neutral point (cart_pitch=0) and then simply keep increasing pitch (0<cart_pitch<1) to go faster than the wind and switch to the wheels driving the propeller.

How this would all tie into the practical limits on a propeller I don't know. It might be that getting maximum speed in air involves gearing the cart in a way that makes it pointless to take advantage of negative pitch.

Or it might be that I have gotten all of this wrong yet again. :-)
posted by clawsoon at 5:48 PM on July 5


If you started with the front of the blades pointing back (cart_pitch<0) I believe that the propeller could drive the wheels up until the neutral point (cart_pitch=0)

That would indeed work, because doing it would allow the whole drive train to keep spinning in the same direction the whole time, except that Blackbird has a freewheel clutch in the drive train that allows the prop to spin freely whenever it tries to overrun its drive shaft instead of transferring wind power to the wheels.

The reason that the clutch is in there is to make it perfectly plain that Blackbird does not and cannot "cheat" by picking up and smoothing out energy from gusts as Prof. Kusenko confidently and ignorantly asserted that it must be doing in his initial "debunk".
posted by flabdablet at 11:36 PM on July 5 [1 favorite]


This is just a fun physics puzzle to bat around with my inner skeptic, even though physics is not my strong suit at all.

Something I find convincing for myself is the idea of leverage, a la what wibari said above. In the treadmill case, if I try to doubt and think something like, "Okay, it is harnessing power from the treadmill somehow, but couldn't it never *quite* get enough to *gain* on the treadmill", then I think, "Okay, so imagine it being just barely short of gaining on the treadmill, and now imagine it has a much bigger lighter propeller." Intuitively it seems absurd that would only produce some tiny fractional gain. There's leverage going on; imagine a bigger lever.

Other more Deep Though things I confound my inner skeptic with are, "Why is the wind not blowing the ground? There is some differential there that can be harnessed. Like wind turbines don't really create energy out of nothing there's just very external stuff." Another is, "The wind isn't just pushing the car, it's also pushing the air in front of the car to make way for it, it's pushing on the air the propeller is pushing on."

In no part of a downwind run does the prop ever drive the wheels.

This is true, though in a video the Blackbird guy talks about a feedback effect, and it IS sort of a brain teaser how it seems like the thrust from the propeller produces more speed on the wheels which gives more thrust to the propeller etc.

I'm BAD at physics math, I just don't get it, but it seems like there should be some kind of interpretation where a geometric sum explanation might fit. Like, if the gearing is ideally 2:1 where 1" of raw travel gets you 1/2" of bonus distance, but then 1/2" of that bonus distance is more bonus distance, etc., then you get 1"+1/2"+1/4"+... = 2", which is the "right" amount. So a given gearing can go arbitrarily high but still theoretically bounded. And if your ratio is over 1, it starts going backwards because now one side is just easier to push than the other, like the water wheel example. Not sure if this is right but it seems to fit what I understand.
posted by fleacircus at 2:57 AM on July 6 [1 favorite]


Also I've watched a few of Xyla Foxlin's videos and holy hell she does some meticulous and labor-intensive projects.
posted by fleacircus at 2:59 AM on July 6 [1 favorite]


in a video the Blackbird guy talks about a feedback effect

That's what finding an operating sweet spot feels like. You can see much the same thing happening when, for example, a two-stroke dirt bike engine achieves enough RPM to get into its power band: the bike suddenly takes off like a cut cat without needing any increase in throttle to make that happen, because an increase in RPM increases power output, which allows for further increase in RPM and up and up it goes.

and it IS sort of a brain teaser how it seems like the thrust from the propeller produces more speed on the wheels which gives more thrust to the propeller etc.

The thing to keep firmly in mind to resolve the tease are the distinctions between speed and force and power. People without much physics background tend to use these terms interchangeably but they're not the same things, and understanding how they relate is really helpful when trying to wrap your head around apparent anomalies like Blackbird.

Power is the product of force and speed. So you can break down a given amount of power as a low force at a high speed, or a medium force at a medium speed, or a high force at a low speed. A gear train is a common physical realization of this principle, and contemplating how a pushbike's gear set lets you choose how to express your available power output as either a high speed on the flat in high gear, or a high force at low speed for hill climbing in low gear, is really helpful for understanding it.

In Blackbird, the drive wheels work like a highly-geared fixie rolling downhill: not much force resisting that motion, but lots of speed, which multiply together as a certain quantity of power fed into the drivetrain.

All of that power, less the inevitable losses, gets fed into the prop. Note well: that's an overall transfer of power, not of force specifically or of speed specifically, from the wheels into the prop. Some of that power does get lost along the way, and this is what makes Blackbird not a perpetual-motion nonsense machine.

The prop, in turn, operates like a bike in low gear: the power fed into it resolves as less speed than at the wheels, because the prop is engaging with a medium that's moving slower with respect to the cart than the ground is, but more force. Not magic, just gearing.

And even though the power fed into the prop will always be a little less than what's collected from the wheels because losses, there will still be a gearing that lets the prop exert more force than the wheels, provided only that the cart has to push through air less quickly than it rolls over the ground. Which will be the case whenever there's a wind blowing over the ground in the direction the cart is going.

And since the prop is thereby pushing forward with more force than the wheels are dragging backward, the net force points forward and the cart accelerates.
posted by flabdablet at 5:13 AM on July 6 [1 favorite]


Well it's confusing to physics professors and aerodynamic engineers too, so I don't think just tightening in the 101 definition solves the brain teaser and not really a useful response to what I was saying.
posted by fleacircus at 7:21 AM on July 6


Once the 101 clicks, it does solve the brain teaser. However, which one of the dozen explanations makes the 101 click is different for everyone.
posted by clawsoon at 7:55 AM on July 6 [1 favorite]


fleacircus: Like, if the gearing is ideally 2:1 where 1" of raw travel gets you 1/2" of bonus distance, but then 1/2" of that bonus distance is more bonus distance, etc., then you get 1"+1/2"+1/4"+... = 2", which is the "right" amount. So a given gearing can go arbitrarily high but still theoretically bounded.

I think you're on to something, since the formula for the sum of a geometric series:

sum = constant / (1 - ratio)

...ends up being the same as the formula I worked out using a different method:

cart_speed = wind_speed / (1 - cart_pitch)
posted by clawsoon at 8:01 AM on July 6


I have made a quick and dirty mechanical model.

I spent three days trying and failing to get a cart ratio over ~1/6 (i.e. cart_speed = ~6/5 * wind_speed). Even getting a cart ratio of 1/5 proved to be too much for these cheap plastic gears. Past a certain amount of force, they would get dramatically stickier. I tried many tiny adjustments, many different combinations of gears, and grease. Nothing got me past ~1/6. Hopefully with metal gears I'll have more luck.
posted by clawsoon at 11:22 AM on July 9 [3 favorites]


Thanks for the intro to Ms. Foxlin, who is awesome! "For some reason, NASA hasn't tested the terminal velocity of a Ms. America crown yet."
posted by Slothrup at 6:42 PM on July 9 [1 favorite]


Hopefully with metal gears I'll have more luck

If you can find a 2:1 bevel gear, you could halve the ratio between the wheels and the intermediate shaft driving the bevel. That should cut friction losses a bit, both by reducing the meshing inefficiency inherent in large wheel:pinion ratios and by reducing the spin rate of the intermediate shaft in its bushings.
posted by flabdablet at 7:23 AM on July 10


If you can find a 2:1 bevel gear

I've since switched from bevel gears to a crown and pinion. I think that the bevel is theoretically more efficient, but in practise the crown and pinion seems to be dealing better with the slight shifts in position that come with the changing forces on the screw. I do have a thrust bearing in there, but it seems like I'd have to do more to keep bevel gear clearances consistent.

It also helped to replace the bent shaft I was using between the bevel gear and the screw with a straight one, lol...

I'm thinking of using a pair of rack gears as rails. That should (I think) make it easier to have the wheels-to-ground friction be larger than the screw-to-nut friction.

What seems to be my biggest remaining problem is screw-to-nut stiction under load. It's just hard for the screw to get going when it's being pushed on. Switch from plastic to brass? PTFE lube? Graphite powder? Spend lots of money for a proper ball screw? White grease and baby oil have both helped a bit, but haven't solved it.
posted by clawsoon at 8:09 AM on July 10 [1 favorite]


What seems to be my biggest remaining problem is screw-to-nut stiction under load.

Makes sense, because that's where the vast bulk of sliding contact is in the drive train. Perhaps a useful analogue to drag in a prop?

Super smooth small-diameter stainless steel thread running in a Delrin nut with a bit of graphite is probably going to be about as good as it gets without going full ball screw. Careful with oil based lubes on Delrin, they make it swell.
posted by flabdablet at 8:30 AM on July 10 [1 favorite]


What's the friction tradeoff with a small diameter thread with small pitch turning fast versus a large diameter thread with large pitch turning slowly? (Versus a small screw turning slowly but with the high slope needed to get a large pitch?)

I don't know where I'd get small, super-smooth stainless steel and a Delrin nut (or how much I'd pay for that), but I do have some 2mm rod around here with brass nuts that I could try with 5x the gear ratio I've got now...
posted by clawsoon at 8:49 AM on July 10


meshing inefficiency inherent in large wheel:pinion ratios

Does this mean I'd be better off with multiple moderate ratios instead of one big ratio? Or is that an "it depends" thing?
posted by clawsoon at 9:27 AM on July 10


Maximum practicable ratio for spur gears in a single stage is usually taken to be about 7:1, which already involves quite a lot more sliding contact between teeth than you get at lower ratios.

Frictional force in a sliding contact is calculated as the coefficient of friction for the materials involved (static and sliding coefficients are different, which is why stiction is a thing) multiplied by the force normal to the contacting surfaces. Contact surface area theoretically cancels out, but in practice, larger surfaces will have a higher coefficient of (especially static) friction because of greater opportunities for contaminants and irregularities to help them bind together.

So a screw thread with a given pitch angle, subjected to an axial applied force between thread and nut, is going to see a frictional rotation-resisting force that's proportional to the coefficient of friction between thread and nut (which is set by choice of materials and surface finish), the axial force, and the cosine of the thread pitch angle. That force is then going to translate into a torque proportional to the thread's diameter.

So if what you need is a nut that moves distance D along a thread per rotation, and what you have instead is a thread with a pitch of D/5, and you gear the thread up by 5:1 to get the effective pitch you need, then you're (a) imposing a thread pitch angle cosine that's higher than using the correct thread would get you and (b) multiplying the frictional torque by a factor of 5 in the gearbox. In effect, the gearbox effectively scales the entire thread up, both in pitch and diameter, by a factor of 5 and then adds gear friction losses on top.

Small thread diameter (to minimize the conversion of frictional force into torque) and coarse pitch (to lower the cosine of the pitch angle) running at low speed (to minimize the conversion of frictional torque into lost power) would seem to be the way to go.

And according to this table of coefficients of friction, Teflon (PTFE) is probably the material of choice for both thread and nut. If you don't have a proper lathe, perhaps you could fabricobble a thread cutting jig out of gears and Lego that's good enough for Teflon?
posted by flabdablet at 10:40 AM on July 10


Actually I think I've missed some steps around the way the along-the-helix friction force translates to lost torque. There's a sine or tangent somewhere I'm sure I've left out. Will have to sit down with pencils and draw vectors and not lose sight of the aim of maximizing the efficiency of conversion between torque and axial force.

Shouldn't be that hard - a screw is just a wedge wrapped around a cylinder, after all.
posted by flabdablet at 10:48 AM on July 10 [1 favorite]


I could be wrong, but the part about wanting a higher thread pitch angle seems like it might (?) be wrong. I'm mostly basing that on the idea that a 0 degree thread pitch angle would contribute 0 to frictional load, while a 90 degree thread pitch angle (a spline) would bring the screw to a stop.
posted by clawsoon at 11:01 AM on July 10


(I'm also guessing that for upwind operation, where the nut drives the screw instead of the screw driving the nut, a higher angle will have lower friction, via the same reasoning.)
posted by clawsoon at 11:04 AM on July 10


I just went to look up friction on an inclined plane and realized that I'm not sure whether the principle force is the perpendicular one from the torque on the screw or the parallel one from the axial load and got confused. And then they were in the closet making babies and I saw one of the babies and the baby looked at me.
posted by clawsoon at 11:26 AM on July 10


Based on this, I got that the excess force available to turn the screw is the axial_force times this, where .5 is the cart_ratio, .1 is the coefficient of friction, and x is propeller_pitch/propeller_circumference. It is suggesting a pitch-to-circumference ratio of 2-ish, which is much higher than I expected.

I did all of the algebra tired, though, so I probably got it wrong. If anybody feels like checking my work to see if I got the right answer...
posted by clawsoon at 3:26 PM on July 10


I think I had an extra term in there. Maybe this instead.
posted by clawsoon at 4:12 PM on July 10


I now have my mechanical models able to achieve all of the modes of motion: Upwind and downwind both slower and faster than the wind, and locking up at the critical prop-to-wheel ratio.

There's some pretty interesting math in there (adding an infinite number of numbers! dividing by zero in real life! changing direction just by making the wheels bigger or smaller!) so if I end up making a proper video out of it one of these weeks I might post it to Projects.
posted by clawsoon at 10:33 AM on July 20 [2 favorites]


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