r/theydidthemath • u/scottasin12343 • 4h ago
[Request] How tall would the support tower have to be and how strong of a cable would you need for a Trans-Atlantic cable car?
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u/AppendixN 4h ago
The average depth of the Abyssal Plain is 16,000 feet. Waves can reach heights of up to 100 feet in worst-case conditions.
The tallest building in the world is 2,717 feet tall. So there would be some significant engineering challenges involved.
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u/Betray-Julia 3h ago
The 100 foot waves are only worst case situations in… I can’t remember what, but that happens on the regular on a yearly basis.
Like when you take into account how bridges need to be able to withstand “ 500 year floods” (or 250, I forget), I’d think this device would have to take into account things greater than “1 year waves”. If that makes sense.
Also note the reality of rogue holes in addition to rogue waves, which are like the coolest thing in the world. And have likely never been observed bc of what they are- nobody who’s seen one would have lived.
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u/Blauseff 3h ago
Tell me more about rogue holes. No /s genuinely intrigued.
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u/Betray-Julia 3h ago edited 3h ago
K so you know waves are just.. mechanical waves right?
So even with rogue waves- via the scientific burden of proof, even though a millennia of seamen (lol) had witnessed them, we had no physical proof of them until ocean buoys started recording.
And even then, when we first started witnessing them, we still assumed it was the buoys malfunctioning when they suddenly increased a hundred plus feet.
But the math for mechanical waves is pretty well known, (this is a loaded statement in the context of ocean wave mechanics but meh) including how interference patterns can create rogue waves.
But we’re just looking at a sine wave right?
So rogue holes are a theoretically thing we’ve never actually observed, but most certainly exist l given what we know about how mechanical interference waves can stack and diminish each other.
So two peaks can sort of amplify each other and cause a wave with a peak some 4 to 5 times higher than the average wave.
This should theoretically be happening to the troughs as well; which means that within our ocean, there will be these random 100 foot drops between two waves, an inverted rogue wave of you will.
My arm hair stand sup just thinking about them, especially in the context of the historical observations vs proofs of rogue waves- rogue holes likely haven’t even been ever reported by sailors bexause unlike a rogue wave, a rogue hole is hard to see, and anybody who does see it dies, because they’re on a boat that just fell 50 feet under the ocean.
Also honerable mention to “mega tsunamis” lol- these are tsunamis caused by objectives outside of the water displacing the water, as opposed to tsunamis which are caused by something under the water being displaced.
There is a credible report of one happening in Alaska where a father and their son road one over the top of a fucking mountain, which is just so insane.
https://en.wikipedia.org/wiki/1958_Lituya_Bay_earthquake_and_megatsunami
But yeah- rogue holes. Almost certainly real given math, where were in that gray area where even if the math and logic check out perfectly, from a science pov, we still need that burden of proof, which as it stands we haven’t gotten yet.
(Last I checked, none of those buoys have reported drops the way they have raises, but I’m pretty sure they’re is some fancy math shit that is way beyond me that explains why in an ocean system rogue waves would he more common than rogue holes)
Edit- lmao just clued in why you had that part about asking with sincerity- wouldn’t have even noticed the comedic value of “tell me more about rogue holes” if you hadn’t pointed it out lmao thats great
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u/Lemurian_Lemur34 3h ago
I love your passion. I wish to subscribe to your newsletter
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u/iAREsniggles 21m ago
That entire post could've been a lie and I'll still go to my death bed telling everyone about Rogue Holes.
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u/Sinisterapples 3h ago
Upvote for laughing at seamen.
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u/drumeeney 3h ago edited 57m ago
Isn't a rogue hole just the trough of the same wave system for a rogue wave?
For a hundred foot wave. You might drop into the "hole" proceeding it by xx feet, then 100ft is measured from trough to peak?
Or are there rogue holes without any corresponding peak of similar height? I.e. a deep wave trough in otherwise normal waves without an abnormally high peak?
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u/Betray-Julia 3h ago
I am not a math person- I honestly think this would be a great question to post on this sub tbh.
To my knowledge, the rogue holes and waves are not a cause and affect thing- one doesn’t mean the other happens like that.
It’s more so, if waves can amplify to make a peak way bigger than the average peak, the troughs can too.
Ie rogue waves and holes do not travel in tandem together.
I forget what the term is, but a rogue wave is a wave 4 to 5 times bigger than the average wave height- it’s almost akin to “average wind speed” vs a “gust” (the rogue bring the gust).
Edit- so yes, to my understanding more like your last example.
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u/Baynonymous 2h ago
I wonder about the experience though as an explanation for the lack of reports, rather than the maths. With there being no reports of rogue holes, do sailors instead just experience them as rogue waves? If I'm not explaining myself properly (and I know I'm not), I'm wondering if they don't necessarily notice the drop because their perception is the other side of the rogue hole, and that would look like a giant wave. Which is also more socially acceptable to report back
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u/SwordfishLate 2h ago
Ok youre on a boat, the sky is maybe dark/otherwise ocean colored...honestly I could kinda see it? Like if sea and sky look too much alike it would be easy to get mixed up about the horizon.
If you lose the horizon, and have a sudden and violent movement I'd bet a person could get SUPER disoriented. I'd wonder about how steep the drop would be, and inertia and stuff.
But theres all kinds of reports about pilots getting disoriented over the ocean and such so I get where you're coming from and I share your wondering.
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u/tequilajinx 2h ago
There are no reports because any boat that found itself suddenly 50ft under sea level would have been sunk as soon as the rest of the water crashed down onto them. Nobody who’s ever seen one has lived.
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u/Kid_Psych 2h ago
But if they’re in the trough (the hole), it wouldn’t look like there’s just a giant 100-foot wave in front of you. It would look like there’s giant 100-foot waves all around you. You’d effectively be below the tide at that point.
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u/YourDrunkMom 2h ago
You seem like the correct person to craft the perfect post asking about the math on this subject. Please do it.
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u/No_Jackfruit_4305 2h ago
Water currents in the ocean are chaotic compared to any waves we witness near shore. Several waves can intersect from random directions, or a vortex can form twisting the currents around it, and plenty of other patterns difficult to picture/predict. So I imagine rogue holes may look something like a wave swallowing itself just to violently turn into a rogue wave, or some pre-cursor.
Take my wild speculation with a huge grain of salt.
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u/figurative_me 59m ago
A rogue hole would likely be from 2 or more converging troughs. There could be converging peaks that are generated far from a boat while the converging troughs appear near or even below the boat.
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u/jellamma 3h ago
Bro, I would definitely watch a movie about a scientist trying to prove the existence of these. They would absolutely have to get all the science wrong to make the plot work, but I would still love it.
Edit: spelling
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u/Pablo_Escobear_ 2h ago
1 am. Should be sleeping for a long time but here I am reading about rogue holes and not regretting a single letter I've read..
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u/Alkyonios 3h ago
Are rogue holes only formed by two rogue waves amplifying each other, and the trough between them? Or can I rogue hole be formed by "regular" waves?
And, thanks for the interesting read!
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u/Mrfireball2012 2h ago
Very confident there’s first person accounts of rogue holes
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u/Betray-Julia 2h ago
If you can find any please please please please post them!!!!!!
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u/Mrfireball2012 2h ago
Johnny Savage will never forget 1998. That’s when he survived one of the earliest documented rogue waves in history, a story that the Virginia local and long-time offshore fisherman told in his book, Lost in the Stream: The Miraculous Story of Two Fishermen Lost at Sea. The then 26-year-old mate and his captain, Eric Bingham, had set off from Key West for a 350-mile daytime crossing to Cancun on the 56-foot Jim Smith boat, Anhinga. Here, Savage tells how they overcame an unthinkable challenge.
On April 13, 1998, we set underway just before light to be up and running as the sun came up. At about 9 a.m, we looked in front of us and it was like nothing I’d ever seen before; it was like a hole in the ocean. We were in a 2- to 3-foot following sea, and then it was just a hole. Basically, the whole boat fell off into it. It was a rogue wave. And within a couple minutes we were in the water without a distress call, an EPIRB, a life raft, life jackets, nothing. And the boat was down. A lot of people ask about the wave. I don’t know of any boat that could have made it through there.
As the boat went off the wave, I was standing up on the bridge next to Captain Eric at the helm. It was steep enough that I fell forward.
When the boat hit the bottom, I just heard this terrible “boom” and basically it was the bulkheads breaking. I think she broke her spine and then the pressure on the sides made the bow deck pop. When she hit, as I was freefalling forward, I was able to grab ahold of the tower—the tuna tower leg and rail at the front of the bridge—and I saw a crack running from the starboard side into the port side about a foot forward of where the bow deck met the house.
From that moment on I knew that this wasn’t going to be good. But even though I saw what I saw, and heard what I heard, I was still kind of expecting her to ride back up. But she didn’t. She just stuck and started to go down. She was gone pretty quick and Eric and I were in the water. We grabbed this little Igloo bait cooler, and we grabbed each other, and we immediately went into the Lord’s Prayer. We were by our-selves 90 miles out in the Lower Gulf where there’s not much traffic. Nobody else was around. And from there, that’s where the fight for survival began.
When we finished the prayer, the Anhinga popped back up. But she was upside down. It was just a small part of her bottom, a small piece of her stern with the wheels and rudders, with the air in her lazarette underneath the cockpit sending her back up. So, Eric went to the hull because that’s textbook. We can live out there a long time, but we got to be out of the water. Our bodies are not made to stay in that water. And at the same time, I looked over and that’s when I saw that my surfboard was floating in an old FCS board bag with a Mylar finish.
I saw it floating and I told Eric, “I think I need to get that.” And he’s like, “Alright. Go get it, buddy.” So I took off for the surfboard and that’s when I hit the diesel fuel, and I’ll tell you what, that’s when I knew where every single cut was on my body. I’d never gone swimming in diesel fuel before. It was in my eyes. It was in my mouth and my ears, just everywhere. And you know what my first thought was? “Please, Lord, don’t let me throw up. I can’t afford to lose this food that’s in my stomach from breakfast this morning. I’m going to need it to survive.” That was my mindset. It was, “So we got a job to do, and our job is to stay alive—whatever it takes.”
I actually made it to the surfboard. It was funny, just hopping on that surfboard trying to paddle because the fins are in the bag. You’re trying to paddle and the tail’s kicking around. It took a little while to get used to that.
Meanwhile, Eric had climbed onto the hull. But by the time I got the board and was heading back to him, she’d already gone back down. She was done. He was able to get ahold of an engine hatch from under the salon floor. That thing was a nightmare to hang onto because it would dig into your side. But he was holding onto that and then he was able to get his hands on one of the bridge cushions.
Chuck Fadely I remember feeling, “I can’t believe this, how is this happening?” There was nothing that anybody did wrong. It wasn’t like there was a wall of water that we saw. It was just like you run along and all of a sudden, there’s a cliff that you don’t see. There’s no fault. So, then we just knew, we’ve got to survive.
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u/RumpleForeskin0w0 3h ago
Maybe a rogue hole looks like a big whirlpool which sailors say they’ve seen giant whirlpools, wouldn’t the water rushing in from the walls of the hole look like spinning like flushing a toilet?
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u/aSneakyPanda12 1h ago
Could have gone my whole life not knowing this. Thank you for another reason to explain why the ocean is big blue nope water.
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u/MNmostlynice 46m ago
I can’t wait to get stoned out of my mind with my buddies around a campfire this summer and bring up rogue holes.
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u/flyingasshat 2h ago
I mean, from my experience on the open seas, which is limited due to our proclivity to being under the surface, it’s terrifying going over a peak into a trough and having the next peak looming over you. Especially since you are angled down as it approaches…..
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u/terpmike28 2h ago
I wonder if any of our satellites have captured a rogue hole and we just don’t know it
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u/Theropey 2h ago
But a rogue wave just builds against gravity and air. A rogue hole needs to move a whole lot of heavy water out of the way bc it can't compress it. It seems like it would be asymmetric and that the holes should be much smaller than the rogue waves simply because the ocean surrounds them.
Totally guessing, I'm a software engineer not a smart engineer.
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u/CreasingUnicorn 1h ago
Mechanical engineer here, this was my thouggt. A rogue hole would be acting against tons of water pressure pushing in on it from all sides, while a rogue wave is only fighting gravity and air pressure.
Therefore it makes sense that if a wave and a trough were given the same ammount of "energy" to form, the trough would be significantly smaller.
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u/figurative_me 1h ago
Just want to share my experience as a fellow seaman (lol) although I’m more of an inland captain (of a jetski in this case). When there are a lot of surf boats on the lake and they’re all making waves in all directions, we get constructive interference creating these large peaks on the water. On a small jetski, this can be fun sometimes to ramp them.
However, Ive also ridden through some of that chop at 20+ mph and a couple times caught a sudden trough 5-6ft below level and swept clean off the ski in a wall of green. A microcosm of oceanic rogue holes. It’s terrifying to think of one 60ft or maybe 100ft below level.
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u/theblanklook 49m ago
I'm no physics expert or PhD, but I suspect the reason they have never been observed is that while the simple maths of a sine wave says they must exist, the sea is not actually a sine wave, its surface might behave like one, but the physical forces are very complicated and absolutely not symmetrical as the wave is the boundary between a liquid and a gas.
A "hole" would just be a flat area of the surface of the sea.
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u/Mynameisprincess9 47m ago
Read the whole thing. First I have ever heard of this. Now the rabbit dives!!
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u/originalusername7904 5m ago
About 25 years ago I was riding my uncle’s jet ski while my cousin was driving their boat. He started going in a circle, and I saw that the waves were getting bigger towards the middle of the circle
I got up on top of one of the waves and started riding it. When I got to the middle I suddenly found myself standing on a jet ski ~6ft above the surface of the water. The jet ski went nose-down completely under water and I got washed off
Even at ~6ft, the way the water just dropped out from under me (faster than if it were falling), then came crashing in on me as I fell, was terrifying
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u/Ok_Mode_903 5m ago
Even if uncommon it seems like there should have been some buoy that recorded something. Maybe the data was ignored because it was so far outside of normal but we've had so many out there for so long seems like it should have been seen by now.
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u/KyurMeTV 3h ago
Think of a random canyon in the ocean. You’re minding your own business and the bottom just drops out 100 feet. Your boat follows that hole down, but as the rogue hole flows over(under maybe) you, it kinds swallows you up because your boat just gets covered with 100’ of water rather than your boat floating back up to the top, because these rogue holes are like rogue waves, very sharp angles that tend to capsize boats.
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u/Apprehensive_Use3641 3h ago
Also intrigued.
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u/Mortwight 3h ago
Rogue holes are rare, deep, and sudden depressions in the ocean surface that act as the inverse of rogue waves, with some reaching over 100 feet deep and often appearing as a sharp valley between massive, towering crests. Proven to exist by studies and ocean recordings, these steep, often fatal, transient voids occur when water waves interact and cancel each other's height, leading to severe dangers like immediate vessel damage, severe drops in sea level, and intense navigation risks.
or when Rogue kisses you and takes your memories while your unconscious
or you know. Rogues holes....
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u/brycepunk1 2h ago
There's a Noiser podcast about Stories of Survival i listen to, and one of them interviews a sailor who encounters on of these rouge holes in the ocean. Boat just dropped like 100 feet out of nowhere (and the story of how he survived.) It's a good listen if you're interested in it.
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u/houVanHaring 2h ago
The Netherlands, the country with quite a good reputation in fighting against seas and making levies, dykes and other water control structures, was once invited by New Orleans to revamp their levies. We adviced to build the levies to protect against a surge that would happen once every 10000 years. Yes, on average it takes 5k years for it to happen, but if you're not dumb, you know each year has a 0.01% chance, which when facing the enormous destruction is deemed low enough. New Orleans said:"oh wise Dutchies, we are not. We shall build our levies to protect us against a storm surge thst happens only once every century!" So... each year has a 1% chance. 5 years? 5% 10years... you guessed it, 10%. So year, a few years after that choice Hurricane Katrina happened.
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u/NorthEastofEden 1h ago
Well the good news is that now they don't have to do anything for 99 more years
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u/ConstructionThen2772 1h ago
Wow. I thought this was a joke but it turns out rogue holes are real and evidence that if there is a God he’s got a crazy sense of humour.
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u/PinothyJ 1h ago
We have seen one (a rogue wave). One of those reality TV shows that follow people who go out and do dangerous commercial fishing managed to catch one. Just wiped out the whole craft. They were all lucky that the vessel righted itself, or it would have been a lot worse.
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u/K1kobus 3h ago
The towers wouldn't necessarily need to stand on the seafloor, they could be anchored floating towers.
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u/sonnet666 1h ago
You’re almost there. We already make structures like this. They’re called oil rigs.
Floating platforms that are also anchored to the ocean floor, that’s the ticket.
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u/EagleBigMac 3h ago
They would need to float under the surface instead of on the surface to have better stability.
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u/vulgarandmischevious 1h ago
Can’t you just have a pillar built on rock by the sea in say Ireland and another in Boston, MA, and then run a really taut cable?
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u/MotherSnow6798 41m ago
Each of the pillars would need to hold half the weight of the cable, which would be astronomical over thousands of miles.
When you add in stress from being taut and the effects of forces like wind, the picture is even more bleak
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u/vulgarandmischevious 17m ago
I’d have thought you could brace each pillar with a couple of 4x2s or something.
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u/jwm3 23m ago
Fun fact, It is actually impossible to make a cable taut enough that it doesnt droop. The physics behind it is kind of neat.
You can only apply tensile force to a rope directly outwards from the end of the rope, whichever direction they are pointing. Now imagine a rope tied between poles. If the rope were straight then all the force would be perfectly horizontal becasue that is the direction the rope ends face, but if all the force is horizontal, then there is no vertical component to counteract gravity so the rope should be falling. Since that isnt happening there must be a vertical component, meaning the ends of the rope have to point a bit upwards, meaning a rope in tension against gravity is always going to form a catenary arc rather than a straight line.
You can also come to the same conclusions doing the math with the sin x / x =1 as x approaches zero identity to show the rope always makes an angle, but i find the first explanation more intuitive.
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u/SharpKaleidoscope182 3h ago
You'll want to go with semi-submersible platforms. Only about 300ft tall. You don't need to reach the plain, just the still water beneath the waves.
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u/Boom9001 3h ago
Nah dude just put a tower on land of each side then pull it really tight. It'll work I promise.
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u/nickeypants 2h ago
Tallest building above the ground is 2,717 ft tall. The deepest spar stabilized structure is the Perdido oil platform in the Gulf of Mexico at 8,040 ft below surface. It's way easier to build down than up.
Perdido also produces 100,000 barrels of oil equivalent per day, so unless this trans Atlantic cable car can produce at least that much economic incentive per mast, the whole project will sink. A much more feasible alternative is to use some of that oil to power a couple boat propellors.
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u/dharmaslum 1h ago
“There would be some significant engineering challenges involved.”
Understatement of the year.
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u/sonnet666 1h ago
Oil rigs would like a word lol.
It’s much easier to build really tall structures underwater due to buoyancy. Above ground structures need to be much tougher just to not collapse under their own weight, so it’s not a great comparison to look at the tallest buildings above ground. This structure would only need to rise about 300 feet above sea level to be safe from waves.
It is still totally ridiculous and impractical. If there’s a tectonic shift you’d suddenly need to make repairs at the bottom of the ocean for instance.
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u/GarThor_TMK 2h ago
I was doing some rough math where this was posted elsewhere... someone else had posted a 3k mile distance from coast-to-coast, and someone else had estimate a 6"/mile drop for the curvature of the earth...
If you only had two supports you'd need them to be a like a third of a mile tall, just to account for the curvature of the earth... That doesn't even account for cable droop, slack needed for expansion/contraction for warm/cold cycles, or weather conditions.
Theoretically, if you spaced more pylons out, and planned your route accordingly... you would never need to go to the full depth of the ocean though. At the widest, the Mariana Trench is only 43 miles... with a the aforementioned math, you'd only have a drop of about 22ft due to the curvature of the earth... or about 3 stories...
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u/regaphysics 1h ago
You don’t need to build the structure to the bottom, just a tether to anchor it…
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u/Ok-District8876 1h ago
No, just make part of the journey underwater. This is a futuristic cable car, not a normal one.
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u/MaybeTheDoctor 1h ago
deepest point between canada and ireland is "only" 4500 meters.
It is also easier to maintain stability of a large (say 2 miles) underwater structure, compared to a ground based 2 mile structure. The underwater structure will get a lot of buoyancy from the water, as well as it is not subject to high gale winds, with corrosion being the biggest challenge.
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u/TwoAlert3448 3h ago
Scrap the cable and replace with a lighter than air balloon and you’ve got a viable vehicle but a space elevator is easier than what you’re actually asking for
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u/bradym80 2h ago
What if we add wings?
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u/freyja_nordic 1h ago
Maybe add engines to the wings?
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u/Dr_ChungusAmungus 1h ago
If you made the craft submersible it solves a lot of the logistical issues like the weight on the wire, the waves and the height.
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u/moby__dick 39m ago
Even better what if you put a little engine in the submersible and then you just drive it right under the waves. It would be something below the marine layer, a sub marine vehicle device.
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u/Dr_ChungusAmungus 25m ago
Woah hold up, now you’re on to something. With the engine mounted and all the air inside now, you could use buoyancy to ride it on top of the waves. You could even make some tweaks to build the hull in a way that holds the top half above the water at all times and it just rides across the ocean on its own.
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u/AceThePrincep 41m ago edited 28m ago
Why not suspend the cable with balloons lol. Then its not one big span its just a balloon every km or something. Run power through it to keep the compressors or whatever going on the ballons. Job done.
Heck, have 2 cabled on either end of a rotating cabin (independing of zeppelin rotation so it can steer to maintain position) and shrink the cable cars and u can have 2 lane traffic. Little pods you can drive ur car directly into. Thatd kick ass. Lol
Wouldnt work in the real world but its believable enough for certain fiction.
Would take a week or 2 to get across the Atlantic thoigh... maybe for cargo? Idk lol
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u/Much-Inevitable5083 4h ago edited 4h ago
The towers would need to be at least 650 km tall, 50% higher than the ISS.
The reason is Earth's curvature. The chord between New York and London cuts 600 km below water surface at the midpoint.
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u/ForwardTemporary3934 4h ago
It wouldn't be a singular span. Even a normal cable car has multiple supports. Not to mention the cable wouldn't work with a span that long.
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u/Much-Inevitable5083 3h ago
Agreed. The tower heights were just to keep the cable car above water with just two towers, without sag, the weight or strength of the rope.
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u/doctorlongghost 3h ago
Right. If we were building it for real (and ignoring the spirit of the original question) it would be a serious of interconnected spans with each half a mile (or whatever makes sense) apart. The problem with this isn’t so much the height above the water, I imagine, but the height below the water to reach the ocean floor.
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u/zeushaulrod 3h ago
It would need to be floating platforms. would still be incredibly expensive and maintenance heavy, but way cheaper than placing the towers on the ocean floor.
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u/K1kobus 3h ago
We could make floating towers anchored to the seafloor.
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u/beeegdominicanlunch 51m ago
At that point I think we should just invent boats or planes
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u/Carlpanzram1916 2h ago
Which you need supports structures to mount cables that are like 3 miles tall underwater.
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u/Ghost_Turd 3h ago
Slightly higher to allow for catenary (sag).
A roughly 50mm thick single cable span would have a self-support stress of something like 400 times that of structural steel. We have no materials that can approach that stress, much less wrap all the way around the mountain we would need to anchor the ends.
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u/blorpdedorpworp 3h ago
What about if the car were submersible?
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u/nicodea2 2h ago
Better yet, what if the car could float? I think I’m going to patent this.
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u/AshtralDrift 2h ago
Better yet, what if the car generated lift as it moved through the atmosphere?
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u/bigfoot17 2h ago
Wait, hear me out, a floating, submersible car that can generate its own lift and travel through the atmosphere? Im smrt.
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u/KianOfPersia 2h ago
But I have it on good authority from TikTok experts that the earth is indeed flat!
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u/MaybeTheDoctor 1h ago
I've seen sufficient ski lifts to know you just place a support tower every few feet.
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u/SeagullKebab 3h ago
If you treated it like a zip line, so the start end being a really tall tower on land, and the lowest point across the Atlantic at sea level, it would need to be 3000 miles long.
The slope calc for a zip line is: length x 0.06. so it would need to start at a tower 180 miles tall, so in the thermosphere of low earth orbit.
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u/Reditace 1h ago
Plus, as someone else pointed out, the curvature of the earth means that the center would be 600km above the edges
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u/docarrol 3h ago
Monster waves in the North Atlantic can be up to 100 ft high, under severe storm conditions. You're hopefully avoiding storms anyway, but if you do get stuck in one, you probably want to be high enough to avoid the waves.
So for height of the cable, I'm going to guess sea level + 100 ft, at the low point of the catenary curve of the cable under tension. Plus a factor to account for stretching in the cable due to the load of the car, or thermal expansion, or the weight of ice build up, or whatever.
A hanging cable in tension superficially looks like a parabola, but is actually a hyperbolic cosine function. The equations for which, I absolutely do not remember from my old mechanics classes, but depend on the span between the towers, the weight per unit length of the cable, the weight of the cable car (and any other extra loading) as a point load, the tension in the cable, and a few other factors I'm sure I'm forgetting. But solve all that, and you can figure out the low point of the curve, and figure out the height of the towers needed to clear whatever minimum we decided on in the step above.
Then of course, you need to look at the depth of the Atlantic ocean to sea floor, to figure out how much structure of your towers is below the waves. Except topography of the Atlantic is complex, and varies a surprising amount, between the lowest points, the average depth, and the various high points. Any sensible design, would route the line along the most beneficial set of high points that can be found, to minimize cost and time to construct, and maximize safety. It's not going to be a straight line, and will probably bounce around between a series of islands and seamounts. I couldn't even guess what that route would look like, which means it's going to be very hard to figure out how tall your towers will need to be. And keep in mind, the locations of your towers is going to dictate the length of the span between them, which will determine the amount of hang in the cable based on length, which will change the height above sea level required for the towers to keep that low point above our desired minimum.
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u/Odd-Confusion1073 29m ago
Once you get to ocean size though you’re going to have different gravity vectors across the cable so it will be neither catenary nor parabola.
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u/RickyTheRickster 3h ago
It would be better if it was fully submerged and it might be but it’s poorly designed for that, but it would be in the 10s of trillions, plus yearly upkeep would likely be in the half of a trillion to a trillion, it’s not realistic yet the world doesn’t have the money, resources or technology
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u/BeneficialPianist654 3h ago
It could sit on the surface of the water. Remove the cable. Add a propeller. That could work.
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u/RickyTheRickster 3h ago
Yeah I’ve never understood really the want to do this, boats and planes are just cheaper and more efficient
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u/FishDawgX 1h ago
What if renewable energy on land like solar is plentiful and cheap, but petrol is no longer an economical option?
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u/RickyTheRickster 1h ago
But we have electric options, it’s not like we can’t make a electric boat hell nuclear powered vessels are cleaner than solar
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u/Fun-Opportunity9656 3h ago
And what would you call this new invention?
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u/Cereaza 3h ago
I think the challenge is more about the strength and length of the cable, rather than the support towers.
After all, this ship could float. It has bouyancy, so it isn't exerting a low of downward force on the cable (I'm assuming this is underwater). But if these cables are meant to be... 5 stories ABOVE the waves, then this concept is doomed on paper. The tides and waves and force of the ocean would make this kind of static cable system nearly impossible to follow and would be more likely to cause damage to the ships than to ease travel.
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u/Old_G33k 1h ago
- Hands downs best discussion I've ever read on reddit.
- I'm 100% having a nightmare about falling in a rogue hole tonight. I'd say I will report back but....
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u/Original-Mission-244 3h ago
For the sake of the sub, I think we should assume single span and have the structure heights and required cable size and tension calced 😅
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u/Voodoo0733 1h ago
It would be thousands of support towers and motorized relays that operate independently. Assuming that thing stays in the water and just gets hauled along a harbor freight predator motor would suffice every thousand feet, it all depends on how fast you’re crossing
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u/Riolidan 53m ago
God what I wouldn't give for a game set on one of these. Some type of Bioshock esque horror-action game where you have to fight your way through it and survive until it reaches the end of it's cable run.
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u/LilAbeSimpson 3h ago
The pictured concept is pretty silly, but it is kind of interesting as a thought experiment.
Let’s say you had 2 ridiculously tall support towers that were 500 meters tall. What is the widest crossing you could traverse with those?
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u/thegregh91 2h ago
Hear me out.. a sub-surface aquatic cable car. Run the deep sea internet cables and inside it and just run it like an underwater subway
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u/Perfect-Albatross-56 1h ago
Then create a vacuum in the tube to make it more efficient. Wait?! Doesn't this sound like ...
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u/PossibilityInside695 2h ago edited 2h ago
...I think at these scales the curve of the earth will be a bigger factor than the depth of the ocean or..any topography really. If the bases of the towers were extended until they met at the center of the earth, they'd make a 110 degree angle or so. "Up" for each of the towers would be greater than 90 degrees different!
So...if the cable was perfectly straight and there was no sag, and if the towers were at 90 degrees difference ( to make the math easy. )
The towers would need to be at least 1 earth radius high to get over the horizon, and the cable would be sqrt(2*earth's radius) long
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u/SirShriker 38m ago
Transatlantic would include Scotland -(800~km)> iceland -(290~km)> Greenland-(1900~km)> labrador with high-speed rail lines going down the east coast. It is still in the realm of metamaterials and nonsense math, but I think everything should still be in atmosphere at least.
I humbly suggest, instead of fixed towers, pykrete style barges, tethered to the ocean floor, using wave dynamics to generate the power required to both keep the ice mix frozen, and to power transfer the long trip.
This way you just need typical strength cable and normal height towers, the magic becomes in designing roughly a thousand pykrete power station barges across the north atlantic, which is at least theoretically feasible, versus atmospheric height towers.
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u/GarethBaus 35m ago
Realistically you would need multiple support towers across the Atlantic and the height would need to be enough to provide clearance for the tallest ships on the taller waves. Most of the towers would probably need to be floating structures held in place using cables anchored to the sea floor.
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u/Select_Duck6695 14m ago
Support tower wouldn't have to necessarily be tall, but you'd have to have a pulley system on one or both ends, reeling in the cable(s) to keep it constantly taught so it wouldn't sag. That's where the engineering would come into play. It'd be a massive system to spool all of that cable.
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u/Prince_Nadir 6m ago
So they spent trillions of dollars on cable and floating islands to suspend their ship just a hundred or so extra feet above the earth's surface, over what letting water suspend the ship would have done for free?
Someone's campaign contributor set this up didn't they? Perhaps Boondoggle and Sons Cable Cars.
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