Episode 510

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N00b13
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Episode 510

Postby N00b13 » Sun Mar 31, 2019 7:15 am

To settle this once and for all. The liftling capacity of helium is .069 lb/ft^3. Say 15ft^3 per lb. A locomotive weighs 300-400 thousand lbs. So we are talking 4.5-6 million cubic feet of helium. A balloon 248 to 273 feet wide. Just for neutral buoyancy. For the medically inclined 80-90 meters. For everyone way too fucking big.
Last edited by N00b13 on Sun Mar 31, 2019 7:18 am, edited 1 time in total.
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Re: Episode 510

Postby Azhrei Vep » Sun Mar 31, 2019 7:16 am

N00b13 wrote:To settle this once and for all. The liftling capacity of helium is .069 lb/ft^3. Say 15ft^3 per lb. A locomotive weighs 300-400 thousand lbs. So we are talking 4.5-6 million cubic feet of helium. A balloon 248 to 273 feet wide. Just for neutral buoyancy.

That is a substantially smaller balloon than I would have expected.
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Re: Episode 510

Postby N00b13 » Sun Mar 31, 2019 7:27 am

Azhrei Vep wrote:
N00b13 wrote:To settle this once and for all. The liftling capacity of helium is .069 lb/ft^3. Say 15ft^3 per lb. A locomotive weighs 300-400 thousand lbs. So we are talking 4.5-6 million cubic feet of helium. A balloon 248 to 273 feet wide. Just for neutral buoyancy.

That is a substantially smaller balloon than I would have expected.

Ok just for context the worlds largest airship the flying bum (yes really) has 1.3 million cubic feet of helium. It's not a sphere like the one in my calculations so it's as long as an american football feild.
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Re: Episode 510

Postby Knaight » Mon Apr 01, 2019 1:54 am

Azhrei Vep wrote:
N00b13 wrote:To settle this once and for all. The liftling capacity of helium is .069 lb/ft^3. Say 15ft^3 per lb. A locomotive weighs 300-400 thousand lbs. So we are talking 4.5-6 million cubic feet of helium. A balloon 248 to 273 feet wide. Just for neutral buoyancy.

That is a substantially smaller balloon than I would have expected.

It's a substantially smaller balloon than you'd get - these numbers assume the balloon itself is neutrally buoyant. Said balloon needs, at minimum, some sort of propulsion system, connection to the train, and of course the mass of the balloon itself.

I'm going to assume that the attachment is an airtight seal with the train itself, which largely removes the gondola mass. Using the Goodyear Wingfoot 3, the current cutting edge blimp the envelope is 19,780 lbs for 297,527 cubic feet. That's 15 cubic feet per pound, at that scale. How that scales up depends mostly on how much thicker the material gets as you scale up. I'd bound it at either a constant or at 15*(volume/297527 cubic feet)^(2/3), assuming constant thickness and thus getting a surface area/volume relation.

Solving this properly is roughly analogous to the rocket equation (fuel with weight that needs more fuel, lifting gas with balloon weight that needs more lifting gas) with some pretty dramatic differences in exponential coefficients such that scaling up actually works for you. I'm too lazy to do that*, but let's take that 4.5 million cubic feet. Using the most generous scaling we get 92 cubic feet per pound of envelope. That's 48,913 pounds. At the least generous scaling we get 299166 pounds. Obviously I don't have that many sig figs here, so call it 50 thousand and 300 thousand for the range.

So, to support the weight we need somewhere between an eighth of it that needs to be fully supported on the low end or a balloon the mass of the train. Those are total mass fractions of 1/9 to 1/2, which a quick geometric sum to deal with the rocket equation analog** gets you 1/8 or 1. That's anywhere from 56 thousand pounds to 800 thousand pounds. Back to volume scaling - the worst scaling scenario is really easy to calculate, where the 800 thousand pounds works out to 12 million cubic feet. The best case one is a little more convoluted, but treating it like a dimensional analysis problem gets 4.5 million * (9/8)^(3/2), or 5.4 million.

Using the 6 million figure instead those are 7.16 million or 16 million instead. It's a blimp the size of 18 to 53 regular blimps by volume, given extremely generous conditions. Given the actual gondola mass on a blimp suggests that it would take a fleet of a good 115 regular blimps minimum to do the lifting, that suggests it's a fair bit bigger. About 35 million cubic feet on the high end, 9 million on the low end. It all depends on blimp fabric, and my experience with materials and eyeballing it suggests it's probably about 15 million cubic feet. Still over 11 times as big as the world's largest airship. Trains be heavy, yo.

*Properly, anyways.
**This would be the effective but kind of improper method.
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Re: Episode 510

Postby N00b13 » Mon Apr 01, 2019 4:22 am

Knaight wrote:
Azhrei Vep wrote:
N00b13 wrote:To settle this once and for all. The liftling capacity of helium is .069 lb/ft^3. Say 15ft^3 per lb. A locomotive weighs 300-400 thousand lbs. So we are talking 4.5-6 million cubic feet of helium. A balloon 248 to 273 feet wide. Just for neutral buoyancy.

That is a substantially smaller balloon than I would have expected.

It's a substantially smaller balloon than you'd get - these numbers assume the balloon itself is neutrally buoyant. Said balloon needs, at minimum, some sort of propulsion system, connection to the train, and of course the mass of the balloon itself.

I'm going to assume that the attachment is an airtight seal with the train itself, which largely removes the gondola mass. Using the Goodyear Wingfoot 3, the current cutting edge blimp the envelope is 19,780 lbs for 297,527 cubic feet. That's 15 cubic feet per pound, at that scale. How that scales up depends mostly on how much thicker the material gets as you scale up. I'd bound it at either a constant or at 15*(volume/297527 cubic feet)^(2/3), assuming constant thickness and thus getting a surface area/volume relation.

Solving this properly is roughly analogous to the rocket equation (fuel with weight that needs more fuel, lifting gas with balloon weight that needs more lifting gas) with some pretty dramatic differences in exponential coefficients such that scaling up actually works for you. I'm too lazy to do that*, but let's take that 4.5 million cubic feet. Using the most generous scaling we get 92 cubic feet per pound of envelope. That's 48,913 pounds. At the least generous scaling we get 299166 pounds. Obviously I don't have that many sig figs here, so call it 50 thousand and 300 thousand for the range.

So, to support the weight we need somewhere between an eighth of it that needs to be fully supported on the low end or a balloon the mass of the train. Those are total mass fractions of 1/9 to 1/2, which a quick geometric sum to deal with the rocket equation analog** gets you 1/8 or 1. That's anywhere from 56 thousand pounds to 800 thousand pounds. Back to volume scaling - the worst scaling scenario is really easy to calculate, where the 800 thousand pounds works out to 12 million cubic feet. The best case one is a little more convoluted, but treating it like a dimensional analysis problem gets 4.5 million * (9/8)^(3/2), or 5.4 million.

Using the 6 million figure instead those are 7.16 million or 16 million instead. It's a blimp the size of 18 to 53 regular blimps by volume, given extremely generous conditions. Given the actual gondola mass on a blimp suggests that it would take a fleet of a good 115 regular blimps minimum to do the lifting, that suggests it's a fair bit bigger. About 35 million cubic feet on the high end, 9 million on the low end. It all depends on blimp fabric, and my experience with materials and eyeballing it suggests it's probably about 15 million cubic feet. Still over 11 times as big as the world's largest airship. Trains be heavy, yo.

*Properly, anyways.
**This would be the effective but kind of improper method.

Wasn't going to go down this rabbit hole as there lies madness but you also have to account for the square cube law as the ship gets bigger. Volume increases faster that surface area when you scale something up.

That said I'm impressed with Goodyear's blimp. Looking at the numbers you gave gives a .003lbs of envelope per cubic meter of gas.
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Re: Episode 510

Postby clintmemo » Mon Apr 01, 2019 10:17 am

Train dirigibles and "Dome of IC"

This episode was a Christmas present to long-time listeners.


I also do the "we always jack around at the beginning of the session so why fight it" thing when I GM but I run my games on Roll20 and discord plus I have an extra added distraction of a dog that always wants attention when I start to game. So what I have been doing lately is setting up the game and hopping on discord about 15 minutes before the game starts, then taking my dog for a walk. That way when people get on discord, we can talk and catch up, but I tell them "I'm finishing up Odie's bonus walk, I'll be back at my PC in a few minutes."
Then it's
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Re: Episode 510

Postby Wayne » Mon Apr 01, 2019 11:14 am

Looking at all this math can I just say I love you guys. You have made my day.


Also after recently seeing it on the way to Dan's house we had a conversation about the Goodyear Blimp and I looked up one very important detail. There are no bathrooms on the blimp. You must have an iron bladder to be a pilot.
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Re: Episode 510

Postby clintmemo » Mon Apr 01, 2019 6:19 pm

Or an empty 2 liter bottle.
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Re: Episode 510

Postby Dan » Tue Apr 02, 2019 1:48 am

N00b13 wrote:Ok just for context the worlds largest airship the flying bum (yes really) has 1.3 million cubic feet of helium. It's not a sphere like the one in my calculations so it's as long as an american football feild.

So once it's made into an ellipsoid, it sounds like we're talking about a blimp -- not the size of a football field -- but about the size of a football stadium.
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Re: Episode 510

Postby GinDragon » Tue Apr 02, 2019 2:24 pm

clintmemo wrote:Or an empty 2 liter bottle.

Or a disregard for the people below you.


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