/sci/ - Science & Math

[Anonymous No.4354623]

Sup /sci/

Lets say I have a sphere with an internal pressure of 10kPa sitting at regular sea-level pressure of 101.3Kpa. How do I calculate the crushing pressure on the skin of the sphere due to the greater external pressure?

[Anonymous No.4354628]

I'm not sure what you mean by "crushing pressure". Do you just mean the difference in pressure across the membrane? 91.3kPa.

[Anonymous No.4354635]

>>4354628

So I can just convert the difference in pressure of 91.3kPa to psi and that's it?

[Anonymous No.4354638]

Calculate the pressure from the air pushing on the outside of the balloon.
Calculate the pressure from the air pushing on the inside.
Subtract.

[Anonymous No.4354637]

>>4354635
Yep

[Anonymous No.4354649]

>>4354637

Okay cool, I get 13psi. Does the size of the sphere come into play at all or will the force exerted on the membrane always be 13psi regardless?

[Anonymous No.4354666]

>>4354649
Pressure is force/area, so yes

but >imperial units

[Anonymous No.4354695]

>>4354666

So if I have two spheres, one with a 1m diameter and the other with a 100m diameter but both at 10kPa, the pressure on the membrane won't always be 13psi? In other words, does the size of the sphere change the pressure per unit area?

I'm just trying to figure out if a "vacuum" airship would be feasible. I put "vacuum" in brackets because a true or near vacuum would obviously be impossible. However, regular atmospheric air at a pressure of 10kPa would provide lift intermediate to that of hydrogen and helium. So I want to figure out whether it would be possible to make a rigid frame with a membrane that can both withstand the pressure difference and be lighter than the displaced air at the same time.

[Anonymous No.4354739]

bamp for some help

And fuck you to the guy that just started a vacuum airship thread 5 minutes after I did.

[Anonymous No.4354784]

>>4354695
>>4354739

If you're trying to work out how feasible a vaccuum lifting cell is, but you're not sure about

>Does the size of the sphere come into play at all or will the force exerted on the membrane always be 13psi regardless?

Then you aren't going to get very far.

Better people than you have already done the maths.

[Anonymous No.4354786]

>>4354695

You can't make a Vacuum Zeppelin.
I like your approach though, layering progressively lower pressures.
But it won't work.

[Anonymous No.4354816]

>>4354784

That's why I came here for some help.

>>4354786

Why? Will the skeletal structure and membrane always be heavier than the weight gained by reducing the pressure inside the structure? What is it exactly?

[Anonymous No.4354820]

something like this? and hope that each layer only has to be strong enough to hold off a small amount of the external pressure but is still light enough that over all it floats?

[Anonymous No.4354825]

>>4354816
>Will the skeletal structure and membrane always be heavier than the weight gained by reducing the pressure inside the structure?

The buoyancy increases as the cube of the radius of the body.

The mass of material required to construct it scales as the square of the radius.

We know from >>4354666
that the strength of the material must be the same no matter the size of the body.

[Anonymous No.4354831]

>>4354825

>The mass of material required to construct it scales as the square of the radius.

No

[Anonymous No.4354839]

>>4354820

That's pretty interesting but that's not what I had in mind at all.

1m^3 of air at 101.3kPa is 1184g
1m^3 of hydrogen gas at 101.3kPa is 82g
1m^3 of helium gas at 101.3kPa is 164g

Based on this it's obvious why hydrogen and helium provide so much lift. Now here's the kicker:

1m^3 of air at 10kPa is 117g

10kPa is a far cry from an actual vacuum but a volume filled with air at this pressure would still provide better lift than helium. So you would need a lightweight skeletal structure covered in a membrane with a few vacuum pumps embedded in it. You can use these to suck out enough air to get to 10Kpa of regular air mixture inside the structure and you're good to go.

So what I'm trying to determine is whether such a lightweight structure and membrane is feasible.

[Anonymous No.4354840]

If you do the calculations, you'll see that using vacuum instead of hydrogen has only a very small gain in buoyancy, even assuming a membrane of negligible weight.

Hydrogen is already so much lighter than air, that using a vacuum has almost no benefit, you'd still need a massive structure to lift useful cargo.

[Anonymous No.4354880]

I've found a relevant paper here:

http://iopscience.iop.org/1367-2630/13/4/045020/pdf/1367-2630_13_4_045020.pdf

To be honest, I don't like materials science enough, and my past attempts to enlighten /sci/ by actually doing the maths have always been thankless and depressing, but this should contain the information that OP needs to work out whether his vacuum zeppelin is theoretically possible. Here is a screenshot of the relevant part of the paper.

You can work out some expression that depends on the strength of the material and the radius of the sphere, and so on.

[Anonymous No.4354887]

>>4354840
IIRC if you assume you can just use a magic membrane that weighs nothing you get a 9% increase in lift by using hard vacuum.
You can't do it though because the pressure on the membrane is so high that it will always crumple.
A better goal would be to use hot Helium...

[Anonymous No.4354889]

>>4354840

Way to not read the thread. What I'm trying to argue here is that using regular air at low pressure of about 10kPa provides substantial lift without having the drawbacks of a near-vacuum airship (which is impossible imo) and none of the drawbacks of hydrogen (leakage and flammability) or helium (expensive).

[Anonymous No.4354903]

>>4354880

Thanks for the source but that stuff is way over my head. I will save it and bring it up with some of my eng friends. I'll get their opinion and see what they think.

[Anonymous No.4354925]

>>4354889

10kPa inside the gas sphere still means a 90kPa difference between the inside and outside.
Take a plastic 2l bottle, pour in a little boiling water and screw the cap on... when the water and air in the bottle cool, the bottle gets crushed... try and stop this with out making the bottle any heavier.

[Anonymous No.4354986]

>>4354925

I love that gif.

>10kPa inside the gas sphere still means a 90kPa difference between the inside and outside.

I know. I just can't figure out what that really means in reality. Is it too much for a lightweight skeleton covered by a strong skin to handle?

[Anonymous No.4355000]

>>4354986
>Is it too much for a lightweight skeleton covered by a strong skin to handle?

Yes.

[Anonymous No.4355001]

>>4354903

What the fuck? How can you not understand? The equation is right there in the screenshot, and you know what all the symbols mean from the text.

You need the Young's modulus of the material, which you can look up. You need the radius and wall thickness of the sphere, which you can decide for yourself, and you need the pressure, which you know because you know atmospheric pressure.

How is it possible to not understand this? Are you telling me you can't substitute numbers into a simple equation, yet you sit around daydreaming about problems like this that you'd have no hope of solving without some very basic physics? Did you come here wanting someone to spoon-feed you the answer to your question after they took all the maths out of it?

Everyone in this thread seems to be basing their arguments around conjecture, or something they remember reading somewhere. Nobody actually considers the numbers, or even what trend something will follow. Thank you, thread, for reminding me why /sci/ is such a shit hole.

[Anonymous No.4355010]

>>4355001

Calm down, it's ok.
Noone read you're wall of text.
Why don't you sum up quickly.

[Anonymous No.4355017]

>>4355010

You are a wall of text?
I'm an idiot.

[Anonymous No.4355030]

>>4355017

No you where right the first time; you use the apostrophe to signify it belongs to something like their's, your's, etc.

[Anonymous No.4355048]

>>4355030

no, I was wrong... I fully admit my error, it happens, it was just a typo... it's very easy to type the wrong word when things are homophones.

Back to vacuum balloons.

[Anonymous No.4355125]

>>4355001

OP here. I'm not good at math or physics and I probably wouldn't be able to do those calculations properly, but your source is just not very relevant. I've already said numerous times that the airship would be a lightweight skeleton (of undetermined shape) covered by a skin (that has lots of tensile strength). I only used spheres in the beginning of the thread for the sake of simplicity. So the deformation of spheres without an internal skeletal structure is just not relevant to any of this.

No need to get upset.

[Anonymous No.4355150]

>>4355125
the up shot of everything is that you can't make the sphere light enough and strong enough at the same time.

For a large sphere the pressure quickly adds up to holding back hundreds of tonnes with tiny amounts of material that just ends up buckling.

[Anonymous No.4355153]

>>4355000

K... but how do you know?

[Anonymous No.4355174]

>>4355153

um... because we don't have materials that are strong enough to support 10,000 kg/m^2 in compression while being very very light?

You've said you're bad at maths but do you want some numbers?

[Anonymous No.4355216]

>>4355174

So when looking for materials that can withstand high pressures per unit area, should I be looking at their tensile strength?

[Anonymous No.4355231]

>>4355216

More like compressive strength, since the air is on the outside.

[Anonymous No.4355233]

>>4355174

Oh and the 90kPa difference would lead to 9,140kg of force per m^2, so it's a bit less than 10,000kg.

And yes, I'd like as many numbers as you can give me lol.

[Anonymous No.4355248]

>>4355231

But the membrane will be some sort of a fabric rather than a rigid shell. So when it's being compressed the fibers of the stuff will be stretched, which makes me think tensile strength would be more relevant no?

[Anonymous No.4355319]

>>4355248

True, that's so if you have a rigid framework inside. Then that framework will depend on its compressive strength.