# Hydrogen balloon logic

#### GTeclips

Joined Feb 18, 2012
96
Hello everyone.

I am trying to figure out the lifting capacity of my hypothetical balloon.

It will be a 300'x75' cylinder. I know there are many variables as to how much weight one foot cubed of hydrogen can lift, but by what I have heard (Correct me if I am wrong), it is somewhere in the ball park of 0.07 lb.

I am using ((pi*radius squared*length)*Lift of 1' cubed hydrogen).

So I figure first, 75 / 2 = 37.5

Next, 37.5 Squared = 1406 (I am rounding)

Then, 1406 x pi = 4,418

Next, 4,418 x 300 = 1,325,359

Lastly, 1,325,359 x 0.07 = 92,775

This leads me to believe the gross lifting weight of the balloon will be around 46 tons.

Is my math correct here? Thank you for viewing!

*Edit* Derp, I just realized that this should have gone under math... Really sorry for that.

#### t_n_k

Joined Mar 6, 2009
5,455
Presumably you mean a 300' long cylinder of 75' diameter. If so you are correct.

A rigid containment vessel of that size would probably weigh some tons, so you'd obviously lose some of the potential lifting capability.

When are you planning to be airborne?

#### WBahn

Joined Mar 31, 2012
26,398
1 mole of dry air at STP occupies 22.4liters and has a mass of basically 29g while the a mole of hydrogen has a mass of 2g (and helium 4g). Thus the bouyancy of a mole of hydrogen when surrounding by dry air at STP is about 27g (and helium is about 25g).

Converting 22.4l to cubic feet is straightforward since 1l is 1000cm^3 = (10cm)^3. So we just multiply that (inside the parens) by (1in/2.54cm)(1ft/12in) and we get that 1 mole of an ideal gas at STP occupies 0.791ft^3. Turning to the mass, 27g (which is basically one ounce, or 1/16 lb) can be converted to pounds using (2.2lb/1000g) (close enough for our needs). So 27g is 0.0594lb. The bouyancy is therefore 0.0594lb/0.791ft^3 which is 0.075lb/ft^3 (and just a little less, namely 0.070, for helium).

Beyond that, your computations look reasonable to me. It would really help if you carried units.

#### GTeclips

Joined Feb 18, 2012
96
Thanks guys!

When are you planning to be airborne?
Well, right now I am just dreaming... Back in reality, I would imagine the cost of a rigid airship of those specs would cost in the high millions to make depending on the materials you use.

Beyond that, your computations look reasonable to me. It would really help if you carried units.
Yeah, my mathematical equation writing is quite poor. XD

#### GTeclips

Joined Feb 18, 2012
96
I just got another question that came to my mind.

Now I know that the frame of a rigid airship is typically made of aluminum, but would it be possible to construct it of wood to suppress the cost, and if that was possible, what would be some of the pros/cons.

#### Wendy

Joined Mar 24, 2008
22,547
I remember reading a SciFi story where a company built a hollow sphere of metal in space and had it enter the earth atmosphere in a controlled way, where it floated. It was to cut down on transportation costs for delivering a big chunk of metal from space.

#### GTeclips

Joined Feb 18, 2012
96
So, I'll take the wood theory as a no?

#### WBahn

Joined Mar 31, 2012
26,398
I remember reading a SciFi story where a company built a hollow sphere of metal in space and had it enter the earth atmosphere in a controlled way, where it floated. It was to cut down on transportation costs for delivering a big chunk of metal from space.
Back long before the first successful balloon flights, among the first notions was to use an evacuated metal sphere. They principle and theory and capability was well understood. The only problem is that, to keep it from imploding, the sphere's structure ends up being heavier than the air it displaces. With modern structures and materials, it might possibly be a different story; I don't know if anyone has looked at the problem, but I suspect they have.

#### #12

Joined Nov 30, 2010
18,223
Funny thought experiment...We were manufacturing ultra-thin wall titanium vacuum containers but we couldn't keep them on the shelves. They kept floating up to the ceiling.