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Lifting ability of Duchess Delthak

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Lifting ability of Duchess Delthak
Post by Nathanael Gray   » Thu Apr 09, 2020 4:09 pm

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I’ve always loved the care and thoroughness with which David lays out the specs of Safehold’s technological achievements. But I think I’ve caught a mathematical goof regarding the new Charisian airships in Through Fiery Trials. On page 283 of my hardback copy, the Duchess Delthak is described; it is remarked that “hydrogen was dangerous. . .But while helium was far safer, it was also far rarer. . .It also offered less lift—only half as much.”
Although a qualifier is stated—“given the practical design and operational differences between hydrogen- and helium-filled airships”—I don’t think that would be enough to justify the “half as much” proportion of lift. I suspect that David momentarily confused the fact that helium gas weighs twice as much as an equal volume of hydrogen gas with the idea that doubling the bouyant gas weight would halve the bouyant lift. Not so. The actual lift is the difference in weight between the bouyant gas and the air that it displaces. I have forgotten the figure for Safeholdian air, but I assume it is not greatly different from Terran air, which is a roughly 4:1 mix of nitrogen (atomic weight 14, diatomic molecular weight 28) and oxygen (atomic weight 16, diatomic molecular weight 32). Let’s say air has an average molecular weight of 29. The diatomic molecular weight of hydrogen is 2, while the monoatomic molecular weight of helium is 4. The difference between hydrogen and air is 27. The difference between helium and air is 25. So, an airship with a volume of hydrogen that could lift 27 units (ounces, pounds, tons), would, if instead filled with helium, lift 25 units, or 93% as much, not 50% as much. Not all that big a difference. So the main problem with helium would be the difficulty of obtaining enough of it.
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Re: Lifting ability of Duchess Delthak
Post by rocket_scientist   » Fri Apr 10, 2020 1:31 am

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I must admit that I too tended to think of helium as having half the lift of hydrogen. But I believe that your reasoning is correct, the amount of lift is the difference in weight between the lifting gas and the weight of the displaced volume of air. Note that weight, not mass is correct this time. Lift is a force, like pounds, and the amount of lift is also a function of the local gravity. The amount of lift is the weight of a unit volume of air minus the weight of a unit volume of lifting gas times the total volume of the lifting gas (balloon). Thus for hot air, the difference is very small and a large balloon is needed. At the other extreme, if the 'balloon' was rigid enough to maintain a vacuum the lift would not be infinite, just the weight of the displaced air minus zero.

And on Safehold there are many barriers to helium balloons. First off I am not even sure if they would even know that helium exists let alone its physical properties unless they are spelled out in one of the books of the WRIT. Second, without access to a helium reservoir like the helium trapped in natural gas fields in the US, they would not be able to get any helium. If they did have a source they would probably not have the ability, within the proscriptions, of separating the helium from whatever else it is mixed in with and then no ability to concentrate it to nearly pure helium. Third, they would clearly not have the ability to compress it enough to keep the storage tanks from being nearly as big as the balloon. Fourth, since unlike hydrogen which binds to many other substances, helium can't be bound to some other substance for easier storage and then unbound (generated) on-site so that all those big storage tanks would have to be hauled to the launch site. And that does not even include the fact that as hard as it is to keep hydrogen in a balloon it is even harder to keep helium inside. Just remember all those rubber helium balloons that look wilted within a few hours and even the aluminized mylar balloons look deflated in just a few days.

Sorry, more than you need to know about something that was not used in the book anyway. But it does further explain why RFC would use hydrogen instead of helium for the new 'demons in the air'.

Mike
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Re: Lifting ability of Duchess Delthak
Post by Nathanael Gray   » Sat Apr 11, 2020 7:29 am

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Good points. I had only thought about the difficulty of obtaining helium in the first place. IF enough helium even exists on Safehold, I'm sure OWL could tell them where to look and how to get at it, but that doesn't mean it would be easy, or even possible with permitted technology. But I had not thought about the storage and handling difficulties.
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Re: Lifting ability of Duchess Delthak
Post by rocket_scientist   » Sat Apr 11, 2020 12:46 pm

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With the permeability of helium through any possible balloon envelope material, I can just see the observation balloons being back on the ground again in just an hour or two because they had lost too much helium!

Mike
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Re: Lifting ability of Duchess Delthak
Post by WeberFan   » Sun Apr 12, 2020 6:45 am

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Great thread. Got me to thinking...

Found a wealth of information here:

https://www.airships.net/helium-hydrogen-airships/

Very good comparison of the use of hydrogen in airships versus helium - plusses and minuses.
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Re: Lifting ability of Duchess Delthak
Post by Nathanael Gray   » Wed Apr 15, 2020 3:40 am

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Excellent site, Weberfan. It does confirm what I said, but then goes on to explain how if you consider only PAYLOAD, you CAN be looking at a 50% loss, or even more, since payload is only a portion of the gross weight. In fact, it gives a hypothetical example where the reduction is more than 100%. But it is still true that the raw lifting ability of helium is about 93% of hydrogen.
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Re: Lifting ability of Duchess Delthak
Post by Loren Pechtel   » Wed Apr 15, 2020 7:15 pm

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Nathanael Gray wrote:Good points. I had only thought about the difficulty of obtaining helium in the first place. IF enough helium even exists on Safehold, I'm sure OWL could tell them where to look and how to get at it, but that doesn't mean it would be easy, or even possible with permitted technology. But I had not thought about the storage and handling difficulties.


It exists, the same place it exists on Earth--natural gas wells. Not only are they not using natural gas now, but separating it is beyond their tech, also. You have to liquefy the natural gas (note: critical point is 190K--you need a lot of chilling, not just pressure) to separate it. I don't think you need any prohibited technologies unless it's needed for quality control.
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Re: Lifting ability of Duchess Delthak
Post by phillies   » Wed Apr 15, 2020 10:01 pm

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Loren Pechtel wrote:
Nathanael Gray wrote:Good points. I had only thought about the difficulty of obtaining helium in the first place. IF enough helium even exists on Safehold, I'm sure OWL could tell them where to look and how to get at it, but that doesn't mean it would be easy, or even possible with permitted technology. But I had not thought about the storage and handling difficulties.


It exists, the same place it exists on Earth--natural gas wells. Not only are they not using natural gas now, but separating it is beyond their tech, also. You have to liquefy the natural gas (note: critical point is 190K--you need a lot of chilling, not just pressure) to separate it. I don't think you need any prohibited technologies unless it's needed for quality control.


It is much simpler to isolate the helium by passing the well output through a double pipe. The outer cylinder is metal. The inner cylinder is a specifically chosen plastic (several choices here). The well output goes down the center. The helium but not the hydrocarbons can pass through the plastic to the coaxial space.
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Re: Lifting ability of Duchess Delthak
Post by WeberFan   » Thu Apr 16, 2020 3:04 pm

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phillies wrote:It is much simpler to isolate the helium by passing the well output through a double pipe. The outer cylinder is metal. The inner cylinder is a specifically chosen plastic (several choices here). The well output goes down the center. The helium but not the hydrocarbons can pass through the plastic to the coaxial space.

What you describe sounds like a molecular sieve. The helium atom is a very small one and will pass through most things that other atoms / molecules won't. If you find a material with the correctly sized interstitial spaces, then it should be pretty straightforward.

Owl could likely identify the right material.

Build a "double pressure vessel" like a large-sized double boiler. Make the outer vessel out of an impervious material and the inner vessel out of "material X" that has the right sized interstitial spaces. Put the natural gas in the outer vessel under high pressure (as high as you can get it) and wait until the Helium passes through the shell of the interior vessel. You'll have to draw it off periodically into an appropriate impermeable vessel to keep the delta-P as high as possible between the two vessels.

Rather like membrane-based desalination I would think. Depending on the field, most natural gas fields have a concentration of 2-7% helium, with a bias toward the lower number. There are a rare few with a concentration around 10%.

The molecular sieve method wouldn't be as commercially efficient as the cool under pressure method, though.
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Re: Lifting ability of Duchess Delthak
Post by rocket_scientist   » Wed Apr 22, 2020 2:26 am

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I looked at the webpage cited above and was confused or concerned about a number of statements in it. So I looked more closely and found a second online document that filled in many of the gaps. The rest of this post gets into some very boring detail, so I will summarize here and you can skip the rest if you desire. Using the data for LZ 129, commonly known as the Hindenburg I can clear things up. First I will limit it to an apples to apples (red delicious to granny smith) comparison so I will ignore the two extra cells LZ 129 had that were specifically intended to be used for helium and limit both the hydrogen and helium to 200,000 cubic meters of gas giving roughly 202,000 kg for hydrogen and 187,000 kg force equivalent lift for helium, giving a 7% ratio. Once you add the same airframe, gas bladders, engines, flight crew and accommodations, avionics, empty fuel and ballast tanks you usee up 47% of the total lift. A maximum fuel load of 65000 kg brings the 'fixed' weight to 85% of the total lift (30,000 kg cargo lift) and with a 7% decrease in total lift which means %92 used up and only 8% left(15,000 kg cargo lift). This then explains the '50% lift from helium as you get from hydrogen comment. The reason I said red delicious to granny smith is that if you were designing two zeppelins with the same gas volume, one with hydrogen and one with helium you would probably tweak the lower lift zeppelin to reduce airframe weight slightly, cut a few corners in the crew cabin, etc. Even 7% smaller engines that consumed fuel 7% more slowly and dropped the airspeed enough to reduce fuel consumption would reduce the max fuel load by 7,800kg making the helium zeppelin slower but over 3/4 the cargo lift of the hydrogen.

A second comment was that you rarely had pure gases for lift and that helium would be at 88% but did not say 88% of what or why helium would be more susceptible to contamination than hydrogen. The 88% did appear to be used later on that webpage but never documented, so I have dropped the initial helium lift slightly.

I short, for rigid bodied (zeppelin) helium provides 50% of the cargo lift compared to hydrogen, but only if the 'fixed' weight was 85% of the total lift. But in the book they use non-rigid blimps with no airframe, no engines, and no fuel so the parasitic weight may be as little as 30% of the total lift which would put helium at 90% of the lift of hydrogen!


Great Boring Detail:
Using web document https://ntrs.nasa.gov/archive/nasa/casi ... 018803.pdf which compares the LZ line of zeppelins, focusing on the Hindenburg. Using kg as the force equivalent in Earth's gravity field, the lifting gas volume of the Hindenburg was 200,000 cubic meters (ignoring the two extra cells in the middle that were intended to be used when helium was the lifting gas). The total raw lift for hydrogen was 202,000 and for helium 187,000 with ratio of 187000/202000 = 92.6%.

category parasitic weight weight added hydrogen net lift helium net lift lift ratio airframe, gas bags, outer skin 78,430 202000-78430=123570 187000-78430=108570 108600/123600=88%
engines, pods, pylons, gondola 15,950 123600-15950=107600 108600-15950= 92600 92600/107600=86%
fuel&water tanks, avionics, crew 12450 107600-12450= 95150 92600-12450= 80150 80150/ 95150=84%
transatlantic fuel (?) 65,000 95150-65000= 30000 80150-65000= 15000 15000/ 30000=50%

The parasitic weight, everything accept the cargo was 47% without fuel and 85% with a full load of fuel. This means that the remaining lift for cargo was the difference between two large numbers and small changes to the either total weight or the raw lift can have a large impact on the cargo carrying capacity (note the helium 50% lift case). It is hard to nail down the exact maximum fuel, the 65 tons seems to be a fair consensus. This second-largest single item for weight could be changed by reducing (or increasing) the range or slowing down (or speeding up) the estimate 140 feet/sec speed.


The LZ 130 was initially designed for hydrogen and had a 70 bed cabin, but when redesigned for helium scaled down to 40 beds with other weight reducing measures. This may also be the source of the 'half the lift with helium'.

P.S. I am sorry if this causes a digression into posts about the Hindenburg, but it was the only example I found with sufficient detail to generate the '50% lift from helium' case.
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