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During WW1 U Class Zeppelins had hydrogen cells that contained 55,795 cubic meters of gas.

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According to Peter Kämpf's excellent, detailed explanation of Zeppelin mechanics they began missions with their hydrogen cells filled with roughly 33% hydrogen. The rest of the volume contained air. Because hydrogen expands as air pressure falls starting at 33% allowed Zeppelins to reach high altitudes without rupturing their gas cells.

However given the constants below I'm not sure how 33% hydrogen produced enough lift to get a Zeppelin off the ground.

Sea Level, 0 Meters:

Temp Celsius: 15°

Temp Kelvin: 288.15°

Pressure Pascals: 101,325

Gas Moles per cubic meter: 42.29

Air mass per cubic meter: 1.221 Kg

Hydrogen mass per cubic meter: .085 Kg

55,795 cubic meters of gas cells * 33% full = 18,412 cubic meters hydrogen

18,412 cubic meters of displaced air mass = 22,481 Kg

18,412 cubic meters of hydrogen = 1,566 Kg

Useful lift = 22,481 kg - 1,566 kg = 20,915 Kg

The empty weight of a U class Zeppelin was 25,750 Kg. That's without fuel, ballast or bombs. If useful lift was less than empty weight how did it take off?

At 5,000 meters altitude useful lift stays the same because although the hydrogen cells expand and displace more air the atmosphere is less dense and has less mass per cubic meter. Lift at 0 meters altitude is the same as lift at 5,000 meters altitude.

Another detail I found interesting is that according to Wiki the U Class Zeppelin produced 64,750 Kg of useful lift.

When I plug in numbers at sea level that suggests that the gas cells were filled to the top with 100% hydrogen.

55,795 cubic meters of gas cells

55,795 cubic meters of displaced air mass = 68,126 Kg

55,795 cubic meters of hydrogen = 4,743 Kg

Useful lift = 68,126 Kg - 4,743 Kg = 63,383 Kg

However if the hydrogen cells were filled to 100% it couldn't climb without bleeding hydrogen all the way up. It should be noted that at 5,000 meters the air is thin and useful lift drops by almost half.

Altitude, 5,000 Meters:

Temp Celsius: -17.5°

Temp Kelvin: 255.65°

Pressure Pascals: 49,586

Gas Moles per cubic meter: 23.33

Air mass per cubic meter: .674 Kg

Hydrogen mass per cubic meter: .047 Kg

55,795 cubic meters of gas cells at 100% full

55,795 cubic meters of displaced air mass = 37,605 Kg

55,795 cubic meters of hydrogen = 2,622 Kg

Useful lift = 37,605 Kg - 2,622 Kg = 34,983 Kg

34,983 Kg of lift is maybe barely enough to stay afloat with fuel, ballast and bombs.

But even if they did it this way when the Zeppelin descended the Hydrogen cells would be mostly empty and would fill with air causing the ship to gain weight and crash.

At 0 meters

55,795 cubic meters of gas cells filled with 66% air = 36,825 cubic meters

36,825 cubic meters of air mass = 44,963 Kg!

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  • $\begingroup$ Maybe, you should have extended your first question. However: But even if they did it this way when the Zeppelin descended the Hydrogen cells would be mostly empty and would fill with air causing the ship to gain weight and crash. No! The weight would be the same, as I wrote before. A balloon does not gain weight, if you inflate it with air It creates lift if you fill it with hydrogen, it looses lift if you remove some hydrogen, but if you add air, nothing happens. $\endgroup$
    – sweber
    Oct 10 '20 at 17:42
  • $\begingroup$ @sweber But if you add water to a ship this increases the mass and it sinks. If you add air to a hydrogen cell isn't that the same thing? $\endgroup$ Oct 10 '20 at 17:46
  • $\begingroup$ Putting water into a ship means removing air... Keep in mind: Everything displaces air, and observed weight is real weight minus weight of displaced air. If the weight is negative, it causes lift. The hydrogen displaces only half the air at groundlevel, but the air weights twice as much than at altitude, so the lift is the same. And since air weights the same as air, it contributes nothing to the weight / lift. $\endgroup$
    – sweber
    Oct 10 '20 at 18:11
  • $\begingroup$ @sweber Maybe I don't understand a basic concept. The gas cells start 100% filled with air. This makes them heavy. However before takeoff hydrogen is pumped into them which is light. The difference gives the airship lift. But if you did the reverse and pushed air into the hydrogen cells (as would happen during a descent with mostly empty cells) wouldn't this reduce lift until the ship crashed? $\endgroup$ Oct 10 '20 at 18:36
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    $\begingroup$ @myNewAccount: Yes, you're missing something very important. The gas cells do not (or at any rate should not) EVER contain air, because hydrogen mixed with air is explosive. They start out EMPTY, like a balloon before you blow it up, and are filled with hydrogen, which then expands and contracts due to outside air pressure. $\endgroup$
    – jamesqf
    Oct 11 '20 at 2:51
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The gas bags always contained close to 100% hydrogen. No air was supposed to be in them. On the ground, the bags were only partially filled because of the high air density and pressure. The rest of the internal volume of the Zeppelin was filled with air which could enter and escape the hull through the many gaps and venting openings.

Compare that to a weather ballon. On the ground, the big envelope is nearly empty and only a small bubble of lifting gas (today mostly helium, but hydrogen would work even better) sits at the top. Only that the nearly empty ballon is in clear sight, while in a rigid airship the half full gas bag is hidden behind the rigid hull covering.

One cubic meter of hydrogen weighs only 90 grams compared to one cubic meter of air at 1.225 kg under standard atmospheric conditions. With the same amount of hydrogen a balloon will have the same lift, regardless of altitude, because its lifting gas will displace a bigger volume but the same mass of air as it expands with altitude. With Zeppelins, fine tuning of lift by adding dynamic lift is possible but limited to maybe 5%-20% of the ship's mass (more for smaller and faster ships and at lower altitude). By growing larger, the mass to volume ratio of Zeppelins decreased, so the latest WW I ships could be built light enough to fly with their gas bags only one third full.

Civilian airships rarely flew higher than 2000 m high and had to circumvent higher mountain ranges because they filled their gas bags to maybe 80% on the ground. Flying higher was not considered worth the reduction in payload and fuel that would result from less lifting gas.

Compare that to the wartime Zeppelins. They were in a continuous arms race for higher altitude with the British aeroplanes which were sent out to chase them. And until 1918 the most modern Zeppelin designs were ahead. The limited altitude of older ships also meant that many were scrapped after one or two years of service. The table below shows the maximum altitude at which the gas bags were filling out the available volume of the ships. The list below gives the maximum altitude of the best ship of each series and the density ratio shows the degree to which the gas bags could be filled on the ground to achieve that altitude. Note that they still carried tons of water ballast and ordnance when flying that high.

Table of selected airships

LZ 112 tried with speed what could not any longer be achieved with altitude: It had 7 more powerful engines where older ships had only 5 and could cruise at 131 km/h as opposed to the 100 km/h of the older ships. The diminishing returns of flying higher and the stress of spending close to a day at -40°C and without a pressure cabin or a pressure suit made higher flight altitude impossible. What also held progress back was the size of airship hangars: Since LZ 62 the maximum diameter could not grow beyond the 23.9 m of the last wartime ships, so their volumetric efficiency went down when they grew larger by adding length.

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  • $\begingroup$ Peter thank you so much for your information. After thinking about your answers I think I understand. The hydrogen cells always displaced a more or less fixed volume of outside air. Airships were rigid and because the bags were attached to the frame they retained their shape and displaced approximately the same amount of outside air even when they were half filled with hydrogen. Is that more or less correct? Although a pressurized cabin would have been heavy I wonder if it would have been worth experimenting with since Zeppelins could reach 7,000 or 8,000 meters. $\endgroup$ Oct 11 '20 at 22:42
  • $\begingroup$ @myNewAccount: I hope you meant to say "The hydrogen cells always displaced a more or less fixed mass of outside air". The outer shape was rigid and the gas bags had variable volume, depending on atmospheric pressure. One big advantage of Zeppelins was that you could walk around the ship. Each engine had mechanics tending them during flight. Repairs of the engines and the structure were done in the air. Pressurizing all those stations was prohibitively expensive in terms of weight. $\endgroup$ Oct 12 '20 at 4:24
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    $\begingroup$ @myNewAccount: The hull displaces those 55795 m³, but the bags inside are flexible and the volume they took up depended on how much hydrogen was in them and the atmospheric pressure. They would displace their maximum volume at maximum altitude and proportionally less at lower altitude. A ship with full gas bags on the ground would not be able to climb, or it would lose lift when venting lifting gas. A Zeppelin was never filled up to create those 64750 kg of lift, they were just filled until the ship was balanced. For an U-class this would mean the bags were half full on the ground. $\endgroup$ Oct 13 '20 at 7:23
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    $\begingroup$ @myNewAccount Please don't hesitate to ask a new question - comments are poor for explanations. Yes, only as much hydrogen as needed to lift the loaded ship would be allowed, or the ship would have risen uncontrollably up to its maximum altitude (Prallhöhe in Zeppelin speak). The elevator was only for controlling pitch, steering up or down was done with the engines. At low speed, the elevator function is even reversed. $\endgroup$ Oct 13 '20 at 17:11
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    $\begingroup$ @myNewAccount: When the lifting gas is at a temperature equilibrium with outside air, the same mass of hydrogen in the bags will keep the ship balanced at any altitude. With altitude the volume of this mass expands until the gas bags fill all of the ship's available volume at maximum altitude. $\endgroup$ Oct 13 '20 at 17:13
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Some physic experiments

Let's assume we have a 1m³ container of negligible weight at sealevel. It displaces 1m³ of air, and this air weights 1.22kg.

When filled with hydrogen at ambient pressure, this hydrogen weights 0.08kg. The lift is 1.22kg - 0.08kg = 1.14kg.

Now let's bring the container to an altitude where pressure is just 50%, and let's ignore temperature. 1m³ air at that pressure weights 0.61kg. With the hydrogen, still at full pressure, the lift is 0.61kg - 0.08kg = 0.53kg.

Let's now bleed half of the hydrogen, until it reaches ambient pressure. The remaining hydrogen weights 0.04kg, and the lift is 0.61kg - 0.04kg = 0.57kg. It increased by just 0.04kg!

The container is now brought back to ground. The lift is now 1.22kg - 0.04kg = 1.18kg. Next, 0.5m³ air is let in, to equalize air pressure, and the hydrogen compresses to 0.5m³. Overall, the container now contains 0.61kg air and 0.04kg hydrogen, the lift is 1.22kg - (0.65kg + 0.04kg) = 0.57kg. This is the same as at altitude!


What does this mean for airships?

If the entire volume of an airship is filled with hydrogen at the ground, it would loose about half the lift at that altitude. Since it can't withstand the over-pressure, it had to bleed off half of the hydrogen, which doesn't change lift much. And if it returns to ground, letting air in to maintain ambient pressure, it would still have just half the initial lift, not more, not less.

Instead, the volume of an airship is filled partially at ground, and the gas is allowed to expand at altitude. This way, it starts with low lift, but it maintains this lift during the entire flight.
Rigid airships like those in question contain gas cells inside the hull, which were inflated partially and could expand during flight.
For non-rigid airships (blimbs), it's usually quite the opposite: The lifting gas is directly under the hull, and there are cells filled with air.

Now, looking at your numbers: The LZ95 weights 23.000kg. This needs about 30% hydrogen to fly. Add some more hydrogen, and it can carry some load.

I guess

  • Maximum lift is when filled 100% with hydrogen, though it can't climb to higher altitude
  • Maximum altitude can be reached only with almost no load.

Remember: An aircraft has a maximum speed, maximum load and maximum range. But not all at once.

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  • $\begingroup$ Your last line is absolutely correct. When I read the specs on ww1 - ww2 aircraft if they carry a lot of bombs they probably aren't flying very far. $\endgroup$ Oct 11 '20 at 22:44

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