# Airships in a world with 1/3 gravity but 3 times the mass of atmosphere?

In the first question I posted here on Worldbuilding Stack Exchange, I asked if lifting gas would be more effective on a world with 1/3 of Earths gravity but with the same atmospheric composition as here on earth. To my surprise I learned that there would be no difference. I admit I was disappointed; but, the answer did encourage me to do more research.

In my research I learned that a lighter gravity planet like Mars with 1/3 of Earth's gravity would need at least 3 times the mass of atmosphere here on earth to have a surface pressure of 14.7 psi. With that in mind, would airships on a world with 1/3 gravity and the same surface pressure as earth (14.7 psi) but 3 times the mass of atmosphere have higher lifting capacity than here on earth or would it stay the same due to the lower gravitational pull reducing weight and buoyancy?

• Before you go too far, it may be fair to mention that a world with low gravity would not be able to hold such an atmosphere – Andrey Nov 13 '18 at 22:51
• @Andrey Remember, surface gravity varies from escape velocity by a factor of the planet's radius. Surface gravity is $Gm/r^2$, while escape velocity is $\sqrt{2Gm/r}$. It is possible, with a relatively large radius and low mass, to have high enough escape velocity to keep even hydrogen gas in the atmosphere while having a low surface gravity. Example: Saturn. – kingledion Nov 14 '18 at 0:10
• Tyler, I changed the wording of your question to make it more scientifically accurate. Atmospheric surface pressure is proportional to $mg$. If you triple the mass of the atmosphere column above any point($m$), but divide surface gravity ($g$) by three, you end up with the same net pressure, so long as your column of atmosphere is the same. Also, your last question was a totally different topic, and should be answered separately, so I removed it. But, be warned, I'm pretty sure that has been asked before on this site. – kingledion Nov 14 '18 at 0:18
• @Andrey Titan is a world with a much lower surface gravity than Earth, but a more massive atmosphere than Earth ( about 20% more massive ). – StephenG Nov 14 '18 at 2:35

# How to make airships lift more

What you really want to know is, how to make an airship lift more.

The lift of an airship's gas envelope is calculated as follows:

$$\text{lift} = \left(\rho_{air} - \rho_{gas}\right)V$$

Since density ($$\rho$$) is in units of $$\text{kg/m}^3$$ and volume ($$V$$) is in units of $$\text{m}^3$$, the lift is measured in kilograms. Kilograms are a unit of mass, not weight, so they are independent of the force of gravity.

But note, they are also independent of the atmospheric pressure (mostly)! If your planet has a high air pressure, then your lift envelope must have a corresponding high pressure in order to counterbalance the force of the atmosphere, or else it will be collapsed. In accordance with the ideal gas law, pressure and density are related. The ideal gas law is commonly $$PV = nRT$$, which can alternately be $$P = \rho\bar{R}T$$. Since $$\bar{R}T$$ can be assumed constant, density of both air and lift gas vary the same way with pressure, so pressure can be ignored.

Let me briefly discuss an alternative, which is to have a rigid lift envelope filled with vacuum. Using known materials, this isn't practical, but if you have magical/futuristic materials, you could set $$\rho_{gas}$$ to zero.

# Conclusion

There are three ways to change the lifting power of your airships.

• Increase the volume of the lift envelope, i.e. make a bigger airship.
• Lower the density of your lift gas. Since there is nothing less dense than hydrogen, you can't lower this any further, unless you use futuristic materials and vacuum. On the other hand, heating the gas relative to the air will reduce its density; this is the principle behind a hot air baloon. Still, you definitely can't lower this any more than zero.
• Increase the pressure independent density of the atmosphere, relative to Earth. This means adding more heavy molecules to the atmosphere, like Argon, Carbon Dioxide, sulfurous gasses, or water vapor.

I you want a planet where the same airship lifts more relative to Earth, the last bullet is your only option.

• @theRiley Warm air is better than cold air...hence hot air balloons. – kingledion Nov 14 '18 at 1:39
• @theRiley You are confusing me. I say all that in my answer. What are you getting at? – kingledion Nov 14 '18 at 1:48
• @theRiley Look at the equation. Does not a hydrogen balloon lift more than a balloon with air in it? Because hydrogen has lower density. Does not a hot air balloon lift more than a balloon with regular temperature air? Hotter gasses have lower density. A lower density lift gas will lift more. – kingledion Nov 14 '18 at 1:55
• It consistently freaks me out that a more accurate way to say ‘low density things rise to the top’ is ‘high density things will push their way to the bottom’, yet nobody ever puts it that way. – Joe Bloggs Nov 14 '18 at 7:37
• Major error. Density of both air and lifting gas is PROPORTIONAL TO pressure. Say your air density is 1 kg/m3 and your lifting gas is 0.2 kg/m3. Buoyancy on a 1m3 balloon is 0.8kg * gravity. As you point out, since gravity also applies to the load you're carrying, that cancels out. But if you double the air density, the air is 2 kg/m3 and the lifting gas is 0.4 kg/m3, so you get 1.6kg worth of lift on a 1m3 balloon! In other words, addition/subtraction doesn't cancel out multiplication/division. – Tristan Klassen Dec 26 '18 at 18:50

Change in gravity does not change how much you can lift, that is, if density of air particles does not change.

On your smaller planet I would expect it to be smaller, as more mass to atmosphere will give you surface presure, but density of air will be less, as with less gravity air will be spead in bigger volume and more even (altitude). With same composition of air, living things would care for less dense air = less O2 or CO2 per volume.

If 1/3g and same air density. Your airships would have same lift and would be able to go higher. You would have more surface presure somewhere in 2-3 times range. Oxygen toxicity - with same % of oxygen will start to show at 2.5-3 normal presure. Nitrogen narcosis: 2-3 normal presure, mild symptoms aka one martini.

I would go somewhere in between. For more precise answer you may go to something like Physics stack.

• "Go higher" is a good point. Assuming a low gravity planet having the same surface air pressure as earth (which I do not think is impossible), then the reduction in pressure with increasing altitude would be smaller than on earth. So it might be feasible for your airship to cruise at twice the height of Everest without losing lift and without the occupiers needing oxygen masks. – Penguino Nov 13 '18 at 23:50

I may be wrong here but

isn't what determines buoyancy the difference in internal overall vessel density to the external fluid density. Like a concrete boat floats because it displaces enough space that the vessels overall density is less than the surrounding waters.

So gravity doesn't matter because it is uniform in the system, what matters is the construction of your airship.

Since the surface pressure is the same, isn't the overall volume irrelevant.

Then again I suppose the volume could matter as it could raise the respective ceiling height of the craft. But that would depend a lot on how the planets pressure layers form, is it a smooth gradient or does it have curves. I think temperature and chemistry would then play a roll as well on this aspect.

The volume would not affect ground inhabitants.