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All credit for this idea goes to Calliban.
It appeared in discussion of space elevators for the Moon.
If a tube where stretched between the Lunar L1 point and the surface, and if a gas were pumped into the tube at the bottom, then the gas could lift a capsule in a manner similar to industrial pneumatic tubes used for many years to move documents between locations in a large building.
On the Moon, since vacuum is the environment, gas would have to be pumped into the tube to move the capsules.
However, on the return trip, the gravity of the Moon could help the capsule to compress the gas, while slowing the velocity of the capsule as it approaches the surface of the Moon.
This system could provide a comfortable ride for human passengers.
The velocity of the capsule on the up side would be limited to the speed of sound of the gas chosen for the application, but that would still be a respectable velocity for a trip from the Moon.
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This post is reserved for an index to posts that may be contributed by NewMars members over time.
Post #6: Isaac Arthur video on space elevators
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The simplicity of this idea is certainly a strength. Problems I can see:
1. How much gas would be needed to push a projectile up a 60,000km long pipe?
2. If velocity cannot exceed the speed of sound (you could do better using hydrogen), then the projectile velocity is limited to 340m/s. Using hydrogen, you could get up to about 1km/s. But even at 1km/s it will take 16.7 hours for the projectile to reach the top.
3. When the projectile exits, you have a long open tube full of gas. You could shut a flap to prevent it from leaking into vacuum after the projectile has passed. But you then need to recompress the gas into a bottle at the base of the tower ready for the next shot. How long will that take? At least as long as it took to fire the shell - 16.7 hours. Probably a lot longer.
So you need a lot of gas to push the shell up the tube, a lot more than the shell would mass. And it would be a long time (days) between shots.
A slightly different take on your proposal would be a plasma cannon. In that case, the gas is an electrically conductive ionised plasma at temperatures of 10,000+ K. Probably ionised and heated by electric arc. In that case, you don't need to save the gas, because you can use something abundant on the moon. The tube would need to be a magnetic coil, creating a magnetic flux tube to contain the plasma. The mass of the required plasma would be much reduced, because the temperature is so high.
I think the problem again comes down to weight. But unlike the gas gun, the plasma gun doesn't need to travel up the entire length of the tube because it can accelerate the projectile to much higher velocity. It could kick the projectile to escape velocity within a barrel length less than a km. So you probably wouldn't need the space elevator. Just some way of keeping the projectiles on course for L1 / L2.
Last edited by Calliban (2024-10-09 11:34:37)
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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For Calliban re #3
Thank you for giving this new topic a welcome push.
The velocity of sound of hydrogen at STP is given as 1280 m/s.
Calculator Soup gives a time of 47929 seconds.
An ordinary calculator shows that value as 13.3 hours.
I think what's throwing us off is the idea of constant velocity...
Dr. John Hunter's projection for performance of his gas launcher is about 7 km/s.
Search Labs | AI Overview
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A projectile launched from one of Dr. John Hunter's gas guns can reach velocities exceeding 7 kilometers per second (km/s), which is roughly equivalent to 4.3 miles per second; this high speed is achieved by utilizing a light gas propellant system, allowing for significant acceleration of the projectile within the barrel.
Key points about Dr. Hunter's gas guns:Clearly the velocity of a projectile is not limited by the velocity of sound in the gas.
What determines the velocity is the pressure of the gas on the base of the projectile.
The prospects for a pneumatic tube space elevator at the Moon would improve if a way could be imagined to build pressure behind the capsule during the lift.
(th)
Search Labs | AI Overview
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The velocity of sound in hydrogen gas at STP (Standard Temperature and Pressure) is approximately 1280 meters per second.
Explanation:Formula:
The speed of sound in a gas is calculated using the formula: v = √(γRT/M), where γ is the adiabatic index, R is the ideal gas constant, T is the temperature, and M is the molar mass of the gas.
The distance given for Lunar L1 is 61,350 kilometers.
Then, the distance between the Moon and the Lagrangian point L1 equals 0.1596003*R, that is 61350 km. Consequently the Earth-to-L1 distance equals 0.8403997*R, that is 323050 km. 2) The distance between the Moon and the Lagrangian point L2 equals 0.1595926*R, that is 61347 km.
Locations of the five Earth-Moon Lagrangian points, namely ...
ResearchGate.net
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Lunar escape velocity is 2.38km/s. If your gun can rapidly accelerate a shell to that speed over a short distance, then we don't need to keep pushing after that speed is reached. The pressure behind the projectile would rapidly fall off. As it climbed, it would slow down, trading gravitational potential energy for kinetic energy. Which is what we want to happen, as the projectiles need to have slowed upon reaching L1/L2.
If hydrogen (or another suitable propellant) can be sourced abundantly on the moon, I think this could work. A chemical bipropellant would work. LOX/H2 has an exhaust velocity of 4500m/s. Even much lower performing propellants have exhaust velocities greater than lunar escape. This is because molecular velocity is much greater at typical combustion temperatures.
******
Sulphur (when burned to sulphur dioxide) has an energy density of 9.23MJ/kg. If burned rich, it would produce a hot vapour rich in sulpur vapour with a molecular weight of 32. It is probably the most abundant volatile on the moon, but isn't really superabundant. Concentration in lunar mare soils is still <1%. Aluminium burned in oxygen has much high energy density. But aluminium is energy intensive to make.
Push the hot gas through a DeLavelle nozzle and the pressure drop converts thermal energy into kinetic energy. Sulphur dioxide has a molecular weight of 64, which is 2x sulphur. Typically, a rocket engine is 30% efficient at converting heat into kinetic energy of exhaust.
Qe = 0.3 x Qc = 0.3 x 9.23 = 2.769MJ/kg sulphur or 1.3845MJ/kg SO2.
An estimate of exhaust v:
V^2/2 = 1,384,500.
V = 1664m/s.
Not quite enough for S/O2 propellant alone. Maybe we could add something else to the mix to get the flame temperature higher? An electric arc cannon is possible. In that case we don't have to burn the sulphur just heat it to a crazy temperature. The exhaust molecular weight halves, so gas velocity increases by ~2^0.5 = 1.4x. That might just be enough.
Last edited by Calliban (2024-10-09 13:19:31)
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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Isaac Arthur created a 30 minute video about space elevators for the Moon.
https://www.msn.com/en-us/news/technolo … fba8&ei=64
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This topic is set up with a focus upon the use of gas to lift capsules from the lunar surface to L1.
The velocity that might be achieved by such a capsule might appear to be limited by the speed of sound of the gas used for the lift, but I am uncomfortable with that theory, because hydrogen can travel faster than it's own speed of sound. I decide to ask Google's Gemini (v2.0 in this case) and it came up with a useful analogy to help:
Conversation with Gemini
Hi Gemini! Thanks for your help with many previous questions! In this one, I am hoping you might be able to help an older person with preconceptions about the speed of sound as a factor in the velocity of acceleration of an object in a tube. The preconception is that the object in the tube can move no more rapidly that the speed of sound of the gas in use to propel the object. I think this belief may be in error under certain circumstances. I offer in support of this idea, that hydrogen gas moving as a body can move faster than the speed of sound within the body. For a trivial example, a container of hydrogen in orbit is travelling far faster (with respect to the Earth) than the speed of sound inside the container. I have a scenario to offer for your consideration, after you have a chance to take in this opening text.
***Hello! It's great to reconnect and assist you again. Your intuition about the object potentially exceeding the speed of sound within the propelling gas under specific conditions is spot on. Your analogy of the orbiting hydrogen container beautifully illustrates that the bulk motion of a substance isn't limited by the internal speed of sound. The speed of sound governs the propagation of pressure waves within a medium, not the overall velocity of the medium itself or an object propelled by it.
I'm very interested to hear the scenario you have in mind. Please share it whenever you're ready!
***The proposal at hand is the use of a pneumatic tube to lift objects from the surface of the Moon to the L1 point. Setting aside the engineering challenges, let's focus on the idea of lifting a capsule using a supply of gas. Our correspondent offers the suggestion that the body to be lifted can move no more rapidly than the speed of sound of the gas used for the lift. I am disappointed to think that the speed of sound of a gas would prevent the gas from expanding into the tube at a velocity greater than that of sound inside the gas. To me that limit is counter intuitive. What is your assessment?
***Ah, lifting objects from the Moon to L1 using a pneumatic tube – a fascinating concept!
You are absolutely correct to question the idea that the capsule's velocity would be strictly limited by the speed of sound of the propelling gas. Your intuition here is sound (pun intended!). The speed of sound in the gas dictates how quickly pressure changes propagate within that gas. It doesn't inherently limit the overall speed that the gas itself, or an object propelled by it, can achieve under the influence of a sustained force.
Think of it this way: imagine pushing a long train. The speed at which the force propagates down the train (analogous to the speed of sound) is determined by the couplings and the mass of the cars. However, if you keep applying a constant force with a powerful enough locomotive, the entire train can eventually reach a speed much higher than the speed at which the initial push traveled down its length.
In the context of your pneumatic tube on the Moon:
Gas Expansion: The speed at which the gas expands into the tube is related to the pressure differential and the geometry of the system. While pressure waves within the expanding gas will travel at the speed of sound, the bulk flow of the gas itself can certainly exceed this speed, especially in a vacuum where there's no atmospheric drag. This is what happens in the exhaust of a rocket engine, for example.
Capsule Acceleration: The capsule's acceleration depends on the force exerted on it by the expanding gas and its mass (F=ma). As long as a sufficient pressure difference is maintained to provide a continuous force, the capsule's velocity can increase over time, potentially surpassing the speed of sound within the gas.
The speed of sound of the gas is a crucial factor in the design of the pneumatic system. It will influence things like the rate at which pressure can build up and equalize, and the characteristics of any shockwaves that might form within the tube. However, it doesn't act as an absolute speed limit for the propelled object.
Therefore, your correspondent's preconception that the capsule's speed is capped by the speed of sound of the gas is likely incorrect. The final velocity of the capsule will be determined by the thrust provided by the expanding gas over the length of the tube, taking into account factors like friction and the mass of the capsule.
What are your thoughts on this assessment? Perhaps you have some specific parameters of the scenario in mind that we could explore further?
***Thank you for providing the ** very ** helpful analogy of the moving freight train! I'll post your reply and hope it is helpful to a few of our readers.
***You are most welcome! I'm so glad the train analogy helped to clarify the concept. It's always rewarding to find ways to make these kinds of physics principles more intuitive.
I truly hope my explanation proves useful to your readers. If any further questions or related scenarios come up as a result of your discussion, please don't hesitate to bring them my way. I'm always happy to explore these fascinating ideas further!
I think the limiting factor for velocity is the pressure applied to the gas, and NOT to the speed of sound within the gas itself.
I think that probably holds true for a cannon launcher as well.
My hope is that NewMars members will take up this interesting physics question. I think the true limit is the speed of light.
Our (human) observations over centuries are a massive body of knowledge that (I suspect) obscures the truth in this situation.
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