Air Hockey On the Moon ( Part 2)

Air Hockey on the Moon Getting: Part 2 Further into the math

In the post “Air Hockey On the Moon (TFN)” we started to outline the idea of launching cargo from the moon using a massive pneumatic trackway. Today we are going to go a bit deeper into the math associated with the design of the trackway. As a brief refresher, escape velocity is the minimum velocity required for getting into orbit around a celestial body. On planet Earth escape velocity is 11.2 km/s or about 25,000 mph, that means if the Earth had no atmosphere and you fired a cannon ball horizontally at 11.2 km/s it would enter into orbit. To get an object to orbit around the moon you need to get it up to 2.38 km/s (just over 5300 mph). The Lunar Launch System outlined in the first post is intended to reduce the net cost of launching materials from the moon. Let us look at how different parameters might impact our design.

The “joy” of engineering and physics is messing around with your variables. (I mean I get a nerdy joy out of this but I won’t speak for everyone) Changing a relatively small parameter for one element can have massive consequences in your final design. Using the equations for simple acceleration we have three basic variables we can easily mess around with. To keep everyone on the same page initial Velocity is assumed to be zero and time is effectively a relationship between acceleration and the velocity at launch so we don’t need to think about time.

The length of the track, velocity when leaving the track, and acceleration are all technically up for grabs, so the question emerges, what variables do you consider most important? In the first post in this series we emphasized a maximum acceptable acceleration to achieve Lunar escape velocity. If we assumed that our cargo, in this case people, are limited to accelerating at 29.4 m/s^2, our trackway would need to be over 96 km long to get our crew into orbit. Building a 96 km long trackway seems daunting so what if we didn’t? By increasing our maximum possible acceleration or reducing our launch velocity requirements we can reduce our track length. Or alternatively we can say, “Hey I can only build a 30 km long launch track on the moon, what can I do with it?” All of these options are mathematically viable so let’s see what changing things around looks like.

First we can look at our maximum acceleration, what happens if we aren’t worried about squishy humans?

This chart shows how fast the launch velocity would be for a range of accelerations and various track lengths.

For a cart able to accelerate at 1 G you would need a track almost 290 km long to get up into orbit. Even at 10 G’s of acceleration, the track would need to be about 29 km long to achieve escape velocity. Well then what happens when we decide can’t even be bothered to make it so humans would survive launching, but some form of cargo might be ok? Let’s zoom in a bit on our chart.

When we start to get into the 100+ G’s territory our track lengths start to seem far more manageable. A launch system capable of boosting its cargo at 100 G’s (980 m/s^2) could achieve escape velocity with only 2890 meters of track way, a bit shy of two miles. Zooming in even more, and assuming our cargo can survive 10,000 G’s (98000 m/s^2) you only need 28.9 meters of track (that’s less than 1/3 of a football field).

Obviously (sarcasm), we should just build a stubby track that accelerates super hard.

Yes, we could make a short hard accelerating track, but there are some other considerations. If your only goal is to just get as much mass off the surface of the moon as cheaply as possible, a high acceleration system does in fact makes sense. Launching lots of mass cheaply isn’t exactly where a linear accelerator like the Lunar Launch System would be most useful. For high gee friendly cargo types you start to look at designs like canons or centrifuges. Cannons and centrifuges have the benefit of being built using fewer overall materials than an open trackway would likely require. One earth-based company SpinLaunch is working to develop a centrifuge that will provide much of the initial thrust that a rocket requires to get into Earth Orbit. With respect to canons, the 16 inch guns on WW2 destroyers were 20 meters in length and could launch projectiles massing between 850-1200 kg at velocities up to 820 m/s. Considering changes in our understanding of manufacturing and the advantage of not needing to worry about air resistance, it would be fairly reasonable to develop a lunar canon capable of launching cargo into lunar orbit. Whether we could use oxygen like our air hockey concept is another story entirely.

Cannons and centrifuges make the most sense when they are launching large volumes of very standardized cargos. Cannons start to lose their appeal when want to change your cargos size. A cannon’s barrel diameter is hard to change after you build it. For cargo that has a smaller diameter than the cannon, no worries you can use a sabot to make sure that everything works. If your cargo needs to have dimensions larger than the barrel, you need to go to an alternative launch solution.

Centrifuges are a bit more flexible, launching from an airless body like the moon means that the dimensions of your cargo is less of a concern, so long as the centrifuge is rated to the mass of the cargo you want to launch you are good to go. In an ideal scenario a centrifuge launcher would work like an Olympic athlete performing the hammer throw, spinning up cargo at the end of a cable or throwing arm, when the time is right the centrifuge system would simply release the cargo towards its intended orbit. A centrifuge potentially benefits from the simplicity of its physics. Need to decrease the g-forces on your cargo, you could design the centrifuge to use a flexible tether that could be slowly let out to help decrease the G load as the cargo was accelerated. Where this approach runs into risks is how much tension your launch tethers can withstand. (honestly I need to crunch some numbers, it may be the better approach, but one crazy idea at a time)  Strong cables certainly exist, the question is whether those cables are cost effective to either import from Earth or fabricate locally.

The Lunar Launch System idea is aimed at scenarios where a lunar facility wants to maximize the utility it gets from their orbital launch infrastructure. Cargo launched from the Lunar Launch System may not get into orbit solely on the energy provided by the system’s track way, but all cargo would have the potential to see some form of mass savings.

Assume we can only build a 30 km long trackway near our lunar base, what do our launch capabilities look like? For 10+G rated cargo, the track is more than long enough. For cargos rated to 1-9 Gs we would be unable to achieve escape velocity just using the Lunar Launch System track, but we are still able to get a bit of a boost. Even if your cargo was only able to accelerate at 1 G would be moving at 766 m/s, more than 2x the speed of sound. In practical terms this means that a 30 km long track is certainly able to start to help reduce how much fuel a space craft needs to carry to get itself into orbit.

Making the LLS a viable solution for a future lunar base is more than saying, “yeah, we have a design that can help clients get stuff into orbit”. If it was that easy, humans would already be strip mining the far side of the moon for helium 3 because folks will “totally” be buying all of that helium that currently has relatively limited uses. To make LLS work financially the design needs to go beyond ease of manufacturability, it needs to be able to minimize the time from when testing is validated to the time where revenue can be produced.

Fortunately, all of those charts we looked at earlier should give the business types hope, even if it hasn’t quite clicked for them (honestly if you aren’t following me that’s on me). While a large and complete trackway has a certain amount of appeal to most of us, you don’t need to build 10’s of km of track to see launch functionality. An 800 m long track would be long enough that a cargo capable of surviving 100+ Gs of acceleration could achieve 1/2 escape velocity or more depending on the track acceleration. That means researchers could increase the volume of research samples they could send to Earth. As sections get added the variety and volume of cargo would steadily increase.

Increasing the length of acceleration trackways is nothing new to the American defense industry. Rocket sled tracks have been used to test various types of equipment for over 80 years. The world’s largest rocket sled trackway the Holloman High speed Test Track is over 15 km in length and has been added to and improved over the last 70 years. The Holloman High Speed Test Track has the world record for rocket sleds, where a test sample was accelerated to Mach 8.6 or 2880 m/s, which is faster than Lunar Escape velocity. This is a good sign that our launch system is technically feasible (well except for some concerns about how our oxygen system will work, and geometry and uhh economics, and well, really lots of stuff.)

More to come.

TLDR: Depending on what criteria our Lunar Launch System emphasizes its capabilities/dimensions will change

-Longer Tracks mean lower acceleration requirements

-lower launch velocities means either lower acceleration or lower track lengths, but it does mean you need to have a booster to make up the difference between launch velocity and escape velocity

-higher accelerations make centrifuges and cannons make more sense, so long as you focus on simple cargo types

-build the track in sections in such a way that you can start launching some types of cargo before everything is done.

-rocket sled trackways on Earth have accelerated payloads to speeds higher than Lunar Escape Velocity,

TLDRtTLDR: More track means more speed, math say it work (kinda)

NASA Lunar Module Ascent Stage (dry mass 2445 kg, propellant 2376 kg, total 4821 kg) https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1969-059C

https://en.wikipedia.org/wiki/Rocket_sled longest rocket sled track according to Wikipedia was 15 km  long and built in 1959

https://en.wikipedia.org/wiki/Orders_of_magnitude_(acceleration) just a fun list of things and how fast they accelerate

The background image that I used for the render came from NASA’s flickr page. A reminder to so many folks, the government has an amazing depth of publicly available information for free that you can use to make art and get creative.

https://www.flickr.com/photos/nasa2explore/9675391060/in/album-72157635384998736/