The Nonlinear Library LW - The economics of space tethers by harsimony
Aug 22, 2024
22:36
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: The economics of space tethers, published by harsimony on August 22, 2024 on LessWrong.
Some code for this post can be found here.
Space tethers take the old, defunct space elevator concept and shorten it. Rockets can fly up to a dangling hook in the sky and then climb to a higher orbit. If the tether rotates, it can act like a catapult, providing a significant boost in a location where providing thrust is expensive. Kurzgesagt has a nice explainer and ToughSF has a great piece explaining the mechanics and some applications.
Tethers make it cheaper to explore space, but how much cheaper? Let's look at the benefits.
Tether materials and characteristic velocity
The key performance metric for the tether material is the characteristic velocity:
Vc=2Tρ
Where T is the tensile strength and rho is the density.
The stronger and lighter the material is, the faster the tether can spin, boosting payloads to higher speeds and saving more fuel. This quickly leads to thinking about exotic materials. Hexagonal boron nitride! Carbon nanotubes! I'm not immune to this kind of speculation, so I've added an appendix on the topic. But as I argue in another part of the appendix, we already have good enough materials to make a space tether. The potential gain from studying exotic materials is actually pretty small.
For what it's worth, I like glass fibers. They're pretty easy to make, the material can be be sourced in space, they can handle large temperature ranges, and they're resistant to atomic oxygen environments and UV [1]. They can also get pretty good performance, S-2 glass fibers have a characteristic velocity close to 2 km/s while the best currently available material clocks in at 2.7 km/s.
Now let's look at why the speed of the tether matters.
Delta V and fuel savings
Rockets have to reach a certain speed in order to orbit any object. For low earth orbit, that's roughly 7.9 km/s; that's over Mach 20 here on Earth. The change in velocity, or delta V (dV), required to reach orbit is the currency of spaceflight. You can essentially map out the solar system based on the delta V needed to reach different places:
Source
It takes a lot of fuel and engineering to get a payload up to these speeds, making launches expensive [2][3]. Tethers are exciting because they can wait in orbit and offer a rocket some extra delta V. A tether spinning at 1.5 km/s in LEO can grab a rocket moving at 5.8 km/s and release it at 8.8 km/s:
Source
It takes a while to visualize how these work. Staring at this gif helps:
Source
Even a small delta V boost saves a lot of fuel. That's because the total fuel required for a mission increases exponentially with delta V requirements, as we can see from the Tsiolkovsky rocket equation:
ΔV=Ispg0ln(mimp)
I_sp is the specific impulse of the rocket, g_0 is the gravitational acceleration (often just called *g *in Earth's gravity), m_i is the total initial mass of the rocket including fuel, and m_p is the payload mass of the rocket after the fuel has been expended. Note that m_p includes both the literal payload and the mass of the rocket itself.
Rearranging to see the exponential:
mi=mpexp(ΔVIspg0)
m_i is the sum of the payload mass m_p and the fuel mass m_x. We can rewrite the above in terms of fuel mass:
mx=mp(exp(ΔVIspg0)1)
By offering a free delta V boost, tethers can save literal tons of fuel. If the tether is spinning at a certain velocity V_t, the tether provides a boost twice that size. You can subtract that boost from the dV requirements for the rocket:
ΔV'=ΔV2Vt
The new initial mass is:
m'i=mpexp(ΔV2VtIspg0)
The new fuel requirement is:
m'x=m'imp=mp(exp(ΔV2VtIspg0)1)
As an example, let's imagine a tether orbiting in LEO [4] at an orbital velocity of 7.5 km/s and spinning at 2 km/s. Our rocket only needs to reach 5.5 km/s in order to be boosted to 9.5 km/s. A Starsh...
Some code for this post can be found here.
Space tethers take the old, defunct space elevator concept and shorten it. Rockets can fly up to a dangling hook in the sky and then climb to a higher orbit. If the tether rotates, it can act like a catapult, providing a significant boost in a location where providing thrust is expensive. Kurzgesagt has a nice explainer and ToughSF has a great piece explaining the mechanics and some applications.
Tethers make it cheaper to explore space, but how much cheaper? Let's look at the benefits.
Tether materials and characteristic velocity
The key performance metric for the tether material is the characteristic velocity:
Vc=2Tρ
Where T is the tensile strength and rho is the density.
The stronger and lighter the material is, the faster the tether can spin, boosting payloads to higher speeds and saving more fuel. This quickly leads to thinking about exotic materials. Hexagonal boron nitride! Carbon nanotubes! I'm not immune to this kind of speculation, so I've added an appendix on the topic. But as I argue in another part of the appendix, we already have good enough materials to make a space tether. The potential gain from studying exotic materials is actually pretty small.
For what it's worth, I like glass fibers. They're pretty easy to make, the material can be be sourced in space, they can handle large temperature ranges, and they're resistant to atomic oxygen environments and UV [1]. They can also get pretty good performance, S-2 glass fibers have a characteristic velocity close to 2 km/s while the best currently available material clocks in at 2.7 km/s.
Now let's look at why the speed of the tether matters.
Delta V and fuel savings
Rockets have to reach a certain speed in order to orbit any object. For low earth orbit, that's roughly 7.9 km/s; that's over Mach 20 here on Earth. The change in velocity, or delta V (dV), required to reach orbit is the currency of spaceflight. You can essentially map out the solar system based on the delta V needed to reach different places:
Source
It takes a lot of fuel and engineering to get a payload up to these speeds, making launches expensive [2][3]. Tethers are exciting because they can wait in orbit and offer a rocket some extra delta V. A tether spinning at 1.5 km/s in LEO can grab a rocket moving at 5.8 km/s and release it at 8.8 km/s:
Source
It takes a while to visualize how these work. Staring at this gif helps:
Source
Even a small delta V boost saves a lot of fuel. That's because the total fuel required for a mission increases exponentially with delta V requirements, as we can see from the Tsiolkovsky rocket equation:
ΔV=Ispg0ln(mimp)
I_sp is the specific impulse of the rocket, g_0 is the gravitational acceleration (often just called *g *in Earth's gravity), m_i is the total initial mass of the rocket including fuel, and m_p is the payload mass of the rocket after the fuel has been expended. Note that m_p includes both the literal payload and the mass of the rocket itself.
Rearranging to see the exponential:
mi=mpexp(ΔVIspg0)
m_i is the sum of the payload mass m_p and the fuel mass m_x. We can rewrite the above in terms of fuel mass:
mx=mp(exp(ΔVIspg0)1)
By offering a free delta V boost, tethers can save literal tons of fuel. If the tether is spinning at a certain velocity V_t, the tether provides a boost twice that size. You can subtract that boost from the dV requirements for the rocket:
ΔV'=ΔV2Vt
The new initial mass is:
m'i=mpexp(ΔV2VtIspg0)
The new fuel requirement is:
m'x=m'imp=mp(exp(ΔV2VtIspg0)1)
As an example, let's imagine a tether orbiting in LEO [4] at an orbital velocity of 7.5 km/s and spinning at 2 km/s. Our rocket only needs to reach 5.5 km/s in order to be boosted to 9.5 km/s. A Starsh...