(now for part 2 of
"The Polls Are In")
At its most basic,
rocket science sounds really easy, just get something going fast enough that it
will leave a planet's atmosphere. Once you start accounting
for things like cost efficiency it starts getting harder. Over the past
20 years, the barriers to launching into orbit have dropped dramatically, with
companies like Blue Origin, Rocket Labs, and SpaceX competing against
traditional launch firms, prices have started to come down. Space tourism
is still out of reach for much of the world's population, but for businesses
that need satellites affordably transported into orbit, times have never been
better. A key driver in lowering the barrier of entry to launching a
rocket comes from a combination of being able to launch smaller/lighter satellites
with more affordable rockets themselves.
There are
several ways to make a rocket more affordable, better manufacturing techniques,
reusing components, large volumes of production, and making a rocket's engines
more efficient. For each of these cost-saving techniques, there are
countless proposed approaches to make improvements. Making rocket engines
more efficient is an incredibly complicated challenge, where engineers must
account for the chemical reaction creating thrust, the heat produced by the engine,
moving fuel fast enough to keep everything moving, and countless other subtle
variables. One possible way to enhance engine efficiency is to make the
rocket's exhaust hotter, hotter exhaust equals more thrust for a given amount
of fuel*. Scientists Arthur Kantrowitz and Wolfgang Moekel realized that
the boost of higher exhaust temperatures didn't necessarily have to come from
the reaction of rocket fuel and its oxidizer. In the 1970's they
proposed using lasers to enhance the exhaust temperature of a rocket.
Instead of having to carry rocket fuel and liquid oxygen, these laser enhanced
rockets would only need to carry a propellent, like water.
Laser
thermal rockets would benefit from having a relatively safe first stage if
engineers noticed any problems with the rocket, they could simply turn off the
lasers supplying the heat power and drastically reduce the risks faced by those
near the launch site. This boost to safety comes with a cost, having
enough powerful lasers to heat water to high enough temperatures to propel a
decent sized rocket would be incredibly capital expensive, consequently, laser
thermal rockets have been relegated to small scale academic research.
What laser enhanced rockets need is a path from academia to industrial
use. Enter the electric turbopump.
Turbopumps are what you
think they are super powerful pumps inside of rockets that help to make sure
that there is always the right amount and mix of fuel and oxidizer. For
the Saturn 5, these turbopumps were truly
massive, producing 41 MW of power (55,000 brake horsepower) to move 58,560
liters (15,471 gallons) of rocket fuel and 93,920 liters (24,811 gallons) of
liquid oxygen. To generate all this power it was necessary for engineers
to make a complicated design that diverted some of the energy of the rocket
motor to powering the turbopump. The aerospace company Rocket Labs has
recently broken with industry traditions and developed the Rutherford Engine a rocket engine that uses
a battery-powered turbopump. This innovation of a battery-powered
turbopump is possible due in part to improvements in battery energy
density. While development is very exciting for the small satellite
launch community, the energy requirements of fluid pumping for larger rockets
make this innovation unlikely to scale if batteries are used as the energy
source for the turbopump.
Larger rockets would
need a lot of power to run their turbopumps. For the Saturn 5's first
stage you have 5 engines needing 41 MW of pumping power each. Each of
these engines will need to run for 168 seconds, and assuming a safety margin of
12 extra seconds of burn time, let's say the pumps need to be able to run for
180 seconds (3 minutes). We also need to assume that powering the
turbopumps is only 90% efficient, meaning the electrical systems for each
turbopump would need to supply 45.6 MW of power. Putting all our
variables together we see that our 5 engines, consuming 45.6 MW each, for 180
seconds would require 41.04 GJ** of energy. That's a lot of energy, to
put things in comparison a Tesla
Model 3 with the largest battery option has a 75 kWhr battery
which holds about 270 MJ (0.27 GJ). Our new Saturn 5 would need 152 Tesla
Model 3 battery packs to run its turbopumps for all of 3 minutes. It gets
more complicated, traditional batteries have a maximum discharge rate; it would
be unlikely that we could design a battery pack that would be able to go from
100% charge to nothing in only 3 minutes***.
Instead of batteries
what if our turbopumps got most of the electricity from power wirelessly sent
from base stations?
Keeping our requirements
from the previous section of 5 engines each needing 41 MW of pumping output
running for a period of up to 180 seconds, but now we have a different
consideration make sure we can safely transmit sufficient power to run the
pumps while keeping the system's weight to less than that of using
batteries****. The two most popular long-distance/low loss means of
transmitting energy wirelessly are lasers and microwaves. Converting
laser light into electricity is currently estimated to have an efficiency
from 40-50+% that means that if your system needs
1 watt of power, your laser will need to have an output of about 2 watts.
Documentation on using microwaves to transmit DC power has been harder to come
by, but values as high as 95% are listed on Wikipedia. Conversion efficiency is
important from a heat management standpoint, the less efficient the conversion
process, the more heat the vehicle's design will need to account
for.
Beyond conversion
efficiency, engineers would need to account for the maximum flux the receivers
can handle. Flux is a measure in Watts per Square meter of how much
energy an object can handle, for example, certain plants are adapted to grow in
shade, they are happiest when they get soft indirect light if the plant gets
too sunlight, they could end up damaged. For something like a Saturn 5 to
get its 205 MW of power to the turbopumps, our 40% efficient panels would need
to be absorbing over 512.5 MW of laser energy*(5). The Saturn 5's first
stage was 41 meters tall and 10 meters in diameter, we are going to assume at
any given moment about 200 square meters of the first stage will be able to
absorb our laser's energy. To achieve our model's requirements our panels
would need to be able to handle 2.5625 MW/m^2, for sake of comparison sunlight
in space produces about 1360 watts/m^2. The power receivers would
need to handle 2000x more energy than sunlight.
We should keep in mind
that the estimated power hitting the receiver assumes that the lasers are
targeting a flat surface. A more detailed analysis would factor in the
curvature of the rocket, where only a small percentage would experience the
2.56+MW/m^2 of peak laser radiant flux.
At this point this post
is already way longer than I originally planned, it turns out rocket science is
hard and I hadn't done any actual deep analysis until I started writing and I
would like to give this concept the analysis I feel it deserves. What to
expect in the next post.
A rant about the square
cubed law, the Saturn 5 has less area per unit mass than say a Falcon 9 or an
Electron rocket, this means the lasers need to power the Saturn 5 pumps would
need to have a much higher energy density when hitting the side of the
rocket. The 9 Merlin Engines on a Falcon 9 have 7.5 MW turbopumps. The Electron Rocket from
Rocket Labs has 9 Rutherford Engines, with each engine requiring roughly 75 kW to power their turbopumps (37 kW for
oxygen, 37 kW for fuel)
A proposed timeline for
how commercialization might go (start small and build)
Thoughts on cost
efficacy of this proposal (it would depend on many market forces and how
long investors are willing to amortize costs)
I hope this was an
interesting start
*there are probably some
exceptions to high exhaust temperature vs produced thrust, but from this
rocketry 101 article from NASA it appears this is generally the case https://www.grc.nasa.gov/WWW/K-12/rocket/rktthsum.html
**GJ is shorthand for
gigajoule or 1 billion joules, lots of energy MJ is a megajoule 1 million
joules
***This is to
acknowledge that supercapacitors are a thing, while they have a lower energy density,
they can discharge that energy much faster than a traditional battery
can. So yes, they are a thing, and yes, they might be part of the
solution, but giving supercapacitors their proper depth would make this article
way way too long
**** I mean technically the most important
comparison is competitiveness with traditional turbopump launches, but c'mon,
do you guys want a book? (seriously if you do let me know)
*(5) this is just
the laser hitting the spacecraft, depending on energy lost to the atmosphere we
could be seeing some really big lasers being needed to get power to the
spaceship
*(6)
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