Altitude compensation on the Falcon 9 first stage and applications.
In post
#86 in this thread is an argument for how two copies of the Falcon 1 first stage combined together using a single Merlin engine with an altitude compensating nozzle could be SSTO. I had forgotten though that the first stage of the Falcon 1e, which SpaceX wants to move to for small launches anyway, has about twice the propellant load of the Falcon 1's first stage so it could form the SSTO.
Aerospike nozzles.
So how to get the altitude compensation? The aerospike[1],[2] is the most extensively studied method of altitude compensation so to get to this quickly it would be nice if this could be used. However, the aerospike (or plug nozzle for the shortened version) requires a toroidal combustion chamber. This would require significant modification of the engine.
However, one concept for getting an aerospike engine uses multiple small chambers arranged around a central spike. This was the idea for the X-33/VentureStar[3]. It was also used earlier on the Beta SSTO concept of Koelle[4],[5]. This could be conveniently used on the Falcon 9 first stage because of its multiple engines. The idea would be to greatly shorten the nozzles on the Merlins and arrange them around a central spike.
We need an estimate of the mass of the Falcon 9 first stage. This environmental assess- ment report on the SpaceX Grasshopper VTVL test vehicle[6] gives on p. 7 (page 17 according to the numbering as a PDF file) the Falcon 9 first stage kerosene load as 24,900 gallons and 38,900 gallons of LOX. Using a density of .820 gm/cc for kerosene
and 1.14 gm/cc for LOX, this amounts to about 245,000 kg propellant for the first stage.
Falcon 9 with aerospike nozzle becomes SSTO.
SpaceX has said the Falcon 9 first stage has a better than 20 to 1 mass ratio. This would give it a first stage dry mass of 13,000 kg. But this is using the Merlin 1C engine. From the thrust level and thrust/weight ratio[7] for this engine we can estimate its mass as about 650 kg. The Merlin 1D is supposed to be lighter, estimated as 440 kg. Using these brings the dry mass down to 11,000 kg.
The question is what would be the weight with the truncated nozzles and aerospike? A complaint against the aerospike used on the X-33 is that it had a worse T/W ratio than other LH2/LOX engines. However it had been planned for the full VentureStar version to use lightweight ceramics for the aerospike, expected to double the T/W ratio to about 80 to 1, better than the SSME's. With the advances in ceramics necessitated by the research and test flights with the hypersonic vehicles such high temperature lightweight ceramics should be further along now than they were with the VentureStar. For instance, the method of transpiration cooling using ceramics should make rocket engine combustion chambers and nozzles lighter and more reusable[8]. So I'll assume the total engine weight remains the same with the aerospike.
As before I'll use the Merlin Vacuum Isp in calculating the delta-V and take the required delta-V to orbit as 9,150 m/s for kerosene engines. Then we can get 6,000 kg payload:
342*9.8ln(1 + 245/(11 + 6)) = 9,167 m/s.
An SSTO is best utilized as a reusable though. Estimates of the added weight of reentry/landing systems are in the range of 28% [9]. However, with modern materials this probably can be cut to half that. Then the payload will be reduced to about 4.5 metric tons.
"An increase of 10% in Isp corresponds to an increase in 100% in payload."
This example illustrates well the importance of altitude compensation. Using it we are able to increase our engine Isp by 10% or more, to the extent we can achieve an SSTO with significant payload. Note that because of the rocket equation just being able to increase the Isp by 10% is no trivial feat. A rule of thumb among propulsion engineers is that "an increase of 10% in Isp corresponds to an increase in 100% in payload"[10]. I'll illustrate this with a single stage vehicle. A common estimate is that a kerosene-fueled SSTO needs a mass ratio of 20 to carry significant payload. Let's say a Falcon 9 sized rocket had instead high efficiency engines such as the NK-33[11] with an Isp of 331 s. You would need three of these. These have better thrust/weight than the Merlin 1C. So the dry weight is reduced to about 11 mT. Then it could carry a payload of 4.5 mT:
331*9.8ln(1 + 245/(11 + 4.5)) = 9,150 m/s.
With vacuum optimized nozzles high efficiency engines such as the NK-33 can get an Isp at 360+ s. Ten percent higher Isp than 331 s is at 364 s. Using this as the Isp allows a payload of 9.4 mT: 364*9.8ln(1 + 245/(11 + 9.4)) = 9,150 m/s.
Falcon Heavy with aerospike matches Phase 1 SLS a hundred times cheaper.
Interestingly an improvement in payload using altitude compensation also applies to staged vehicles. A preliminary calculation showed that with a two-stage vehicle you can increase your payload in the range of 25% to 30%. The improvement can be even better if the vehicle uses parallel staging, perhaps up to 50%. This is because with parallel staging the second stage still has to use the same nozzles as a lower stage because they still fire from the ground.
I'll illustrate this with the Falcon Heavy. SpaceX has said its side boosters will achieve a 30 to 1 mass ratio[12]. Reportedly the lower stages also will be stretched to hold more propellant. A posting on the NASASpaceFlight forum suggests a stretched version of the Falcon 9 will have 480,000 kg gross mass[13]. I'll estimate the stretched Falcon 9 based boosters as having a 435 mT propellant load and 15 mt dry mass. The central core stage has to be stronger since it holds the upper stage as well as the heavy payload. I'll take the dry mass for this lower core stage as 20 mT with the same 435 mT propellant load.
For the upper stage, I'll take the propellant load as 30 mT and the dry mass + fairing as 6 mT. For the vacuum Isp of the Merlin 1D I'll take the announced 310 s, and for the Isp of the upper stage, that of the Merlin Vacuum, 342 s. Then we can lift a payload of 51 mT:
310*9.8ln(1 + 2*435/(2*15 + 435 + 20 + 36 + 51)) + 310*9.8ln(1 + 435/(20 + 36 + 51)) + 342*9.8ln(1 + 30/(6 + 51)) = 9,155 m/s.
Now suppose we use altitude compensation to be able to get 342 s vacuum Isp for all the engines. Then we could lift 70 mT:
342*9.8ln(1 + 2*435/(2*15 + 435 + 20 + 36 + 70)) + 342*9.8ln(1 + 435/(20 + 36 + 70)) + 342*9.8ln(1 + 30/(6 + 70)) = 9,150 m/s
This means we could get a 70 mT launcher from essentially the same vehicle as the Falcon Heavy by using altitude compensation on the engines. SpaceX has said they intend to sell the Falcon Heavy for the range of $80 to $125 million per launch. The modifications to the aerospike nozzle should be relatively low cost compared to designing a whole new engine so the price should still be in this range.
Compare this to the estimates of the costs of the SLS program:
Space Launch System.
"Program costs.
During the joint Senate-NASA presentation in September 2011, it was
stated that the SLS program has a projected development cost of $18
billion through 2017, with $10B for the SLS rocket, $6B for the Orion
Multi-Purpose Crew Vehicle and $2B for upgrades to the launch pad and
other facilities at Kennedy Space Center. An unofficial NASA
document estimates the cost of the program through 2025 will total at
least $41B for four 70 metric ton launches (1 unmanned in 2017, 3
manned starting in 2021). The 130 metric ton version should not be
ready earlier than 2030."
http://en.wikipedia.org/wiki/Space_Launch_System#Program_costs
If that estimate for the total costs of the SLS is correct then that's $10 billion per launch for the interim 70 mT payload vehicle. That's two orders of magnitude higher than the Falcon Heavy with altitude compensation.
Reusable first stage Falcon 9 with aerospike also serves as a reusable booster.
This is for the expendable version of the Falcon stages. However, another benefit of the reusable version is that it could serve as the first stage of the reusable booster program (RBS) of the Air Force[14].
Reusable Falcon 9 with aerospike also as next-generation shuttle.
Another interesting possibility is suggested by the recent report of investigations of bringing back the shuttle as a commercial satellite launcher[15],[16]. My view is that the shuttle orbiter is too heavy for that role, ca. 80 mT in dry mass. This cuts greatly into the payload capacity. According to the reports the investigations also considered building their own shuttle but using the advancements made since the shuttle was designed. Then the reusable Falcon SSTO could be used to launch small payloads or even crew capsules. It could be modeled on the aerodynamic design of the shuttle since the aerodynamics for that are so well studied. Since kerolox has an overall density about 1,000 kg/m^3, the propellant could fit within the 300 m^3 shuttle-sized payload bay[17]with 55 m^3 left over. For a cargo only version we could also use the 75 m^3 sized volume of the crew cabin, for a total of 130 m^3.
The stretched version of the Falcon 9 first stage to be used for the side boosters of the Falcon Heavy are expected by SpaceX to have 30 to 1 mass ratio. The improved mass ratio over the current Falcon 9 first stage is probably coming from the fact that making your rocket larger in general improves your mass ratio, the fact that the new Merlin 1D is lighter, and also the fact the boosters do not have to support the weight of the upper stage and payload of the full vehicle. Using a 435 mT propellant load and a 15 mT dry mass, this could launch 15.3 mT: 342*9.8ln(1 + 435/(15 + 15.3)) = 9,155 m/s. If you take the reentry/landing systems mass with modern materials as 14% of the dry mass this takes up 2.1 mT from the payload, so to 13.2 mT. To scale up the space shuttle design for a 435 mT propellant tank compared to a 245 mT tank, the linear dimensions would only have to be scaled up by 20%.
Bob Clark
1.)Aerospike Engine.
http://www.aerospaceweb.org/design/aerospike/main.shtml
2.)Nozzle Design.
by R.A. O'Leary and J. E. Beck, Spring 1992
http://www.rocketdynetech.com/articles/nozzledesign.htm
3.)Aerospike engine.
http://en.wikipedia.org/wiki/Aerospike_engine
4.)Beta, A Single Stage Reusable Ballistic Space Shuttle Concept.
Based on a study contract of the German Federal Ministery for Education and Science, Bonn (RFT 1017).
May 1970
Space Division, Messerschmitt-Bolkow-Blohm ( MBB), Munich, Germany.
http://www.spacefuture.com/archive/beta_a_single_stage_reusable_ballistic_space_shuttle_concept.shtml
5.)A Cost Engineered Launch Vehicle for Space Tourism.
D E Koelle
TCS-TransCostSystems, Ottobrunn, Germany.
IAA-98-IAA.1.5.07
http://www.spacefuture.com/archive/a_cost_engineered_launch_vehicle_for_space_tourism.shtml
6.)Draft Environmental Assessment for Issuing an Experimental Permit to SpaceX
for Operation of the Grasshopper Vehicle at the McGregor Test Site,Texas.
September, 2011
http://www.faa.gov/about/office_org/headquarters_offices/ast/media/20110922%20SpaceX%20Grasshopper%20Draft%20EA.Final.pdf
7.)Merlin(rocket engine).
http://en.wikipedia.org/wiki/Merlin_%28rocket_engine%29
8.)Ceramic Materials for Reusable Liquid Fueled Rocket Engine Combustion Devices.
http://ammtiac.alionscience.com/pdf/AMPQ8_1ART06.pdf
9.)Newsgroups: sci.space.policy, sci.space.history, sci.astro, sci.physics
From: Robert Clark <rgregorycl...@yahoo.com>
Date: Tue, 4 Oct 2011 10:04:42 -0700 (PDT)
Subject: Re: Elon Musk's SpaceX to build 'Grasshopper' hover-rocket
http://groups.google.com/group/sci.physics/msg/f3b4c27da1f13027?hl=en
10.)Discovery of New Molecule Could Lead to More Efficient Rocket Fuel.
ScienceDaily (Dec. 22, 2010)
http://www.sciencedaily.com/releases/2010/12/101222071831.htm
11.)NK-33.
http://www.astronautix.com/engines/nk33.htm
12.)SPACEX ANNOUNCES LAUNCH DATE FOR THE WORLD'S MOST POWERFUL ROCKET.
http://www.spacex.com/press.php?page=20110405
13.)Re: Falcon Heavy Master Update Thread.
http://forum.nasaspaceflight.com/index.php?topic=24711.msg723410#msg723410
14.)Doing a 180 - AFRL's Rocket-back Pathfinder.
Posted by Graham Warwick at 4/7/2010 7:52 AM CDT
http://www.aviationweek.com/aw/blogs/defense/index.jsp?plckController=Blog&plckScript=blogScript&plckElementId=blogDest&plckBlogPage=BlogViewPost&plckPostId=Blog:27ec4a53-dcc8-42d0-bd3a-01329aef79a7Post:1553afc7-cc1e-4b5e-9a6c-ced39704d348
15.)Next Gen Shuttle-Capable vehicle interest as secret effort to save orbiters ends.
December 19th, 2011 by Chris Bergin
http://www.nasaspaceflight.com/2011/12/next-gen-shuttle-vehicle-secret-effort-save-orbiters-ends/
16.)Atlantis Journal – Epilogue.
by MLD on Dec.19, 2011, under Commercial Space, Space Exploration, Space Policy, Space Shuttle Program
http://www.marylynnedittmar.com/?p=1303
17.)Space Shuttle orbiter.
Shuttle Orbiter Specifications.
http://en.wikipedia.org/wiki/Space_Shuttle_orbiter#Shuttle_Orbiter_Specifications