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Sunday, April 13, 2014

Sample Return Missions from Enceladus, Europa, Titan, Ceres, page 1.

Copyright 2014 Robert Clark 

 Gravity measurements from Cassini have provided further evidence that Enceladus has a subice liquid ocean. It is being regarded now as a prime target in the search for extraterrestrial life. The question is how to reach that ocean through what may be 40 km of ice. There have been various proposals for drills. However, NASA has modeled the plumes seen to arise from the "tiger stripes" on Enceladus as coming from vents that attach to the ocean below. Then a simpler method may be to reach the ocean by traveling through these vents. 



This graphic shows how the ice particles and water vapor observed spewing from geysers on Saturn's moon Enceladus may be related to liquid water beneath the surface. The large number of ice particles and the rate at which they are produced require high temperatures, close to the melting point of water. These warm temperatures indicate that there may be an internal lake of liquid water at or near the moon's south pole, where the geysers are present.

 In this model the temperatures don't have to be particularly high, just near the melting point.
 This method may work to reach subsurface liquid water for other outer solar system bodies expected to have them such as Europa, Titan and Ceres.

 As a feasibility test we might try it to explore subsurface though deep-sea hydrothermal vents here on Earth. 


 According to this model the temperatures might reach a maximum of 400 °C. If we can develop a robot to travel through these conditions quite likely it would also work in the conditions for the vent systems of these outer solar system moons.

In an upcoming blog post I'll discuss how the Falcon Heavy at a 53 metric ton(mT) payload capacity and the first version of the SLS at 70 mT could each be used to conduct sample return missions from these outer solar system moons.

     Bob Clark  

Tuesday, March 25, 2014

"Golden Spike" Circumlunar Fights, Page 2.

Copyright 2014 Robert Clark

 In the blog post "Golden Spike" Circumlunar Flights, I suggested that the Falcon 9 1.1/Dragon could do a circumlunar mission with a half-sized Centaur, of ca. 10 mT propellant load, to do the translunar injection.
 Interestingly it might be possible to do without even needing the extra in-space stage. Elon Musk has said through his Twitter account that the 13 mT payload capability was actually a reduction of the F9 V1.1's true capability due to reusability considerations. Gwynne Shotwell confirmed this on a TheSpaceShow interview on Friday, Mar. 21 at about the 9 minute mark. She said the quoted payload on their web site for the F9 v1.1 is about 30% less than that of a one-use version.
 This would put the expendable version in the range of the 16.6 metric tons to LEO given on NASA's site:

NASA Launch Services Program's
Launch Vehicle Performance Web Site.

 The point is this would be just about at the payload capability to do translunar with the Dragon using just its onboard Draco, or upgraded SuperDraco, thrusters. On the "NASA Launch Services Program" site, click the link for the Performance Query Tool and select the Falcon 9 and "elliptical" orbit option. Enter in 36000 km for the altitude corresponding to geosynchronous transfer orbit (GTO) and 28.5 degrees for the orbital inclination corresponding to launch from Cape Canaveral. Then the calculator gives the payload to GTO as 5745 kg.

 As shown here the delta-v to GTO is 2,500 m/s:


 Then translunar injection (TLI) at 3,100 m/s would only require an additional 600 m/s delta-v. The Dragon has a dry mass of 4,200 kg and a propellant mass of 1,290 kg. SpaceX has not released the Isp of the hypergolic thrusters on the Dragon, but they typically are in the 320 s range in vacuum. Then it could carry 1,800 kg payload to the 600 m/s needed to reach TLI:

320*9.81ln(1 + 1290/(4200 + 1800)) = 610 m/s.

  Actually that 1,800 kg payload would put the total mass beyond the 5745 kg capacity to GTO. Smaller payload say in the 250 kg range would be doable.
 Such missions would be important to do since at a perhaps $120 million total launch price for the Falcon and Dragon it would show lunar missions are possible without requiring huge launchers such as the Saturn V, Ares V or SLS.

   Bob Clark


UPDATE, April 1, 2014:

 On TheSpaceport.us forum, DocM informed me via PM that in an environmental impact statement SpaceX gave the propellant load for the Dragon as 1,388 kg. This would raise the max payload to reach 600 m/s delta-v to 2300 kg. Again though this would put the total mass outside the range that could be lofted to GTO. Likely you would still have to limit the payload to ca. 250 kg or so.

  
 


 

Sunday, March 16, 2014

Short travel times to Mars now possible through plasma propulsion.

Copyright 2014 Robert Clark


 Robert Zubrin wrote a critique of the plasma propulsion system VASIMR here:

The VASIMR Hoax
By Robert Zubrin | Jul. 13, 2011
http://nextbigfuture.com/2011/12/tiny-solar-cell-could-make-big.html

 The primary criticism is that it would require unrealistically lightweight nuclear propulsion. However, Zubrin doesn't even like the idea of fast propulsion to allow short travel times to Mars. He argues in favor of using 6 month or more one-way travel times to allow free return trajectories at Mars. But the health disadvantages of long travel times such as radiation exposure, bone and muscle loss, and the recently found eye damage and vision loss suggest we should investigate such short travel times.

 Now we find there is also another reason: mechanical breakdowns on such missions of 2 or more years round trip length, such as found with the coolant system on the ISS.

 Note that the argument about free return trajectories does not hold with respect to planets with atmospheres. The Apollo missions did do a free return around the Moon, but there was no non-propulsive method to slow down at the Moon. On return to the Earth though, even Apollo had a trajectory that would send it off into space if the angle was too shallow or plunging too steeply into the Earth's atmosphere to burn up if the angle was too steep. The same could be used in addition to the propulsive method whose high efficiency would also allow it to be used for slow down at Mars.

 So it is important to note we may have a short term power source instead of nuclear power, for plasma propulsion such as Vasimr at the needed lightweight.

 The key point is that the power source does not need to be nuclear. According to Zubrin's article on the Vasimr it requires a power source of 1,000 watts per kg power density. This is 100 times better than what has been done with nuclear space power at 10 watts per kg. However, it is only 10 times better than standard solar space cells at 100 watts per kg. Actually more recent space solar cells get 200 watts per kg, so it is only needs to be 5 times better than those.

Now the key fact is that solar cells can put out more power if they have more concentrated light shone on them. Estimates of how much power solar cellls put out are based on the solar insolation at the Earth's distance from the Sun. But if that light is concentrated they can put out more power. In fact some Earth solar power systems get more power by using inexpensive mirrors or lenses to concentrate light over a larger area rather than using expensive solar cells over that larger area.

A disadvantage is this increases the loss due to heat and also if the light is too intense it can overload the solar cells so they don't work at all. However a recent report claims they can use concentrated light at thousands of times higher than solar insolation:

SEPTEMBER 07, 2013
Stacked Solar Cells Can Handle Energy of 70,000 Suns.
This work is important because photovoltaic energy companies are interested in using lenses to concentrate solar energy, from one sun (no lens) to 4,000 suns or more. But if the solar energy is significantly intensified – to 700 suns or more – the connecting junctions used in existing stacked cells begin losing voltage. And the more intense the solar energy, the more voltage those junctions lose – thereby reducing the conversion efficiency.

Several reports in fact claim solar concentration at hundreds to thousands of Suns:

FEBRUARY 20, 2009
Breakthrough Solar Concentrator:low cost with high efficiency.
http://nextbigfuture.com/2009/02/breakthrough-solar-concentratorlow-cost.html

FEBRUARY 17, 2011
Concentrated solar power at half the cost of thin film solar.
http://nextbigfuture.com/2011/02/concentrated-solar-power-at-half-cost.html
DECEMBER 16, 2011
Tiny Solar Cell Could Make a Big Difference
http://nextbigfuture.com/2011/12/tiny-solar-cell-could-make-big.html

This will be dependent on having lightweight mirrors or lenses. However another key fact is that the parabolic mirrors do not have to be telescope grade accuracy. Indeed you can find on the net videos of amateurs making their own homemade solar furnaces that also require light to be concentrated to high intensity. These homemade mirrors can be as simple as aluminum foil spread onto a cardboard frame and still concentrate light to generate thousands of degrees. Not requiring high accuracy for the mirrors suggest they can be made lightweight.

DARPA is also funding lightweight space lenses:

DECEMBER 08, 2013
DARPA shoots for 20 meter folding space telescope.
http://nextbigfuture.com/2013/12/darpa-shoots-for-20-meter-folding-space.html

 Another example of how lightweight we could make the mirrors is actually to be tested in space:

Gossamer sail set to deorbit satellites.
By Jenny Winder | 30 December 2013


http://www.sen.com/news/gossamer-sail-set-to-deorbit-satellites

 This solar sail has 25 square meters at only 2 kg weight. Let's suppose we only need 10 times solar concentration. This should already be within the capacity of currently used solar cells to accommodate since recent research is in the 100's to 1,000's of Suns range.
At 10 times solar concentration this means the solar cells have 2.5 square meters area in order for the mirror reflecting area to be 10 times greater. If they were 100% efficient this would be 2500 watts of power under standard solar illumination, i.e., without concentration. Solar cells though typically are only in the range of 30% efficient. So they would give 750 watts under standard solar illumination. At a 200 watts per kg power density now reached for space solar cells they would weigh 3.75 kg.
Now we are assuming the sail concentrates 10 times greater surface area onto the cells, so under this concentrated illumination they will put out 7,500 watts. The total weight of the cells and sail would be 5.75 kg. And the power to weight efficiency would be 1,300 watts per kg, sufficient for the Vasimr.

 The question though is would extra mass be needed to dispense the extra heat. Low power concentrators don't need these cooling systems:

Concentrated photovoltaics.
Low concentration PV (LCPV)
Low concentration PV are systems with a solar concentration of 2-100 suns.[5] For economic reasons, conventional or modified silicon solar cells are typically used, and, at these concentrations, the heat flux is low enough that the cells do not need to be actively cooled. The laws of optics dictate that a solar collector with a low concentration ratio can have a high acceptance angle and thus in some instances does not require active solar tracking.
http://en.wikipedia.org/wiki/Concentrated_photovoltaics#Low_concentration_PV_.28LCPV.29

 We only need about about 5 times concentration with currently available space solar cells without significant loss of efficiency from the solar cells to get the needed specific power.

 For simplicity and to maintain the light weight we might want to use these low power concentrators. However, there might be lightweight, passive cooling systems that could be used for the high power concentrators, that can reach hundreds to thousands of Suns, that with the higher degree of concentration would still have a light weight at high power.

These methods would concentrate sunlight onto solar cells. However, solar cells are typically low efficiency, in the range of 30%. Another advantage of concentrators is that increase the efficiency. The latest ones can get 44.7% efficiency and researchers believe they can reach above 50%.

 Another method would eliminate the need for solar cells. That is to use a solar furnace. These can get temperatures as hot as the surface of the Sun by concentrating sunlight. By thermodynamics very high temperatures correspond to high efficiency conversion of heat to other forms of energy, 90% and above.

 An additional problem with plasma thrusters though is the high weight compared to the thrust they put out. For VASIMR the thrust to weight ratio can be calculated to be in the range of only 1 to 4,000. See for example this report for the mass of the thruster per given power on p. 2  and the thrust per power on p. 3:

Low Thrust Trajectory Analysis (A Survey of Missions using VASIMR® for Flexible Space Exploration - Part 2).
http://www.adastrarocket.com/VASIMR_for_flexible_space_exploration-2012.pdf

 Other plasma thrusters however, such as the Hall effect thruster have better thrust weight ratios, ca. 1 to 200. A recent advance may even improve on that. This report discusses "nested channel" Hall effect thrusters, which have been shown to achieve the same thrust at a lower weight:

Developmental Status of a 100-kW Class
Laboratory Nested channel Hall Thruster.
IEPC-2011-246
Table 1, Example of concentrically NHT specific mass and footprint savings, p. 5.
http://pepl.engin.umich.edu/pdf/IEPC-2011-246.pdf

 The three-channel thruster in this table only weighs 320 kg. There is an inverse relationship between Isp and thrust as shown in the graph in Fig. 3 of this report on p. 3. So for the high of 5,000 s Isp in this table, the thrust would be 36 N. Still this is a 1 to 90 thrust to weight ratio, quite good for plasma propulsion. In comparison, at a 1 to 4,000 thrust to weight ratio, the VASIMR thruster would weigh nearly 15,000 kg.

 In addition to the thruster though plasma propulsion systems need a power procession unit (PPU). This transforms the low voltage put out by solar cells, usually just a few volts, to the hundreds of volts needed for plasma propulsion. The PPU mass is often comparable to that of the thruster itself.

 However, there may be methods to reduce or eliminate this extra mass. One method might be to put the solar cells in series like with batteries to build up the voltage. There is the question though if the solar cells can handle this higher voltage. Another possibility might be to use the recent advances in nanotechnology to produce a lightweight PPU. For instance quantum dots can transform low frequency light to high frequency light. It might possible to adapt this method to transform low voltage to high voltage.

 An exciting upcoming development is the Sunjammer solar sail scheduled for launch in January, 2015:

Solar Sail Demonstrator.

http://www.nasa.gov/mission_pages/tdm/solarsail/solarsail_overview.html#.UyWr7IUcbOw


 
 This sail will have an area of 1,200 sq. m. at only a 50 kg weight. At perihelion, the solar irradiance is about 1,400 watts per square meter. This would give a maximum possible power of close to 1.7 megawatts at 100% efficiency. If using the new 44.7% efficiency solar concentrator cells, this would be 750 kwatts.

 Then as early as next year we can test high power plasma propulsion systems that can make manned missions to Mars at travels times of weeks rather than months.


  Bob Clark

Wednesday, January 29, 2014

Transitioning SpaceShipTwo to liquid fueled engines: a technology driver to reusable orbital launchers.

 Copyright 2014 Robert Clark


 A new book by Tom Bower on Richard Branson, “Branson: Behind the Mask”, claims the hybrid engine on SpaceShipTwo still does not have enough power to get the vehicle to the altitude for suborbital flight. Doug Messier on his blog ParabolicArc.com has been reporting on the technical problems developing the hybrid engine for some time.

 There has been much speculation actually that Virgin Galactic will have to transition to a liquid fueled engine to achieve suborbital flight. In point of fact, independent studies have shown that SS2 by switching to liquid fueled propulsion, can be suborbital on its own without even needing the carrier craft WhiteKnightTwo:

SpaceShipTwo could be single stage to suborbit says ESA firm


Reusable Space Plane Idea Intrigues Europeans.
Rob Coppinger, SPACE.com Contributor
Date: 01 May 2012 Time: 04:30 PM ET
The Vinci suborbital space plane's structure and cryogenic fuel and oxidizer tanks are depicted in this illustration.
Credit: ESA

  This would be by using the hydrogen-fueled Vinci engine. The Vinci is soon to be introduced on the Ariane 6. However, the existing HM-7 engine used on the cryogenic version of the upper stage of the Ariane 5 could also be used. The advantage of this is that it has been in use for decades and is well-characterized. You would probably need to place an extra one on the Ariane 5 upper stage to be able to lift the SS2. Still the engine and the stage are already developed and the cost of the addition of an extra engine should be comparatively small. The development cost of the SS2+WK2 combo has reportedly reached into the few hundred million dollars range. In contrast, the addition of an already existing engine to an already existing stage should be simpler, quicker and far cheaper than creating a new engine, hybrid, from scratch.

 The reason for the choice of the hybrid for the SS2 rather than a higher performance liquid-fueled engine was the idea that a hybrid engine could not explode. However, the accident in 2007 at Scaled Composites due to a nitrous oxide explosion has destroyed that misperception. Indeed because of the instability of nitrous oxide one team involved in developing a rocket propelled car suggests nitrous should not be used for passenger flight:

Observations and comments on Cal/OSHA report (Inspection No: 31081103) on fatal accident at Mojave test site of Scaled Composites at the Mojave Air and Space Port, 26th July 2007.
While it is most advisable to apply the established safety protocols relating to liquid oxygen, such protocols, in themselves are not sufficient to ensure the safe handling of Nitrous Oxide. The unique physical properties of N2O require further protocols above and beyond those used for liquid oxygen.
Safety protocols for N2O, in a rocket motor system, should include (in addition to the protocols used for Liquid Oxygen)

   * The detailed study of materials compatibility of all components in the system
   *  Avoidance of high temperatures at all points in the system
   * Stirring of large tanks
   * Avoidance of the gaseous phase both during apparatus filling and in use
   *  Purging of lines and valves immediately prior to ignition
   * Not using any component that may have previously absorbed N2O –   especially fuel grains

We are not confident that, even with these additional precautions, that we yet know enough about N2O to consider it a safe oxidiser for use in passenger flight. In the light of what we do know, safety must remain a major concern.
http://www.knightsarrow.com/rockets/scaled-composites-accident/


  Then the SS2 hybrid engine should no longer be considered to have an advantage over a liquid fueled engine. Then the fast and low cost development possible, especially with using an already existing engine, should push the decision to using liquid fuel. In fact by doing so SS2 probably could already have been flying by the originally announced date of the first suborbital test flights of 2007.

 The importance of their making that decision then and of their making that decision now goes far beyond that of just suborbital rockets however. If you look at the specifications of the cryogenic Ariane 5 upper stage, you see it could be propelled, with the SS2 aeroshell around it, well above the speed needed for suborbital flight. In fact it could be in the high Mach range envisioned for example for the X-33. A stage like that though could be used for a reusable first stage booster for a two-stage to orbit system.

 Now, since the first stage is generally much larger and costlier than the upper stage, a reusable first stage could significantly cut the cost to orbit of a two stage system. This in fact is what DARPA wants with its reusable spaceplane program.


 So Virgin Galactic giving SS2 a liquid fueled propulsion system could have a system to satisfy the requirements for DARPA's reusable spaceplane. In fact, it could already have had such in 2007.


   Bob Clark

Sunday, December 1, 2013

Will the SpaceX push to reusability make Arianespace obsolete?

Copyright 2013 Robert Clark

 By deciding on the solid-fueled Ariane 6, ESA is, unwittingly, betting on SpaceX to fail on reusability. For if SpaceX succeeds then the solid-fueled Ariane 6 becomes obsolete, with billions of dollars and years wasted. ESA would then have to start all over again to develop a liquid-fueled version which can be made reusable:

Musk lays out plans for reusability of the Falcon 9 rocket.
October 3, 2013 by Yves-A. Grondin
Quote:
“The most important thing is that we now believe we have all the pieces of the puzzle (for recovery). If you take the Grasshopper tests, where we were able to do a precision takeoff and landing of a Falcon 9 first stage and you combine it with the results from this flight where we were able to successfully transition from vacuum to hypersonic, through supersonic, through transonic and light the engines all the way through and control the stage all the way through.
“We have all the pieces necessary to achieve a full recovery of the boost stage.”

Falcon 9 first stage in a controlled descent toward the Pacific Ocean. At this point, the stage was about 3 meters (9.8 feet) above the water. (Credit: SpaceX)


  I think it's a bad bet on ESA's part.

 Arianespace has already taken seriously the competition SpaceX offers for their expendable rockets:

SpaceX Challenge Has Arianespace Rethinking Pricing Policies
By Peter B. de Selding | Nov. 25, 2013

Quote:
“I have sent a signal to our customers telling them that I could review our pricing policy, within certain limits,” Israel said in an interview with Les Echos, a French financial newspaper. “I think they have appreciated this.”
Israel’s comments came on the day when Space Exploration Technologies Corp. (SpaceX), after a decade of rattling Arianespace’s cage, is preparing its first-ever launch into the geostationary transfer orbit used by most commercial telecommunications satellites, and the place where most commercial revenue is made.
SpaceX Chairman Elon Musk taunted Arianespace again on Nov. 24, the day before his company’s scheduled launch of the SES-8 satellite owned by SES of Luxembourg.
“Unless the other rocket makers improve their technology rapidly, they will lose significant market share to the Falcon 9,” Musk said in a news briefing.
SpaceX President Gwynne Shotwell added: “Competition is always a good thing. It keeps people sharp. They [Arianespace and other competitors] may not look at it that way, but hopefully they’ll come to appreciate it in the future.”
...
“I am looking at our pricing policy and if we must adapt it to the competition, we will,” Israel said. “We’ll look at the overall efficiency of the Ariane business with a view to optimizing it.”
Israel said there are more small telecommunications satellites being designed now than ever, a fact he attributed in part to the arrival of SpaceX, which has stimulated the market.
http://www.spacenews.com/article/launch-report/38331spacex-challenge-has-arianespace-rethinking-pricing-policies
 IF SpaceX succeeds in cutting prices by reusability, then no readjustment of the pricing will be effective. SpaceX is already undercutting them on pricing and if reusability really does cut the SpaceX prices again by a factor of 4 to 10 then ArianeSpace simply will not be able to compete.

 This will be all due to ESA's decision to go backwards in technology and not forwards in selecting a solid-fueled version of the Ariane 6. Every other space agency in the world will be able to adapt their liquid fueled rockets to make them reusable to match SpaceX's pricing. Only ESA will be left behind - both technically and economically.

 This becomes really bad because they will no longer have the smaller satellites to partially pay for the Ariane 5 launches. This could mean they also lose their entire Ariane 5 market as well! Their entire market for any of their launches will be gone all due to the choice to move backwards in technology.

 Ironically, this would mean their real reason for selecting the solid-fuel Ariane 6 would have no meaning as well. The actual reason why France and Italy want the solid-fueled Ariane 6 is to help defray the costs of the solid-fueled ballistic missiles of the French military and the solid-fueled Vega rocket largely built in Italy. But if SpaceX succeeds in cutting costs by reusability then neither the solid-fueled Ariane 6 nor the Vega, will be used because they will be priced far outside the market. So neither of them will wind up defraying the costs of other solid-fueled rockets in Europe anyway.

 Interestingly, IF SpaceX succeeds in their next test of reusability in Feb. 2014, this might provide an incentive for ESA to at least "hedge their bets" and engage in some development research of adding a second Vulcain to the Ariane 5 core. Then they would not be years behind the other space agencies in the world IF SpaceX succeeds in cutting costs by reusability. 


  Bob Clark

Thursday, November 7, 2013

The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO, Page 2.

Copyright 2013 Robert Clark

 Though in the first test flight of the new version of the Falcon 9, the F9 v1.1, they did not stably "land" the first stage, SpaceX is optimistic they can solve the problem to get a reusable first stage:

SpaceX Hit Huge Reusable Rocket Milestone with Falcon 9 Test Flight (Video).
By Mike Wall, Senior Writer   |   October 17, 2013 02:01pm ET
Combining information from the Falcon 9 v1.1's maiden flight and the ongoing Grasshopper tests should help bring a rapidly reusable rocket closer to reality, SpaceX officials said.
"SpaceX recovered portions of the [Falcon 9 v1.1's first] stage and now, along with the Grasshopper tests, we believe we have all the pieces to achieve a full recovery of the boost stage," they wrote in the Oct. 14 update.
http://www.space.com/23230-spacex-falcon9-reusable-rocket-milestone.html

 SpaceX also plans to transition the half-scale Grasshopper VTVL test vehicle to a full scale Falcon 9 first stage:

Final flight of Grasshopper v1.0 sets new record.
By Brian Dodson
October 14, 2013
http://www.gizmag.com/grasshopper-retires-altitude-record/29384/

 This article says this "Grasshopper 2", as it were, would have all 9 engines of the regular F9 first stage. However, discussions on other forums have said it would only have 3 engines. That would make sense since on stage return, you are using at most 3 engines, and moreover this way, you would not be risking an expensive 9 copies of the Merlins during these Grasshopper test flights.

 Still, in point of fact there would be an advantage of using all 9 engines on this first stage Grasshopper, and with a full propellant load. In November, 2012 Elon Musk gave a lecture in London at the Royal Aeronautical Society.




 About 30 minutes in, he gave the propellant fraction of the new Falcon 9 v1.1 first stage as around 96%, or perhaps 95.5%. The 96% propellant fraction number gives a 25 to 1 mass ratio. But at an Isp of 311 s for the Merlin 1D, the rocket equation gives a delta-v of 311*9.81ln(25) = 9,800 m/s. Since the delta-v to orbit is only about 9,100 m/s, this would allow a significant amount of payload. Then using the 9 engines and the full propellant load on the F9 first stage would allow in fact not just a VTVL test vehicle, but in fact a fully reusable and fully orbital vehicle.  Amusingly, about 36 minutes into Elon's lecture someone asks a question about what he sees as the next big breakthrough in rockets after full reusability. Elon thinks for awhile and can't come up with an answer. He finally jokes maybe warp drive. Ironically, he already has the next big advance: a reusable SSTO.
 
In the blog post "The Coming SSTO's: Falcon 9 v1.1 first stage as SSTO" I had already discussed the F9 v1.1 first stage being used as a SSTO. But there I actually used the side boosters of the Falcon Heavy, which are based on the F9 v1.1 first stage, since they were supposed to have such a high mass ratio, at 30 to 1. However, this information in Elon's lecture on the first stage of the F9 v1.1 suggests it itself would have a surprisingly high mass ratio.
 We'll enter this data into Dr. John Schilling's launch performance calculator to estimate the payload it could carry. On the SpaceX page on the Falcon 9 v1.1 the vacuum thrust is given as 6,672 kN. The Merlin 1D has a vacuum Isp of 311 s. We need to know the propellant mass of the F9 v1.1 first stage.

  I found the propellant loads for the Falcon 9 v1.1 first stage and second stage in this environmental impact report: 

Draft Environmental Impact Statement: SpaceX Texas Launch Site. 
http://www.faa.gov/about/office_org/headquarters_offices/ast/environmental/nepa_docs/review/documents_progress/spacex_texas_launch_site_environmental_impact_statement/media/SpaceX_Texas_Launch_Site_Draft_EIS_V2.pdf  

  They're given on page 66, by the PDF file page numbering:

First and Second Stages  
The first stage of the Falcon 9 is approximately 12 ft by 150 ft, and includes nine Merlin 1D engines. The Merlin engine produces 146,000 lbs of thrust and contains a pump-fed gas generator cycle, turbine exhaust roll control, and hydraulic thrust-vector control. The first stage consists of aluminum LOX and RP-1 tanks that hold approximately 62,000 gallons (gal) of LOX and 38,000 gal of RP-1. The second stage is approximately 12 ft by 41 ft, not including the fairing and payload, and uses one Merlin vacuum engine. The fairing (the top portion of the vehicle where the payload is encapsulated) would be 17 ft by 35 ft, and a smaller version may also be used. The second stage consists of approximately 15,000 gal of LOX and 9,000 gal of RP-1 in tanks with a common bulk head.  

 The conversion factor between gallons and liters is 1 gallon to 3.7854 liters. So the amount of LOX in liters is 62,000*3.7854 = 234,700 liters, 234.70 m³. And the amount in liters of RP-1 is 38,000*3.7854 = 143,800 liters, 143.8 m³. The density of LOX is 1140 kg/m³ and the density of RP-1 is 820 kg/m³. So the total mass of propellant is 1140*234.7 + 820*143.8 = 385,500 kg. This is in the range of what has been estimated for instance on Ed Kyle's site of ca. 389 metric tons (mT): 

Space Launch Report:  SpaceX Falcon 9 v1.1 Data Sheet. 
http://spacelaunchreport.com/falcon9v1-1.html#components  

 However, there is a significant difference from the estimates and the actual propellant load of the second stage. Using the same conversion factors and densities, the total propellant for the second stage is 92,670 kg, whereas Kyle gives it as approx. 64 mT.  

 Take, optimistically, the propellant fraction of the F9 v1.1 first stage as 96%, corresponding to a mass ratio of 25 to 1. Then the dry mass is 16,040 kg, which I'll round to 16,000 kg.  In the calculator input the vacuum values for the Isp and thrust, as it takes into account the reduction at sea level. Select "No" for the "Restartable Upper Stage" option, otherwise the payload will be reduced. Select Cape Canaveral as the launch site at a launch inclination of 28.5 degrees to match the latitude of the launch site. Then the calculator gives an estimated payload of 5,147 kg: 

Mission Performance:
Launch Vehicle:   User-Defined Launch Vehicle
Launch Site:   Cape Canaveral / KSC
Destination Orbit:  185 x 185 km, 28 deg
Estimated Payload:   5147 kg
95% Confidence Interval: 1242 - 9908 kg

 This is surprisingly high for a stage using engines without an especially high Isp. However an SSTO reaches its best performance when using altitude compensation. Let us suppose we use altitude compensation so that the engines on the first stage have the same vacuum Isp as the Merlin Vacuum at 340 s. 
 Note that because of the higher Isp, the thrust is also increased. On that SpaceX page on the Falcon 9 v1.1, the thrust of the single Merlin Vacuum on the upper stage is given as 801 kN. So 9 would have a thrust of 7209 kN, which I'll round to 7,210 kN. Select "Optimal" in the calculator for the "Trajectory". Then the calculator gives the result:

Mission Performance:
Launch Vehicle:   User-Defined Launch Vehicle
Launch Site:   Cape Canaveral / KSC
Destination Orbit:   185 x 185 km, 28 deg
Estimated Payload:   12068 kg
95% Confidence Interval:   7319 - 17788 kg
 This is remarkable as being near the payload cited by SpaceX for the full two stage Falcon 9 v1.1 of 13,150 kg.  

 But for a fair comparison we should see also how high the payload would get for the two stage F9 when altitude compensation is also given to the first stage. The calculation here is made difficult by the fact that we don't know the propellant fraction of the upper stage, so we can't calculate the dry mass from the known propellant mass of 92,670 kg.
 For the upper stage much smaller than the first stage, the mass ratio would not be as great. It is known that as you scale up a rocket the mass ratio improves. The reverse is also true, when you scale down a stage the mass ratio becomes worse. The acceleration at burn out for just an empty upper stage, and payload would also be rather high. Then I'll take the mass ratio for the upper stage at only 10 to 1, giving a 9,200 kg upper stage dry mass. Let's calculate first what the calculator gives as the payload for the present case using the standard Merlin 1D at 311 s Isp. The calculator gives:
Mission Performance:
Launch Vehicle:   User-Defined Launch Vehicle
Launch Site:   Cape Canaveral / KSC
Destination Orbit:  185 x 185 km, 28 deg
Estimated Payload:   13831 kg
95% Confidence Interval: 10061 - 18407 kg
 Rather close to the actual value of 13,150 kg. Now we'll calculate it for the case where the first stage has been given altitude compensation to get a 340 s Isp. We'll change the Isp input to 340 s and also increase the thrust to 7,210 kN as before. Then the calculator gives:


Mission Performance:
Launch Vehicle:   User-Defined Launch Vehicle
Launch Site:   Cape Canaveral / KSC
Destination Orbit:  185 x 185 km, 28 deg
Estimated Payload:   17056 kg
95% Confidence Interval: 12781 - 22223 kg
 This is a significant increase but not nearly as dramatic as the increase for the SSTO case. For the SSTO case the payload more than doubled. But for the TSTO case it increased by less than 25%.

 This could mean the SSTO could approach that of the TSTO on a cost per kilo basis. Elon Musk has said the Falcon 9 first stage takes up about three-quarters of the cost of the Falcon 9:
Musk lays out plans for reusability of the Falcon 9 rocket
October 3, 2013 by Yves-A. Grondin 
Performance hit for reusable rockets:
Musk also addressed the performance hit that results from reserving propellant for landing the first stage.
“If we do an ocean landing (for testing purposes), the performance hit is actually quite small, maybe in the order of 15 percent. If we do a return to launch site landing, it’s probably double that, it’s more like a 30 percent hit (i.e., 30 percent of payload lost).”
...
Musk believes that the most revolutionary aspect of the new Falcon 9 is the potential reuse of the first stage “which is almost three-quarters of the cost of the rocket.”

http://www.nasaspaceflight.com/2013/10/musk-plans-reusability-falcon-9-rocket/
 This would put it at about $40 million out of the $54 million for the full rocket. Then the cost per kilo for the SSTO would be $40,000,000/12,068 = $3,314 per kilo, while for the TSTO it would be $54,000,000/17,056 kg = $3,166 per kilo.

 The benefits of the SSTO would be even more dramatic in the reusable case. In the Nasaspaceflight.com article Elon says the loss in payload for the F9 for returning just the first stage to the launch site was about 30%. This is interesting because he said in another interview the loss in payload for returning both stages would be a loss of about 40%:

Elon Musk on SpaceX’s Reusable Rocket Plans.
By Rand Simberg
February 7, 2012 6:00 PM

Despite the dangers, Musk is clearly a fan of the rocket-powered approach. He told PM that SpaceX has come up with a solution to make both the lower and upper stages of the Falcon 9 reusable. (The Dragon capsule that will fly atop the rocket has already demonstrated that it can be recovered in the ocean after it splash-lands with a parachute, though SpaceX is building vertical-landing capability into that as well.)
The key, at least for the first stage, is the difference in speed. "It really comes down to what the staging Mach number would be," Musk says, referencing the speed the rocket would be traveling at separation. "For an expendable Falcon 9 rocket, that is around Mach 10. For a reusable Falcon 9, it is around Mach 6, depending on the mission." For the reusable version, the rocket must be traveling at a slower speed at separation because the burn must end early, preserving enough propellant to let the rocket fly back and land vertically. This also makes recovery easier because entry velocities are slower.
However, the slower speed also means that the upper stage of the Falcon rocket must supply more of the velocity needed to get to orbit, and that significantly reduces how much payload the rocket can lift into orbit. "The payload penalty for full and fast reusability versus an expendable version is roughly 40 percent," Musk says. "[But] propellant cost is less than 0.4 percent of the total flight cost. Even taking into account the payload reduction for reusability, the improvement is therefore theoretically over a hundred times."

http://www.popularmechanics.com/science/space/rockets/elon-musk-on-spacexs-reusable-rocket-plans-6653023 


 These two quotes together could mean the payload loss from making the upper stage also reusable is 10%, assuming Elon was being consistent between the two quotes. Then a question arise: would the payload loss from the making the SSTO reusable also be just 10% of the payload? 

 This doesn't seem likely, for if you changed the relative sizes of the first and upper stages while keeping the payload the same, then the extra added components for the upper stage such as heat shield, landing legs, and propellant reserve for landing should also change. It should not stay as the same 10% of the payload, regardless of the size of the stage. So we'll need to do use some other sources to see how much payload would likely be lost under the reusable SSTO case.

Payload Lost for a Reusable SSTO.

 We need a heat shield, landing legs, and reserve propellant for the landing. This interesting discussion between noted space-historian Henry Spencer and a former manager for both the DC-X and X-33 programs, Mitchell Burnside Clapp, is about the relative benefits of horizontal versus vertical landing of RLV's:

Horizontal vs. vertical landing (Henry Spencer; Mitchell Burnside Clapp).
http://yarchive.net/space/launchers/horizontal_vs_vertical_landing.html 

 Burnside Clapp conservatively estimates the propellant that needs to be kept on reserve for the landing amounts to about 30 seconds of engine firing. Spencer optimistically estimates it might be as low as 10 seconds. I'll estimate it as 20 seconds. Assume the engine used for the landing has similar sea level Isp as the Merlin at 282 s. But this is not for the full firing of all engines as would be needed for takeoff of a fully loaded rocket. 

 We'll assume we only need enough thrust for the dry mass of the stage, as the needed reserve propellant is a small proportion of this. Taking the dry mass of the first stage as 16,000 kg, 157,000 N, the flow rate of such an engine would be (flow rate) = (thrust)/(exhaust velocity) = 157,000N/2370m/s = 57.5 kg/s. And the propellant for a 20 second burn would be 1,150 kg, 7% of dry mass.

 For the heat shield, it will be the PICA-X material of SpaceX. The mass for this heat shield  used for the Dragon has been estimated in the range of 226 kg. However, the video SpaceX has released of a reusable Falcon 9 shows a heat shield on the upper stage that extends partially down the side of the stage. Then I'll estimate the mass as double that of the Dragon at 550 kg.

 For the landing gear the example of the lighweight gear for the B-58 suggests it can be as low as 1.5% of the landing weight:

Landing gear weight (Gary Hudson; George Herbert; Henry Spencer).
http://yarchive.net/space/launchers/landing_gear_weight.html 


 With lightweight composites this might be reduced to 1% of the landed weight, 160 kg. The total of all three of these extra systems for reusability would then be 1,860 kg, about 12% of the 16,000 kg dry weight. 

 This would need to be subtracted off from the delivered mass to LEO. Then the reusable F9 v1.1 first stage would have a payload to LEO of 10,200 kg.

Comparsion of Costs of Reusable SSTO, Partially Reusable TSTO, and Fully Reusable TSTO.

  First, under the partially reusable case of just the first stage being reusable, this would subtract off 30% of the payload, so from 17,056 kg to 11,940 kg. Now assume the first stage is reusable 10 times and this cuts the cost of that stage by a factor of 10, so to $4 million per flight. Then the upper stage being expendable would be $14 million, i.e. $54 million - $40 million, and the total cost would be $18 million per flight, at a cost per kilo of $1,500 per kilo.


 Now compare to the reusable SSTO case. Again assume 10 uses at a cost of $4 million per flight. Use the reusability loss estimate above that lowers the payload to LEO to 10,200 kg. Then the cost per kilo would be only $390 per kilo(!)

 Perhaps a fairer comparison though would be to the fully reusable TSTO case. This would cut the payload by 40% so from 17,056 kg to 10,230 kg. Since we're using the full rocket 10 times, assume the cost is cut to $5.4 million per flight. This would be a cost per kilo of $527 per kilo. So the reusable SSTO would carry about the same payload but at a better cost per kilo.

 Admittedly though this conclusion is based on very rough estimates for the propellant reserve needed for landing and the mass needed for the heat shield for a long rocket stage compared to that of a capsule.


   Bob Clark

 

Thursday, October 31, 2013

A SpaceX Heavy Lift Methane Rocket.

Copyright 2013 Robert Clark

 SpaceX has announced development of a new 300 metric ton (mT), 660,000 lb, thrust engine, the Raptor:

SpaceX Could Begin Testing Methane-fueled Engine at Stennis Next Year.
By Dan Leone | Oct. 25, 2013

 This is supposed to be used for a proposed heavy lift rocket to be used for manned Mars missions. However, I'm not a fan of the 9 engine arrangement used on the Falcon 9, and even less so of the 27 engines proposed for the Falcon Heavy. I would hope that SpaceX would transition to the larger engines for these rockets as well.

 We can do an estimate of the size and payload capacity of the methane-fueled heavy lift rocket. Previous statements from SpaceX have suggested the core of the rocket might be 7 meters wide. However, I wanted to use an 8 meter wide core to make use of the tooling used for the shuttle external tank to save on costs. If we used the same size tank as the shuttle ET then we can calculate the mass of propellant could be carried as methane-lox instead of hydrogen-lox by comparing their densities.

SSTO Case.

 This report by Dr. Bruce Dunn gives densities and performance data on several propellant combinations:

Alternate Propellants for SSTO Launchers.
Dr. Bruce Dunn
Adapted from a Presentation at:
Space Access 96
Phoenix Arizona
April 25 - 27, 1996
http://www.dunnspace.com/alternate_ssto_propellants.htm

 In Table 1 the density of methane-lox is 828 kg/m^3 and for hydrogen-lox, 358 kg/m^3. So the same volume would hold 2.4 times more methane-lox. This would put it in the range of 1,700 mT for the methane-lox. Actually it would probably be a little more than this because likely SpaceX would use common bulkhead design for the tank which would mean it could hold more propellant.

 There have been some estimates proposed for this launcher that use 7 copies of Raptor engine on the core. This many probably would be needed when you take into account the reduction in thrust at sea level if using a 1,700 mT sized tank. However, I wanted to keep the maximum number of engines on a core to be at most what was used on the Saturn V at 5 engines. Therefore I'll reduce the propellant load to 1,000 mT.

 For the dry mass, note that Elon has said that the Falcon 9 v1.1 first stage has a propellant fraction in the range of 96%, for a mass ratio of 25 to 1. As you can see in Dunn's Table 1 the density of methane-lox is about 80% that of kerosene-lox. So I'll estimate the mass ratio for the core as 20 to 1. This will put the dry mass of the core at 52,630 kg, which I'll round off to 50,000 kg.

 The vacuum thrust in kilonewtons for 5 Raptors will be 5*300*9.81 = 14,715 kN. We'll calculate the payload for this core stage first as an SSTO. Input these numbers into Dr. John Schillings Launch Performance Calculator. Select "No" for the "Restartable Upper Stage" option, otherwise the payload will be reduced. Use the default altitude of 185 km. Select Cape Canaveral as the launch site with an orbital inclination of  28.5 degrees to match the latitude of the launch site. Then the Calculator gives the result:

Mission Performance:
Launch Vehicle:  User-Defined Launch Vehicle
Launch Site:  Cape Canaveral / KSC
Destination Orbit:  185 x 185 km, 28 deg
Estimated Payload:  42487 kg
95% Confidence Interval:  28319 - 59338 kg

 Two stage case.  

 For the two stage case, I'll take the the upper stage as using a single Raptor and at 1/5th the size of the first stage, so at 200 mT propellant mass and 10 mT dry mass. Enter in 2,943 kN for the thrust of a single Raptor in the column for the second stage and select "Optimal" for the trajectory. Then the Calculator gives:

Mission Performance:
Launch Vehicle:  User-Defined Launch Vehicle
Launch Site:  Cape Canaveral / KSC
Destination Orbit:  185 x 185 km, 28 deg
Estimated Payload:  77569 kg
95% Confidence Interval:  64244 - 93424 kg

  However, for this upper stage likely you won't be able to get as good a mass ratio as the first stage since it would undergo a higher acceleration as the propellant is burned off. This would require a stronger and therefore heavier structure. Then the payload would be reduced below this, though likely still above ca. 70 mT.

Cross-Feed Fueling for Multiple Cores.

 For higher payloads we'll use a combination of 2 or 3 cores. For both of these we'll use cross-feed fueling. To emulate cross-feed fueling with the Schilling Calculator, note that during the parallel burn portion of the flight the propellant for the center core engines is coming from the side booster stage(s). This ensures that the center core will have a full propellant load during its solo burn portion of the flight, after the side booster(s) are jettisoned. 

 So the total amount of propellant burned during the parallel burn portion, is that of the side booster(s) only. But the Schilling Calculator assumes the amount of propellant burned in the center core during the parallel burn is the same as the amount burned in each side booster. So enter in the Calculator for the booster propellant load a fraction of the actual propellant load of a core equal to the number of side boosters divided by the number of cores. So if you're using 2 cores with one used as a side booster enter in the Calculator booster column 1/2 the amount of the actual core propellant load. And if using 3 cores with 2 used as side boosters, enter in 2/3rds the actual core propellant load in the booster section. This will ensure the Calculator interprets the total propellant burned during the parallel burn portion is that of the actual side booster(s) only.

 But you also want the Calculator to take the amount of propellant burned during the center core's solo burn portion of the flight as that of a full propellant load. Since it is already taking it to have burned the same amount as what the side boosters have burned during the parallel burn portion, add this amount onto the actual propellant load of a core and enter this into a first stage column of the Calculator. For the other specifications for both booster(s) and center core such as Isp, dry mass, and thrust enter in the actual values.

2 Core Version.
 Here one core will be used as a side booster. As described above, to emulate cross-feed fueling enter in the Calculator only 500,000 for the propellant load of the booster. Enter in though the actual dry mass of 50,000 kg, actual thrust of 14,715 kN, and actual Isp of 380 s. And for the center core, enter in the first stage column for the propellant 1,500,000 kg, but the real dry mass, thrust, and Isp values. Also use all the actual values for the second stage. Then the Calculator gives the result:

Mission Performance:
Launch Vehicle:  User-Defined Launch Vehicle
Launch Site:  Cape Canaveral / KSC
Destination Orbit:  185 x 185 km, 28 deg
Estimated Payload:  145339 kg
95% Confidence Interval:  121566 - 173707 kg
 This is surprisingly high. However, another consideration besides the fact that the second stage mass ratio likely won't be as good as used here, is that as propellant is burned off during the parallel burn portion, the engines will have to be gimbaled because the propellant is only coming from the side booster stage. This will reduce the payload somewhat.

3 Core Version.
 Here two cores will be used as side boosters. As discussed, to emulate cross-feed we'll enter in the booster column for the propellant load, 2/3rds the actual amount, so only 660,000 kg. And for the center core's propellant load, enter into the first stage column 1,660,000 kg. All the other specifications are given their actual values. Then the Calculator gives:

Mission Performance:
Launch Vehicle:  User-Defined Launch Vehicle
Launch Site:  Cape Canaveral / KSC
Destination Orbit:  185 x 185 km, 28 deg
Estimated Payload:  211268 kg
95% Confidence Interval:  177052 - 251940 kg

  Remakably high. Twice the payload of the SLS at about the same gross mass.

   Bob Clark