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Tuesday, August 22, 2017

Orbital rockets are now easy, page 2: solid-rockets for cube-sats.


Copyright 2017 Robert Clark

Introduction.
  In the blog post "Orbital rockets are now easy", I argued that with altitude compensation, liquid-fueled orbital rockets become within the capabilities of most university undergraduate labs.

 Here I'll argue solid-fuel rockets can also be built by amateurs to reach orbital space.

 I was impressed by this university teams launch to 144,000 feet of a suborbital solid-fuel rocket:

USC Rocket Propulsion Laboratory Breaks Record.
Amy Blumenthal | March 16, 2017
Student-run RPL launches rocket of own design to 144,000 feet.
https://viterbischool.usc.edu/news/2017/03/usc-rocket-propulsion-laboratory-breaks-record/

  However, using essentially "off-the-shelf" components, you can get a 3-stage solid rocket of comparable size to actually reach orbit. Moreover, I was surprised to see after running a launch simulation program that you don't even need altitude compensation to accomplish it.

 By essentially off-the shelf, you could use solid-rocket motors sold to amateurs but with an addition of a lightweight carbon-composite casing that amateurs such as the USC team already have been making themselves for their own rockets.



 You would have Cesaroni Technology, or other solid motor manufacturer, make their motors with only a thin aluminum case, not meant to hold the full combustion chamber pressures. The amateurs would then make the carbon composite case rated for the full combustion chamber pressure.

 Cesaroni also makes commercial sounding rockets with carbon composite casings but this is likely to be more expensive than if the amateurs make it themselves.

Specifications.
 This motor by Cesaroni Technology, or similar motors by other manufacturers, could form the basis of the orbital rocket:




  This motor though only has a mass ratio of about 2.5 to 1, adequate for amateurs doing high power rocketry test flights, but not for an orbital rocket. However, you can save about half of the weight of the aluminum casing used by replacing it by carbon composite.

 Cesaroni was able to do this for the suborbital rocket SpaceLoft they constructed for UP Aerospace, Inc.:

CTI rocket motor successfully powers the launch carrying the ashes of astronaut and James Doohan - April 30, 2007.
On April 28th, a Spaceloft™XL rocket successfully completed a round-trip space flight launched from Spaceport America. This rocket was developed by UP Aerospace Inc. of Hartford, Conn. The rocket carried a wide variety of experiments and payloads, which included the cremated remains of Star Trek's "Scotty", James Doohan and NASA astronaut and pioneer Gordon Cooper. In addition, the cremated remains of more than 200 people from all walks of life were onboard. Also flown into space on the SL-2 Mission were dozens of student experiments from elementary schools to high schools to universities - from across America and worldwide - as well as innovative commercial payloads.
The flight was a successful demonstration of the rocket motor developed and built by Cesaroni Technology Incoporated (CTI). CTI started the design process in September of 2005. CTI specializes in low cost propulsion systems for military and space applications and used its experience to develop an affordable, reliable propulsion system for the rocket. The motor has a carbon fiber composite case and a monolithic solid propellant grain that is bonded to the casing.
Watch the post-launch coverage as carried by local television station KRQE here (9 Mb)
Watch the launch as carried by the BBC here (1 Mb)
Watch pre-launch coverage as carried by CTV Toronto here (9 Mb)
Watch pre-launch coverage as carried by CBC Toronto here (9 Mb)
Technical data for the UPA-264-C rocket motor


 So we'll assume the Cesaroni Pro150 can get a 0.8 propellant fraction by using carbon composite casing. We'll round off the propellant mass to 20 kg, and take the dry mass as 5 kg. We'll take this as the third stage of our rocket.

 For the lower stages, the size of stages commonly are in the range of 3 to 5 times larger than the succeeding stage. We'll take the second stage as 4 times larger than the third stage at a 80 kg propellant weight and 20 kg dry weight. For the first we'll take it as larger by an additional factor of 4 to a 320 kg propellant weight and 80 kg dry weight.

 Now for the specific impulses for the stages. This commercial solid motor has a similar sea level Isp as the Cesaroni solid rocket motor Pro150:

Star 37.
Thiokol solid rocket engine. Total impulse 161,512 kgf-sec. Motor propellant mass fraction 0.899. First flight 1963. Solid propellant rocket stage. Burner II was a launch vehicle upper stage developed by Boeing for the Air Force Space Systems Division. It was the first solid-fuel upper stage with full control and guidance capability developed for general space applications.
AKA: Burner 2;TE-M-364-1. Status: First flight 1963. Number: 180 . Thrust: 43.50 kN (9,779 lbf). Gross mass: 621 kg (1,369 lb). Unfuelled mass: 63 kg (138 lb). Specific impulse: 260 s. Specific impulse sea level: 220 s. Burn time: 42 s. Height: 0.84 m (2.75 ft). Diameter: 0.66 m (2.16 ft).
Thrust (sl): 33.600 kN (7,554 lbf). Thrust (sl): 3,428 kgf.
http://www.astronautix.com/s/star37.html

 So we'll estimate the vacuum Isp of the Cesaroni Pro150 to be in the Star 37's range of 260 s. However, rocket stages can get higher vacuum Isp's by using longer nozzles. A 285 s Isp is not uncommon for solid rockets motors with vacuum optimized nozzles, such as the Star 48.

 So we'll take the Isp for the second and third stage as 285 s.

 For the thrust, we'll take the thrust of the third stage as the same as the Pro150 of 8 N, and assume the thrust for the second and first stage scale according to their size so to 32 N and 128 N, respectively.

 Now use Dr. John Schilling's launch performance calculator to estimate the payload.

 The input page looks like this:


 Note there some quirks of this program you need to be aware of if you use it. First, always use the vacuum values for the Isp's and thrust numbers, since the program already takes into account the diminution at sea level. Second, always set the "Restartable Upper Stage" option to "No", rather than the default "Yes", otherwise the payload will be reduced. Third, always set the launch inclination to match the launch site latitude, otherwise the payload will be reduced. This is related to the fact that changing the orbital plane involves a delta-v cost. So for the Cape Canaveral launch site, the launch inclination should be set to 28.5 degrees.

Now, here's the result:




 So a payload to LEO of 7 kg. And this with standard nozzles, no altitude compensation required.

Structure.
  To save costs, I'm envisioning making the components as much "off-the-shelf" as possible. But among its standard products Cesaroni offers the Pro150 as the largest motor. So to get the larger second and first stages, we would have to combine multiple copies of this motor.

  I could cluster them in parallel, but for the first stage that would be 16 of them, and you would have the problem of simultaneous ignition with that many motors.

  So what I'm envisioning is take 4 copies of the Pro150 stacked vertically one on top of the other for the second stage, then cluster 4 of these second stage motors in parallel for the first stage.

 The question is though about the vertical stacking is how much the thrust scales in this case. If for the solid motors the propellant burned from the bottom upwards, then the thrust would be the same as for a single motor, you would just get 4 times longer burn time.

  But that's not how large solid motors work. Actually, they have a hollow region in the center so the propellant burns from the inside surface, proceeding outwards. In this case, you have a greater amount of propellant being burned per second because of the larger vertical surface area with the stacked segments. In fact, the thrust scales linearly with the number of segments.

 By the way, the reason why I don't just also stack the first stage vertically, is because of the thinness of the rocket that would result. The Pro150 is about 3 feet long and 1/2 foot wide. If you stacked vertically 16 for the first stage, 4 for the second, and 1 for the third, that would be a rocket 63 feet high but only 1/2 foot wide, for a ratio of length to width of over 120 to 1.

 This ratio of length to width is called the "fineness ratio". Rocket engineers don't like for it to be higher than about 20 to 1 because of the severe bending loads that would result. The upgraded version of the Falcon 9 has been noted for its long, skinny profile, and has a fineness ratio of about 20 to 1. The Scout solid rocket had a fineness ratio of about 24 to 1. Solid rockets can support a higher fineness ratio because their thicker walls can withstand higher loads. Still, 120 to 1 would very likely be too high.

  So to avoid this I decided to form the first stage by clustering in parallel four copies of the second stage. Note here these four clustered motors arranged around the second stage will provide the full thrust for the first stage while the central second stage motor will not fire until the four clustered motors are jettisoned.

 It would be possible though to get a single vertically stacked motor using multiple segments if the segments were shorter, resulting in a smaller rocket. For instance, there is a market for cubesats at only 1 kg mass to orbit. If you made the solid motor segments only about 1/2 foot long by cutting the Pro150 into 6 segments, you could take one of these smaller segments as the third stage, 4 segments for the second stage, and 16 segments for the third stage.

Cost.
 The Cesaroni Pro150 retails for about $3,000 and in general the Cesaroni solids cost in the range of $100 per kg of the motor mass:

Cesaroni O8000 White Thunder Rocket Motor.   
$3,099.95
Product Information
Specification
Brandname:  Pro150 40960O8000-P                  Manufacturer:  Cesaroni Technology
Man. Designation:  40960O8000-P                    CAR Designation:  40960 O8000-P
Test Date:  4/10/2008                                   
Single-Use/Reload/Hybrid:  Reloadable             Motor Dimensions mm:  161.00 x 957.00 mm (6.34 x 37.68 in)
Loaded Weight:  32672.00 g (1143.52 oz)         Total Impulse:  40960.00 Ns (9216.00 lb/s)
Propellant Weight:  18610.00 g (651.35 oz)       Maximum Thrust:  8605.10 N (1936.15 lb)
Burnout Weight:  13478.00 g (471.73 oz)          Avg Thrust:  8034.50 N (1807.76 lb)
Delays Tested:  Plugged                                      ISP:  224.40 s
Samples per second:  1000                                  Burntime:  5.12 s
https://www.csrocketry.com/rocket-motors/cesaroni/motors/pro-150/4g-40kns-reloads/cesaroni-o8000-white-thunder-rocket-motor.html

 So take the cost of the third stage, derived from the Cesaroni Pro1050, as $3,000, and the second stage 4 times larger as $12,000, and the first stage larger by an additional factor of 4 as $48,000. So $63,000 for a smallsat launcher with a 7 kg payload to orbit.

Applications.
 Several universities have created their cubesats and smallsats to be launched piggyback on large rockets such as the Falcon 9. However, the solid rocket launcher formed from essentially off the shelf components could be built by any interested university itself thus creating their own launcher and satellite.

 Despite the small size of such satellites, and their low construction cost, the launch cost is still not cheap when sent piggyback. SpaceX for their latest incarnation of the Falcon 9 is charging about $60 million for a 20,000 kg payload to LEO, about $3,000 per kilo. But the price is much higher than that for small payloads that have to ride piggyback on launchers. For instance Spaceflight Industries charges about $100,000 per kilo to book such flights. But a 1 kg cubesat launch would only cost in range of $9,000 for one of these dedicated solid-rocket launchers.

 The remaining entrants to the Google Lunar X-Prize will have to pay expensive launch costs for their spacecraft to the Moon. But with the university teams using their own solid rocket launchers, the launch costs would be so cheap the teams could afford to make many attempts to win the lucrative $30 million prize to soft-land on the Moon, and many more teams could have remained in the race.

 Also, both DARPA and the Army funded programs to develop such small dedicated launchers (liquid fueled), with their ALASA and SWORDS programs. But both their programs failed. They wanted to get about 25kg to 50kg to orbit for a launch cost of $1,000,000, about $20,000 to $40,000 per kilo. But the small size solid rockets will be able to beat this price, moreover will be more operationally responsive by using solid rockets. In a follow up post I'll discuss the payload can be more than doubled by using altitude compensation reducing the per kilo cost even further.


National security implications.
 Recently, there has been some discussion on creating Ultra Low Cost Access to Space (ULCATS). See for instance this study:

FAST SPACE: LEVERAGING ULTRA LOW-COST SPACE ACCESS FOR 21ST CENTURY CHALLENGES.
http://www.airuniversity.af.mil/Portals/10/Research/documents/Space/Fast%20Space_Public_2017.pdf

 Most of the discussion has been about how this would improve U.S. capabilities. But surprisingly little has been about what are the national security implications of any university world-wide and many knowledgeable amateur groups world-wide launching their own rockets to orbit.

 To prepare for this, which will be here like tomorrow, this discussion must begin now.


    Bob Clark

Note: thanks to former aerospace engineer and math professor GW Johnson for helpful discussion on this topic on the NewMars.com forum:

Amateur solid-fueled rockets to *orbital* space?
http://newmars.com/forums/viewtopic.php?id=7763




10 comments:

  1. Hi!

    If I understand correctly, a stack of commercially available solid rocket motors with a casing modification can put 1kg into orbit for only $9000. They key is the carbon fibre weave that allows for high pressure casings combined with high mass ratio. Has there been other non-amateur attempts at using this technique for solid rocket motors?

    How would the $9000 change if the first stage is replaced by a conventional RP-1/LOX rocket with gimballed nozzle and ground ignition? It might increase launch flexibility and reliability.

    ReplyDelete
    Replies
    1. The large aerospace companies have used carbon composite casings for solids such as the GEM solid boosters. But these are for lower stage boosters.

      Some solid rocket stages have gotten surprisingly high mass ratios though by using titanium casings in the range of 20 to 1 such as the Star 48.

      These though are for launchers that cost millions of dollars. I'm aiming for orbital launchers for small payloads that may cost only tens of thousands of dollars per launch.

      About replacing the solids with liquid fuels, this would be doable but more of a technical challenge. I discussed this possibility in the prior "Orbital rockets are now easy" post.

      Bob Clark

      Delete
  2. Nowhere is achieving the 25,000 mph escape velocity mentioned. Please show the math to achieve that to support your thesis.

    ReplyDelete
    Replies
    1. As Robert Heinlein said, once you reach orbit, you're halfway to anywhere.

      To get a spacecraft to escape velocity, you replace the LEO payload mass with a small in-space stage.

      I estimated using another solid rocket stage, you can get about 1/3rd the LEO payload to escape velocity.

      Delete
  3. Solids have high acceleration and shor burn times. This is a big penalty for small solids... see:
    https://e-reports-ext.llnl.gov/pdf/321763.pdf

    ReplyDelete
  4. Thanks for the reference. I'll take a look at it.

    Someone else reminded me that the Cesaroni Pro150 only has a burn duration of 5.1 seconds. That means that the proposed 3-stage rocket would reach orbit in only 15 seconds!

    Quite a bit shorter than the ca. 10 minute flight times to orbit of most orbital rockets. This high acceleration and speed would induce a high rate of drag, so this may require the first stage to be given a slower burn rate.

    In any case, the payload estimator I used is statistical in nature, i.e., doesn't actually do trajectory simulations.

    So I'm asking anyone with trajectory simulation programs such as OpenRocket or RockSim to do a run on the proposed configuration to see if it can actually reach orbit.

    Bob Clark

    ReplyDelete
  5. Best solution is probably a 4 stage, with a long coast between stage 1 and stage 2. IE stage 1's job is to just get it up out of the atmosphere....

    Its VERY hard to make a small long burn solid. The solid fuel regression rate is pretty much fixed within an order of magnitude for any efficient mix.

    So if you are burning 5mm /sec a 5 sec burn needs 25mm of burn.
    If you do an end burner you have serious heavy insulation issues.

    Easy to get long burns in something the size of a shuttle solid, really hard to get good mass fraction and long burn in a 2" diameter rocket motor.. (the 5mm/sec is a number I pulled out of the air, I'm not a solids, guy and that number could be wrong by a factor of 10. , but I'm friends with solids guys and I don't usually hold that against them ;-)


    ReplyDelete
    Replies
    1. Agree with you about the 4-stages. Most solid orbital launchers do.

      Getting to high altitude with solids is doable by amateurs as the example of the solid rocket constructed by USC undergrads shows.

      Cesaroni Technology does make some longer burning motors, of about 14 second duration. There are also certain additives you can add to the propellant to slow down the burn rate.

      Bob Clark

      Delete
  6. As a first cut don't need trajectory sim...
    Just calculate vacuum DV given ISP, and mass fractions for each stage. Is the number larger than the required number in the paper I posted? If not its not getting to orbit.

    So JUST the Pro-150 motor quoted above has a DV of empty motor of 1949m/sec...

    Given that if I make each stage 10X smaller than prevouse stage and make the stage wt ZERO except the motor I need 6 Stages to get to orbit given the small solids losses....

    Something is really wrong with your model..

    Assume 32672 loaded wt . Add 50% for next stage to both loaded and empty wt. This give me a stage DV of 1094 m/sec.

    Assuming 10Km/sec needed I get 9.14 stages.
    Assuming its launched from a balloon for zero drag of gravity losses I need 6.85 stages.

    This is assuming ZERO wt for payload, structure, guidance anything..... Just using the stock motors that would be in the zero drag case 7 stages and 511 motors.....


    % next stage 10 50
    Loaded Wt 32672 35939.2 49008
    final Wt 13478 16745.2 29814
    ISP 224.4 224.4 224.4

    1949.219141 1681.219048 1094.089946
    5.130259492 5.948064896 9.140016358
    3.847694619 4.461048672 6.855012269

    Stage # 10 2
    1 1 1
    2 10 2
    3 100 4
    4 1000 8
    5 10000 16
    6 100000 32
    7 1000000 64
    8 10000000 128
    9 100000000 256
    511




    ReplyDelete
    Replies
    1. Keep in mind I'm reducing the dry weight by using carbon composite casing instead of aluminum. This is known to be able to reduce the weight of a tank by about one-half.

      Cesaroni was able to improve the mass ratio to 5 to 1 on the SpaceLoft rocket I mentioned in the "Specifications" section this way.

      The carbon composite casing is a key aspect of the design. Redo your calculation with a 5 to 1 mass ratio.

      Also the ideal delta-v to reach orbit has been taken commonly as ca. 9 km/sec, instead of 10 km/sec, though I have also seen the higher value. See here for the lower estimate for the delta-v to orbit:

      Modern Engineering for Design of Liquid-Propellant Rocket Engines, p.12
      http://i64.tinypic.com/14ipea8.png

      and:

      Towards Reusable Launchers - A Widening Perspective.
      H. Pfeffer
      Future Launchers Office, Directorate of Launchers, ESA, Paris
      http://www.esa.int/esapub/bulletin/bullet87/pfeffe87.htm


      Bob Clark

      Delete