### Author Topic: Micro-Rocketry to Orbit?  (Read 92923 times)

#### braddock

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##### Micro-Rocketry to Orbit?
« on: 06/09/2006 08:24 PM »
I just wanted to pose this as a thought experiment to help me better understand the limits of rocketry.

What is the smallest theoretical rocket that can make orbit?  What factor causes the limit?

As far as I can tell, the Tsiolkovsky rocket equation doesn't seem to address the problem of scale.  If I wanted to launch a paper clip into orbit, and I had a 350 Isp micro-machined thimble engine, then I just plug that in and get the same mass fraction that the big boys use.  But this seems intuitively wrong.

I can imagine that atmospheric drag will scale non-linearly with size, but say I hitch a balloon ride up the first 100k feet to avoid most of that...

So is the problem just building a teeny tiny engine of some exotic type?  Or possibly carrying a very high muzzle-velocity gun up on a balloon to shoot my pea into orbit?

#### mlorrey

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##### Re: Micro-Rocketry to Orbit?
« Reply #1 on: 06/09/2006 08:59 PM »
Aerodynamic losses are significantly greater, they do scale not just because of the scale of the vehicle size to the depth of the atmosphere, but that air is "thicker" for small things than for large things (a reason why small objects have lower terminal velocities versus large objects of equal density.)

Simultaneously, gravity losses are greater because a useful orbit is also "higher" if your unit measure is the size of the launcher. At the same time and while structural requirements due to gravitational stresses are less, structural requirements based on pressure (tank pressure, pump pressure, combustion chamber pressure) may not scale that well.
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#### Propforce

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##### RE: Micro-Rocketry to Orbit?
« Reply #2 on: 06/09/2006 11:34 PM »
Quote
braddock - 9/6/2006  1:11 PM

What is the smallest theoretical rocket that can make orbit?  What factor causes the limit?

Certain things are scalable, certain things are not.  Boundary layer is not scalable.  Surface area accounting for aerodynamic drags, however; is scalable (with the suface area!).  Generally speaking, smaller launcher has a higher surface area relative to its size, hence less efficient than a big rocket.

Quote
As far as I can tell, the Tsiolkovsky rocket equation doesn't seem to address the problem of scale.  If I wanted to launch a paper clip into orbit, and I had a 350 Isp micro-machined thimble engine, then I just plug that in and get the same mass fraction that the big boys use.  But this seems intuitively wrong.

Are you launching it as a single stage? two stages?  air launched? balloon launched?  The rocket equation alone does not tell you what the losses are that adds up to the total "ideal" delta-vee.  You'll have to run a 3-DOF trajectory optimization program (e.g., POST, OTIS) with the correct vehicle aero data in order to get a credible design.  In addition, you'll need to get a good idea of your propellant mass fraction that you can design to.  Again, this is where small launch vehicle suffers, as the smaller the vehicle the lower prop mass fraction one is able to achieve because the "fixed" inert weight becomes a larger % of the total weight.  Then you'll need credible "load-path" and structural strength sizing for your rocket.  Is your rocket going to flex like a spaghetti during flight, or is it going to be rigid like a pencil?  Do you model your guidance, control & flight stability adequately? Too many people fail to appreciate how heavy all those avionic boxes weight on a vehicle, and how heavy the wire harnesses are !!

Quote
So is the problem just building a teeny tiny engine of some exotic type?  Or possibly carrying a very high muzzle-velocity gun up on a balloon to shoot my pea into orbit?

Does your "Pea" need to stay intack once to get to orbit?  Does it burn up on the way up due to high aerodynamic heating?  Can your pea handle the high-G load and the high dynamic preesure?

Put it this way, "mother nature" will teach you where the "limits" are !

#### braddock

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##### Re: Micro-Rocketry to Orbit?
« Reply #3 on: 06/10/2006 01:01 AM »
Okay, so far it seems like the show stoppers are:

1) Volume doesn't scale linearly with Surface Area (even if 1/10th the mass may need only 1/10th the fuel, but the scaled rocket will only have ~1/5th the surface area).  Larger relative surface area = larger relative air friction resistance.

2) Also larger relative surface area MAY require larger proportion of weight to be structural (although lower pressures and smaller stresses could mitigate that)

3) Larger relative air viscosity (air is "thicker").  This is what the Micro UAV folks have run into as well (often to their advantage, although probably not to ours)

I'm still rather interested in the case of a balloon or otherwise boosted start at 100k ft where the atmosphere density is a fraction of ground level.  There must be some reason amateur rocketeers haven't taken a shot at orbit from a balloon (the likes of JP Aerospace and others have done balloon launches)?

What _IS_ the smallest rocket to have ever made orbit?

#### mlorrey

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##### Re: Micro-Rocketry to Orbit?
« Reply #4 on: 06/10/2006 03:56 AM »
Quote
braddock - 9/6/2006  7:48 PM

Okay, so far it seems like the show stoppers are:

1) Volume doesn't scale linearly with Surface Area (even if 1/10th the mass may need only 1/10th the fuel, but the scaled rocket will only have ~1/5th the surface area).  Larger relative surface area = larger relative air friction resistance.

2) Also larger relative surface area MAY require larger proportion of weight to be structural (although lower pressures and smaller stresses could mitigate that)

3) Larger relative air viscosity (air is "thicker").  This is what the Micro UAV folks have run into as well (often to their advantage, although probably not to ours)

I'm still rather interested in the case of a balloon or otherwise boosted start at 100k ft where the atmosphere density is a fraction of ground level.  There must be some reason amateur rocketeers haven't taken a shot at orbit from a balloon (the likes of JP Aerospace and others have done balloon launches)?

What _IS_ the smallest rocket to have ever made orbit?

Ah, good question. The US NAVY's NOTS program,  which in 1960-62 launched Caleb rockets from underwing an F4D-1 Skyray (not the later F-4 Phantom, different plane model), made 7 launches, with three failed launches. One of the successful launches, according to range radar, had sufficient downrange velocity to attain orbit, however payload telemetry failed, so achievement of orbit could not be confirmed. Project staff assert they made orbit.

There was also the earlier Project Pilot, also put on by the NOTS program, which made 10 attempts to loft a 1 kg payload. All failed, though one was also claimed to have reached orbit, though telemetry also failed in this instance.

The Caleb was a four stage solid fuelled rocket. The goal of the project was to achieve an air launched ASAT weapon. Total Mass: 1,350 kg (2,970 lb). Core Diameter: 0.60 m (1.96 ft). Total Length: 4.90 m (16.00 ft). Payload: 7.00 kg. Empty weight: 224 kg. Fuel fraction:  0.829. Isp (sl): 204 sec. Isp (vac) 250 sec.

Theoretical:
The smallest launcher that never flew, but could have reached orbit, would have been Dr. Gerald Bull's GLO-1B cannon launched missile, http://www.astronautix.com/lvs/glo1b.htm
which he had developed to be launched from his 16 inch gun system at his Carribean island test site. Bull's larger Babylon Gun, to be built for Saddam Hussein had Bull not been assasinated by the Mossad prior to the Gulf War, would have theoretically lofted 1,000 lb into LEO via a missle launched through its 36 inch bore.

Actual confirmed: The Russian Shtil launcher seems to me to be the smallest launcher that has put payloads reliably into orbit. This vehicle is a Sea Launched Ballistic Missile essentially of similar size as SpaceX's Falcon 1 launcher.
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#### braddock

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##### RE: Micro-Rocketry to Orbit?
« Reply #5 on: 06/10/2006 01:17 PM »
Very interesting.  I found an article on Project Pilot that suggests that it actually achieved orbit twice, although the telemetry reports were ify.  Only source of this article seems to be in an old mailing list archive: http://www.uoregon.edu/~stevev/sd-archive/raw/sd1998-3.txt (search for NOTSNIK)

So a 16' x 2' air-launched solid (Caleb) can at least theoretically get a 15 lb payload to orbit, with a payload-to-mass ratio of .5%.  Can't find altitude info on Caleb, but Project Pilot was launched at 41k feet.

http://www.astronautix.com/graphics/n/nots.jpg">

Interesting lower limit example.

And I spent a couple hours last night reading about Dr. Bull's Project HARP gun-launched rockets, which was also fascinating.  Astronautix has an excellent series of articles on that.  http://www.astronautix.com/articles/abroject.htm

I still don't have a good idea of what defines the lower limit for an air-launched orbital launch vehicle, however.  Caleb seems to have a reasonable payload mass fraction for a solid (although by my figures Pegasus is closer to 2%, but is also much more refined).

If 2'x16' (=~50 cu ft of propellent if cylindrical) lofts 15 lbs, then I could naively expect that an 8ft x 6 inch rocket could loft a half pound payload (8ft x 6in =~ 1.5 cu ft of propellent =~ (50 cu ft)/30).

This would seem to quickly cut things down to the capabilities of amateur rocket folks?  But yet I don't see them orbiting small payloads, so I must be missing something still?

#### Jim

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##### Re: Micro-Rocketry to Orbit?
« Reply #6 on: 06/10/2006 02:14 PM »
Cost of the aircraft

#### mlorrey

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##### Re: Micro-Rocketry to Orbit?
« Reply #7 on: 06/10/2006 08:47 PM »
Quote
Jim - 10/6/2006  9:01 AM

Cost of the aircraft

True. For those "amateurs" with big bank accounts, I know where to get flight capable Mig-21 aircraft, delivered to your location, for under \$100,000.00. The Mig-21 has higher speed, altitude, and payload capacity than the Skyray, so one ought to be able to replicate Project Pilot and/or Caleb relatively easily.

So, any takers?
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#### mlorrey

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##### RE: Micro-Rocketry to Orbit?
« Reply #8 on: 06/10/2006 09:05 PM »
Quote
braddock - 10/6/2006  8:04 AM

Very interesting.  I found an article on Project Pilot that suggests that it actually achieved orbit twice, although the telemetry reports were ify.  Only source of this article seems to be in an old mailing list archive: http://www.uoregon.edu/~stevev/sd-archive/raw/sd1998-3.txt (search for NOTSNIK)

So a 16' x 2' air-launched solid (Caleb) can at least theoretically get a 15 lb payload to orbit, with a payload-to-mass ratio of .5%.  Can't find altitude info on Caleb, but Project Pilot was launched at 41k feet.

http://www.astronautix.com/graphics/n/nots.jpg">

Interesting lower limit example.

And I spent a couple hours last night reading about Dr. Bull's Project HARP gun-launched rockets, which was also fascinating.  Astronautix has an excellent series of articles on that.  http://www.astronautix.com/articles/abroject.htm

I still don't have a good idea of what defines the lower limit for an air-launched orbital launch vehicle, however.  Caleb seems to have a reasonable payload mass fraction for a solid (although by my figures Pegasus is closer to 2%, but is also much more refined).

Well, you've got to decide what your fuel choice is (ergo, your Isp), how many stages (less stages is less complex, but more stages is easier to get payload to orbit), as well as your air launch altitude and speed.

The NF-104 program is a good example of a rocket-equipped jet aircraft doing zoom maneuvers on a consistent, even daily, basis, and is the basis of the various RASCAL proposals. I've read that one attempt was made to launch an upper stage from an NF-104 into orbit, but it failed. The USAF tended to look at the NF-104 with a bit of distain given its concurrence with the X-15 program, and despite the excellent work done by Capt Bob Smith on the program, but it was sabotaged by Chuck Yeager's quest for more glory in his waning years, when he crashed one of the aircraft because he refused to follow Smiths instructions in the flight profile.

I think a reasonable case could be made for a kerosene/lox or kerosene/H2O2 fuelled two stage vehicle to be dropped from a Mig-21 at 40kft and Mach 2. The standard payload of the 21 is 2,000 kg of missiles plus a 23 mm cannon and ammo. If the cannon, radarset, and obsolete avionics were stripped out, you could probably get the max upper stage GTOW up to 4,000-5,000 kg. That should allow an upper stage payload in orbit of about 50-75 kg.

Let the Mig-21 do the climb before release, so a Pegasus-style wing would be unnecessary.
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#### Zachstar

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##### Re: Micro-Rocketry to Orbit?
« Reply #9 on: 06/10/2006 09:53 PM »
Might find this interesting http://www.microlaunchers.com/home.htm

#### mlorrey

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##### Re: Micro-Rocketry to Orbit?
« Reply #10 on: 06/11/2006 08:12 PM »
Quote
Zachstar - 10/6/2006  4:40 PM

Might find this interesting http://www.microlaunchers.com/home.htm

It is interesting what micromachinery is being made. Just the other day I was chatting with a fellow at a company that produces MEMS chip liquid cooling devices, made by diffusion bonding hundreds of leaves of 1-3 mil metal, each with their own micro cut patterns.
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#### Jim

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##### Re: Micro-Rocketry to Orbit?
« Reply #11 on: 06/11/2006 11:33 PM »
Quote
mlorrey - 11/6/2006  3:59 PM

Quote
Zachstar - 10/6/2006  4:40 PM

Might find this interesting http://www.microlaunchers.com/home.htm

It is interesting what micromachinery is being made. Just the other day I was chatting with a fellow at a company that produces MEMS chip liquid cooling devices, made by diffusion bonding hundreds of leaves of 1-3 mil metal, each with their own micro cut patterns.

The problem is micromachinery doesn't work very well with fluids.  The same reasons that there are no small jst engines, would be the same for turbo pumps.  Reynolds numbers don't scale.

#### mlorrey

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##### Re: Micro-Rocketry to Orbit?
« Reply #12 on: 06/12/2006 05:13 AM »
Quote
Jim - 11/6/2006  6:20 PM

Quote
mlorrey - 11/6/2006  3:59 PM

Quote
Zachstar - 10/6/2006  4:40 PM

Might find this interesting http://www.microlaunchers.com/home.htm

It is interesting what micromachinery is being made. Just the other day I was chatting with a fellow at a company that produces MEMS chip liquid cooling devices, made by diffusion bonding hundreds of leaves of 1-3 mil metal, each with their own micro cut patterns.

The problem is micromachinery doesn't work very well with fluids.  The same reasons that there are no small jst engines, would be the same for turbo pumps.  Reynolds numbers don't scale.

What makes you think there are no small jet engines? I know a number of modellers who fly jet engines in the 10-100 lb thrust range, and a number of institutions, including MIT, are developing MEMS turbine generators for powering remote devices, many of which are being developed for Army infantry use:

http://www.enme.umd.edu/SSSC/pdf/update/Transducers%2097%20-%20Paper.pdf
http://www.enme.umd.edu/SSSC/pdf/update/HH2000-Turbine.pdf
http://www.enme.umd.edu/SSSC/pdf/update/MEMS%2099%20-%20Paper.pdf

In fact, turbines reach adiabatic efficiencies of 70% and are able to maintain supersonic turbine speeds while maintaining laminar flow, with Reynolds numbers up around 20,000. The one MIT is working on is an 80 watt turbogenerator, with a turbine disc diameter of about 3-4 mm. The full engine assembly is 1 cm dia.

NASA is also working on a "steam" turbine, using Xenon as the working fluid, which is heated by various processes: fuel cells, solar concentrators, radiothermal devices, etc.
http://www.nasatech.com/Briefs/Jan03/NPO20933.html

The reason for this is because at the microscale, gasses flow with the viscosity of liquids at macro scales.
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#### Jim

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##### Re: Micro-Rocketry to Orbit?
« Reply #13 on: 06/12/2006 10:46 AM »
Efficent small jet engines

#### cpooley

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##### Re: Micro-Rocketry to Orbit?
« Reply #14 on: 06/12/2006 06:32 PM »
Braddock emailed me asking about Microlaunchers.  It is a plan to devekop commercial space access via a launcher to place 1 pound spacecraft to escape.  That was thought do-able 10 years ago.  Now more easily (eg 1-gram RC plane linket to in my site).
1.  starting small because starting "big" has always failed--too expensive, risky
2.  to escape-- LEO too crowded, not enpugh new things to do with that--there's a solar system to check out.  (A ML could orbit maybe 3 Cubesats)
------------------------------
Most of the problems related to small scale have to do with aerodynamisc.  The 1st stage will be inefficient.  I'm assuming 10% GLOW for upper stages.  The upper stages, starting in vacuum, can operate more like "normal" size rockets.
---------------------------
The engineering of this looks very attainable.  Currently raising the funding for the "chapter written in fire and metal".

Charles Pooley  http://www.microlaunchers.com

#### braddock

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##### RE: Micro-Rocketry to Orbit?
« Reply #15 on: 06/15/2006 03:33 AM »
Super Loki to LEO?
~~~~~~~~~~~~

Okay, as a kind of culmination of what I've leared here, let me see if I can launch a large glass marble (18g) into LEO.

I'd appreciate it if the folks here could point out any flaws in my logic or math here, since this is my first attempt at using the rocket equation.

Fantasizing, I figure I could fit an integrated microchip die with on-board solar cells and an imager and simple lens, and LED for optical communications, and guidance into something the size and weight of a glass marble (18g) pretty easilly with a custom VLSI design.

I take an existing Super Loki sounding rocket, and replace the usual 6 kg instrumented "dart" payload with a second stage small rocket to get me into LEO.  Take off weight is only about 75 lbs.

I assume the Loki will get my second stage above around 200,000 feet; above enough air resistance that I can ignore drag and use the straight rocket equation.

I'll assume an Isp of my solid second stage of only 200 secs.
This would make my exhaust velocity:

Ve = 200*g0 = 200*(9.8 m/s/s) = 1960 m/s

I'll assume ignition of my second stage at apogee of 200k feet with an initial velocity of 0 m/s.
I'll therefore use a delta V from standstill to LEO of
dV = 9.5 km/s

Mass Fraction: http://upload.wikimedia.org/math/4/d/b/4db710073244697d25c8520051a7bd03.png">

Plugging in the right-hand-side, I get a mass fraction of .992
Ie, 99.2% of my second stage mass has to be propellant for this work.

With a second stage mass of only 6 kg, this means that my stage structure and payload must have a mass of only 47 grams.  18g of that is my marble, leaving 29g for structure.

This is clearly not much margin, but it would seem plausible that not much more than a Super Loki and a solid second stage can get a very small payload to orbit.

Comments and corrections?

#### meiza

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##### Re: Micro-Rocketry to Orbit?
« Reply #16 on: 06/15/2006 09:31 AM »
You probably don't need 9.5 km/s when starting at high altitude? You're talking about essentially SSTO performance. 8 km/s would give mass fraction of 0.98 and 120 g of empty mass. It would be wiser anyway to get some horizontal velocity from the first stage too and stage at lower altitude while you still have vertical and horizontal speed. (Lessens gravity losses.) So perhaps you can calculate both stages as giving about 5 km/s deltav. The payload of the first stage is the fully fueled second stage, it would prolly be smart to make it heavier than 6 kg. And use three stages.
And how are you going to have maneuvering and guidance in a 29 g or even 120 g empty weight rocket? You have to maneuver to lift the apogee (you can't reach the orbit with a pure gun from ground since the perigee will always be inside earth). Maybe if you shot the Loki straight up and then the upper stage was positioned sideways and then spun up...

#### Monroe

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##### Re: Micro-Rocketry to Orbit?
« Reply #17 on: 05/28/2011 11:33 PM »
Old topic but maybe we can give it a kick.

Team Prometheus is attempting to orbit a 20 gram payload launched from 100,000ft.

Our attempt is based on project "Pilot" The exception being balloon launched from a Zero Pressure Balloon. The rocket weigh's about 150lbs, is 5 stages. Is unguided by mechanical means just like Pilot. The third stage fires by horizon location it's spin stabilized. The final stage nozzle is under the noze cone due to the spin when the rocket reaches the other side of the world it will be facing the right direction. The last stage circularizes the orbit.

Monroe

#### Tcommon

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##### Re: Micro-Rocketry to Orbit?
« Reply #18 on: 05/29/2011 02:39 AM »
As far as I can tell, the Tsiolkovsky rocket equation doesn't seem to address the problem of scale.

you can scale a rocket, but you can't scale the planet.

Reynolds numbers don't scale.

Reynolds numbers are dimensionless

similitude can be hard to visualize.

#### JohnFornaro

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##### Re: Micro-Rocketry to Orbit?
« Reply #19 on: 05/29/2011 03:27 PM »
The SR-71 is my favorite plane, but the F-104C is a close second.  If Chuck Yeager was trying to "sabotage" that program up there, he certainly chose a risky way to do it!

But anyhow, this is a great discussion.  Here is my "affordable" miniature idea.  I'd like to land the smallest possible lunar lander at one of the Apollo sites, photograph it a half dozen times, and successfully transmit the images back to Earth on an open channel.

I lost the envelope, but it seemed at the time that an F1 would do it.
Sometimes I just flat out don't get it.

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