To what extent might a booster designed to place an extremely light weight "micro" satellite with radio transmitter, say 100 grams for the sake of argument, be scaled down before factors such as increased aerodynamic drag on smaller objects, mass ratios etc. make such a venture impossible ? Has anyone done speculative calculations for such as project ?
In general there's a minimum size of rocket that can place nothing other than itself in orbit (because of the energy requirements to accelerate the rocket's own parts to orbital velocity while lifting it to orbital altitude--at mostly the same time or problems occur). There are diminishing returns as the payload sizes gets smaller and you asymptotically approach the smallest possible rocket given the technologies you apply to it, which leads to a couple preliminary conclusions:
- Existing small launchers will end up being pretty good models of what the limits are
- Being a secondary payload is generally much cheaper than flying primary on a small rocket, so small rocket development hasn't taken off, so we haven't seen a lot of real exploration of the limits of small rocketry; you're usually stuck with thought experiments
That said, there have been a few papers on this, so I'll share what I've found, minus frankly distressing amounts of link rot. I want to say I've seen a study at least once, too, but am having trouble finding one in my notes. The motivations are typically putting up payloads the size of cubesats or smaller, e.g. http://www.news.cornell.edu/stories/2014/04/cracker-sized-satellites-launch-orbit
I came across a lot of this a few years ago while toying around with the idea of an orbital rocket that could be transported inside a typical 42-foot semi trailer. That never became a design or paper, but maybe some day.
Dimotakis et. al concluded in 2000 that a 100lbm payload, which would be in the nanosatellite weight class, could be put into LEO for $300,000 per launch with an aircraft-launched two- or three- stage chemical rocket. https://fas.org/irp/agency/dod/jason/leo.pdf (I think that conclusion's nonsense, but it sure looks like they got paid for that paper and there certainly were companies thinking of doing exactly that for a while, but I think the price of being a secondary payload has dropped since then...)
A Smithsonian Air&Space article primarily about Mars Sample Return concurs with the drag limitations stated in the comments:
A terrestrial rocket has to push through a plug of air equivalent to a 30-foot column of water, and physics dictates that the smallest vehicle capable of moving all that atmospheric mass without paying a penalty in momentum is about 30 feet long.
There are several places I've heard that the Japanese Lambda 4S is the "smallest ground based launch vehicle to put a satellite into orbit" (quoted from the link soon to follow). http://orbitalaspirations.blogspot.com/2011/10/japanese-lambda-4s-launcher.html does a good job breaking down the rocket equation math for the launcher. I'd imagine its numbers could be beaten by actually having guidance (which it didn't!) and swapping out the solid rockets for more efficient motors after the first stage, but there probably isn't a ton of margin to win. She's about 10 tons and 55 feet long.
Vector Space Systems is working on Vector-R, a 50kg to LEO launcher, at 12m tall x 1.2m diameter, 5000 kg design dimensions, though those figures change from page to page in the site... http://vectorspacesystems.com/technology-4 http://vectorspacesystems.com/technology-5
Rocket Labs' Electron is 16x1.2m for 150kg to a 500km sun-synchronous orbit. Somewhat more payload and to a higher orbit, similar-ish size https://www.rocketlabusa.com/
JAXA is planning to launch the SS-520-4, 9.54m x 0.52m, 2600kg at launch, lofting 3kg of 3U cubesat to (for TRICOM-1) an orbit of 180kmx1500km. All per http://spaceflight101.com/ss-520-4-smallest-orbital-rocket-set-for-launch/ This is based on a sounding rocket, and I'd expect any orbital rockets at this size to be similar--sounding rockets with very small upper stages added to them.
Astra's Rocket 3 family is 11.6m long, placing it solidly in the same class as the other rockets listed here. The SS-520-4 beat it to making a successful orbital launch (and is also smaller), and none of the Rocket 3 launches have been entirely successful as of early 2021, but I think it deserves to be listed.
Experimental Launch of World’s Smallest Orbital Space Rocket ends in Failure
While they have called it the "World’s Smallest Orbital Space Rocket", so far it hasn't put it's payload into orbit yet.
above: SS-520-4 rocket ready for launch. From here, Photo: JAXA
above: SS-520-4 rocket. From here, Image: JAXA
SS-520-4 is a three-stage solid-fueled rocket standing 9.54 meters tall, measuring 52 centimeters in diameter and weighing in at 2,600 Kilograms – smaller and lighter than any previous ground-based orbital launch vehicle. It is based on the SS-520 sounding rocket design, modified with a small third stage tasked with injecting a payload into Low Earth Orbit.
above: TRICOM-1 in Launch Configuration. From here, Photo: JAXA
above: Person with TRICOM-1 for scale - in this case Professor Hiroto Habu of the Japan Aerospace Exploration Agency. Image from here.
I'm no rocket scientist, but I have it from two real rocket scientists that no launcher under about one metric tonne can get anything to orbit, at least if it has to start from the Earth's surface. Air launch can theoretically help, though, if it can bypass a lot of the atmosphere. There were some experiments back in the late 1950s at China Lake with multi-stage solids launched from fighter jets. They might have put small payloads into orbit, but at the time, they lacked the telemetry and tracking to verify orbit. Back then, it was hard to make anything practical with such small payload mass limits, so the approach was abandoned. Those limits aren't what they used to be, though -- significantly functional satellites fit in the cubesat format and perhaps smaller. CubeCab is trying this fighter-plane air launch approach again, planning to exploit the F-104's flight ceiling (in excess of 50,000 feet, with some versions going much higher) and launching one 3U cubesat at a time. Mach 2 isn't a very big fraction of orbital velocity, but it also helps a little. I'm not sure how big CubeCab's stack is, but it's probably much lighter than 1 metric tonne.
One force which makes launch to orbit difficult is aerodynamic force, primarily drag. Drag is directly related to the Aspect Ratio of the rocket, which is its length divided by its diameter. The Aspect Ratio determines the aerodynamic reference surface area, and like a sailboat, the longer and thinner the rocket the better. Attached is a drag profile for a typical ascent which I've plotted from CFD simulation of a 42" diameter launch vehicle using Matlab.
To complete the answer, realize the mass ratio (initial mass/final mass) will determine the delta-V that the rocket can attain. Initial mass includes the structure and payload and propellant.
The required delta-V for a mission is determined by the destination orbit, drag, and launch site (angular velocity of earth adds to delta-v). The required delta-V dictates the mass of propellant required. The mass of propellant and its density dictates the required volume of the tanks. Since a rocket is mostly tanks, the volume of the tanks dictates the size of the rocket. The designer needs to decide the diameter of the tanks, and voila! The length of the rocket is determined.
Going back to my original concern, a design with a high Aspect Ratio, that is a long rocket with small diameter, will face less drag in its flight. The plot shows that drag for the vehicle I modeled sees maximum drag at around Mach 1.3, which is the point of maximum dynamic pressure (Max Q). This is also the point of maximum structural loading. However, a long, thin rocket having high Aspect Ratio may not have the structural integrity to fly through Max Q without damage and/or loss of control. So this factor would be the limit on how small the diameter of a rocket could be.
I believe the Black Brandt sounding rocket has the largest Aspect Ratio of any operational vehicle, but it is a suborbital rocket.
- Arthur Greensite, Analysis and Design of Space Vehicle Flight Control Systems
- Hill and Peterson, Mechanics and Thermodynamics of Propulsion