Quote of the Day

Our educational system is like an automobile which has strong rear lights, brightly illuminating the past. But looking forward, things are barely discernible.

— Hermann Oberth, German rocket theoretician, describing the German education system in the 1920s. He was bitter because his doctoral thesis on rocket propulsion was deemed utopian. His work became the basis of all spaceflight today. In my opinion, his criticism of the German educational system could be applied to the US education system today.

I just read a news article about Japan launching a 3 kg satellite into orbit using a 9.7-meter-long, two-stage rocket called the SS-520 (Figure 1). The 9.7 meter length was interesting to me because I recalled an Air & Space magazine article from 1999 that stated that the smallest rocket capable of achieving Earth orbit would be "about 30 feet long." Since 9.7 meters is 31.8 feet long, it appears that Japan's SS-520 is very near the lower size limit for rocket that can put an object into Earth orbit.

The size limit for an orbital rocket is driven by the amount of momentum lost because of atmospheric drag. As with artillery projectiles, larger rockets are more efficient in retaining momentum against drag. For a given shape, larger rockets are more aerodynamically efficient because frontal area increases by the square of the linear dimensions and volume (and mass) scales by the cube of the linear dimensions (see this detailed discussion). Drag is a function of the frontal area of the rocket, thus larger rockets have more mass (and momentum) relative to their drag. Another challenge with implementing a small launch vehicle is the difficulty of efficiently implementing a high specific impulse, liquid-fuel system because of the overhead of all the pumps, plumbing, and cooling.

Because I am still tied up with my cabin project, I have not gone through the minimum-sized orbital rocket calculations myself. Air & Space magazine states that:

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.

Historically, the orbital launch market has been dominate by customers who want to put large payloads into space. The advent of CubeSats has created a market for these small rockets. For example, a company called Rocket Lab uses their Electron rocket to launch small groups of CubeSats.

NASA has been researching the smallest rocket that can return a sample from Mars to Earth. According the Air & Space magazine article, the smallest orbital rocket is "about the size of a pencil" for essentially zero payload. NASA's Mars return mission is targeting a 1 pound payload and the mass is about 170 kg. Having lower gravity and a much thinner atmosphere make the job of getting into Mars orbit much easier than getting into Earth orbit.

People have been discussing these small rockets for many years. In fact, people have tried to motivate innovation in this area with the N-Prize, which is focused on putting a small payload (10 - 20 grams) into Earth orbit for less than 1000 *£* . For an excellent discussion on micro-rocketry, see this forum thread. The following Google talk on microlaunchers is also useful.

Figure 2: Microlaunchers – The Case for a New Generation of Very Small Spacecraft. |

"A terrestrial rocket has to push through a plug of air equivalent to a 30-foot column of water."

But at the top of Kilimanjaro the pressure is half what it is at sea level, and, the top is very accessible compared with other mountains. It's also close to the equator, another bonus for space launches.

So why isn't the world of space exploration beating a path to Tanzania.

A little bit more ambitiously you could also build a few miles of linear accelerator track with a gradual upturn near the top.

People certainly do launch rockets from high altitudes to reduce the size of the plug of air they must push through. The most common way is to launch the rocket from a high-altitude airplane. See this Wikipedia discussion about the Pegasus system, which has had 43 launches and is still operating today.

As far as horizontal rail launches, I have never seen that used in real life. However, it does appear in science fiction. The most famous case is from the movie When Worlds Collide. The photo below shows how the ramp shot was done with a model.

mark

Excellent post. Highly interesting to me since I've been employed as a systems engineering supporting NASA and MILSATCOM space missions for some year, and have a growing interest in cubesats. On the other end of the (size) spectrum, did you get a chance to view the live feed of the Falcon Heavy launch yesterday?

That was incredible! SpaceX is re-creating the feelings that the country had during the Apollo days. The two boosters landing nearly simultaneously almost seemed like something out of a science fiction movie. My youngest son and I spent quite a bit of time last night discussing SpaceX and their plans for Mars. I sure hope Musk can pull it off.

mark

The question of what the smallest orbital launcher could be is one that I've looked at for a few years now.

One problem is that I'm not sure that there's a definitive answer unless the question is constrained appropriately. What is theoretically possible could be different than what is practically possible. Practical limiting issues are largely associated with the practicality of developing small upper stages.

Without air resistance, I don't believe that there is a lower theoretical limit other than the performance of the rocket stages (e.g. total delta V). John C Whitehead did a paper on this:

How Small Can a Launch Vehicle Be?

John C. Whitehead

http://www.redyns.com/Reference/MinLaunchVehicle.pdf

And he points out that the trajectory itself is significant in answering that question.

Ignoring the practicality issues, the issue then becomes one of "what is the minimum integrated air drag that can be encountered over a shape's flight during ascent." Having a long, skinny rocket will reduce this drag versus a short, squat rocket. So, I think that the question must be constrained to an established practical limit on the length of the rocket. A good upper limit on practical length to diameter ratios is about 20:1 (Length:Diameter) but it could be more, as well. The Length:Diameter ratio is also known as the "fineness ratio." So, the question becomes "what is the minimum drag that could be encountered by a 20:1 L:D ratio shape integrated over its complete ascent to orbit?" Another presumption/constraint is that it is from sea-level to a "reasonable" low orbit (say 125 statute miles altitude). Alternatively, the answer might be parametric on the fineness ratio.

But, it all comes down to what is "practical." What is practical for me may not be practical for you (available dollars and facilities and infrastructure establish the limits of practicality). If we had a budget of billions the answer is different than if we only have a budget of hundreds of thousands.

Personally, I think that the answer is in the range of a 3 stage rocket with about 100 kg total take-off weight. But that rocket is not practical to build (the upper stages are practically too small to build). I personally think that the smallest practical rocket is about 600 kg.