|MadSci Network: Physics|
Let's tackle this question in two parts (in rocketry jargon, I guess that would make this a two-stage question). The first part of the answer is simple, direct, and to the point: the size of an ideal rocket, given the size of the payload, is computed as follows (according to the NASA guide to Practical Rocketery, available here):
R = P/.06where R is the total mass of the rocket and P is the mass of the payload. This just says that, for an ideal rocket, the size of the payload should be 6% of the total size of the rocket. So, plugging in your requirement of a 20lb payload gives us a weight for the rocket of approximately 333lbs (although mass and weight aren't the same thing at all, they are still proportional in the usual way). A rocket this small would probably be a couple of meters tall. As far as rockets go, this is much smaller than the smallest NASA launch vehicle, the Scout, which weighs in at a hefty 46,620lbs and stands 23meters tall! You can compare this to other launch vehicles at Bryant, Oosthuizen, and Sellens' excellent site.
Okay, what about the second part? I must admit that I'm a little unclear on exactly what you're interested in... e.g., would you like to know how much extra thrust is needed to take a 20lb payload into orbit? Or would you like to know the total amount of thrust required for the rocket, fuel, and payload? Also, exactly how high an orbit did you want it to go into? So the second part of the answer really depends on what you are specifically looking for. The good news is that in order to research these specifics, you can avail yourself of the Internet since there is a TREMENDOUS amount of information available on the Net.
Two great resources are the sites linked above (be sure to explore the different areas of these sites as they have tons of information hidden in their nooks and crannies). Once you've exhausted these two sites, give Yahoo a try... maybe doing a search like "+rocket +payload" (or for specific things like the rocket equation, specific impulse, etc.). I'm sure you'll be amazed at the amount of information you will find. And if you still haven't found what you're looking for, you might want to pick up a good introductory physics book for the basics of rocket motion (e.g., pp.207-208 of Physics for Scientists and Engineers by D.C. Giancoli). Finally, if you're having a hard time wading through all that information, please feel free to drop me a line (at firstname.lastname@example.org) and I can go into it in more detail.
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