An Orbital Vehicle Part 1

What does it take to build an orbital vehicle?
My interest is in something really small say a nano sat launcher. This is going to require more performance than a larger rocket as air drag has so much more effect. I'll start with John Whiteheads paper. For a LOX Hydrocarbon stage to get to a 200Km orbit he says we need ~9500 m/sec Delta V and for a 1T vehicle. This paper claims this was a simple analysis, and I always like to cross check. From the Falcon 1 Users guide table 2-1 we get the following:

2nd stage:

1200lb empty

8900 lb propellant

400kg (880lb) payload

317s ISP

Using the rocket equation I get 5173 m/sec DV

1st stage:

3000 lb empty

47380 propellant

10980 lb Payload(The 2nd stage)

300 s ISP

Using the rocket equation I get 4353 m/sec DV

Total DV 9526 m/sec

Extrapolating in the "How Small" paper we get about 9250 for a Falcon 1 sized vehicle. So I have a source to give me some target numbers and have independently verified that the numbers are not wildly off. So we need to design a vehicle with 9700 m/sec of Dv to go orbital.

The 180 sec LLC vehicles needed 1765m/sec DV. So orbit is a whole bunch harder. We could use the LLC L1 level of technology and stage 5 times this would weight 750K lbs. Clearly we need to do better. All but the first state will run in vacuum, they don't need to throttle, we don't need landing gear, so we should be able to do a lot better. My initial spread sheet says its quite possible with a three stage H2O2/Hydrocarbon vehicle. To do it in 2 stages would require developing a lightweight pump or making the vehicle really big. I'm going to refine my inital guess and publish it in the next week or so.