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

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.

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J. Whitehead treats the vehicle as an integrated from ground to orbit, as do most. For Microlaunchers I prefer to separate the firt stage from the vacuum operating upper stages. The staging would be at 60 Km with a vertical velocity of 900 m/s and horizontal of 1000 m/s including Earth rotation.

The upper stages become easier to plan, as the gravity and aerodynamic losses can be very much smaller, more redictable--not much more than orbit velocity minus 1000 m/s

The separately designed first stage (TAV) will be about 90% of the gross liftoff weight, and can be tested separately.

To do it in 2 stages would require developing a lightweight pump or making the vehicle really big.Are you thinking of doing it all pressure-fed then? That would be an interesting data point. Beal wanted to do that. HC/peroxide could be very well suited for pressure-fed first stages. High density would reduce the mass penalty and peroxide being noncryogenic should help with using composites.

I am the annonymous 2 posts ago--password problem. A 3 stage launcher can be all pressure fed, with the chamber pressure of stages 1-3 10,5,2 atmospheres respectively.

For one Cubesat,a GLOW of 100-200 Kg appears to be enough.

You need to know some other stuff if you want to do the math.

* Thrust and weight of the engines for each stage.

* Practical numbers for the propellant tank scaling.

The first lets you calculate the propellant-mass dependent term. The second lets you calculate the gross-mass dependent term. With that you can apply Kirk Sorensen's stage estimate equations.

http://selenianboondocks.com/2010/02/pf-expressions-example/

And there's more posts in that series that help you come up with the values for lambda/phi.

Judging from Blue Origin vehicle pictures released so far, is it possible they are trying a three stage vehicle with disposable second stage and vertical landing recoverable first (booster) and third (crew) stages?

The diagrams released by Blue Origin are for a 1 stage suborbital vehicle and do not include the capsule. Word on the street is that they are also working on orbital stuff but nobody knows (or is allowed to tell). I suppose you could consider the capsule a separate stage but in terms of performance it isn't since it doesn't have propulsion for anything other than abort.

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