What is the most number of stages, including fractional stages?

Question

Falcon 9 clearly has two stages, but the smaller two-stage Electron has a "kick-stage" so some might call that 2.5. The question Quantitative benefits of Atlas II's engine-dropping or 1.5 staging? and Would there be any advantages for a rocket with two “half stages”? deal with half-stages as well, and counting stages is even a challenge in CZ-5 plus YZ-2 put SJ-17 in GEO - third stage or separate spacecraft?

Yet there are several questions here about single stage to orbit (SSTO) and the sentiment is that this would be a good goal for a future launch vehicle. Saturn V had three stages and some have argued here that it's more than three if you count the whole mission.

Question: Why is there such a large range of stage numbers, including fractional stages?

Answer 1

There actually aren’t that many different stage counts, but the variation comes because different missions have different delta-v requirements, and different propulsion technologies yield different amounts of delta-v per stage.

The definition of “half stage” is not totally clear. It’s mostly used to refer to the Atlas and Atlas II strategy of dropping engines but not tankage; it’s also sometimes used to describe the very common use of boosters that ignite concurrently with a first stage but which have a significantly shorter burn time, and are dropped before the first stage burns out.

The size of the stage doesn’t make it a half-stage. Upper stages are always smaller than lower stages, typically at a mass ratio of around 1:4 or 1:5. If you have two stages plus a “small kick stage” you have three stages, period.

Saturn V used two stages (and a little bit of the third) to reach Earth orbit, and needed the third to go to the moon. The usual payload of the Saturn V was Apollo, which consisted of two spacecraft: the one-stage CSM and the two-stage LM. The complete Saturn-Apollo stack therefore included six stages, but Saturn V should be thought of as a three stage rocket.

“Two-half” stages and half-upper stages as proposed in recent questions don’t actually exist.

Modern liquid fueled launchers designed to send payloads to LEO or to geosynchronous transfer orbit generally have two stages. Sometimes boosters are added to the first stage; if the boosters and core both ignite at liftoff, it’s debatable whether those count as an extra stage or as part of the first stage. If the core doesn’t start at ground level ignition, the boosters are the first stage, the core second stage, as in Titan III (but the Titan III-IVs with SRBs usually referred to the boosters as 'stage zero' to avoid having to rename the Titan II's first stage).

Launchers that rely mainly on solid fuel stages, and some older liquid fueled rockets, have too low specific impulse and/or too heavy stage dry mass to reach Earth orbit using only two stages, so they have three or even four stages.

Answer 2

Yet there are several questions here about single stage to orbit (SSTO) and the sentiment is that this would be a good goal for a future launch vehicle.

The ultimate goal is to be able to reuse the entire launch vehicle, because that has the potential to be a lot cheaper than having to build a new rocket every time.

One of the ways to do that is an SSTO vehicle. There have been lots of studies for winged SSTO vehicles. If you need a wing to land the vehicle like an airplane, you can use that wing during takeoff as well.

The problem with winged SSTO is that it's at the edge of what's possible:

• with every engine type available today, you need a very light, but large structure: the payload and structural mass fractions need to be low.
• this includes a heat shield that has to be easily reusable, yet light.
• many SSTOs were designed around an engine that can use ambient air at low altitudes, then switch to working as a rocket engine at high altitudes. This is a difficult concept to get to work right.

So to get an SSTO working, you'd need to invest huge amounts of R&D, and it'd take a long time to recoup those costs even if your vehicle was as cheap as promised. That amount of money just wasn't available in the space industry at any time after the Apollo program.

Then SpaceX showed it's possible to land a rocket stage without using wings, by landing vertically using the rocket engines. This opened up a new path to reusability without resorting to SSTO.