[rst]

The video actually shows two stages and the Dragon capsule, which is payload. As to the use of staging, there are several reasons:

1) During the late stages of the boost, the one second stage engine is pushing only its single engine, fuel and tankage. You're no longer dragging around the nine engines of the first stage and their tanks. That weight saving means you get a lot more delta-V for each unit of expended fuel.

2) The engines themselves are also different. Rocket nozzles designed for optimal performance at sea level aren't optimal for high-altitude or vacuum conditions; those optimal for vacuum won't work at sea level (their exit pressure is so low that the exhaust has trouble pushing air out of the way). And compromise designs aren't optimal in either environment.

3) In the proposed SpaceX reuse architecture, they don't need to protect that long, thin first-stage tank from re-entry at orbital velocity. It's not clear how they could.

[lutze]

Good answer, thanks.

I've been playing too much Kerbal Space Program, I assumed the first stage had already reached orbital velocity.

[mikeash]

KSP is great fun and extremely educational, but it makes things way easier than they are in real life, presumably for the sake of fun.

One way this is done is by making Kerbin a lot smaller than Earth. Specifically, over ten times smaller. This reduces the speed needed for low Kerbin orbit to around 2000m/s, while low Earth orbit needs around 8000m/s.

A factor of four in speed probably already sounds bad, but it's much worse than one might naively expect. The amount of fuel needed to accelerate a given payload to a particular speed grows exponentially with the target speed. A typical rocket engine exhaust velocity, both in KSP and real life, might be 4000m/s. When the target velocity is half the exhaust velocity, as is the roughly the case with Kerbin, then you need about 40% of your rocket's mass to be fuel. In other words, you can orbit about 60% of your total mass. When the target velocity is double the exhaust velocity, as is roughly the case with Earth, you need 86% of the initial mass to be fuel, so you can only orbit about 14% of the rocket.

In other words, if you're putting 1000kg into orbit, then in KSP you need about 700kg of fuel, while on Earth you need over 6000kg of fuel. For a single stage rocket, that 1000kg that you're putting into orbit includes fuel tanks and engines. You need much bigger engines and fuel tanks to lift 7000kg than you do to lift 1700kg, so a lot of that 1000kg you get into orbit is going to be empty fuel tanks and spent engines, not actually useful stuff.

Staging lets you work around this problem by letting you reduce the amount of useless junk you put into orbit. By dropping large amounts of empty fuel tank and spent engine early on, you no longer have to lift it all the way up, and you have more orbited mass left over for actually useful widgets.

A single stage that goes from ground to orbit isn't too hard in KSP. On Earth, it's right at the limits of technology. Nobody has operated a rocket as a single stage to orbit, but a couple of pieces of larger rockets are theoretically capable of reaching orbit from the ground on their own if flown by themselves. It's possible, but the amount of useful payload that such a thing can put into orbit is so small that it's not cost effective.