How does the economics of orbital refueling vs bigger rocket work?

SpaceX plans to refuel Starship in orbit for Moon and Mars missions. According to some other questions here, it seems like they would need 6 tanker Starships to send 1 Starship to Mars.

At a glance, a whole SIX tankers to get only 1 to Mars sounds huge. They need to launch 7 full stack Starships with Super Heavy boosters. Use all that fuel and weight from Super Heavy boosters to escape earth 7 times. To get just one Starship to Mars.

One proposed alternative I keep hearing about would be to use an even bigger rocket, so you don't have to refuel. For example, you could have side boosters. The counter argument I hear against this is that Starship is already too big, adding even more boosters would mean it would need way too much fuel for just one launch.

So yes, it would need a lot of fuel too launch a full fueled up Starship with additional boosters. I understand that.

So my question is: is that extra fuel required to launch a fueled up second stage + more boosters really more than all the fuel required for SEVEN full stack Starship launches?

How can we calculate that? How do the economics work out?

Or maybe the whole thing is actually not about the fuel economics at all? And they're planning Orbital refueling more because it's probably an easier engineering challenge than figuring out how to strap even more boosters to what is already the biggest rocket planned? So they're willing to pay extra fuel cost and launch time as a trade off, as something they have higher confidence they can actually pull off?

• How about getting more isp already? That's the only way you keep from just brute-forcing things even further. – ikrase Mar 29 at 6:51

Starship carries about 1200 tons of propellant. If we assume that each of the tankers and the mission ship contributes an equal amount of the total propellant at Earth departure, the tankers are contributing about 1020 tons.

For most orbital launchers, there's a ratio of about 20:1 from liftoff mass to mass in low Earth orbit, though it varies quite a bit by the launcher design. Almost all the liftoff mass is fuel.

To get a fully fueled Starship into orbit on a single launch, therefore, you'd need around 20,000 additional tons of launcher -- not just some strapped-on boosters as an afterthought, but the equivalent of another 4 Starship+Superheavy stacks, at least -- probably more if the big booster needs to be recoverable.

So our options are to make one rocket 5 times as big as Starship+Superheavy, or seven SS+SH. As you note, this is already the biggest rocket ever to reach the bent-metal stage of development. The "Megaheavy" you'd need to make this work in a single launch would need a vastly larger factory to construct the tanks in, vastly larger assembly building, vastly larger launch pad, and so on. It would not surprise me to find that if you run the numbers, 7 SS+SH could cost much less than the Megaheavy.

In your question, you refer to fuel economics and fuel costs. Bear in mind that the cost of the fuel itself is a relatively small part of total launch cost (about US\$1.4M for a full-up Starship+Superheavy launch). Most costs (fuel, engines) scale close to linearly with mass, while some others scale sub-linearly (electronics, personnel management, paperwork). But a few, like finding a place to build and launch a rocket that size, increase faster than linearly with mass. • Musk gives an estimate of <\$500k propellant costs here: twitter.com/elonmusk/status/1258580078218412033. Apart from that, a rocket 5x as large as Starship using the same technology would have a payload ~5x as large, which falls quite a bit short of lifting a fully-fueled Starship. – Christopher James Huff Mar 29 at 2:45
• Musk gives a lot of interesting estimates; the only mass-specific price I could find for methane (\$1.35/kg) was from 2016. – Russell Borogove Mar 29 at 4:58
• My proposed Megaheavy wouldn't be simply a scaled SS/SH. There's no scaled-up Megastarship that dispenses the Mars-mission Starship and then lands. The payload fraction is thus very different. – Russell Borogove Mar 29 at 5:01
• Does it somehow manage reuse while doing this? Because that'll impact the economics just a tiny bit... – Christopher James Huff Mar 29 at 12:50
• Yeah, with full reusability you might well approach 7x mass. I don't think you can quite make it at 25000 tons all-up with similar mass fractions to SS+SH. I'll edit to clarify that. – Russell Borogove Mar 29 at 19:58