Exactly why does Starship need to be this big for interplanetary travel?

Question

As discussed in several answers to Isn't Starship way too big? Starship's unusual size is due to it being intended for missions to the Red Planet. But why?

Even a smaller ship could satisfy the delta-V for a crewed interplanetary mission.

Surely a ship need not carry 100 people to prevent psychological problems. Surely, a more modest number such as 10 would satisfy.

A larger fleet of smaller ships could carry the same payload as one large ship

Pros:

• Economies of scale drives production costs down.
• Safety due to multiplied experience over several vessels and flights.
• Reduced development cost and risk.

Cons:

• Not everything scales. For example, regardless of size, each individual ship needs a fixed amount of avionics, at least one commander, etc.
• Some large items of cargo may not be carried.

Answer 1

A lot of launch costs are independent of rocket size. It's no cheaper to clear the flight path for a smaller rocket, for example. It also takes a lot longer to do 10 launches instead of one large launch, and spaceflight is full of cases where you have limited launch opportunities. A larger vehicle will have higher throughput and lower costs per kg.

Smaller vehicles are harder to reuse. SpaceX looked at reusing the second stage of the Falcon 9, but the payload penalty would have been severe. Square-cube scaling means things like TPS scale roughly with the vehicle's surface area, not its mass, and gauge issues mean that many parts of a smaller vehicle are not as lightweight as would be optimal, because they'd be too small and fragile. Parts of Starship's skin will only be 3 mm thick. Scale it down to Falcon 9's size and the skin will only be about 1 mm thick. This would be difficult to weld and easy to damage...even a small scratch could greatly weaken it...and you'd probably have to pressurize the structure to support itself and everything attached to it. Similar issues also affect ability to efficiently carry many cargos.

Finally, Starship is not meant to carry 100 people to the moon or Mars in its initial missions. It will carry a much smaller number of people, along with plenty of supplies and equipment. The large size of the vehicle means a huge mass budget for additional supplies, redundant airlocks and elevators, a dedicated medical facility, and so on. A minimal-mass alternative would necessarily be much less well-equipped and able to handle unexpected issues.

Answer 2

Why not both?

You've correctly identified that there are two economies of scale - the first being in production (the more we produce, the cheaper it gets) and the second being payload per flight (the more we carry, the cheaper it is).

The problem is you think starship is attempting to do the second, at the cost of the first. This is not correct. Starship is doing both - it's intended to carry huge amounts of cargo basically anywhere AND do so at scale with many units being produced.

Building 100 Starships/year gets to 1000 in 10 years or 100 megatons/year or maybe around 100k people per Earth-Mars orbital sync

https://twitter.com/elonmusk/status/1217990326867988480 (Thanks @Robyn for the source!)

I like to think of it like the 747 - big, ambitious, and yet an everyday workhorse.

Answer 3

When sending something to Mars, it seems space agencies wait until Mars is about to reach the closest distance to Earth.

from: https://en.wikipedia.org/wiki/Launch_window

Sending one mission instead of dozens would open up additional launch sites as well since the preferred launch window is limited.

Answer 4

Going to Mars is going to need a lot of cargo.

Elon's plan is to send 2 starships of cargo to Mars before any crewed mission. (He's been uncharacteristically consistent on this, given how much he usually changes his mind.) Even for Elon (let alone NASA) this is a minimum safety requirement. I'd want to see the propellant factory up and running and at least one of those starships being refueled for the return flight before I would consider sending humans there.

Starship requires 1200 tonnes of propellant. Given 2 years between launch windows and assuming the Sun shines half the time on Mars, that means generating 38 grams per second of propellant during daylight. That may not sound much but requires about 600kW of electrical power. A solar photovoltaic array of that size would be 6000m2 on Earth (more on Mars) and may fill up all of the 2 starships itself. You'll say that with a smaller ship you'd need less solar cells. But at the scale of the proposed starship a mini nuclear reactor (similar to those found on nuclear submarines) becomes a viable option (though one you'll never hear Elon talk about at the moment.)

Also, what are people going to do when they get to Mars? I would guess the first crew will be around 10 very brave people, not 100 as the risk is too high. But if they go, you can bet there will be plans for them to be gainfully employed when they get there. Doing all kinds of exploration and experiments, as well as building habitats for the next group of Martian explorers. Several hundred tonnes of cargo to keep a crew of 10 occupied (and happy) for what will necessarily be a mission of several years doesn't seem too much at all.

2 starships does not mean 2 launches

The whole Starship to Mars concept is based on refuelling in low earth orbit. It will take around 6 to 8 launches per starship to fully fuel the first 2 cargo ships. So you're looking at a campaign of 12 to 16 launches just to send the 2 advance starships full of cargo. This would be followed 2 years layer by another campaign of 12 to 16 launches to send 2 more starships with a crew (as I said above, probably just 10 people plus a load of cargo.) All in all that's 24 to 32 launches to make the most of a 10 person mission.

Starship is not that big compared to its competition

While Elon's goal is to go to Mars, the way of making money to get there is to use Starship as a workhorse provider for Earth orbit missions. The original plan for a 12 metre diameter rocket was, in my opinion, excessive. But the Starship currently being developed has very similar capacity to LEO to the USA's SLS, China's Long March 9 and Russia's Yenisei so it's clear that others believe a rocket of this size (even an expendable one) will be needed in the foreseeable future.

Answer 5

The ratio of total mass to propellant mass becomes better the larger the fuel tank is, therefore a bigger tank provides more delta-v.

(I.e. the tank has less dry mass per amount of propellant it can hold the bigger it is).

The reason for this is that the volume of a cylinder or sphere scales roughly with the square of its radius, while its surface only increases proportionally to its radius. (This is also the reason why elephants have such big ears - they need to somehow increase their body surface to cool down their huge body volume.)

Looking at the Tsiolkovsky rocket equation

we can see that the delta-v depends on the ratio of total mass m0 to fuel mass mf, so a lower dry mass gives us bigger delta-v (if we keep the efficiency of the rocket engine the same).

Lets take some numbers from https://forum.nasaspaceflight.com/index.php?topic=50049.0 to see how this scaling works. According to this forum entry, Starship has a diameter of 9 meters and uses steel that is 3.97mm thick and has a density of 7907kg/m³.

For simplicity, lets imagine the Methane tank is a simple steel cylinder without any internal support struts, anti-slosh baffles, bulkheads etc. If the Methane tank is a 16,5 meters high cylinder with 9 meter diameter, this gives a surface area of:

r = 4,5m h = 16,5m

A = 2πrh+2πr^2

A = 466,52 + 127,23 = 593,75 m²

and a volume of:

V = πr^2h

V = 1049,86 m³

The steel skin of the tank has a mass of

M = 593,75 m² x 0,00397 m x 7907 kg/m³ = 18638,28 kg

So to hold propellant in a 9 meter diameter cylinder we need 18638,28 kg / 1049,86 m³ = 17,75 kg of steel per m³ of propellant

For Starship 2 tanks with 18 meter diameter have been proposed.

r = 9 m h = 16,5 m

A = 933,05 + 508,93 = 1441,99 m²

V = 4198,74 m³

The steel skin of the 18 meter tank has a mass of

M = 1441,99 m² x 0,00397 m x 7907 kg/m³ = 45265 kg

To hold propellant in a 18 meter diameter cylinder we only need 45265 kg / 4198,74 m³ = 10,78 kg of steel per m³ of propellant

Note how the surface area of the bigger tank is not even 3x as large as that of the smaller tank, while its volume is 4x larger.