# How heavy can a fuel tank get before making it heavier is a liability under any circumstances?

This Question may bend the boundaries of this community a little, since it's mostly about hypothetical rockets that would never be built.

Considering a filled fuel tank has to withstand a lot of force to escape earths gravity, I wondered if there's a sweetspot where the material needed to stabilize a bigger fuel tank is too heavy to be accelerated for longer/stronger by the additional fuel it allows the tank to hold. I don't want to go into dropping empty tanks, amount of engines, aerodynamics or how you'd steer this (possibly) gigantic tower of metal.

Just imagine the tank is magical, getting smaller by burning fuel, lots of gigantic chemical engines to burn all that fancy fuel (let's not mention the others), whatever fuel you like and whatever material you like.

• Your title and final line appear to be asking different questions. Can you clarify? Nov 13, 2019 at 15:52
• To clarify why they are different, your fuel tank is rarely going to be the same material as your rocket. The fuel will be stored in tanks, internally, bolted to an external structure or mounting with MMOD or shielding around that. Nov 14, 2019 at 4:55
• To pile on as well, the material of your tank is rarely the limiting factor when it comes to tank design. It is more a question of "What is the volume limit to store this propellant at the right pressure?" "Can we avoid excessive ullage?" "What flow rate does the system require?" If we theoretically limit the case to a magical tank, we would want a tank with the lowest Surface Area to Volume Ratio (A Sphere) and can grow it to the limiting factor of where the mass of the added prop + the material mass for the surface area to contain that prop volume cancels out w/ the energy the prop gives. Nov 14, 2019 at 5:04
• You would also want seperate tanks for your fuel, oxidizer, and pressurant. Nov 14, 2019 at 5:05
• "What is the 'limit' of the best material to build a rocket with?" given how context-sensitive "best" is, and the number of different kinds of "limits", I think your question isn't very well formed. Presumably this is still related to your questions elsewhere about launching a chemical rocket from a super-earth with a 1.5G surface gravity? Nov 14, 2019 at 10:35

Sort of. Note that this answer will be incomplete and only consider $$\Delta V$$, not strength. Don't accept it, since I expect a better one will come along.

First, there is the obvious limit that we can't make fuel tanks infinitely thin and infinitely strong. Second, there is the obvious limit that we can't make a fuel tank that has no internal volume that still produces $$\Delta V$$ (that is, if it has no internal volume, it's just a solid block of material which is in theory the strongest you'll be able to get).

After some manipulation, I computed $$\frac{\Delta V}{v_e}$$ as:

$$\frac{\Delta V}{v_e} = \ln\big(1+\frac{\rho_{fuel}V_{internal}}{\rho_{tank}V_{shell}}\big)$$

and plotted it against $$V_{tank}$$. I assumed a spherical, stainless steel tank of outer radius 1m filled with kerosene. I ended up with this graph:

Now, obviously a tank isn't just fuel, but the numbers on the graph don't matter much and the shape of the graph does. We can get some insight here:

1. There is an obvious maximum $$\Delta V$$ that is obtained when the tank is infinitely thin. The inner volume cannot be larger than the outer volume. This is the "ideal" max.
2. As expected, if the tank were just a solid block, there would be no fuel and therefore no $$\Delta V$$
3. This graph does not maximize except at its endpoint. That is, it doesn't have a hump in the middle and then start going back down. This is straight from the rocket equation - the more fuel you have and the less dry mass, the faster you can get

So, in terms of the sweet spot: if you also consider material strength, there is some minimum strength, and therefore minimum amount of material, you will need. This cuts off your maximum $$\Delta V$$. You may still produce a tank that has more material than that which is strictly needed, but never less. As a result, the sweet spot is exactly the amount of material required to handle the flight. (Yes, I know I didn't entirely answer this question, that's why I recommend not accepting it. It's partial, not complete)

• thanks a lot for your time Nov 28, 2019 at 12:59