The ratio of total mass to propellant mass becomes better the larger the fuel tank is

(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

So to hold propellant in a 18 meter diameter cylinder we 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.

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.

The ratio of total mass to propellant mass becomes better the larger the fuel tank is

(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 weight 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 = 2πrh+2πr^2

A = 933,05 + 508,93 = 1441,99 m²

and a volume of

V = πr^2h

V = 4198,74 m³

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

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

So to hold propellant in a 18 meter diameter cylinder we 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.

The ratio of total mass to propellant mass becomes better the larger the fuel tank is

(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

So to hold propellant in a 18 meter diameter cylinder we 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.