A tank's weight is proportional to volume, not surface area, assuming equal pressure and material strength.
The weight of a full tank, yes.
The weight of an empty tank, no. An empty tank is mostly a shell, and the size of that shell corresponds to area.
Also, you often can't just simply stretch tanks - you need to increase thrust. Otherwise your payload drops because of lower T/W and more gravity losses in early flight.
I am assuming that Elon Musk's 5-10% estimate takes things like this into account.
Incidentally "early flight" in this case is very early. At the ground, oxygen levels are a bit over 20%. But as you go up, oxygen drops off faster than nitrogen, so oxygen intake falls off slower than drag. At some point you'll gain nothing. I do not know what that point is, but the oxygen/nitrogen level is part of why it is most efficient for commercial airlines to fly at around 9 km high. So it is really just a few km that you get a potential benefit. But your top speed at that moment is a pretty small fraction of what you need to get to orbit.
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A tank's weight is proportional to volume, not surface area, assuming equal pressure and material strength.
The weight of a full tank, yes.
The weight of an empty tank, no. An empty tank is mostly a shell, and the size of that shell corresponds to area.
Also, you often can't just simply stretch tanks - you need to increase thrust. Otherwise your payload drops because of lower T/W and more gravity losses in early flight.
I am assuming that Elon Musk's 5-10% estimate takes things like this into account.
Incidentally "early flight" in this case is very early. At the ground, oxygen levels are a bit over 20%. But as you go up, oxygen drops off faster than nitrogen, so oxygen intake falls off slower than drag. At some point you'll gain nothing. I do not know what that point is, but the oxygen/nitrogen level is part of why it is most efficient for commercial airlines to fly at around 9 km high. So it is really just a few km that you get a potential benefit. But your top speed at that moment is a pretty small fraction of what you need to get to orbit.
Nope, the shell. In a bigger tank (similar material and pressure) the shell has to be thicker. It's mathematically trivial.