Excluding the atmosphere, delta vee is exhaust velocity times the logarithm of the mass ratio. The mass of a pressure vessel is proportional to its volume. So if you double the propellant, also tank volume doubles and also tank mass doubles. No clear scale related terms there. Gravity also is not affected by scale, gravity losses are strictly related to mass.

But air resistance is different. It is a surface effect and thus related to scale. It's roughly proportional to the frontal area of the rocket. Hence, if you grow a rocket and keep its shape intact, the air resistance grows only as square, but the other factors like mass grow as cube. So bigger rockets have a smaller proportion of their delta vee spent on air resistance losses.

That's also why sounding rockets are so skinny. Air resistance dominates there. (They are also accelerating faster since they are rail launched and don't have active gimbal guidance, which makes it even worse)

You can think of a medium sized orbital rocket, and then if you shrink it, the only way to keep its payload to total mass rate the same is to keep the air resistance losses same related to the total mass - ie keep its original length and only shrink it sideways.

> A terrestrial rocket has to push through a plug of air equivalent to a 30-foot column of water, and physics dictates that the smallest vehicle capable of moving all that atmospheric mass without paying a penalty in momentum is about 30 feet long.

This doesn't make sense - they're talking about momentum, but then conflating that with a length rather than a mass

The momentum to length thing comes from Newton's approximation for impact depth, which basically states that the distance a high speed projectile can penetrate something is a function of its density and length. Something like an asteroid or needs a certain minimum length to make it through the atmosphere without slowing down below the speed of sound.

It has nothing to do with rockets though, as rockets are not high velocity projectiles - they are powered vehicles and most of the time they are in the atmosphere they're not even going that fast. For space launch this condition would only be relevant if you're being shot out of a massive cannon or something.

https://en.wikipedia.org/wiki/Impact_depth