3 ms·

Is there a theoretical lower limit to the size of an orbit-capable launch vehicle if the payload size keeps shrinking?

Sanzig 5y ago
On earth, about 30 feet in length due to the atmosphere, although I will admit I don't have a firm intuition for why this is the case. [1] https://www.airspacemag.com/space/the-one-pound-problem-718812/ https://www.airspacemag.com/space/the-one-pound-problem-7188...
- fnord77 5y ago
  > 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
  - jjk166 5y ago
    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 https://en.wikipedia.org/wiki/Impact_depth
- Gravityloss 5y ago
  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.
jjk166 5y ago
There isn't really a theoretical minimum size, but with the best chemical propulsion possible you're going to have an initial to final mass ratio of about 5. Now that final mass needs to include the structure of the vehicle, so you can cheat a little bit with staging but you can't make it go to zero. In practice, the smallest orbital launch vehicle ever launched required 2600 kg to launch a 4 kg payload. Turns out that the smaller a rocket is, the less mass efficient it gets.

On earth, about 30 feet in length due to the atmosphere, although I will admit I don't have a firm intuition for why this is the case. [1] https://www.airspacemag.com/space/the-one-pound-problem-718812/ https://www.airspacemag.com/space/the-one-pound-problem-7188...

fnord77 5y ago
> 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
- jjk166 5y ago
  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 https://en.wikipedia.org/wiki/Impact_depth
Gravityloss 5y ago
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.

jjk166 5y ago

There isn't really a theoretical minimum size, but with the best chemical propulsion possible you're going to have an initial to final mass ratio of about 5. Now that final mass needs to include the structure of the vehicle, so you can cheat a little bit with staging but you can't make it go to zero. In practice, the smallest orbital launch vehicle ever launched required 2600 kg to launch a 4 kg payload. Turns out that the smaller a rocket is, the less mass efficient it gets.