Re:Musk explains why SpaceX prefers clusters of small engines
by Robotbeat on Thursday February 08, 2018 @03:15PM
(#16335214)
Pressure vessel equation means structural efficiency is invariant based on volume but we're talking (to zeroth order) area, thus smaller pressure vessels (nozzles, chambers, etc) are more structurally efficient (at the large size limit...).
To expound: Mass ∝ Volume, Volume ∝ length^3.
Thrust ∝ cross sectional area, area ∝ length^2.
Thus, Mass ∝ Thrust^(3/2), or:
Thrust to weight ratio ∝ sqrt(thrust) for a single engine.
> The point being that, if your nozzles are 9 times smaller, they're only 9 times lighter.
This is incorrect, for the reason I shared earlier. Thrust is proportional to cross section, not volume. Thus scaling laws (at some point) favor smaller engines. (Note that this is assuming we're already big enough that we have full combustion and are not experiencing minimum gauge issues, etc.)
My knowledge doesn't come from being a SpaceX enthusiast. In addition to having a physics degree, years ago I was part of a very early-stage startup (never got off the ground) at one point looking at launch vehicles, and so I read Sutton's Rocket Propulsion Elements (a very nice introductory text, I highly recommend) among others and did a bunch of scaling analysis. (SpaceX would've been a competitor.)
To expound: Mass ∝ Volume, Volume ∝ length^3.
Thrust ∝ cross sectional area, area ∝ length^2.
Thus, Mass ∝ Thrust^(3/2), or:
Thrust to weight ratio ∝ sqrt(thrust) for a single engine.
> The point being that, if your nozzles are 9 times smaller, they're only 9 times lighter.
This is incorrect, for the reason I shared earlier. Thrust is proportional to cross section, not volume. Thus scaling laws (at some point) favor smaller engines. (Note that this is assuming we're already big enough that we have full combustion and are not experiencing minimum gauge issues, etc.)
My knowledge doesn't come from being a SpaceX enthusiast. In addition to having a physics degree, years ago I was part of a very early-stage startup (never got off the ground) at one point looking at launch vehicles, and so I read Sutton's Rocket Propulsion Elements (a very nice introductory text, I highly recommend) among others and did a bunch of scaling analysis. (SpaceX would've been a competitor.)