Troy:
I got all that but your comments led me to realize my “error”: I kept the
L/D constant whereas this storytelling clearly requires that length remain
constant.
If, consistent with actual tankage, the length increases as a function of
increasing diameter, then the volumetric rule remains correct.
Bill
On Wed, 29 May 2019 at 18:21, Troy Prideaux <troy@xxxxxxxxxxxxxxxxxxxxx>
wrote:
Oops
and the volume (not mass) of the wall is its cross-sectional area * length.
Multiply that by density to gather mass.
Troy
*From:* arocket-bounce@xxxxxxxxxxxxx [mailto:arocket-bounce@xxxxxxxxxxxxx
<arocket-bounce@xxxxxxxxxxxxx>] *On Behalf Of *William Claybaugh
*Sent:* Thursday, 30 May 2019 9:00 AM
*To:* arocket@xxxxxxxxxxxxx
*Subject:* [AR] Volumetric ratio
It has previously been asserted on this list that while the surface to
volume ratio of a rocket declines as diameter increases (by the square); it
is not the case that rockets become relatively lighter as diameter
increases because the wall thickness required to hold a constant pressure
increases as diameter increases; or at least that is what I have previously
understood.
This has gnawed at my ankles for some time, so, because my shop is down
today to bringing in more power, I sat down this afternoon and gave this
some thought.
Numerically, it does not appear to be so: the mass to diameter ratio
increases by a factor of four with every doubling of the diameter.
I assume that the wall thickness doubles with a doubling of diameter to
hold a constant pressure and that wall density is constant. I am
accordingly led to conclude that tank mass decreases by the square (not
linearly) as diameter increases.
Have I misunderstood the previous claims about there being no “volumetric
effect” with scale?
Bill
