Bill,
As you double the diameter of your pressure vessel, your wall thickness does
indeed need to double to accommodate the same pressure rating, but remember the
cross-sectional area of your vessel’s volume will increase by 4 and the
*cross-sectional area of your wall* will also increase by 4.
So as the dimensions (diameter & wall thickness) increase linearly, the
cross-sectional areas of such will increase by the square – because they’re
*areas* and the mass of the wall is its cross-sectional area * length.
Troy
From: arocket-bounce@xxxxxxxxxxxxx [mailto: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
