Bill,
The length shouldn’t make any difference to that particular disagreement.
Where the scaling of the length is an issue is with the cube-square law which
is more of an influence to *drag* scaling ie. if you scale your diameter up but
maintain a constant length, the vehicle’s mass & volume scale to the square,
not the cube, so there won’t be any *relative* drag reductions with scaling
diameter as opposed to scaling all 3 dimensions.
Troy
From: arocket-bounce@xxxxxxxxxxxxx [mailto:arocket-bounce@xxxxxxxxxxxxx] On ;
Behalf Of William Claybaugh
Sent: Thursday, 30 May 2019 11:16 AM
To: arocket@xxxxxxxxxxxxx
Subject: [AR] Re: Volumetric ratio
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
<mailto: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>
[mailto:arocket-bounce@xxxxxxxxxxxxx] On Behalf Of William Claybaugh
Sent: Thursday, 30 May 2019 9:00 AM
To: arocket@xxxxxxxxxxxxx <mailto: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
