Bill, note I said “constant length” not constant L/D ratio for the last reply.
My point was (getting back to the original query) that a scaling of the
diameter of a pressure vessel will yield a mass increase *per unit length*
that’s a square of the scaling (or of the linear ratio of diameter1 to
diameter2) to maintain an equal pressure rating. Whether you scale the length
with that or half that or double that doesn’t change the fact that your wall
cross-sectional area increases to the same exponent to the cross-sectional area
of the vessel’s inner conduit thereby yielding no weight/pressure rating
benefit for doubling the diameter.
Apologies if wires were crossed.
Regards,
Troy
From: arocket-bounce@xxxxxxxxxxxxx [mailto:arocket-bounce@xxxxxxxxxxxxx] On ;
Behalf Of William Claybaugh
Sent: Thursday, 30 May 2019 12:58 PM
To: arocket@xxxxxxxxxxxxx
Subject: [AR] Re: Volumetric ratio
Troy:
Let’s try an example:
Consider two cylinders of diameter 1 and 2, respectively and w/ a L/D ratio of
5. I get a surface area of 15.7 and 62.8 respectively and volumes of 3.92 and
31.4; the resulting surface to volume ratios are 4.0 and 2.0, respectively:
the smaller cylinder has twice as much surface per unit volume.
If I assume a wall thickness of 1 and 2, respectively, and a density of 1 (for
convenience) then they “weigh” 15.7 and 125.6, a factor of eight difference.
It looks to me like doubling the diameter and the wall thickness is producing a
square / cube outcome for constant L/D.
What am I missing?
Bill
On Wed, 29 May 2019 at 19:49, Troy Prideaux <troy@xxxxxxxxxxxxxxxxxxxxx
<mailto:troy@xxxxxxxxxxxxxxxxxxxxx> > wrote:
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>
[mailto:arocket-bounce@xxxxxxxxxxxxx ;<mailto:arocket-bounce@xxxxxxxxxxxxx> ] On
Behalf Of William Claybaugh
Sent: Thursday, 30 May 2019 11:16 AM
To: arocket@xxxxxxxxxxxxx <mailto: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
