[PSUBS-MAILIST] K3000 spherical shell calculations

Wed Apr 16 11:12:32 EDT 2014

Hi  Les, 
The  basic formula for the volume of a sphere is .  Don't accidentally  
plug in the diameter instead of the radius (I've done that).  To simplify the 
formula, convert the 4/3  to a decimal carried to as many places as you wish 
for accuracy:   1.333333.  So it now reads V=1.3333  π r3.  Since π = 
3.14159 (rounded), you can go ahead and multiply  it by your 1.333333 to get 
4.1888.  Your simplified formula now reads V = 4.1888 x  r3  or V = 4.1888 x r x 
r x  r.  You can use that simplified formula for  calculating the volume of 
any sphere by plugging in the r3.  The 4.1888 is a  constant. 
In  your case since the diameter of the sphere is 2 meters, your radius is 
1 meter  and the volume of your sphere is 4.1888 cubic meters.  Having the 
simplified formula saves a  lot number crunching when you are calculating 
different sizes.  If you can set up a spreadsheet  containing that formula it 
will be even easier.  You can also use that formula to  calculate the volume 
of a hemispherical tank head on a cylinder by dividing it  by 2. 
To  calculate the volume of a cylinder, first calculate the area of a 
circle of that  radius and multiply it by the length.  A  = π r2 .  For your 
radius of 0.6 meters, A = 1.13  m2 or 4.524 m3 for a 4 meter long cylinder.   
Add a hemispherical tank head on the other  end:  V = 4.1888 x  .63 and you 
get a volume of  .905 m3. 
Add  the three figures together: 
Sphere         4.189 
Cylinder       4.524 
Head            0.905 
9.618 m3 Total volume 
As  you can see, these figures pretty well match up with Sean’s.  Your sub 
would have to weigh at least  9858 kg (21,688 lb) in air in  order to 
submerge in sea water.  Adding external ballast tanks will not reduce that figure. 
 Adding internal ballast tanks will  reduce it by the weight of the water 
in those internal  tanks. 
Don’t  worry about dumb questions.  I’ve  had a few.  If anything I’ve 
written  above is inaccurate, someone will correct it for the benefit of all.  
I wanted to keep it simple instead of  adding too much detail.  That can be  
done later. 
Best  regards, 
Jim  T.

In a message dated 4/16/2014 12:58:11 A.M. Central Daylight Time,  
personal_submersibles at psubs.org writes:

Les, the total mass of the trimmed-out craft will  be exactly the 
displacement volume of your proposed craft multiplied by the  density of seawater, if 
you expect to be neutrally buoyant.  Back of  envelope calcs:  a 2m sphere 
is 4.189 m^3, a cylinder 1.2m OD x 4m is  4.524 m^3, for a total of 8.713 
m^3. Multiplying by 1025 kg/m^3 (seawater  density) gives 8930.825 kg.  
Subtract some for the common volume, add  some for superstructure, conning tower 
etc., but that's the ballpark.  Or  are your worried about the dry weight of 
the steel used in  construction?

Sean

On 2014-04-15 23:25, Personal  Submersibles General Discussion wrote:

Hello everybody ,anybody, Les here ,  
Attatched myself to this email for convenience  (similar subject) been away 
from psubs for quite some time wanting to start  again.
Now it might sound dumb, but I tried to follow  the calc sheet for material 
and depth etc with ring stiffeners but  ufortunately had a few problems, 
perhaps a sample calc attached to it would  assist me and maybe others on how 
to use it correctly? 
In between time I do need to get a rough  indication of the thickness of 
steel  and  approx size  of  ring stiffener size and quantity, to roughly  
calculate the weight of what I wish to build, to see if what I  want to do is 
feasible or not...WEIGHT IS CRITICAL for my project  
Can anyone help me please my reqirements are;  
A Sphere 2 meters diameter
A Cylinder attached to that 1.2m diameter x  4meters long
 ( I understand there will be a flaring  attatchment to the sphere, however 
at this point for the exercise, just to  calc the min weight that would be 
possible on these two items would be an  indicator for me andd give me a 
mental appreciation of my limitations  )
The desired depth is 300m, ( 984ft )  ( 452 psi ) or I could settle for 250 
meters( 820ft ) ( 379 psi )  both maximum dive depth not crush depth.
Sorry to be  pain but can any-one help me  
Thank you 
Les

P.S. In for a penny in for a pound, guess I  will make myself look 
completely dumb ....just as an indication, with  something like the above how would 
I calculate the   
 volume hence the size required for soft tanks for maximum submergance  

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