Page Index Toggle Pages: [1] 2  Send TopicPrint
Hot Topic (More than 10 Replies) diameter/weight/length formula? (Read 6681 times)
broken_arrow
Full Member
***
Offline



Posts: 202
Location: Lancaster County
Joined: Aug 12th, 2008
diameter/weight/length formula?
Dec 18th, 2013 at 10:52am
Print Post  
Hi all,
Does anyone know of a mathematical formula for the following theoretical situation....
Can you determine the length of an unknown lead bullet if you have the diameter and the weight of said bullet?
Thanks,
Dave
  

ASSRA #10186 (10-25-2021)
Every Mighty Oak Was Once A Little Nut That Held Its Ground
Back to top
 
IP Logged
 
gunlaker
Frequent Elocutionist
*****
Offline



Posts: 2271
Location: lower mainland, B.C.
Joined: Dec 13th, 2010
Re: diameter/weight/length formula?
Reply #1 - Dec 18th, 2013 at 11:16am
Print Post  
It'll depend a lot on the nose profile of the bullet. 

Chris.
  
Back to top
 
IP Logged
 
Chickenthief
Junior Member
**
Offline



Posts: 81
Location: Here
Joined: Aug 5th, 2013
Re: diameter/weight/length formula?
Reply #2 - Dec 18th, 2013 at 11:30am
Print Post  
WAG is the best without a lot more info!

Number and size of GG's
Nose shape and length
Then youre pretty much there.

But then again alloy is an issue.
Lead = 11,34gram/cc~2843,2grain/cui
Antimony = 6,7gram/cc~1680grain/cui
Tin = 7,3gram/cc~1830grain/cui

For a true wadcutter you can come pretty close:
Weight gives you volume
Diameter gives you area of a slice of bullet
And that leads you to length

Volume = radius x radius x PI x length
Length = volume /(radius squared x 3.1415)

For lead:
example 148grain .357" caliber
Volume = 148/2843,2 = 0.052 cui
Length = 0.052/(0.1875 squared x 3.1415) = 0.052/0.1 = 0.52inch
  
Back to top
 
IP Logged
 
frnkeore
Frequent Elocutionist
*****
Offline



Posts: 7268
Location: Central Point, OR 97502
Joined: Jun 16th, 2010
Re: diameter/weight/length formula?
Reply #3 - Dec 18th, 2013 at 1:35pm
Print Post  
This is a good example of the difference between two bullets of almost the same length. If the 320366 was cast of linotype and the PJ cast of 30/1, there would be even more difference in weight.

  

ASSRA Member #696, ISSA Member #339
Back to top
YIMAIM  
IP Logged
 
joeb33050
Frequent Elocutionist
*****
Offline



Posts: 2613
Location: Marathon, FL
Joined: Apr 20th, 2004
Re: diameter/weight/length formula?
Reply #4 - Dec 18th, 2013 at 3:39pm
Print Post  
Yes. GREENHILL FORMULA WORKBOOK.xls" will estimate bullet length from weight and caliber. PM me your email address and I'll send it.


broken_arrow wrote on Dec 18th, 2013 at 10:52am:
Hi all,
Does anyone know of a mathematical formula for the following theoretical situation....
Can you determine the length of an unknown lead bullet if you have the diameter and the weight of said bullet?
Thanks,
Dave

  
Back to top
 
IP Logged
 
Cat_Whisperer
Frequent Elocutionist
*****
Offline


No 1, 9.3x74R

Posts: 3877
Location: Mountains of Virginia
Joined: Apr 17th, 2004
Re: diameter/weight/length formula?
Reply #5 - Dec 18th, 2013 at 4:31pm
Print Post  
For just an estimate, probably not a bad idea.

Greenhill's formula was for a given bullet shape that likely would be right-much heavier than other bullets - due to nose shape and grooves - but that's a great place to start.

  

Cat Whisperer (trk)
Chief of Smoke
Pulaski Coehorn Works and Skunk Works
Drafted May 1970, Retired Maj. U.S.Army
assra #9885
Back to top
WWW  
IP Logged
 
SSShooter
Frequent Elocutionist
*****
Offline



Posts: 2917
Location: Southern NJ
Joined: Aug 1st, 2010
Re: diameter/weight/length formula?
Reply #6 - Dec 18th, 2013 at 9:51pm
Print Post  
gunlaker wrote on Dec 18th, 2013 at 11:16am:
It'll depend a lot on the nose profile of the bullet. 
Chris.

Indeed. My 38cal Brooks mould casts a 340gr 'Money' bullet and the PJ mould casts a 368gr bullet. Both are 1.423" in length. 
  

Glenn - 2x CPA 44 1/2 w/22LR (Shilen ratchet-rifled & Bartlein 5R rifled), 38-40RH & 38-55WCF (Bartlein 5R rifled) & 40-65WCF (GrnMtn 'X') barrels
Back to top
GTalk  
IP Logged
 
joeb33050
Frequent Elocutionist
*****
Offline



Posts: 2613
Location: Marathon, FL
Joined: Apr 20th, 2004
Re: diameter/weight/length formula?
Reply #7 - Dec 19th, 2013 at 1:30am
Print Post  
Or, the same without Excel:

Bullet length ~ bullet weight/Factor

Bullet weight ~ bullet length * Factor

DIAMETER      FACTOR
0.257      122
0.286      151
0.308      175
0.323      192
0.357      235
0.375      259
0.410      310
0.429      339
0.457      385

The precise relationship depends on bullet shape, number and volume of grease grooves and alloy composition. Close-to-exact relationships can be found using other, more involved arithmetic that is seldom worth the effort.. 
  
Back to top
 
IP Logged
 
joeb33050
Frequent Elocutionist
*****
Offline



Posts: 2613
Location: Marathon, FL
Joined: Apr 20th, 2004
Re: diameter/weight/length formula?
Reply #8 - Dec 19th, 2013 at 8:16am
Print Post  
I doubt both weights-both look too low, and the difference doesn't seem correct.
Does anyone have similar bullets to check weight?



frnkeore wrote on Dec 18th, 2013 at 1:35pm:
This is a good example of the difference between two bullets of almost the same length. If the 320366 was cast of linotype and the PJ cast of 30/1, there would be even more difference in weight.


  
Back to top
 
IP Logged
 
broken_arrow
Full Member
***
Offline



Posts: 202
Location: Lancaster County
Joined: Aug 12th, 2008
Re: diameter/weight/length formula?
Reply #9 - Dec 19th, 2013 at 8:53am
Print Post  
Thanks guys,
Your responses have me a lot closer than my WAG were getting me.
And the simple formula that Joe posted will get me close enough for starters.
Thanks again,
Dave
  

ASSRA #10186 (10-25-2021)
Every Mighty Oak Was Once A Little Nut That Held Its Ground
Back to top
 
IP Logged
 
frnkeore
Frequent Elocutionist
*****
Offline



Posts: 7268
Location: Central Point, OR 97502
Joined: Jun 16th, 2010
Re: diameter/weight/length formula?
Reply #10 - Dec 19th, 2013 at 1:02pm
Print Post  
joeb33050 wrote on Dec 19th, 2013 at 8:16am:
I doubt both weights-both look too low, and the difference doesn't seem correct.
Does anyone have similar bullets to check weight?



frnkeore wrote on Dec 18th, 2013 at 1:35pm:
This is a good example of the difference between two bullets of almost the same length. If the 320366 was cast of linotype and the PJ cast of 30/1, there would be even more difference in weight.




Joe, I also own the bullet molds and the bullets.

Frank
  

ASSRA Member #696, ISSA Member #339
Back to top
YIMAIM  
IP Logged
 
joeb33050
Frequent Elocutionist
*****
Offline



Posts: 2613
Location: Marathon, FL
Joined: Apr 20th, 2004
Re: diameter/weight/length formula?
Reply #11 - Dec 19th, 2013 at 2:26pm
Print Post  
frnkeore wrote on Dec 19th, 2013 at 1:02pm:
joeb33050 wrote on Dec 19th, 2013 at 8:16am:
I doubt both weights-both look too low, and the difference doesn't seem correct.
Does anyone have similar bullets to check weight?



frnkeore wrote on Dec 18th, 2013 at 1:35pm:
This is a good example of the difference between two bullets of almost the same length. If the 320366 was cast of linotype and the PJ cast of 30/1, there would be even more difference in weight.




Joe, I also own the bullet molds and the bullets.

Frank


Frank;
Would you tell us about sample weights of the two bullets?

  
Back to top
 
IP Logged
 
gunlaker
Frequent Elocutionist
*****
Offline



Posts: 2271
Location: lower mainland, B.C.
Joined: Dec 13th, 2010
Re: diameter/weight/length formula?
Reply #12 - Dec 19th, 2013 at 7:03pm
Print Post  
I haven't looked at how those factors were generated, but obviously with a reference bullet of. Particular shape.  The "money" bullets are a relatively slender tangential ogive with a small hemispherical tip.  I imagine that they'll always come out a bit longer than the formula predicts.  But that's ok, it's still likely useful.  The only way to get a really accurate answer is to calculate the volume by integration.

For reference, I just weighed a Buffalo Arms 324gr "money bullet" in 20:1 alloy.  It is 1.322" long and the formula predicts 1.251".  Still probably good enough for whatever you want it for Smiley

Chris.
  
Back to top
 
IP Logged
 
Cat_Whisperer
Frequent Elocutionist
*****
Offline


No 1, 9.3x74R

Posts: 3877
Location: Mountains of Virginia
Joined: Apr 17th, 2004
Re: diameter/weight/length formula?
Reply #13 - Dec 19th, 2013 at 7:15pm
Print Post  
gunlaker wrote on Dec 19th, 2013 at 7:03pm:
I haven't looked at how those factors were generated, but obviously with a reference bullet of. Particular shape.  The "money" bullets are a relatively slender tangential ogive with a small hemispherical tip.  I imagine that they'll always come out a bit longer than the formula predicts.  But that's ok, it's still likely useful. 
For reference, I just weighed a Buffalo Arms 324gr "money bullet" in 20:1 alloy.  It is 1.322" long and the formula predicts 1.251".  Still The only way to get a really accurate answer is to calculate the volume by integration.
probably good enough for whatever you want it for Smiley

Chris.



Just a few keystrokes when drawn in 3d cad!
  

Cat Whisperer (trk)
Chief of Smoke
Pulaski Coehorn Works and Skunk Works
Drafted May 1970, Retired Maj. U.S.Army
assra #9885
Back to top
WWW  
IP Logged
 
gunlaker
Frequent Elocutionist
*****
Offline



Posts: 2271
Location: lower mainland, B.C.
Joined: Dec 13th, 2010
Re: diameter/weight/length formula?
Reply #14 - Dec 19th, 2013 at 7:57pm
Print Post  
Cat_Whisperer wrote on Dec 19th, 2013 at 7:15pm:

Just a few keystrokes when drawn in 3d cad!


Indeed!
  
Back to top
 
IP Logged
 
Page Index Toggle Pages: [1] 2 
Send TopicPrint