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6,195 ml Capacity 8x68 Taras with LM-102 with 102 mm overall Length and 800 mm Barrel

LM-102

Very high BC Bullet for windy long Ranges

LM-102, 55 mm long, 16 g heavy, BC1000 1,219, for 170 mm Gain twist barrel

Powder Mass [g] Density
[%]
Pressure [bar] Burn rate
[%]
V0
[m/s]
Remark
highest @ muzzle
Alliant Reloder-22 5,16 98,5 4'500 627 100,0 906
Alliant Reloder-25 5,35 103,8 4'472 607 100,0 907
Hogdon H4350 4,86 94,3 4'519 590 100,0 888
Hogdon H4831 5,20 103,3 4'332 619 100,0 894
IMR 7828 5,17 100,9 4'508 634 100,0 912
IMR 7828 SSC 5,17 97,2 4'508 634 100,0 912
Norma MRP 5,20 97,2 4'477 631 100,0 910
Norma MRP 2 5,40 104,2 4'208 650 100,0 902
PCL 517 5,60 101,3 4'548 643 100,0 919
Rottweil R905 5,14 99,2 4'509 630 100,0 903
Path sighted in at 216 m for 265 m ± 5 cm Range
Range [m] 0 50 100 150 200 250 300
Speed [m/s] 915 902 889 876 864 851 839
Path [cm] -5 +1,3 +4,6 +4,7 +1,7 -4,7 -14,5
Wind drift [cm] 0 0,1 0,5 1,3 2,5 4,1 6,0
to 1200 m
Range[m] 0 200 400 600 800 1.000 1.200
Speed [m/s] 915 864 814 761 707 655 605
Path [cm] -5 +117 +186 +196 +139 X -227
Wind drift [cm] 0 2,5 11 25 46 77 116

Throat

Here are the 8x68 Taras Dimensions in a PDF-File. It is a blown out 8x68S with 1° Body taper (full Cone angle) and 2° Throat, tailored for the LM-102. Cases may be neck turned. If so, Dimensions bust be accommodated to keep the 2° Throat at the same location with Respect to the Case, but for the LM-102 this extra Effort is not really necessary. See below, how the first two Drivebands fit in the 2° Throat:

They are dimensioned to fit with +0,01 mm Space Surface-to-Surface or 0,02 mm in Diameter. A Zero Tolerance cannot be designed, as all mechanical Parts are made with Tolerances, the LM-102 not excepted.

One Millimeter moved a 2° Cone changes 0,035 mm Diameter (above is 10(!) mm long). So to adjust for 0,02 mm Diameter either the Throat or the Bullet have to be moved 0,02/0,035 = 0,57 mm or roughly 0,6 mm. That is more than wanted, as the overall Cartridge length is fixed to 84 mm, hence the Name, so some Gap might persist. This Gap will allow to unchamber unfired Rounds, if for some Reason, the intended Shot cannot be fired. So a basic Safety requirement for Shooting ranges is met.

Aerodynamics

LM-102 950 m/s Pressure, click to enlarge

LM-102 950 m/s Pressure Iso-lines, click to enlarge

LM-102 950 m/s dynamic Pressure contour, click to enlarge

LM-102 950 m/s dynamic Pressure Iso-lines, click to enlarge

LM-102 950 m/s Velocity contour, click to enlarge

LM-102 950 m/s Velocity Iso-lines, click to enlarge

Stability


Estimated Drag, BC and Gyroscopic Stability at Standard ICAO Sea Level Conditions
 -----------------------------------------------------------------------------------
  Möller LM-102 Cal. 8.200 mm, 16.0 g
  Ballistic Coefficient Calculated for Drag Function G1
 -----------------------------------------------------------------------------------
      Velocity       Drag Coefficient       RPM and Stability      maximum Twist-
                      Factor of Form        at a Twistlength         lenght
                         and B.C.             of 20,7 Cal.          for s = 1.3
   Mach  m/s   fps    Cw      i    B.C.       RPM        s        Cal.   in.    mm
 -----------------------------------------------------------------------------------
  0,441  150   492  0,076  0,373  0,907      52941      1,11      19,1   6,2   157
  0,514  175   574  0,075  0,373  0,907      61765      1,09      19,0   6,1   156
  0,588  200   656  0,074  0,369  0,918      70588      1,07      18,8   6,1   155
  0,661  225   738  0,074  0,356  0,951      79412      1,05      18,6   6,0   152
  0,735  250   820  0,074  0,329  1,028      88235      1,00      18,2   5,9   149
  0,808  275   902  0,074  0,289  1,172      97059      0,93      17,5   5,7   144
  0,882  300   984  0,078  0,244  1,385     105882      0,81      16,3   5,3   134
  0,955  325  1066  0,104  0,254  1,331     114706      0,56      13,5   4,4   111
  1,000  340  1116  0,211  0,446  0,759     120104      0,62      14,3   4,6   117
  1,102  375  1230  0,201  0,345  0,980     132353      0,67      14,9   4,8   122
  1,175  400  1312  0,238  0,383  0,883     141176      0,76      15,9   5,1   130
  1,763  600  1969  0,203  0,329  1,028     211765      1,14      19,4   6,3   159
  2,351  800  2625  0,168  0,308  1,101     282353      1,28      20,6   6,6   169
  2,939 1000  3281  0,141  0,278  1,219     352941      1,35      21,2   6,8   173
  3,526 1200  3937  0,121  0,243  1,390     423529      1,40      21,5   7,0   177
  4,114 1400  4593  0,105  0,214  1,584     494118      1,44      21,8   7,0   179
  4,702 1600  5249  0,093  0,189  1,788     564706      1,47      22,0   7,1   181
  5,290 1800  5906  0,083  0,170  1,996     635294      1,49      22,2   7,2   182
 -----------------------------------------------------------------------------------  

Achtung! The LM-102 needs at least 900 m/s Muzzle velocity to fly stable from a 170 mm Gain twist barrel. This Note means, it will not fly stable from smaller Cartridges, yielding less Velocity, but from bigger ones. Bigger would not be better, as internal ballistic Efficiency would drop and too long Barrels would be needed.

That drag minimizing Tail introduced  Mac. C. Adams in Langley, November 1951. M. A. Ramaswamy and S. Viswanathan optimized it December 1975 in Bangalore.

One may ask,  why I design so many different shaped Projectiles. Aren't there optimal Solutions? Yes, there are, but the Conditions determine the Optimum. Different Conditions yield different Optimization shapes. This LM-102 is optimized for to deliver 900 m/s Muzzle velocity from a 8x68 Taras Cartridge out of a 80 cm Barrel. Other Projectiles exit for other Conditions. The Barrel shall have a progressive, or gain Twist with final 170 mm Twist length. This slow Twist start is meant to ease Drive bands requirements to reduce Engraving forces and Friction, but still withstand the Shear forces for such high Spinning. The LM-102 will handle that well.

Lutz Moeller, 6th February 2008

Energy calculator

Currently (early 2008) Bisley limits fired kinetic Energy to 4'500 Joule. So watch out for local Range limits an Rules to obey.

Velocity m/s Masse g
Joule

See previous LM-101

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