After noticing that the CV9030 Bushmaster Mk44 AC penetration at longer distances felt too low compared to what I had read I made some serious dive into the wonderful land of APFSDS penetration theory and measurements. I compared the numbers to other autocannons starting with Swedish Bofors 40mm L/70 autocannon used in CV9040.
Contrary to what I stated in the first post I found out that the penetration doesn't depend linearily from momentum or kinetic energy. All other factors being stable the penetration of RHA is proportional to the e^(-1/v^2), where v is the velocity and e is Euler's number (a.k.a. Napier's constant).
When I had gathered the data all around the Internet I found out that the game formula works really well for every other gun than the CV90 guns. I also found out couple of oddities in the OOB which should probably be corrected anyway. The CV90 guns have what is advertised as low drag kinetic penetrators and they seem to retain their penetration capability rather well.
Bushmaster 30mm (note: ammunition may vary on Warfaretech values from others)
Penetration in mm.
Code:
+-----+----------+-----------+-----------------+
| km | Pen (RL) | Pen (OOB) | Source(s) |
+-----+----------+-----------+-----------------+
| 0 | 124 | 120 | Warfaretech |
| 0.5 | 116 | 100 | Warfaretech |
| 0.5 | 115 | 100 | Thesis* |
| 1.0 | 108 | 90 | Warfaretech |
| 1.0 | 100+ | 90 | Nammo |
| 1.0 | 100 | 90 | Thesis* |
| 1.5 | 100 | 80 | Thesis* |
| 1.5 | 100 | 80 | Warfaretech |
| 2.0 | 90 | 70 | Warfaretech |
| 2.0 | 80 | 70 | Thesis* |
| 2.5 | 84 | 60 | Warfaretech |
| 2.5 | 80 | 60 | Thesis* |
| 3.0 | 80 | 50 | Thesis* |
| 3.0 | 76 | 50 | Warfaretech |
+-----+----------+-----------+-----------------+
http://www.nammo.com/globalassets/pd...g_2014_web.pdf
https://www.doria.fi/bitstream/handl...pdf?sequence=1 (In Finnish)
http://warfaretech.blogspot.fi/2014/...ic-cannon.html
* = Thesis gives penetration values for three ranges, which makes the penetration figure probably overestimating at the long end (1500-3000m = 80 mm)
From these values and the Nammo given muzzle velocity I calculated the drag constant c = -0.1145. Using that drag constant and penetration-velocity equation fitting the data to the mathematical model gives the following estimates for penetration:
Code:
s (km) v (m/s) pen (mm)
0.0 1,430 122.0
0.5 1,350 115.0
1.0 1,275 107.6
1.5 1,204 99.8
2.0 1,137 91.8
2.5 1,074 83.6
3.0 1,014 75.3
This data is really well in line with the penetration figures given earlier.
If the penetration @0km is kept at 120mm (OOB Sabot pen: 12) then bumping the Sabot Range to 160 would give the closest response to RL penetration tables:
Code:
s (km) pen (mm) RL
0.0 120 122
0.5 120 115
1.0 110 108
1.5 100 100
2.0 90 92
2.5 80 84
3.0 70 75
The Swedish Bofors 40mm AC had data which seemed to contradict itself until I found out that Swedes have upgraded the APFSDS ammunition in 1997 and again in 2005! Luckily the 1997 change was only to make the round safer for the CV90 crew. Also the data is hard to find, so I only have a couple of sources.
For the 1997 revision Bofors 40mm Slpprj 90LK/97 (Assumed that weapon slot 016 in Swedish OOB is this one, pen=20, sabot range=60)
Muzzle velocity: 1,470-1,480 m/s
"The flight time to 1500m is less than 1.1 seconds." (Gander)
Drag coefficient is thus c=-0.1077 which is almost 10% better than above.
Code:
+-----+----------+-----------+-----------------+
| km | Pen (RL) | Pen (OOB) | Source(s) |
+-----+----------+-----------+-----------------+
| 0 | | 200 | |
| 0.5 | | 170 | |
| 1.0 | 120+ | 140 | Bofors, 2002 |
| 1.0 | 120+ | 140 | Gander, Terry |
| 1.0 | 140 | 140 | SBWiki* |
| 1.0 | 131 | 140 | Collinsj |
| 1.5 | | 120 | |
| 2.0 | | 100 | |
| 2.5 | | 70 | |
| 3.0 | | 50 | |
+-----+----------+-----------+-----------------+
http://www.dtic.mil/ndia/2003gun/boren.pdf
The Bofors Gun by Terry Gander
http://web.archive.org/web/201311150...om/protect.htm
http://www.steelbeasts.com/sbwiki/in...mmunition_Data
* = Reliability questionable
Assuming the 131mm and the initial velocity and flight time are correct I was able to work back to following penetration tables:
Code:
s (km) v (m/s) pen (mm)
0.0 1,465 146.5
0.5 1,388 139.0
1.0 1,315 131.0
1.5 1,246 122.7
2.0 1,181 114.0
2.5 1,119 105.1
3.0 1,061 96.0
Assuming the higher, 140 mm @1km penetration figure we can deduce a safe upper bound:
Code:
s (km) v (m/s) pen (mm)
0.0 1,465 156.6
0.5 1,388 148.5
1.0 1,315 140.0
1.5 1,246 131.1
2.0 1,181 121.8
2.5 1,119 112.3
3.0 1,061 102.6
Adjusting the sabot penetration to 15 (150 mm) and giving sabot range 130 we would reach
Code:
s (km) pen (mm) RL
0.0 150 147
0.5 150 139
1.0 130 131
1.5 120 123
2.0 100 114
2.5 100 105
3.0 90 96
The current round used by Swedes, Bofors 40mm Slpprj 95LK/05
Muzzle velocity: 1,510 m/s
The penetrator is heavier and faster than 1997 version.
Assuming the same drag coefficient as earlier.
Code:
+-----+----------+-----------+-----------------+
| km | Pen (RL) | Pen (OOB) | Source(s) |
+-----+----------+-----------+-----------------+
| 0 | | 200 | |
| 0.5 | | 180 | |
| 1.0 | 170 | 150 | SBWiki* |
| 1.0?| 150+ | 150 | Army-guide |
| 1.0?| 150+ | 150 | Bofors, 2002 |
| 1.0 | 140 | 150 | Odbrana* |
| 1.5 | | 140 | |
| 2.0 | | 120 | |
| 2.5 | | 100 | |
| 3.0 | | 90 | |
+-----+----------+-----------+-----------------+
http://www.army-guide.com/eng/product3367.html
http://www.dtic.mil/ndia/2003gun/boren.pdf
http://www.odbrana.mod.gov.rs/arsena...senal%2048.pdf (in Serbian. Uncertain whether this is a different round, also muzzle velocity stated differs)
Here we assume the 170mm is a good number (shouldn't be less than 160 anyway) and work the equations:
Code:
s (km) v (m/s) pen (mm)
0.0 1,510 188.9
0.5 1,431 179.7
1.0 1,356 170.0
1.5 1,285 159.8
2.0 1,217 149.2
2.5 1,154 138.1
3.0 1,093 126.8
Adjusting the sabot penetration to 19 and giving sabot range 150 (gasp!) we would have
Code:
s (km) pen (mm) RL
0.0 190 189
0.5 190 180
1.0 170 170
1.5 160 160
2.0 140 149
2.5 140 138
3.0 130 127
Which gives slightly lower results around 2km range but it is acceptable as range is anyway so far away that hit probabilities are getting too low to try it.
For this post I made careful checks with other weapons as well:
120mm DM33 L44
120mm DM53 L55
120mm DM63 L55
30 mm 2A42 3UBR6
30 mm 2A42 3UBR8
and all the real world data was well-aligned to the model predictions and OOB penetrations... with an anomaly I found:
BMP-2 uses 2A42 30mm autocannon which has poorly performing AP and sabot rounds (in real life as well as in the OOB). The AP round often used - Finland as well - is (APBC-T) 3UBR6 for which has AP pen 6 and range 80. Then there is a sabot round, APDS 3UBR8, which has sabot pen 8 and range 40. Jane's gives the following penetration data
Code:
s (km) 3UBR6
0.5 35
1.0 28
1.5 22
Rosonboronexport catalogue says
Code:
s (km) 3UBR6 3UBR8
0.7 20
1.5 25
for 60 deg impact. This would translate to 40 and 50 mm but compared to Jane's numbers there seems to be marketing extra in here. Anyway the ~50mm is far from the game given 30mm @1.5km which seems to be a result of a round up as game gives 20mm @1.55km. This lead me to think that the 25mm result has been taken as 0 degree impact as this APDS round has worse performance than the APBC round. The sabot range should probably be bumped up as well.
MODIFY
BMP-2 2A42, multiple nations
Sabot range should be higher, penetration @1.5km approx 40mm
MODIFY
Bofors 40mm L70 AC, Sweden
Starting 2005 the sabot values should be
pen: 19
range: 150
before that
pen: 150
range: 130
to represent the low drag with high sabot range.
MODIFY
Bushmaster 30mm Mk44 AC, multiple nations
sabot range: 160
or alternatively
bump up penetration to 13
range to 130
Note
For all you other nerds over there, math (and physics) is in the attachment.
Re: Sabot range for modern autocannons
Hybrid Mode
