Sabot range for modern autocannons

[dmnt]

I've now done some early analyses and come up with the following findings:

• Bofors L70 40mm has two generations of APFSDS ammunition with differing penetration values.
• Bofors L70 40mm APFSDS ammunition has exceptionally low drag (the penetrator may fly up to 40 km!)
• Penetration data (Bofors 40mm L/70) for differing distances and ammunition generations is hard to find from reliable sources. Unnamed sources agreeing may have a common ancestor.
• Bushmaster 30mm APFSDS has a low drag, but not as low as Bofors L70 40mm's.
• Rheinmetall 120mm APFSDS data on OOB is in accord with the calculations
• This model works well only when the projectile has at least Mach 1.1 speed. All bets are off after that point.

The good news here is that because the model predictions for tank sabot ammunition is well within margin of error in the source data: for Rheinmetall 120mm L/55 DM53 the sabot penetration @3km is modeled at 676 mm vs. 660 mm in the MBT_APCalc.exe. Closer distances are even better aligned, for example @1km 854mm vs. 860mm. This gives me confidence that the model isn't grossly off.

Further checks I made were to check the NSV 12.7mm values given by MIL-STD-662F p. 20. The predicted velocity and observed velocity are within 2.25% of each other. I.e. the small caliber should not affect.

I'll continue with Russian autocannons to see if they follow the suit and the OOB and the model agree there. Then we can say that it is the low drag of these and only these projectiles that require tweaking.

[DRG]

We had confidence in the game model years ago ..... but you have fun

[dmnt]

To clarify, by model above I mean the model I wrote. And BMP-2 2A42 again fits the data and the game data - with a small nuance which I'll address later in the wrap-up (3UBR8 penetration @1.5km). What it looks to me is that the recent APFSDS ammunition has lower drag which can be represented by giving higher sabot range values in OOBs, just as I suspected in the first message.

I'll make a proper post with findings and sources listed later.

[Imp]

One of the questions in the very first post condensed into one sentence:
Is the maximum range for a gun to shoot sabot rounds the actual "range" value even if "sabot range" is greater?

Not sure what you are getting at here
1) If like a tank main gun the range is often 100+ for sabot the shot will never be taken because the hit probability is to low.

2) If what you want to know is if sabot will fire past its range which I seriously doubt then just adjust the sabot range to say 15 & see what happens when you fire at a target at range 16 hexes.

3) Just guessing but sometimes the sabot range might be massaged slightly so the formula gives penetration results that more closely match RL results.
Adjust the range of weapons & look in AP Calc if you want to reverse engineer the formula used.
Penetration of a 100 would probably make the results fairly simple to read.

[Suhiir]

Keep in mind that a weapons max range effects it's hit probability, a weapon with a 120 max range will be somewhat more likely to hit at any range then one with a 100 max range.
And the "sabot range" has significant effects on sabot penetration.

[dmnt]

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.

+-----+----------+-----------+-----------------+
|  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:

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:

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.

+-----+----------+-----------+-----------------+
|  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:

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:

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

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.

+-----+----------+-----------+-----------------+
|  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:

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

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

s (km) 3UBR6
0.5     35
1.0     28
1.5     22

Rosonboronexport catalogue says

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.

[dmnt]

For some reason the attachment refused to attach. Downloadable at http://www.venhola.com/winspmbt/velocity_and_drag.pdf

[scorpio_rocks]

Originally Posted by dmnt

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.

EEK! Please tell me thats a typo!

[dmnt]

Originally Posted by scorpio_rocks

EEK! Please tell me thats a typo!

Yes, it's sometimes hard not to mix the penetration values in OOB (in tens of mm) and penetration values elsewhere (in mm). It's supposed to be "pen: 15"