Bill Jurens’ and Brad Fischer: “Gunnery exercise reports from the WW2 era showed an average TMD of 0.429% with AP and service velocity.”
This translates to 1.716% of range for a 9-gun pattern.
True mean dispersion 0.429% @ 20km = 86m
Average range pattern @ 20km:
9 guns: 86 x 4 = 344m (1.72% of range)
3 guns: 86 x 2.43 = 209m (1.05% of range)
Fast Battleship League Table
North Carolina / South Dakota 16” (40.6cm)/45 Mark 6 dispersion
Bill Jurens’ and Brad Fischer: “Gunnery exercise reports from the WW2...”
Average TMD of 0.383% with AP and service velocity:
True mean dispersion 0.383% @ 20km = 77m (with RPC ≥1943)
Average range pattern @ 20km:
9 guns: 77 x 4 = 306m (1.53% of range)
3 guns: 77 x 2.43 = 186m (0.93% of range)
USS Massachusetts reported 183 - 274m salvo pattern @ 20-24km firing AP rounds during the Casablanca action in 1942, when Massachusetts was still operating with “Follow the Pointer” gun control (i.e. no RPC available).
Average salvo pattern = 227.5m / 2.43 = 93.62m @ average range = 22km = 0.426%
True mean dispersion 0.426% @ 20km = 85m
Average range pattern @ 20km:
9 guns: 85 x 4 = 340m (% of range)
3 guns: 85 x 2.43 = 206m (% of range)
Average TMD of 0.383% with AP and service velocity:
True mean dispersion 0.383% @ 20km = 77m (with RPC ≥1943)
Average range pattern @ 20km:
9 guns: 77 x 4 = 306m (1.53% of range)
3 guns: 77 x 2.43 = 186m (0.93% of range)
USS Massachusetts reported 183 - 274m salvo pattern @ 20-24km firing AP rounds during the Casablanca action in 1942, when Massachusetts was still operating with “Follow the Pointer” gun control (i.e. no RPC available).
Average salvo pattern = 227.5m / 2.43 = 93.62m @ average range = 22km = 0.426%
True mean dispersion 0.426% @ 20km = 85m
Average range pattern @ 20km:
9 guns: 85 x 4 = 340m (% of range)
3 guns: 85 x 2.43 = 206m (% of range)
Bismarck / Tirpitz 38cm/52 SKC/34 dispersion
Actual practice shoots battery spreads indicated 120meters at 20km from 2-gun 38cm gunfire. The same guns had about 140m at 25km. Battery spreads for 4-gun salvos at 25km showed less than 150 meters.
120m / 1.69 * n2 1.414 = 100.4m @ 20km = 0.5%
140m / 1.69 * n2 1.414 = 104.2m @ 25km = 0.417%
150m / 1.69 * n4 1.155 = 102.5m @ 25km = 0.41%
https://www.kbismarck.com/gkdos100a.html W.A.39,16 matches Tirpitz practice shooting very well.
Conversion to US Navy equivalent dispersion values according Delcyros:
https://www.tapatalk.com/groups/warship ... 9-s30.html
With this information it is possible to back-calculate 50% scatter to TMD:
20km: 12.1° elev = 0.5% = 100m x 1.45 = 145m battery dispersion / 1.69 = 85.8m apparent mean dispersion for n8 x 1.069 = 92m (0.458%) TMD @ 20km
23km: 15° elev = 108m x 1.5 = 162m / 1.69 = 95.86 x 1.069 = 102m (0.4455%)
25km: 16.7° elev = 0.44% = 110m x 1.5 = 165 / 1.69 = 97.6 x 1.069 = 104m (0.417%)
28.5km: 20° elev = 120m x 1.5 = 180m / 1.69 = 106x 1.069 = 114m (0.4%)
To put this in relation to 0.429% TMD of the US 16”/50 guns acc. Fischer, Jurens “US Fast battleship gunnery…” we can average this to 0.430% between 20 and 28.5km for Bismarck class, about the range where the US 16” gunnery was also averaged by Fischer, Jurens.
True mean dispersion 0.43% @ 20km = 86m
Average range pattern:
8 guns: 86 x 3.85 = 331m (1.66% of range)
4 guns: 86 x 2.89 = 249m (1.24% of range)
120m / 1.69 * n2 1.414 = 100.4m @ 20km = 0.5%
140m / 1.69 * n2 1.414 = 104.2m @ 25km = 0.417%
150m / 1.69 * n4 1.155 = 102.5m @ 25km = 0.41%
https://www.kbismarck.com/gkdos100a.html W.A.39,16 matches Tirpitz practice shooting very well.
- Bismarck dispersion.jpg (114.15 KiB) Viewed 17531 times
https://www.tapatalk.com/groups/warship ... 9-s30.html
With this information it is possible to back-calculate 50% scatter to TMD:
20km: 12.1° elev = 0.5% = 100m x 1.45 = 145m battery dispersion / 1.69 = 85.8m apparent mean dispersion for n8 x 1.069 = 92m (0.458%) TMD @ 20km
23km: 15° elev = 108m x 1.5 = 162m / 1.69 = 95.86 x 1.069 = 102m (0.4455%)
25km: 16.7° elev = 0.44% = 110m x 1.5 = 165 / 1.69 = 97.6 x 1.069 = 104m (0.417%)
28.5km: 20° elev = 120m x 1.5 = 180m / 1.69 = 106x 1.069 = 114m (0.4%)
To put this in relation to 0.429% TMD of the US 16”/50 guns acc. Fischer, Jurens “US Fast battleship gunnery…” we can average this to 0.430% between 20 and 28.5km for Bismarck class, about the range where the US 16” gunnery was also averaged by Fischer, Jurens.
True mean dispersion 0.43% @ 20km = 86m
Average range pattern:
8 guns: 86 x 3.85 = 331m (1.66% of range)
4 guns: 86 x 2.89 = 249m (1.24% of range)
Scharnhorst dispersion
20km / 10.9° elev 50%LS = 0.84% = 168m x1.45 battery disp=> 244m / 1.69 aparent mean disp. 144m x 1.061 (n9) =152m TMD (0.76%)
25km / 15.5° elev 50%LS = 0.79% = 197.5m x 1.5 battery disp =>296m / 1.69 => 175m x 1.061 (n9) = 185m TMD (0.74%)
29km / 19.9° elev 50%LS = 0.75% = 217.5m x 1.5 => 326m / 1.69 =>193 x 1.061 (n9) = 204m TMD (0.7%)
25km / 15.5° elev 50%LS = 0.79% = 197.5m x 1.5 battery disp =>296m / 1.69 => 175m x 1.061 (n9) = 185m TMD (0.74%)
29km / 19.9° elev 50%LS = 0.75% = 217.5m x 1.5 => 326m / 1.69 =>193 x 1.061 (n9) = 204m TMD (0.7%)
UK 15" dispersion update
After redoing the Scharnhorst numbers, I realised again, that percentual dispersion is better at ranges around the 15°-20° elevation ranges than at lower and higher angles. I will take another look at the UK 15"L42 numbers again, since their dispersion was based on shootings at ranges in the 8° to 10° elevation region. I presume that their dispersion would also be better in the 15°-20° elevation range.
I had adopted the German curvature for the Vanguard comparison, but not for Renown. Therefore, I will do Renown again.
Best regards,
Frank
I had adopted the German curvature for the Vanguard comparison, but not for Renown. Therefore, I will do Renown again.
Best regards,
Frank
UK 15"L42 as precise as US 16"L50 and GE 38cmL52
H.M.S. Hood Association-Battle Cruiser Hood: H.M.S. Hood Reference Materials - ADM 239/137: C.B. 3001 (39) Progress in Naval Gunnery 1939 ( (hmshood.org.uk)
Average spread:
246/15,000 = 1.64%
253/14,000 = 1.8%
(227/11,200 = 2%) excluded for short range
190/14,200 = 1.34%
258/13,400 = 1.93%
226/15,300 = 1.48%
182/14,400 = 1.26%
Average = 1.575% at average range of 14,350 yards = 13.1km
1.575% of 13.1km = 206.35m
Assuming typical 4 gun salvos we can divide 206.35m by 2.89 to get the TMD of 71.4m or 0.545%
13.1km range equals 8.2° elevation for the 15” guns according “Common Ground on Shifting Sands”.
The German W.A.39.16 gives a normalized curve for dispersion / 50% Längenstreuung, which is not equal to TMD, but in the same relation to elevation as TMD.
According that curve, a TMD of 0.545% at 13km (8.2° elevation) would mean a TMD of 0.439% at 20km (14.8° elevation) and 0.422% at 25km (21° elevation).
So, now we can compare TMD at 20km and 25km for Bismarck and UK 15"L42:
TMD @20km:
Bismarck 0.458% : 0.439% UK 15"L42
TMD @25km:
Bismarck 0.417% : 0.422% UK 15"L42
This is a wash with Iowa’s 0.429% at similar ranges.
Average spread:
246/15,000 = 1.64%
253/14,000 = 1.8%
(227/11,200 = 2%) excluded for short range
190/14,200 = 1.34%
258/13,400 = 1.93%
226/15,300 = 1.48%
182/14,400 = 1.26%
Average = 1.575% at average range of 14,350 yards = 13.1km
1.575% of 13.1km = 206.35m
Assuming typical 4 gun salvos we can divide 206.35m by 2.89 to get the TMD of 71.4m or 0.545%
13.1km range equals 8.2° elevation for the 15” guns according “Common Ground on Shifting Sands”.
The German W.A.39.16 gives a normalized curve for dispersion / 50% Längenstreuung, which is not equal to TMD, but in the same relation to elevation as TMD.
According that curve, a TMD of 0.545% at 13km (8.2° elevation) would mean a TMD of 0.439% at 20km (14.8° elevation) and 0.422% at 25km (21° elevation).
So, now we can compare TMD at 20km and 25km for Bismarck and UK 15"L42:
TMD @20km:
Bismarck 0.458% : 0.439% UK 15"L42
TMD @25km:
Bismarck 0.417% : 0.422% UK 15"L42
This is a wash with Iowa’s 0.429% at similar ranges.
-
Bill Jurens
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- Location: USA
Re: Fast Battleship League Table
My thanks for this information, which must have taken some time to compile. It does help to indicate where fact fades into supposition, e.g. regarding the number of guns in salvo, lie.
Your observation regarding dispersion vs range is basically correct; at short ranges most dispersion is due to variations in angle of departure and variations in velocity are relatively unimportant. As ranges increase the dispersion tends to be most heavily affected by variations in initial velocity and/or drag, and variations in angle of departure become relatively insignificant.
One does need to keep in mind that a good deal in hitting depends upon good spotting, so that -- at least in the old days -- a somewhat larger pattern was actually advantageous, i.e. created a higher hit percentage, because it enabled straddles to be identified earlier in the game. Small patterns are advantageous if you have good control over the desired mean point of impact, i.e. you know the range exactly, the time of flight is short, and all guns are properly aligned and produce similar initial velocities. As uncertainty regarding range grows, the number of guns in the salvo decreases, and gun-to-gun consistency goes down, then a larger range pattern ( and a larger True Mean Dispersion) may actually improve the situation.
There are quite complicated equations for this, which I haven't used now in years, but I can try to look them up again.
Bill Jurens
Your observation regarding dispersion vs range is basically correct; at short ranges most dispersion is due to variations in angle of departure and variations in velocity are relatively unimportant. As ranges increase the dispersion tends to be most heavily affected by variations in initial velocity and/or drag, and variations in angle of departure become relatively insignificant.
One does need to keep in mind that a good deal in hitting depends upon good spotting, so that -- at least in the old days -- a somewhat larger pattern was actually advantageous, i.e. created a higher hit percentage, because it enabled straddles to be identified earlier in the game. Small patterns are advantageous if you have good control over the desired mean point of impact, i.e. you know the range exactly, the time of flight is short, and all guns are properly aligned and produce similar initial velocities. As uncertainty regarding range grows, the number of guns in the salvo decreases, and gun-to-gun consistency goes down, then a larger range pattern ( and a larger True Mean Dispersion) may actually improve the situation.
There are quite complicated equations for this, which I haven't used now in years, but I can try to look them up again.
Bill Jurens
Re: Fast Battleship League Table
Thank you very much, Mr Jurens,Bill Jurens wrote: ↑Tue Oct 31, 2023 5:14 pm ....
As uncertainty regarding range grows, the number of guns in the salvo decreases, and gun-to-gun consistency goes down, then a larger range pattern ( and a larger True Mean Dispersion) may actually improve the situation.
There are quite complicated equations for this, which I haven't used now in years, but I can try to look them up again.
Bill Jurens
I would be very thankful. It is always very interesting and educating to read and learn from your knowledge.
If I recall correctly, you also intended to write a follow up on "Common Ground on Shifting Sands", or am I mistaken?
Best regards,
Frank
Scharnhorst vs. Renown @ Day 1939 => 2:2 revisited
Clear day, calm seas. Let’s assume Scharnhorst was cut off by Renown on the retreat from superior forces and Renown has the task to cripple and slow down Scharnhorst at all cost.
Ranging accuracy:
Scharnhorst:
Optical range finders: 10.5m x 50=> 76m @20km
Renown:
Optical range finder: 30ft (12.5m) x 25 => 153m @20km
Battle range: 20km.
Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 152m
Renown: True Mean Dispersion (TMD) @ 20km: 88m
Danger Zones @ 20km:
Scharnhorst’s guns Angle of Fall @ 20km = 16.3° Danger zone vs. Renown 10m high 25m beam = 56m
Renown guns Angle of Fall @ 20km = 20.3° Danger zone vs. Scharnhorst 10m high 28m beam = 55m
Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 56m / (152m + (76m/2)) = 29.5%
Renown: 55m / (88m + (153m/2)) = 33.4%
Projectile times of flight @ 20km:
Scharnhorst: 31s
Renown: 36s
Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 3.80%
Renown: HP = 3.71%
Initial rate of fire to find the range (IF):
i.e. 60s / (ToF + 20s observation + correction time) x no of guns -10% for expected output misses:
Scharnhorst: 9.53 shots per min
Renown: 5.79 shots per min
Rapid Fire rate (RF):
Scharnhorst: 16.23 shots per min
Renown: 10.13 shots per min
Average rate (AR) of fire:
Scharnhorst: 12.30 shots per min
Renown: 7.96 shots per min
Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 4.67 hits per 10 min
Renown: 2.95 hits per 10 min
Scharnhorst would fire a mixture of AP, HE base-fuse and HE nose-fuse rounds at long ranges, when not expecting penetrations and then change to AP round at shorter ranges, when expecting penetrations. Against Renown Scharnhorst would probably start with AP right away.
Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
(Scharnhorst: (7.84+16+21.8kg)/3 x 4.67/ 2 = 35.5kg)
Scharnhorst: 7.84kg x 4.67 / 2 = 18.3kg
Renown: 22kg x 2.95 / 2 = 32.5kg
Side protection system penetration @ 30° inclination:
Scharnhorst could penetrate Renown @ 11km (9in belt) / 20km (6in belt)
Renown could penetrate Scharnhorst @ 3
However Renown could also penetrate Scharnhorst through the upper belt (45mm) and the lower armor deck at >21km.
Summary:
1. Hits: Scharnhorst 4.67 : 2.95 Renown (1:0)
[2.a Explosives: Scharnhorst 35.5kg : 32.5kg Renown (<20% difference ie. Draw 1:1)]
2.b Explosives: Scharnhorst 18.3kg / 32.5kg Renown (0:1)
3. Belt pen: Scharnhorst 11km/20km : 3km Renown (1:0)
4. Deck pen inside 25km: Scharnhorst 0 : 4km (21-25km) Renown (0:1)
Scharnhorst 2:2 Renown
However, tactical circumstances and weather often have greater effect than these numbers. Just look at the action off Lofoten!
Ranging accuracy:
Scharnhorst:
Optical range finders: 10.5m x 50=> 76m @20km
Renown:
Optical range finder: 30ft (12.5m) x 25 => 153m @20km
Battle range: 20km.
Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 152m
Renown: True Mean Dispersion (TMD) @ 20km: 88m
Danger Zones @ 20km:
Scharnhorst’s guns Angle of Fall @ 20km = 16.3° Danger zone vs. Renown 10m high 25m beam = 56m
Renown guns Angle of Fall @ 20km = 20.3° Danger zone vs. Scharnhorst 10m high 28m beam = 55m
Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 56m / (152m + (76m/2)) = 29.5%
Renown: 55m / (88m + (153m/2)) = 33.4%
Projectile times of flight @ 20km:
Scharnhorst: 31s
Renown: 36s
Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 3.80%
Renown: HP = 3.71%
Initial rate of fire to find the range (IF):
i.e. 60s / (ToF + 20s observation + correction time) x no of guns -10% for expected output misses:
Scharnhorst: 9.53 shots per min
Renown: 5.79 shots per min
Rapid Fire rate (RF):
Scharnhorst: 16.23 shots per min
Renown: 10.13 shots per min
Average rate (AR) of fire:
Scharnhorst: 12.30 shots per min
Renown: 7.96 shots per min
Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 4.67 hits per 10 min
Renown: 2.95 hits per 10 min
Scharnhorst would fire a mixture of AP, HE base-fuse and HE nose-fuse rounds at long ranges, when not expecting penetrations and then change to AP round at shorter ranges, when expecting penetrations. Against Renown Scharnhorst would probably start with AP right away.
Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
(Scharnhorst: (7.84+16+21.8kg)/3 x 4.67/ 2 = 35.5kg)
Scharnhorst: 7.84kg x 4.67 / 2 = 18.3kg
Renown: 22kg x 2.95 / 2 = 32.5kg
Side protection system penetration @ 30° inclination:
Scharnhorst could penetrate Renown @ 11km (9in belt) / 20km (6in belt)
Renown could penetrate Scharnhorst @ 3
However Renown could also penetrate Scharnhorst through the upper belt (45mm) and the lower armor deck at >21km.
Summary:
1. Hits: Scharnhorst 4.67 : 2.95 Renown (1:0)
[2.a Explosives: Scharnhorst 35.5kg : 32.5kg Renown (<20% difference ie. Draw 1:1)]
2.b Explosives: Scharnhorst 18.3kg / 32.5kg Renown (0:1)
3. Belt pen: Scharnhorst 11km/20km : 3km Renown (1:0)
4. Deck pen inside 25km: Scharnhorst 0 : 4km (21-25km) Renown (0:1)
Scharnhorst 2:2 Renown
However, tactical circumstances and weather often have greater effect than these numbers. Just look at the action off Lofoten!
Last edited by fsimon on Tue Oct 31, 2023 9:17 pm, edited 2 times in total.
Scharnhorst vs. Renown @ Night 1943 => 3:1 revisited
Let’s assume Scharnhorst’s top radar is not yet shot off by Norfolk.
Both will find each other with radar, but only Scharnhorst can spot for the fall of shots outside of 20km. Renown will chase salvos outside of 20km. Both are now interested in closing to inside 20km, Renown to get into radar spotting range and Scharnhorst to start hitting a maneuvering opponent, while unable to escape due to the Norwegian coast.
Ranging accuracy:
Scharnhorst:
Optical range finders: 10.5m x 50=> 76m @20km
FuMO 26 FCR: 25m, blind fire / spotting to 30km
Renown:
Optical range finder: 30ft (12.5m) x 25 => 153m @20km
Type 284M3/P FCR: 36m, blind fire / spotting to 19km
Battle range: 20km.
…
Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 56m / (152m + 25m) = 31.6%
Renown: 55m / (88m + 36) = 44.4%
Projectile times of flight @ 20km:
Scharnhorst: 31s
Renown: 36s
Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.08%
Renown: HP = 4.93%
…
Average rate (AR) of fire:
Scharnhorst: 12.30 shots per min
Renown: 7.96 shots per min
Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.02 hits per 10 min
Renown: 3.92 hits per 10 min
Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Scharnhorst: 7.84kg x 5.02 / 2 = 19.7kg
Renown: 22kg x 3.92 / 2 = 43.2kg
Side protection system penetration @ 30° inclination:
Scharnhorst could penetrate Renown @ 11km (9in belt) / 20km (6in belt)
Renown could penetrate Scharnhorst @ 3
Summary:
1. Hits: Scharnhorst 5.02 : 3.35 Renown (1:0)
2. Explosives: Scharnhorst 19.7kg / 43.2kg Renown (0:1)
3. Belt pen: Scharnhorst 11km/20km : 3km Renown (1:0)
4. Blind fire: Scharnhorst 30km : 19km Renown (1:0)
Scharnhorst 3:1 Renown
Both will find each other with radar, but only Scharnhorst can spot for the fall of shots outside of 20km. Renown will chase salvos outside of 20km. Both are now interested in closing to inside 20km, Renown to get into radar spotting range and Scharnhorst to start hitting a maneuvering opponent, while unable to escape due to the Norwegian coast.
Ranging accuracy:
Scharnhorst:
Optical range finders: 10.5m x 50=> 76m @20km
FuMO 26 FCR: 25m, blind fire / spotting to 30km
Renown:
Optical range finder: 30ft (12.5m) x 25 => 153m @20km
Type 284M3/P FCR: 36m, blind fire / spotting to 19km
Battle range: 20km.
…
Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 56m / (152m + 25m) = 31.6%
Renown: 55m / (88m + 36) = 44.4%
Projectile times of flight @ 20km:
Scharnhorst: 31s
Renown: 36s
Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.08%
Renown: HP = 4.93%
…
Average rate (AR) of fire:
Scharnhorst: 12.30 shots per min
Renown: 7.96 shots per min
Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.02 hits per 10 min
Renown: 3.92 hits per 10 min
Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Scharnhorst: 7.84kg x 5.02 / 2 = 19.7kg
Renown: 22kg x 3.92 / 2 = 43.2kg
Side protection system penetration @ 30° inclination:
Scharnhorst could penetrate Renown @ 11km (9in belt) / 20km (6in belt)
Renown could penetrate Scharnhorst @ 3
Summary:
1. Hits: Scharnhorst 5.02 : 3.35 Renown (1:0)
2. Explosives: Scharnhorst 19.7kg / 43.2kg Renown (0:1)
3. Belt pen: Scharnhorst 11km/20km : 3km Renown (1:0)
4. Blind fire: Scharnhorst 30km : 19km Renown (1:0)
Scharnhorst 3:1 Renown
Scharnhorst vs. Vittorio Veneto @ Day 1940 => 2:2
Ranging accuracy:
Scharnhorst:
2x FuMG39 FCR: 25m, ranging to 25km
10.5mx50: 67m
Vittorio Veneto:
12m x 25:116m
Battle range: Shooting commences earlier, but main battle range will be 20km
Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 152m
Vittorio Veneto: True Mean Dispersion (TMD) @ 20km: 194m (OTO gun mounts; battles for Littorio with Ansaldo mounts with TMD 148m to follow)
Danger Zones @ 20km:
Scharnhorst’s guns AoF @ 20km = 16.3° Danger zone vs. Vittorio Veneto 10m high 31m beam = 62m
Vittorio Veneto guns AoF @ 20km = 14.1° Danger zone vs. Scharnhorst 10m high 28m beam = 66m
Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 62m / (152m + (67m/2) =33.4%
Vittorio Veneto: 66m / (194m + 116m/2m) = 26.2%
Projectile times of flight @ 20km:
Scharnhorst: 31s
Vittorio Veneto: 30s
Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.31%
Vittorio Veneto: HP = 3.49%
Initial rate of fire to find the range (IF):
i.e. 60s / (ToF + 20s observation + correction time) x no of guns -10% for expected output misses:
Scharnhorst: 9.53 shots per min
Vittorio Veneto: 9.72 shots per min
Rapid Fire rate (RF):
Scharnhorst: 16.2 shots per min
Vittorio Veneto: 10.53 shots per min
Average rate (AR) of fire:
Scharnhorst: 12.3 shots per min
Vittorio Veneto: 10.13 shots per min
Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.3 hits per 10 min
Vittorio Veneto: 3.53 hits per 10 min
Scharnhorst would fire a mixture of AP, HE base-fuse and HE nose-fuse rounds at long ranges, when not expecting penetrations and then change to AP round at shorter ranges, when expecting penetrations.
Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Scharnhorst: (7.84+16+21.8kg)/3 x 5.3/ 2 = 40.32kg
Vittorio Veneto: 10.16kg x 3.53 / 2 = 17.9kg
Side protection system penetration @ 30° inclination:
Scharnhorst belt:
Scharnhorst could pen Vittorio Veneto @ 1km
Vittorio Veneto could pen Scharnhorst @ 5km
However Vittorio Veneto could also penetrate Scharnhorst through the upper belt (45mm) and the lower armor deck at >22km. Hit probability of Vittorio Veneto is only 3.49% and the probability of hitting this section is only ~20% of the danger zone, i.e. ~0.7% probability of hitting through the upper belt. With 100 shots fired in 10 min that is 0.007 probability.
Summary:
1. Hits: Scharnhorst (123 shots) 5.3 : 3.53 (101 shots) Vittorio Veneto (1:0)
2. Explosives: Scharnhorst 40.32kg : 17.9kg Vittorio Veneto 1:0)
3. Belt pen: Scharnhorst 1km : 5km Vittorio Veneto (0:1)
4. Deck pen inside 25km: Scharnhorst 0 : 3km (22-25km) Vittorio Veneto (0:1)
Scharnhorst 2:2 Vittorio Veneto
Scharnhorst:
2x FuMG39 FCR: 25m, ranging to 25km
10.5mx50: 67m
Vittorio Veneto:
12m x 25:116m
Battle range: Shooting commences earlier, but main battle range will be 20km
Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 152m
Vittorio Veneto: True Mean Dispersion (TMD) @ 20km: 194m (OTO gun mounts; battles for Littorio with Ansaldo mounts with TMD 148m to follow)
Danger Zones @ 20km:
Scharnhorst’s guns AoF @ 20km = 16.3° Danger zone vs. Vittorio Veneto 10m high 31m beam = 62m
Vittorio Veneto guns AoF @ 20km = 14.1° Danger zone vs. Scharnhorst 10m high 28m beam = 66m
Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 62m / (152m + (67m/2) =33.4%
Vittorio Veneto: 66m / (194m + 116m/2m) = 26.2%
Projectile times of flight @ 20km:
Scharnhorst: 31s
Vittorio Veneto: 30s
Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.31%
Vittorio Veneto: HP = 3.49%
Initial rate of fire to find the range (IF):
i.e. 60s / (ToF + 20s observation + correction time) x no of guns -10% for expected output misses:
Scharnhorst: 9.53 shots per min
Vittorio Veneto: 9.72 shots per min
Rapid Fire rate (RF):
Scharnhorst: 16.2 shots per min
Vittorio Veneto: 10.53 shots per min
Average rate (AR) of fire:
Scharnhorst: 12.3 shots per min
Vittorio Veneto: 10.13 shots per min
Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.3 hits per 10 min
Vittorio Veneto: 3.53 hits per 10 min
Scharnhorst would fire a mixture of AP, HE base-fuse and HE nose-fuse rounds at long ranges, when not expecting penetrations and then change to AP round at shorter ranges, when expecting penetrations.
Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Scharnhorst: (7.84+16+21.8kg)/3 x 5.3/ 2 = 40.32kg
Vittorio Veneto: 10.16kg x 3.53 / 2 = 17.9kg
Side protection system penetration @ 30° inclination:
Scharnhorst belt:
Scharnhorst could pen Vittorio Veneto @ 1km
Vittorio Veneto could pen Scharnhorst @ 5km
However Vittorio Veneto could also penetrate Scharnhorst through the upper belt (45mm) and the lower armor deck at >22km. Hit probability of Vittorio Veneto is only 3.49% and the probability of hitting this section is only ~20% of the danger zone, i.e. ~0.7% probability of hitting through the upper belt. With 100 shots fired in 10 min that is 0.007 probability.
Summary:
1. Hits: Scharnhorst (123 shots) 5.3 : 3.53 (101 shots) Vittorio Veneto (1:0)
2. Explosives: Scharnhorst 40.32kg : 17.9kg Vittorio Veneto 1:0)
3. Belt pen: Scharnhorst 1km : 5km Vittorio Veneto (0:1)
4. Deck pen inside 25km: Scharnhorst 0 : 3km (22-25km) Vittorio Veneto (0:1)
Scharnhorst 2:2 Vittorio Veneto
-
Bill Jurens
- Moderator
- Posts: 878
- Joined: Mon Oct 18, 2004 4:21 am
- Location: USA
Re: Fast Battleship League Table
Frank Simon wrote:
If I recall correctly, you also intended to write a follow up on "Common Ground on Shifting Sands", or am I mistaken?
No. You are correct. It's being written as an aid to predicting armor penetration, tentatively called "Predicting the Past". I would expect it to be published sometime in the summer of 2023. I have another project on interior ballistics to complete as well, plus illustrations and (a good deal of new text) for the upcoming 3rd edition of Garzke/Dulin Volume II on Allied battleships. If schedules hold, that should be ready by autumn. Then we start on a rework of Volume III, i.e. Axis Battleships.
So I've got my plate full, for sure...
Bill Jurens
If I recall correctly, you also intended to write a follow up on "Common Ground on Shifting Sands", or am I mistaken?
No. You are correct. It's being written as an aid to predicting armor penetration, tentatively called "Predicting the Past". I would expect it to be published sometime in the summer of 2023. I have another project on interior ballistics to complete as well, plus illustrations and (a good deal of new text) for the upcoming 3rd edition of Garzke/Dulin Volume II on Allied battleships. If schedules hold, that should be ready by autumn. Then we start on a rework of Volume III, i.e. Axis Battleships.
So I've got my plate full, for sure...
Bill Jurens
Re: Fast Battleship League Table
That is a full plate I will happily digest.
I am looking forward to this.
Best Regards
Frank
I am looking forward to this.
Best Regards
Frank
Scharnhorst vs. Vittorio Veneto @ Night 1943 => 3:2
Ranging accuracy:
Scharnhorst:
2x FuMO 26 FCR: 25m, blind fire / spotting to 30km
10.5mx50: 67m
Vittorio Veneto:
EC3ter Gufo radar: 150m; max 30km range, poor range and angular resolution no blind fire
12m x 25:116m
Both will find each other with radar, but only Scharnhorst can spot for the fall of shots outside of 20km. Vittorio will chase salvos outside of 20km. Both are now interested in closing to inside 20km, Vittorio to get into star shell illumination range and Scharnhorst to start hitting a maneuvering opponent.
Battle range: 20km.
Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 152m
Vittorio Veneto: True Mean Dispersion (TMD) @ 20km: 194m
Danger Zones @ 20km:
Scharnhorst’s guns AoF @ 20km = 16.3° Danger zone vs. Vittorio Veneto 10m high 31m beam = 62m
Vittorio Veneto guns AoF @ 20km = 14.1° Danger zone vs. Scharnhorst 10m high 28m beam = 66m
Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 62m / (152m + 25m) =35.0%
Vittorio Veneto: 66m / (194m + 116m/2m) = 26.2%
Projectile times of flight @ 20km:
Scharnhorst: 31s
Vittorio Veneto: 30s
Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.52%
Vittorio Veneto: HP = 3.49%
Initial rate of fire to find the range (IF):
i.e. 60s / (ToF + 20s observation + correction time) x no of guns -10% for expected output misses:
Scharnhorst: 9.53 shots per min
Vittorio Veneto: 9.72 shots per min
Rapid Fire rate (RF):
Scharnhorst: 16.2 shots per min
Vittorio Veneto: 10.53 shots per min
Average rate (AR) of fire:
Scharnhorst: 12.3 shots per min
Vittorio Veneto: 10.13 shots per min
Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.6 hits per 10 min
Vittorio Veneto: 3.53 hits per 10 min
Scharnhorst would fire a mixture of AP, HE base-fuse and HE nose-fuse rounds at long ranges, when not expecting penetrations and then change to AP round at shorter ranges, when expecting penetrations.
Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Scharnhorst: (7.84+16+21.8kg)/3 x 5.6/ 2 = 42.29kg
Vittorio Veneto: 10.16kg x 3.53 / 2 = 17.9kg
Side protection system penetration @ 30° inclination:
Scharnhorst belt:
Scharnhorst could pen Vittorio Veneto @ 5km
Vittorio Veneto could pen Scharnhorst @ 5km
However Vittorio Veneto could also penetrate Scharnhorst through the upper belt (45mm) and the lower armor deck at >22km. Hit probability of Vittorio Veneto is only 3.49% and the probability of hitting this section is ~20% of the danger zone, i.e. ~0.7% probability of hitting through the upper belt.
Summary:
1. Hits: Scharnhorst (123 shots) 5.6 : 3.53 (101 shots) Vittorio Veneto (1:0)
2. Explosives: Scharnhorst 42.29kg : 17.9kg Vittorio Veneto 1:0)
3. Belt pen: Scharnhorst 1km : 5km Vittorio Veneto (0:1)
4. Deck pen inside 25km: Scharnhorst 0 : 3km (22-25km) Vittorio Veneto (0:1)
5. Blind Fire: Scharnhorst 30km : 5km Vittorio Veneto (1:0)
Scharnhorst 3:2 Vittorio Veneto
Scharnhorst:
2x FuMO 26 FCR: 25m, blind fire / spotting to 30km
10.5mx50: 67m
Vittorio Veneto:
EC3ter Gufo radar: 150m; max 30km range, poor range and angular resolution no blind fire
12m x 25:116m
Both will find each other with radar, but only Scharnhorst can spot for the fall of shots outside of 20km. Vittorio will chase salvos outside of 20km. Both are now interested in closing to inside 20km, Vittorio to get into star shell illumination range and Scharnhorst to start hitting a maneuvering opponent.
Battle range: 20km.
Gun accuracy @ 20km:
Scharnhorst: True Mean Dispersion (TMD) @ 20km: 152m
Vittorio Veneto: True Mean Dispersion (TMD) @ 20km: 194m
Danger Zones @ 20km:
Scharnhorst’s guns AoF @ 20km = 16.3° Danger zone vs. Vittorio Veneto 10m high 31m beam = 62m
Vittorio Veneto guns AoF @ 20km = 14.1° Danger zone vs. Scharnhorst 10m high 28m beam = 66m
Danger Zones in relation to True mean dispersion and average ranging error = X:
DZ / (TMD+RE) = X
Scharnhorst: 62m / (152m + 25m) =35.0%
Vittorio Veneto: 66m / (194m + 116m/2m) = 26.2%
Projectile times of flight @ 20km:
Scharnhorst: 31s
Vittorio Veneto: 30s
Hit probability with respect to errors accumulating during time of flight:
X / ¼ ToF = Hp
Scharnhorst: Hp = 4.52%
Vittorio Veneto: HP = 3.49%
Initial rate of fire to find the range (IF):
i.e. 60s / (ToF + 20s observation + correction time) x no of guns -10% for expected output misses:
Scharnhorst: 9.53 shots per min
Vittorio Veneto: 9.72 shots per min
Rapid Fire rate (RF):
Scharnhorst: 16.2 shots per min
Vittorio Veneto: 10.53 shots per min
Average rate (AR) of fire:
Scharnhorst: 12.3 shots per min
Vittorio Veneto: 10.13 shots per min
Expected hits per 10 min:
i.e. Hp x AR x 10
Scharnhorst: 5.6 hits per 10 min
Vittorio Veneto: 3.53 hits per 10 min
Scharnhorst would fire a mixture of AP, HE base-fuse and HE nose-fuse rounds at long ranges, when not expecting penetrations and then change to AP round at shorter ranges, when expecting penetrations.
Explosives effects on TGT:
i.e. Explosive filler of round times hits divided by 2 (I expect 50% duds):
Scharnhorst: (7.84+16+21.8kg)/3 x 5.6/ 2 = 42.29kg
Vittorio Veneto: 10.16kg x 3.53 / 2 = 17.9kg
Side protection system penetration @ 30° inclination:
Scharnhorst belt:
Scharnhorst could pen Vittorio Veneto @ 5km
Vittorio Veneto could pen Scharnhorst @ 5km
However Vittorio Veneto could also penetrate Scharnhorst through the upper belt (45mm) and the lower armor deck at >22km. Hit probability of Vittorio Veneto is only 3.49% and the probability of hitting this section is ~20% of the danger zone, i.e. ~0.7% probability of hitting through the upper belt.
Summary:
1. Hits: Scharnhorst (123 shots) 5.6 : 3.53 (101 shots) Vittorio Veneto (1:0)
2. Explosives: Scharnhorst 42.29kg : 17.9kg Vittorio Veneto 1:0)
3. Belt pen: Scharnhorst 1km : 5km Vittorio Veneto (0:1)
4. Deck pen inside 25km: Scharnhorst 0 : 3km (22-25km) Vittorio Veneto (0:1)
5. Blind Fire: Scharnhorst 30km : 5km Vittorio Veneto (1:0)
Scharnhorst 3:2 Vittorio Veneto