Ah, I see. In that case the difference between the two data sets I commented on is likely just differing test conditions, “bench” shooting vs “range” shooting.
Might be worth clarifying that it’s not that naval guns are getting “less accurate” at shorter range, exactly. Sport shooters will be familiar with the idea of measuring accuracy in minutes of arc (MoA or arcmin) with MoA=1 equivalent to shooting a 1-inch group at 100 yards (metric equivalent is mils, with 1 arcmin = 0.30 mil, or a 3 cm group at 100m, but I digress). That’s against a target in the vertical plane however. Against vertical targets, most small arms dispersion patterns are going to be roughly circular around the mean point of impact.
HMD is a measurement of horizontal-plane dispersion; if we used it for rifles, it would be a measurement of when the round hits the ground again at the other end. Because the round is arcing in flight this “beaten zone” will be an ellipse with its main axis along the G-T (gun-target) line, even though it would still have been a circle if the same dispersion pattern had been measured vertically (in flight) like a paper target would do. Ballistic arcs mean small errors in the vertical will lead to larger drift on the ground pattern than in the horizontal.
This means that vertical error is more pronounced at closer range. Basically the ellipse is longer when the trajectory is flatter, so the vertical component of the error makes a bigger difference. As the round’s fall to earth gets farther away, it has a greater vertical component, so the ellipse becomes more circular.
For naval shooting, horizontal ballistic error (just based on the gun’s ballistics, nothing else factored in) is basically linear, but the vertical ballistic error is going to be a non-linear function for this reason. And because the TMD is related to the product of both the length and width of the ellipse (the horizontal and vertical errors), it also becomes non-linear, and you’ll get graphs like those shown. Here’s another one I had which shows some of the same base data I think:
Spoiler
It appears to show some guns get more accurate with range, but a better way of thinking about it might be their dispersion-pattern ellipses are really just getting relatively fatter and more circular, even as they’re growing in overall size with range. Because of this aspect of how TMD is calculated, on this kind of TMD y-axis one should expect a good gun (like Bismarck’s) to curve down and then basically go flat-line with range, whereas an increasingly inaccurate gun (like some of the WW1 weapons shown here) will actually start to curve up at longer ranges.
It’s also worth noting that there’s a lot of graph fitting to not a lot of actual real world data points, as Jurens warned frequently. And that all this is purely the ballistics of an otherwise perfect shot. This is the baseline accuracy which is confounded by all the other factors (particularly fire control system factors, which introduce a whole new error variable).
That said, it can be fun to extrapolate, as Jurens did, from TMD to probability-of-hit, as a back-of-the-envelope estimate of the absolute number of hits one should expect from naval guns, removing all other factor besides ballistics, which for him produced an absolute maximum of a 12% probability of hit by a single gun on a 60m target (that’s about the length of a Flower-class corvette, for reference) at 25000m. Using the same way he did his rough estimate on the same chart above (for 20000m HMDs), you get:
| Ship |
Range |
TMD |
8 gun group |
Hit Probability (corvette) |
| North Carolina |
20000 |
0.383 |
295 |
0.19 |
| Iowa |
20000 |
0.429 |
330 |
0.17 |
| Yamato |
20000 |
0.44 |
339 |
0.16 |
| Bismarck |
20000 |
0.458 |
353 |
0.16 |
| Hood |
20000 |
0.544 |
419 |
0.13 |
| Colorado |
20000 |
0.55 |
424 |
0.13 |
| King George V |
20000 |
0.566 |
436 |
0.13 |
| Rodney |
20000 |
0.57 |
439 |
0.13 |
| Richelieu (postwar) |
20000 |
0.71 |
547 |
0.10 |
| Littorio |
20000 |
0.74 |
570 |
0.10 |
| Scharnhorst |
20000 |
0.76 |
585 |
0.10 |
| Vittorio Veneto |
20000 |
0.98 |
755 |
0.07 |
| Richelieu (WW2) |
20000 |
1.25 |
963 |
0.06 |
Again, that is purely ballistics under otherwise perfect conditions (and also likely has huge error bars on any specific ship considering the data behind it). It would be interesting to know from in-game tests how closely WT gets to this, or whether the prospect of hitting (at most!) 1 in 10 or 1 in 5 rounds in some cases was just too depressingly random and they’ve goosed it to keep battleship games from lasting basically forever.
