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Post by tortugapower on Dec 2, 2019 19:58:43 GMT -6
evil4zerggin you're right, shell impact chance is basically the projection of the shadow of the ship/boat from the incoming angle of the shell. That's also a great way to explain it to others that should be easy to visualize. I was willing to spend the little extra time to calculate full shell trajectories, just so I would know exactly what the final angle is. Instead of taking an actual ship model and projecting it, I did a simplification -- hit boxes. My Iowa-class has three hit boxes, a simplification but it should be "good enough" (by my own definition of it, at least). Here's the breakdown: I have the same measurements approximated for the widths for each of these heights. That leads me to the following hit boxes: I add a depth to these boxes (approximate width of ship, even though the ship profile narrows at the bow/stern, I use 30m everywhere). Now I can check if a shell at a series of (x,y,z) coordinates has passed through the hit boxes. Doing this I should be able to duplicate the results from NavWeaps, for the ship hit ratio for target beam-aspect vs. target bow/stern-aspect. I will show those results next.
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Post by tortugapower on Dec 2, 2019 20:21:40 GMT -6
Theory Post #3A: Looking at Trajectories and Hit-Box CollisionsShort RangeWe saw how splashdown looks like, and that shows us that, yes, splashdown is an elliptical pattern. Does that mean a ship is easier to hit when it is bow/stern-aspect? Not necessarily. Let's take a look at short ranges first. I will focus only on the Iowa-class hit box of deck height -- the blue box in the previous post. I test hit percentages of this hit box first abeam to my firing platform, then bow/stern-aspect. Just like the NavWeaps data shows (and thank you to vidboi for helping me interpret this), the turret horizontal/rotational error is so small, that you are actually more likely to hit a bow/stern aspect. Moving out from ~5km to ~10km, we get to the crossover point** where turret horizontal error is wide enough to miss the beam-aspect. Next post continues with what happens at longer range.
** This crossover point is a derivative of the specific horizontal (rotational) and vertical (elevation) turret errors. I chose 0.1 degrees for both, which gives something reasonable, but I strongly suspect that vertical error should be greater. If someone has values for the dispersion patterns at different ranges (probably on NavWeaps), I'd be happy to choose error values to fit the historical data.
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Post by tortugapower on Dec 2, 2019 20:44:14 GMT -6
Theory Post #3B: Looking at Trajectories and Hit-Box Collisions Long RangeIf you have your T-crossed at short range, it's definitely bad, not even taking the reduction of firepower into account. Let's see what happens at longer ranges. Moving out from ~10km to ~18km, it becomes easier to hit a beam-aspect target, but not by much. If I included hit boxes beyond just deck-height, the disparity should increase to further favor hitting beam-aspect, as horizontal spread is high and end trajectories are pretty steep. Now moving to extreme ranges. The chance to hit a beam-aspect is so much higher at this point, crossing the T is actually a *bad* thing. As in, even considering the enemy ship's firing arcs, your chance to hit them is so much lower that it more than compensates for their reduced firepower. Again, that's for normal distribution for horizontal/rotational and vertical/elevation errors that are equal (sigma_h = sigma_v = 0.1 degrees). What's next? That might be the end of my analysis. It was fun! I'm open to suggestions. I can see William Miller shaking his head because this doesn't take into account human ranging error, and so is missing one of the main sources of shell error. I haven't thought about how to model ranging error's impact on shell error. Let me know if you're interested williammiller or if you have any ideas.
A final note: these are for constant drag vs. altitude, obviously not reality. It should only matter above 1 km, so higher elevations like 15 degrees, which translates to very long targeting ranges (~20km). Nonetheless, I shared these results with a friend, and in the spirit of fraternal correction he said "don't be lazy, [Tortuga]! Put in the real drag!" I have since done so, and the results are impacted at longer ranges, but I haven't replicated these nice plots yet for "real" atmosphere.
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Post by samweston on Dec 2, 2019 22:31:47 GMT -6
Now one thing I wonder. Most time I attempt to cross the T on an enemy formation I end up making more of a curve given that the ships are always moving and I rarely have a single ship in a division. How would that affect such as it places a point of convergence for the shells, as would crossing the T with multiple ships as they are going to be training their guns in a manner to converge the point of impact?
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Post by broadsides on Dec 3, 2019 10:25:50 GMT -6
Is this aimed at a 'game only' calculation or real life. In historical terms the 'elliptical splashdown' effect is manufactured by multiple gunned mounts. example: Target is class X with a 50meter beam and 300meter length, Range 12,000, firing ship has three 3x turrets. target AoB is 90 degrees (broadsides), Turret 1 spreads it's guns so the middle gun is ranged at 12,000 but guns 1&2 are ranged at 11,950 and 12,050. This is based on the 50m beam of the target to produce a spread before any ballistic effects in flight. In an AoB zero degrees (bow/stern aspects) the guns of turret 1 might range 11,900; 12,000; 12,100 or even 11,800; 12,000; 12,200; because of the 300 meter length. Turrets 2 and 3 would be firing a few degrees port/starboard of the target to spread hits 50 meters port and starboard (based on the 50 meter beam) and so forth. In WW2 this was done by spotting corrections, in modern guns can be adjusted (thanks to ballistic radars that determine wind,humidity,temperature...etc effects) and follow up shots can be adjusted to compensate. it is an intended spread to cover the target area to compensate for range/speed/heading estimate errors and target motion during flight. In such a gunnery application 9 shots to cover the target area based on target size to increase the probability of all guns achieving at least 1 hit and several close hits over 9 guns firing at a lesser hit probability per individual gun.
I do not know if the game accounts for this by just increasing the hit percentage as tech develops and still 'firing' each gun individually at the target or makes a number of guns times area covered probability calculation.
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Post by tortugapower on Dec 3, 2019 12:29:44 GMT -6
Thanks for the info, broadsides. With respect to your comment, you can treat my simulations as only representing the gun trained exactly dead-center (with perfect accuracy). This study originates because several people mentioned how "elliptical dispersion pattern means that a target is easier to hit when its T is crossed". I doubted this was always true because an elliptical splashdown pattern does not consider the shell trajectory itself. The conclusion from my results so far is -- for a specific variation of turret elevation and rotation -- the splashdown pattern is elliptical and mostly stretched in the direction of shell travel, as expected. However, there is still a wide range when this elliptical pattern is more likely to hit a beam-aspect target, contrary to what those individuals theorized. I hope my motivation helps explain what I was trying to study here, although I'm happy to explore other trajectory-related items (now that the simulation is already built!).
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Post by rimbecano on Dec 3, 2019 17:29:23 GMT -6
I'd like to see some coverage of range error due to muzzle velocity dispersion.
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swang
Junior Member
Posts: 97
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Post by swang on Dec 3, 2019 21:24:25 GMT -6
I work on the theory of charging forward. When I get superimposed turrets, I immediately change to 2x3 gun turrets. Ending with 2x4 soon after and the advantage of all forward guns.
In this case, crossing my T does my opponents no good. They get a smaller cross section with better angled armor. I get to shoot their big fat sides.
When I need to turn and run from DD s, my secondaries are helpfully in the back. Even if I get crossed from the back, because of the wider angle of fire, a minor angle will still allow me to engage any remaining SoL that is still floating. There usually isn't, but that's probably because I'm playing against the AI.
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Post by tortugapower on Dec 5, 2019 15:50:20 GMT -6
rimbecano Sure, I can do new trajectory plots with hits/misses like above, but also including shells fired at lower velocity. Can you recommend a distribution for the shell velocity? (Maybe something as simple as a half-normal distribution for shell velocity decrease, but even then what magnitude of variation?) Also, I know that some shells were impacted by the turbulence of other shells in the same volley, if you have an idea about the numbers that I might use to simulate that.
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Post by vidboi on Dec 5, 2019 17:33:19 GMT -6
rimbecano Sure, I can do new trajectory plots with hits/misses like above, but also including shells fired at lower velocity. Can you recommend a distribution for the shell velocity? (Maybe something as simple as a half-normal distribution for shell velocity decrease, but even then what magnitude of variation?) Also, I know that some shells were impacted by the turbulence of other shells in the same volley, if you have an idea about the numbers that I might use to simulate that. I believe a new gun would have a velocity variance of 1-2 m/s, and a worn one about 5 m/s. Italian gunnery was particularly affected by this as they had awful quality control on shell and propellant mass
Kudos on the analysis overall, it makes an interesting read and I like the way you've plotted the hitting space. Any chance you could share the code used for this? I'm tempted to have a crack at considering the effects of aiming errors
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Post by evil4zerggin on Dec 6, 2019 19:48:20 GMT -6
Also, I know that some shells were impacted by the turbulence of other shells in the same volley, if you have an idea about the numbers that I might use to simulate that. According to this article, the introduction of delay coils to US battleships in 1934 decreased dispersion by about 40%. Though I'm not sure whether it affected horizontal or vertical more---maybe horizontal, since that's the direction the guns are offset from each other?
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