Discussion: rate of depth change (lengthy)

[Steeltrap]

Hi all. In the spirit of "don't complain without offering a solution", I tender the following:

I've been interested in the rate at which the boat changes depths. Given that the amount of inclination (bow/stern) is very limited graphically, I noticed at low sppeds your sub seems to zoom up and down effortlessly without using compressed air.

I decided to do a few observations to see how long it takes to change depths at various speeds.

Setup
Sub: Gar
Speed: 3, 5 and 7kts
Method: start at periscope depth. Give order to dive to 320ft. Start timing from moment indicated depth starts changing. Level at 250ft using "A" command. Give order to go to periscope depth and commence measuring per above.

Results
@ speed: 3kts 5kts 7tks 3kts 5kts 7kts
Diving Climbing
100-150ft: 18s 19s 17s 150-100ft: 30s 30s 25s
150-200ft: 26s 23s 20s 200-150ft: 28s 25s 22s
200-250ft: 47s 39s 34s 250-200ft: 30s 27s 26s

What becomes immediately significant is that the rate of change of depth is largely unaffected by the boat's speed. There are 2 possible reasons for this:
1. the sim has simply got hard-coded rates of depth changes programmed
2. the angle of inclination gets steeper the slower your speed, but this is not reflected graphically when examining the boat using external view.

What should happen, IMO, is that there should be a direct link between forward speed and rate of depth change. WWII subs largely used forward motion and planes to achieve depth changes. It was possible to use trimming tanks and compressed air to effect depth changes, but this was usually done only in emergencies as it was noisy and depleted compressed air.

The correct relationship is that the rate of change in vertical feet is the following:

change = horizontal speed x tan A, where A is the dive/climb angle.

Put differently, if you want to know how quickly you would change your depth by 1 foot based on different dive angles, the answer is:

@ 25 degrees: change depth 1 foot for every 2.14 feet of forward travel
@ 30 degrees: " " " " " " " 1.7 " " " " "

What does this mean? Well, at 3 kts you travel forward 5.07 ft/s. Therefore, if you are travelling at 3 kts and diving at a 25 deg angle, your rate of change in depth is 2.36 ft/s.
Thus it should take you (50/2.36) = 21.2s to change your depth by 50ft.

Similarly, for an angle of 30 deg, it takes 17.1s to change your depth by 50ft.

Obviously, with your rate of change being a constant based on angle, you should change depth more quickly based on your dorward motion. In fact it is linear, so you will do so in proportion to your changed speed i.e. 7kts is 2.33 times greater than 3kts, so your rate of change will be 2.33 times greater than it is at 3kts.

Looking at the results, you can see that the time taken to dive from 100 to 150ft is 18s on average, which is close to what we'd expect for a dive angle of 30 deg. What isn't clear, however, is why the rates change for deeper dpeths, and why they are so different when decreasing your depth.

It could be the boat climbs at a more shallow angle than it dives. There is also the factor of "levelling off" so that the last 50ft of a change in depth will be slower than the others (note I set my desired depth to 320ft in the tests to try to minimise this factor on diving). The trouble is that the results do not reflect either of these reliably. Indeed, with almost constant results across a given depth band, there seems to be no difference in your rate of dpeth change based on your forward speed, and this is clearly not correct.

Conclusion
It seems there are issues with respect to the way the sim handles depth changes at present. There is no proportional difference between different speeds of the boat and resulting times taken to change depths.
One result of this is that it is artificially easy to evade DDs at lower speeds, as you can change depth just as quickly at 3kts as you can at 7, but obviously you are much quieter at 3kts.

Recommendation
Explore the following:
1. ask devs how depth changes are calculated at present.
2. work out an appropriate model for rates of change in depths based on different forward speeds.
3. ask if there is any way to change the amount of inclination represented graphically in the sim so it looks more realistic.

Final comment
It's interesting to note that SHIII seemed to model this much more accurately in that your rate of dchange of depth was very greatly affected by your speed. If you wanted to change depth quickly, you needed to increase your speed commensurately. This, of course, had implications for remaining silent during evasions.

I hope people find this useful/interesting. I further hope something might be done with it to improve the realism of the sim (I don't have the skills to mod this, but I will post it in the mod forum).

Comments welcome. If I've made significant errors (always possible!), please tell me. I've just nutted this out in the past 15 mins, so entirely possible I'm mistaken (hell, it's 20+ years since I've done any trig!).

Cheers all!