(Yet another) Attempt to make sense of gyro angles

[Von Due]

WARNING. MATHS AHEAD!

Introduction:

I am looking into the torpedo triangle problem where the gyro angle is not zero. As the game documentation offers no information on dimensions needed to work out the solutions, this is going to involve a lot of guesswork, trial and error. Some guesswork may be more educated than others but it will still be guesswork.

The most apparent problem is that SH3 is a game, that is nothing more than computer code and if the developers decided to use other dimensions than the historical accurate ones, or other principles entirely, then historical documents can only highlight issues without being able to offer actual values to put into the various formulas. This is where trial and error comes in, to attempt to deduce which dimensions and principles the game is using so that the non zero gyro angle triangle can be worked out by the player.

As a starting point, when it comes to errors, everything about the game is a suspect until proven innocent. To get anywhere one must make a few choices and assumptions. I will start with the historical accurate data (or what I believe is historically accurate) whereever I can find them, and attempt to work out if the results agree with what the game does.

To avoid this getting completely out of hand, I will limit this to the G7a and G7e torpedos.

Data is primarily nicked from http://tvre.org/en/gyro-angled-torpedoes

Finally, let me just say this entire topic is about torpedo shots where the gyro angle is not zero so no "just set it to zero, it's easier", please as that only makes the thread harder to read without adding anything useful.


General on torpedo runs as described in documents

When a torpedo leaves the tube muzzle, it will travel straight ahead for a short distance called reach (German: gerade vorlauf). This reach is torpedo type specific so when you know the type, you know the reach.
The reach is followed by the turn. The turn angle is the gyro angle. The turn also has a turn radius which is torpedo type specific so when you know the type, you know the radius.
The turn is followed by a final straight run to target. The gyro angle is the angle between the submarine's longitudal axis and this straight line. The distance between the tube muzzle and where the terminal run line crosses the submarine's longitudal axis, is called advance (German: Winkeleinsteuerungsversetzung). The advance is therefor a function of the reach, turn radius and gyro angle, two of which are constant for a given torpedo type.

The G7a and G7e

These torpedos have the same values for reach (R) and turn radius (r).
R = 9.5 meters
r = 95 meters.

The advance (A) for a 90* turn is reach + radius so for these torpedos, the
A = 9.5m + 95m = 104.5m

Generally, the advance for a given gyro angle (g) can be approximated by the formula

A = (R+r) (1 - cos g) according to http://tvre.org/en/gyro-angled-torpedoes

In the case of these two types, this gives

A = 104.5 (1 - cos g)

However, I will use
A = R + r * tan(0.5*g)

Periscope and parallax

The periscope is a fixed distance from the tube muzzle. This distance L is uboat type specific. The game offers no information on the precice distance here. Nor have I been able to find documentation on this value. This means that L + A can not be known. This value is necessary to solve the parallax problem. This may be decucable from in game tests though if a test method can be deviced that will give results accurately enough to being used. More than one method would be preferable to check for agreement between results.

Each submarine in the game has 2 periscopes some distance apart so L would depend on which periscope is used. The parallax effect has been confirmed on the two periscopes but the distance between the two is still unknown. To limit the work, I will only consider the attack periscope of the type VIIB uboat.

Restrictions on aiming

In the game, the gyro angle must be smaller than about 95* to either side of the bow (stern for stern tubes). For contact pistols, the angle between the torpedo path and target hull should be from 85* to 95* (from memory. If anyone has a correction, please post it) to minimize the chance of no detonation. For magnetic pistols, there is no such requirement.

Principles of aiming

When one aim the shot, what one is aiming at is a point P that is fixed relative to the submarine, at a constant bearing from the periscope, at a constant distance. As the submarine maneuvers in the world, this point will follow the submarine so the bearing and distance remain constant.

The moment the torpedo launches, that P leaves a virtual mark Q on the map. This virtual point Q will NOT move with the submarine but keep its position on the world map. Q is a time freeze image of where P was at the moment of launch. It is important to understand that the torpedo will be set to, at some point in the future, reach Q. If the submarine moves during the shot, then P and Q will not be in the same spot and it is only Q that can be considered.

There are 2 bearings to P that must be considered. One is from the periscope, the other from the advance point ahead of the muzzle, which will be L + A meters ahead of the periscope. Because the periscope is some distance away from the muzzle, and because of the advance, the bearing to P from the reach point ahead of the muzzle will be different than the bearing to P from the periscope. This is the root of the parallax problem.

The goal of the gyro angle is to have the torpedo reach Q at some point in time. Q is a mark left by P so P is the intersection of the two bearings that is, the bearing from the periscope (Bp) and the bearing from the far end of the advance (Ba). When the distance to P from the periscope increases at a constant Bp, then Ba will decrease and vice versa for decreasing range. There is a non-linear relationship between range and Ba. There is also a non-linear relationship between Bp and Ba.

Since gyro angle g = Ba, if one can find a function of Bp and range D that reveals Ba, then one has also found g.

Setting up the game's TDC for testing game vs theory

If the target is moving, then it is not enough to know P and therefor also Q. So far I have considered P as the intersection of Bp and Ba but for a moving target, Q must also be where the target and torpedo arrive at the same time. Q must therefor be where Bp, Ba and target course intersect. Furthermore, for contact pistols, it is desireable to have Ba perpendicular to target course, +- 5* but for the sake of more completeness, I will extend the work here to angles outside that window.

If the uboat's course is parallell to target course, then one can set up P beforehand and maneuver the boat so that P tracks the target course. If the uboat's course is not parallell, then P needs continuous update for range and or bearing. For that reason, I will look at cases where the uboat and target travel on parallell courses. Later one can look into the problems with non-parallell courses.

Periscope bearing, TDC and gyro angle

At this point I will remind you that P is where Bp and Ba intersect and that since Ba = gyro angle g, P is at the intersection of Bp and g. Bp defines a line of sight from the periscope, g defines the point P on that line. This means that once you set the range and Bp for P, and the target speed set to zero in the TDC, the gyro angle calculated by the TDC is precicely the angle that defines P. If g changes, then so does P. The opposite however is not necessarily true. This means that for a given P, there exists only one g, but for one given g there exist infinitely many possible P. Which one of these is determined by Bp.

As long as the target speed is zero, then the lead angle will be zero. Lead angle gives a lead bearing Bl. Bl is Bp offset for target speed and relative course. The TDC will always assume the periscope points at Bl. By setting the target speed to zero, Bl and Bp are one and the same and Bp can be read directly off the scale.

By setting target speed to greater than zero, the TDC will change g under the assumption that the periscope is at Bl but by doing so, it changes P. To correct that, you must turn the periscope so that g shows the correct angle for P. This is the angle found at target speed equal to zero.

A quick recap: The TDC is set for desired range to P and by turning the periscope to the desired bearing to P (Bp) with target speed set to zero, the correct gyro angle is found. Next target speed is given to the TDC which will change g and thus P. The periscope is turned so that g is back at the correct angle putting P back to where we want it.

(more to come as I keep working on it, including more on lead angle and ways to figure out true torpedo runtime).

[Von Due]

I am trying to establish the distance L between the attack periscope and the bow tube muzzles.

I set up P at Bp = 270* at 3000m

Totally eyeballing the terminal run back to the 0* bearing line to somewhere near 140 meters from the center of the submarine icon.

Assuming the game uses the correct values for reach and advance, I backtrack the distance L to be in the area of 33.5 m +- 2 meters uncertainty.

I will use 33.5 as my initial guess and look at the consequences, to try to narrow it down to a closer to exact value.

If 33.5 is correct, then L + R is constant and equal to 43m.

Then the side S of the triangle that is on the 0* bearing is

S = 43 + 95 * tan (0.5 * g)

[Von Due]

Made an illustration to the problem with gyro angles as a function of Bp and D.

http://i68.tinypic.com/2hz0io8.jpg

[Von Due]

Digression: Assuming the developers used a similar model as in the illustration but ignored that port and starboard turns would require mirrored models, it might be possible that this would be the reason for the discrepancies between port and starboard turns in the game, yielding so different projections on the attack map. If this is the case, then the model would work for one turn but not for the other. One more on the things-to-check list.

[bstanko6]

I don't believe German torps could travel in a curve and then straighten out, being they were preset gyros.

Firing a torp is no different then a handgun. Trigonometry plays a huge
Role.

If I stand at the range and hold a gun, my hand naturally moves and shakes.

If I pull the trigger, the bullet will travel, and every shake and tremble will throw the trig solution off the greater the distance the bullet travels.

Germans knew this, and ordered their boats to fire under 1000 meters!

Also, setting the gyro on a torp to curve at a greater degree, is like pulling a guns trigger while moving... the degree of error is too great.

This is why we try to get a zero angle every time, to eliminate error.

You are doing a lot of work on this TDC. But I think due to German engineers lack of developing the torp and TDC compared to tanks and planes in WW2, you are better off eliminating error, than solving angle issues.

Torps cost money! Don't be wasteful!

[Von Due]

I don't believe German torps could travel in a curve and then straighten out, being they were preset gyros.

Firing a torp is no different then a handgun. Trigonometry plays a huge
Role.

If I stand at the range and hold a gun, my hand naturally moves and shakes.

If I pull the trigger, the bullet will travel, and every shake and tremble will throw the trig solution off the greater the distance the bullet travels.

Germans knew this, and ordered their boats to fire under 1000 meters!

Also, setting the gyro on a torp to curve at a greater degree, is like pulling a guns trigger while moving... the degree of error is too great.

This is why we try to get a zero angle every time, to eliminate error.

You are doing a lot of work on this TDC. But I think due to German engineers lack of developing the torp and TDC compared to tanks and planes in WW2, you are better off eliminating error, than solving angle issues.

Torps cost money! Don't be wasteful!

Thanks for the input but as I stated in the introduction, this topic is solely for the discussion of shots with gyro angles other than zero and as such, any response here like "don't do that" is only making the thread less readable. If you read the page I provided a link to, then you would have known that according to that page, German torpedos, as well as most other torpedos after WWI could indeed turn. This includes the G7a and G7e. Not only were the torpedos capable, but the submariners including German ones, knew about it and knew how to solve it. However, for tactical reasons, only 90 degree gyro settings were used as alternative to zero degree runs.

[bstanko6]

Sorry I got lost in your MIT dissertation you wrote. Just kidding, I am being funny. I actually started to skim over and I did not read that part about certain responses.

Any way, my concern was over the statement you made in the first paragraph of your second topic:

"The turn is followed by a final straight run to target."

I did not think this is possible for an analog gyro system to do. I can see modern torpedoes straightening out, not WW2 era. That is what I really meant.

I added the trigonometry comments because it is true, you are sending a torp (bullet) with no controls once it is fired, onto a path that cannot be changed. The only thing that changes is your boat moving, the target moving, every wave and sea state your torp travels through, the density of that sea state changing, the resistance of drag onto the outer shell of the torp as it travels through said density, the distribution of steam (or power from battery cell) of torp, all the while you wanted to set a curved path with manual input that may or may not be correct depending on the math of the person who inputs the solution in the first place....

needed to breath there!

When in the end, you can eliminate the bulk of these variables by eliminating the gyro angle, and set it to 0!

[Von Due]

You must remember what the gyroscope is actually doing. Before launch, the gyro is set to an angle to zero degree bearing. The way gyros work, they will want to turn into this new course and stabilize themselves there once they are on the new course. The gyro setting is not a turn rate setting but a course setting, a course relative to the longitudal axis of the torpedo's pre-launch position.

Example: Your boat is on a 250* true course and you fire the torpedo with a 30* port turn gyro setting. That will take the torpedo to the course of 220* true heading. It will not continue the turn after reaching 220* because this is the heading where the gyroscope is not fighting back to correct the course. This is the course that makes the gyroscope happy.

If your true course is 315* true heading, then a 30* port gyro angle will see the torpedo take the true course of 285* true heading.

After this heading is achieved, no more turning takes place and with no turn, there is only a straight run left to do.

[bstanko6]

That's right. You are right! My apologies. I was thinking in an extreme curve where the torp hits the boat while curving.

Thank you for clarifying!

[Von Due]

Referring to the illustration in post #3.

The circle represents the turn. It has 2 tangent lines. The vertical tangent line is the uboat's 0* bearing line. The other going to P is the bearing line for Ba.

The turn starts at the tangent point at the 0* bearing line. The turn then follows the curve until it reaches the 2nd tangent point at the Ba line.

The Ba line must always be a tangent line to the circle. So must the vertical 0* bearing line.

This means the intersection angle i is a function of Bp and D.


The 0* bearing line, the Bp line and the Ba line form a triangle with angles
Bp, i and (180* - g). Regardless of the length of the sides in this triangle, any triangle with this particluar set of angles are all similar and can be treated as one and the same when solving for angles.

With Bp and D as function inputs, one can therefor describe the gyro angle g as a function of Bp and D.

Value of g = g(Bp, D)

The Quest now then, is to find that function...

EDIT: Apparently, German submariners would bring with them tables for parallax correction and I can only find references to numerical methods for estimating the corrections. I can not find any reference to any analytical method which is bad news.

[bstanko6]

Maybe look in USN manuals. I forgot where it is but there
Is a website with historical records for the US navy with manuals.

US subs in WW2 probably had the same issues.

[Von Due]

Thanks for the heads up on those! Will look around and hoping it would be for solutions before their uber TDC entered service.

I am slightly worried now though. If no analytical method is known, then that could mean that it is either proven to be impossible, or it is an NP problem. In both cases, the search would have to end. That would not be what I was hoping for. "Luckily" I am a complete fool and will keep looking until someone smacks me over my noggin with the evidence that there really is no analytical method known.

EDIT: Returning to the same site I found the other data, I discovered that the distance L I was looking for was roughly 28 meters for the Type VII boats. My guess was 33.5. Reality and virtual game reality are 2 different worlds but I will try to put 28 meters to the test and see how the game responds to that.

Another thing I found there was a description on how the TDS's parallax solver worked (sub chapter "Description of the component for calculating the parallax correction" at http://tvre.org/en/torpedo-calculator-t-vh-re-s3 ). Perhaps there is something there that sheds some light on this.

[Von Due]

To put L = 28m to the test, and assuming the reach and turn radius in game were historically accurate or close, I did this test:

Using L = 28 meters, R = 9.5 meters and r = 95 meters.

L + R = 37.5m.

I drew a line on the map straight up for 3000 meter using Pato's bearing and range tool. This line represents the Bp line of sight to P at a distance of 3000m (the line OP in the illustration above).

From the 0m end of the first line, I drew a horizontal line line and marked a point approximately 37 meters from the start, again using Pato's tool and counting the pixels (the vertical line in the illustration, and marking the end of the reach measured from the periscope at 0m).

From this mark, I drew a line approximately 95 meters long straight north. At the end of this line I then drew a circle that now had a 95m radius (the circle and horizontal radius line in the illustration).

From P at the far end of the 3000m line, I drew a tangent line for the gyro angle. Pato's bearing tool showed this line having a bearing of approximately 2.5 degrees (corresponds to the angle i) and the gyro angle g being approximately 92.5 degrees.

This is a very uplifting result as this agrees within the inaccuracies of the drawing and measurements to about 0.1-0.2 degree from what the TDC gives me for the same bearing and range.

It does appear more likely now that the game uses actual dimensions and that one could construct on the map the triangle for gyro angles at any arbitrary Bp and D.

EDIT: Repeated the test with L being my initial guess of 33.5. Changed the position of the reach and the center of the circle accordingly.

The difference for D = 3000 meters was too small to be meaningful but for D = 2000m the result was a closer match between the drawned angle and the TDC computed angle when L was 33.5. This suggests that 33.5 is closer to the length the game uses.

[Von Due]

Found this scan of a translated handbook for Kriegsmarine u-boot commanders
http://archive.hnsa.org/doc/uboat/index.htm#par148

It contains instructions on how to carry out various torpedo attacks including the 90* shot but also, curiously enough a 45* shot. Paragraph 148, II D IV.

It does not describe the calculations but it is an interesting read nontheless.

[La vache]

I am not able to reproduce all mathematical functions.
My source is: Analogrechner auf deutschen U-Booten des Zweiten Weltkrieges: Technikgeschichte und mathematische Grundlagen (https://www.amazon.de/Analogrechner-deutschen-U-Booten-Zweiten-Weltkrieges/dp/3732350339/ref=sr_1_2?s=books&ie=UTF8&qid=1486976287&sr=1-2&keywords=Analogrechner)

The battle picture (Gefechtsbild) Tvh-Re/S3 similar Drawing 12/13 on tvre.org
The formula for the parallax improvement (Parallaxverbesserung) of Tvh-Re/S3

Sin (δ) = x/e * (ω + δ + Δω)

[Von Due]

Thanks heaps, La Vache. Appreciated! Too bad I don't read German and Google translate is as hilariously bad as ever but names of books can be looked into. Again thanks heaps.

Reading up on the parallax correction on that other site and he is not making it easy for the reader, that's for sure.

[Von Due]

I am pretty convinced now the bug on the attack map projection is because the developers forgot to mirror the calculations for port vs starboard turns not to mention they add the same distance into the total more than once.

Here is an experiment you guys can do the next time you fire up SH3.

Set the TDC up for zero everything except distance. Zero target speed, zero gyro angle, everything. Note down the projected time T0 on the attack map in seconds. Also note down the distance D0 you set the run for.

Calculate for 90* port gyro turn the time Tgp:

Tgp = (D0 + 95)/D0 * T0

Calculate for 90* starboard turn the time Tgs:

Tgp = (D0 - 2*104.5)/D0 * T0


Now turn the periscope to set the gyro angle to 90* port and starboard and compare the projected time with the result you calculated. Were they close?

[Von Due]

It appears that adding 4 seconds to the runtime for a straight run will give a good approximation for runtime for a 90 degree turn set at the same distance.

The torpedo travels about 100 meters in 4 seconds on fast speed (avg. speed appr. 44.5 kts). The added distance comes from the turn so the arc of the turn must be about 100 meters. Since the arc length for a 90 degree turn

a = 1/2 pi*radius,

this corresponds to a turn radius of about 63.66 meters which is about 2/3 of the historical accurate turn radius of 95 meters.

The torpedo will travel parallell to line of sight to the 270/90 bearings at a distance of roughly 136 meters. It's not exact but should be accurate enough for medium to large size targets.

More importantly, the runtime and distance between torpedo track and the 270*/90* bearings are the same for port and starboard turns. Only the projection on the attack map is wrong for starboard turns.

[La vache]

Hallo Von Due

According to Rössler (https://www.amazon.de/Torpedos-deutschen-U-Boote-Eigenschaften-Marine-Torpedos/dp/3813208427) the GA (Gradelaufapparat) could only reach a torpedo running angle of ± 90°.
It should be shot with the smallest possible torpedo angle as there was an offset displacement at 90° of ± 35 m. β ≦ 90°


You can set settings such as test sheets. As an example rear shot with 7° parallax angle. LfdNo 15
Distance E = 5hm (500m)
Target direction ω = 66°
Vt = 30 nm/h
Vg = 24 nm/h
AoB ϫ = 60° StB
β = 40°
Result = firing angle ϱ = 280° corrected -180° = firing angle 100°
The deviation of the deflection angle and the shot angle results in a parallax angle δ ~7°

http://fs5.directupload.net/images/170216/p4kd4fix.jpg
http://fs5.directupload.net/images/170216/6wvn8lfq.jpg

[Von Due]

Thanks for that. Has that been verified to work in the game? The main problem with the game is the dimensions that seem to be somewhat off but in a not so predictable way and the main Main issue is the attack map which is way off as a rule of thumb, so to speak. I set up a dummy shot for 3000 meters, gyro angle 315*, intercept angle 135*, target speed 7 kts. The solution projected on the map had a solution for 3750 meters.

Strange also about the 90* only thing as a copy of the commander's handbook has a step by step section on 45* gyro angles if I read that right.

[La vache]

The RW (TDC) shot was the standard solution.
Bow/rear shot, 45° and 90° shot was used in case of TvhRe/TDC failure.

Important for complete solution is the Angel of Bow.
AoB and lead angle arise with Vt Torpedo running track.

For parallax enhancement, Boat speed and command deceleration were automatically calculated. This is probably not considered.

[Von Due]

In the game, speed, speed changes or course changes are definitely not something the TDC keeps itself updated on. I believe that would be the same for the real German TDC. If anyone other than the Americans had position keeping capable TDC, then that would be interesting to know.

I went back to my main character's campaign, in a Type IXB and the dimensions are definitely different but right now I'm questioning the method that worked for the Type VIIB. Attempting to establish where the equivalent point of fire is for the IXB using G7a torpedos on a 90* setting is giving me a mild headache.

[La vache]

I believe that would be the same for the real German TDC.

The component for entering the target bearing also took into account the correction for the angular speed of the U-Boat turn. This correction was connected with the torpedo gyro starting-up delay, which was equal to tv = 0.4 sec. During this time, the gyro of the torpedo was locked in one position. That means that when the U-Boat was turning during the torpedo launch, the longitudinal axis of the torpedo (together with the locked gyro) was turned by the angle tv∗φt, where φt was the angular speed of the turn, which depended on the U-Boat speed and main rudder deflection.

The TvhRe/S3 was connected to the gyro compass.
The rotational speed was calculated automatically, but could also be entered manually.
The SH3 TDC is a simplification.
For example:
The spread angle is entered as the target width in meters (100-200). In SH3, enter the angle directly.
For Fat and Lut torpedoes there were no adjustments at the TvhRe/S3. These were done directly on the torpedo or on an auxiliary board in the bow space.

[bstanko6]

http://www.tvre.org/en/aiming-with-the-periscope

Try this one out in reference to your parallax issue. Hope it helps.

[makman94]

hello Von Due,

i think it is useless trying to find out great accuracy based on sh3's TDC for two reasons.

The first reason is that the game (and eventually TDC) is NOT getting the distance to target or bearing to target from the periscope (the one that player is using) but from the generic node of sub's 3d model. this ,practically, mean that for each sub model there will be different inaccuracies.
you can easily confirm that by looking at a stationary -close to you- target from periscope at a fixed bearing. not at bearing 0° but better,for example, to 270° and watch the bearing that TDC shows.you will need a mod for showing you the 10ths of degrees of bearing for that.then simply,without moving anything, press the lock button to lock the target on periscope and watch that the bearing on TDC is slightly changing and now the bearing on TDC is not exactly the same with the bearing you see on scope. (this is fixable.in my own sh3 set up , i have matched ,at the uboat i am using,all the scopes-uzo 3d nodes with the uboat's generic node for avoiding the above inaccuracies)

the second reason is that sh3 is coming from sh2 which is coming from sh1. sh1 is for american submarines and sh3 is for german submarines. The american submarines were using different Torpedo's Straight Run(SR) and Torpedo's Turn Radious(TR) values for the left or right shots (from this book:https://www.abebooks.com/9781935327073/Submarine-Torpedo-Data-Computer-Mark-1935327070/plp i read that for right shots the values were SR=57.93yards TR=215yards and for left shots the values were SR=32.46yards TR=206yards). I am suspecting that the sh's devs didn't transform the equations (for torpedo aiming) right from sh1 to sh2 and finally to sh3. i am ,also, guessing that this is the reason for the inaccuracies you see at torpedo running times for shots like in the following image (the first reason is not responsible for that issue.this issue is a hardcode error):

http://i65.tinypic.com/bhi2d2.jpg

the image shows the TDC solution at two symmetrical set ups.
at the left, you see that torpedo's run time is 1:13 and at the left you see that torpedo's run time is 1:06.
the two solutions have to be the same but they are not.

ps: propably i am off topic (haven't followed all the posts) but my point is that trying to get very accurate results(-conclusions) based on sh3's TDC is not a safe way.


...If anyone other than the Americans had position keeping capable TDC, then that would be interesting to know.

.....

Japan had one too

[Von Due]

Greatly appreciated post, makman94. As you said, there are errors and the attack map and TDC are both questionable. The goal I would like to reach however is to figure out a way to manually plot lead angles for gyro angled shots, for various speeds and distances. Manually, because a bugged game is not going to do what it's supposed to so in short, find a way to work around the bugs and errors in the game.

[makman94]

Greatly appreciated post, makman94. As you said, there are errors and the attack map and TDC are both questionable. The goal I would like to reach however is to figure out a way to manually plot lead angles for gyro angled shots, for various speeds and distances. Manually, because a bugged game is not going to do what it's supposed to so in short, find a way to work around the bugs and errors in the game.

there is no way to be able to calculate the gyroangle taking in account the parallax correction with a single formula.for that is the need of a computer.

there is a workaround though for those who doesn't want to use the tdc and it is called ''the broken tdc methods'' (http://www.subsim.com/radioroom/showthread.php?t=169935) but in these methods is not taking in account the parallax correction so there will be inaccuracies in very close shots.The method is good for use at shots more than 1500m
At the tutorials for these methods (tutorials can be found in MaGui F.rar), i showed the straight shots and the perfect shots (perfect shot means impact angle = 90°) but you can combine these two methods and create whatever curved shot you like (for any other curved shot you have to choose the desired impact angle-instead of 90°- and proceed).



in case that you are interested in these methods ,

have in mind to take the angle 'x' ,always and in any case, from the tables (not from the RAOBF rings as i am discribing in the notes.the RAOBF rings are good for getting angles <5.71° but if angle 'x' is greater the rings will be off. so get the angle 'x' only from tables)

here is one example how these two methods can be combined:

http://i63.tinypic.com/eg353m.jpg

steps for the above example:
1. get angle lb1 from map (angle lb1 is the angle between yours and target courses).lets say at our example lb1=110°
2. select the impact angle (angle lb2) that you want for your shot (at perfect shots this angle is 90°). then set to gyro G=lb1-lb2 .then set tdc to manual mode from now on.
in our example . lets select impact angle lb2= 80° so we will have G=110°-80°=30° so will set G=30°to tdc and switch it to manual mode from now on.
3. choose the torpedo speed that you will use and look at its table for getting the angle 'x'. for this combined method,the torpedo tables now have at vertical columns the angles lb2. so find the lb2 of our example at vertical columns and the target speed at horizontal lines. the table will give you the angle 'x'.
lets say that our target is moving with speed= 10 knots and we choose to hit him with a 30kts torpedo.from the table,lb2=80° and u=10, so we get angle 'x'=17.2°
4. Shooting bearing = G + x so ,at our example, Shooting bearing = 30° + 17.2° = 47.2°

[Von Due]

Just curious. Those tables you show there (I have them too), how were those values found? Were they all empirically found or were there some sort of algorithm involved? If they were all empirically found then I am impressed! That's a lot of testing.

[makman94]

Just curious. Those tables you show there (I have them too), how were those values found? ....

the tables were created with excel programm,

if you apply the law of sines on the triangle that containes the angle 'x' (look at the image at my previous post) you get :

x = arctan{sin(lb2) / [(u1/u2) + cos(lb2)]} ,where u1=torpedo speed and u2=target speed

and excel gave all the outputs that you see on tables. (i ,then, rounded these outputs to one decimal digit before print them one tables)

[Von Due]

This is where I am confused. See, you said there was no simple way of correcting for parallax but for these angles to really work in-game, the parallax MUST have been accounted for. See the contradiction? That there is a parallax issue in the game, like in the real world, has been confirmed. The game does account for the different positions of tube muzzles, periscopes, advance and equivalent point of fire. That does not imply in any way that the dimensions the game use are the historically accurate dimensions. It only means that the game does distinguish between bearing from tube muzzle and bearing from periscope and that these 2 bearings are different from one another. Tests show that the game does apply the concept of equivalent point of fire, in one shape or the other, even if the game does not follow up on the concept in full.

It does nothing good in knowing what lead angle the torpedo needs, if there is no way the game will allow the player to know how to correct for parallax.

This is the reason I asked if these angles were empirically found.

To use your example:

The triangle shows the lead angle for the torpedo must be 17.2 degrees. This does not help the player as 17.2 degrees is only valid as seen from the equivalent point of fire. From the periscope, the lead angle must be different (smaller in fact) than 17.2. How much smaller is the unknown and the challenge is to find out exactly how to find the lead angle as seen from the periscope.

[Von Due]

Just noticed something peculiar.

I set up the gyro for a 90 degree turn. Which side doesn't matter.

With the auto update on, I make sure the periscope doesn't move and that nothing else on the TDC is altered. Still there is some small movement for the gyro angle in rough weather. With the auto update off, I couldn't notice any change in gyro angle.

This is odd indeed and I'm wondering if the reference points for a fireing solution are floating around much like the bridge/deck gun sight cameras are not fixed to what they should be fixed to. The end effect is, the SH3 submarine might very well have its torpedo tubes not attached to the submarine at all but floating around freely in proximity of the submarine. In that case, all bets are off and angled shots would be impossible to work out.

[makman94]

..... the challenge is to find out exactly how to find the lead angle as seen from the periscope.

as i told you the ''broken tdc methods'' are for those who doesn't want to use the tdc. i also said that are not taking in account the parallax correction so expect inaccuracies at close shots. these methods work fine at long shots.they are not EXACTLY at the point you aiming just becuase the parallax is not in play but at long shots you hit the target. (i have made many many shots with success becuase the difference is not so critical).
But , i see what you are aftering at , and for extreme accuracy these methods are not for you.
The best accuracy you can get,as things are, is to use sh3's tdc becuase it is taking in account the parallax correction.i am afraid that without the use of sh3's tdc you will not be able to get extreme accuracy at your shots becuase it is impossible to solve the firing problem without the use of a computer.there is no single formula for giving you the shooting bearing with the parallax correction in play.
trying to find a workaround for the shooting bearing (with parallax in play) is the same problem with a workaround for getting the gyroangle and this is just not possible without a computer.

my two cents though, i will be huppy if i proved wrong

[Von Due]

Test procedure and results so far:

I mark on the map a representation of the periscope.

Due north of this mark, 135-136 meters north I mark the advance line for a 90* gyro angle. This line is extended west and east so that it intersects the 87.4* and 272.6* marks at the 3000 meters circle on Pato's bearing tool.

I fired torpedos at slow speed setting with 90* turns and timed when the torpedo reached each of the 100 meter marks out to 3000 meters.

Plotting the range from periscope vs time, I did a linear regression and found the expressions for torpedo run time for 30kts, 40 kts and 44 kts for distances between 200 and 3000 meters from the periscope.

t(30) = 0.06543472906*R + 1.683743842
t(40) = 0.0490760468*R + 1.262807882
t(44) = 0.044614588*R + 1.148007165

These regressions had an r^2 apprx = 0.9999 which is very good. Still it should be mentioned that the times can be off by apprx 1 second but for targets 70 meters long, 1 second is within limits even for target speeds of 12 kts.

I then drew a line L from the periscope mark to the advance line and used the distance from the periscope in the above equations to find run time. I noted down the true bearing of this line.

Set target speed to zero in the TDC, and adjusted the range until the attack map displayed the time I calculated while keeping the gyro angle locked at 90*, the actual periscope bearing now matched the measured true bearing of L

I calculated how far the target would travel at 8 kts before reaching the intercept point and drew the target course line for this calculated distance, to find the aim point.

Now I drew the lead angle line from the perscope to the aim point and measured the true bearing to get the lead angle bearing for the periscope.

This bearing did NOT match the TDC suggestion. The two disagreed by several degrees.


I will attempt these manual plots for 90* shots and see if they will give me consistent results.
After setting distance and gyro angle, I will disengage the auto update and set the perscope to the measured bearings.