(Yet another) Attempt to make sense of gyro angles

Von Due · 02-12-17, 10:30 AM

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if the developers decided to use other dimensions than the historical accurate ones, or other principles entirely, then historical documents can only highlight issues without being able to offer actual values to put into the various formulas.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).

02-12-17, 10:30 AM	#1
Von Due Sea Lord Join Date: Jul 2012 Posts: 1,690 Downloads: 30 Uploads: 0	(Yet another) Attempt to make sense of gyro angles 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(0.5g) 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). Last edited by Von Due; 02-12-17 at 11:08 AM.