Doolittle WoS Guide

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\author{Patrick Doolittle}
\title{$\mathfrak{Silent\; Hunter\; 5:}$ \\  $\mathfrak{Wolves\; of\; Steel\; Mod}$  \\
$\mathfrak{Submarine\; Commander's\; Guide}$}
\date{July 31, 2023}
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\begin{document}

\begin{titlepage}
\maketitle
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\section{Introduction}
Silent Hunter 5 is a game released by ubisoft that puts the player in charge of a World War II German submarine. The game takes place in several theaters from the North Sea, East Atlantic, Mediterranean, and the open ocean over the span of the outbreak of the war in September 1939 to it's end in May 1945. Your goal as the U-Boat commander is to direct your crew and operate the submarine's mechanisms to sink enemy vessels both alone and as part of multi-submarine "wolf packs". As the war progresses the technology available to you in terms of your submarine, instruments, and torpedos will improve. The response of the enemy over time will also continually increase, until by the late war there will be significant risk in making any submarine patrol. \\

\textbf{Wolves of Steel} is a \emph{mod} to Silent Hunter 5 that provides modifications to the original game that make it more realistic. Although the original game is playable on it's own, Wolves of Steel adds to the quality of the game as well as making the game a lot easier to play.


\section{U-Boat Operation}

\begin{figure}[H]
\includegraphics[scale=.5]{u505.jpg}
\end{figure}


The U-Boat is a diesel-electric submarine. In Silent Hunter 5 we use various iterations of the German Type VII U-Boat. The Type A U-Boat at full power will do 17 knots on the surface and 6 knots submerged, with later versions being slightly faster. The crush depth of the Type VII was around 200 meters, while the Type C/41 had increased hull strength and could dive even deeper. The batteries on the U-Boat do not have to capacity to permit long distance travel while submerged. In later years U-Boats are equipped with a \emph{snorkel}, a tube extending from a submerged submarine to the surface that permits running the diesel engine without exposing the submarine to visual detection. \\

The Type A is armed with 10 bow torpedos and one that fires from the stern. Type B and later U-Boats instead feature 4 stern torpedos for a total of 14. The U-Boat is also often armed with an 88mm or 105mm deck gun with both armor-piercing and high-explosive ammunition capable of sinking other vessels. However the U-Boat is very vulnerable to cannon fire itself. It is also armed with a single 20mm cannon for deterring air attacks, although in most situations diving when an aircraft is spotted is ideal. Later versions of the U-Boat ditch the deck gun in favor of more anti-aircraft weaponry as aircraft began to become a serious threat to U-Boat operations. \\

U-Boat torpedos come with either electric or steam propulsion. Early models of electric torpedo suffered from very low reliability, but their lack of a wake made them invaluable as steam torpedos could be spotted while in transit and avoided. Torpedos are triggered by either an impact or magnetic fuse. The magnetic fuse suffered from lack of reliability as well, but could be used to strike vessels from below where the torpedo warhead would cause fatal damage. \\

The low silhouette of the U-Boat allows it to make visual contact with other vessels first and maintain the element of surprise by diving before they are spotted. Two \emph{periscopes} allow the submarine to spot enemy vessels and collect data for the torpedo computer while submerged. The U-Boat is also equipped with a \textbf{hydrophone} that in quiet ambient conditions can hear enemy vessels' propellers at up to 20 kilometers away. In later years U-Boats are equipped with surface radars for detecting hostile vessels as well. \\

The U-Boats torpedos have internal gyroscopes for allowing them to maintain a set course upon release. This gyroscope is set with help by a torpedo computer called the \textbf{TDC}, fed with data attained by the periscope in conjuction with the RAOBF, Stadimeter, or by other methods. The TDC calculates the correct trajectory for an intercept course and sets the torpedo's gyroscope so that it follows this course.


\section{Strategy}

\begin{figure} [H]
\centering
\includegraphics[scale=0.25]{reach.jpg}
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The U-Boat is far outgunned and outpaced by other warships. The fastest enemy warship found often on the open sea is the smallest class of warship, the \textbf{Destroyer}, and \textbf{Destroyer Escort}. The destroyer is fast and heavily gunned for it's size. It is also equipped to destroy submarines with depth charges, hydrophones, and sonar. Depth charges are bombs that are set to explode under the surface at the same depth as a submarine to destroy it, and sonar is an active detection device that can find submarines at several km away even when they are not completely silent to hydrophones. For this reason it is advisable to avoid confrontation with hostile destroyers at all costs. Destroyer Escorts are small vessels specifically designed for dealing with submarines, which accompany convoys of merchant vessels on long range voyages. Destroyer Escorts are also armed with anti submarine equipment and are even faster and more numerous than Destroyers.  \\

Another arguably more dangerous adversary of the U-Boat is the enemy anti-submarine plane. Small single-engine planes will strafe and potentially even bomb U-Boats, but longer range twin-engine bombers are more often used for hunting submarines. Enemy anti-submarine bombers will spot the submarine and quickly line up a depth charge bombing run giving you little time to react. For this reason a submarine commander should dive if an enemy aircraft is spotted at long range, and potentially use the 20mm cannon to destroy it if it is too late to dive safely. In areas where attacks by enemy aircraft are common, extreme caution is advised.\\


The primary target of the U-Boat commander will be very large enemy freighters or troop transports. Vessels in excess of 10,000 tons will be the ideal target. A single well-placed torpedo has the power to cripple or sink even the largest vessels and with the high likelihood of misses or duds the value of the ships being fired on should be maximized. Using your limited supply of torpedos on high value targets will maximize the effectiveness of each patrol you make. If you see high value warships such as cruisers, battleships, and especially aircraft carriers, it may be worth making an attack.


\section{Tactics}
\begin{figure}[H]
\centering
\includegraphics[scale=0.25]{attack.jpg}
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Large enemy coal or oil burning vessels such as warships and freighters will create smoke columns visible from many miles away. In good conditions they can also be detected by hydrophone at even longer ranges. The hydrophone can be used to determine the propeller speed of the contact. Slow moving propellers indicate slow moving vessels such as freighters. Conversely, destroyers moving at high speed will have a high propeller frequency. The size and number of enemy ships should be estimated. Using bearing-interception methods to determine the course of the target is advised, as getting within visual range risks being spotted by the target. Since the submarine cannot move very quickly while submerged the best tactic is to use high engine power (full speed or flanking speed) to get ahead of the enemy group while at long range where the U-Boat cannot be detected visually. The contact's course should be estimated and the U-Boat should submerge in a position where it can lie in wait to launch an attack on the target undetected.

\section{Target Motion Analysis}
Ideally, you should be able to find your targets distance and course from beyond visual range. However beyond visual range you only have access to the target's \emph{bearing} through smoke trails or by hydrophone. By recording the bearing to the target at regular intervals, you can gather enough information about the target to find an approximation of the target's distance and course. This is all likely under the assumption that the target is traveling at a constant speed and bearing however. \\

\subsection{Foundations}
The target vessel will be assumed to be following a \emph{linear course}, meaning that it does not change course over time. The target will likely be following a waypoint navigation plan, and will change course at certain points. However within the window of interception it is likely that the target will follow a linear course. \\



\subsection{Three Bearing Method}
When the submarine is not moving, the three bearing method can be used to get a rough estimate of the target's course by taking three bearing measurements at equal time interval. While this method will get you the direction the target is traveling in, it won't tell you how far away the contact is. It also will not be accurate when the submarine is under way. The procedure is as follows:
\begin{enumerate}
\item Ensure that the submarine is almost completely still in the water.
\item Take three bearing measurements ($B1,B2$ and $B3$) at \textbf{equal time intervals}.

\begin{figure}[H]
\centering
\begin{tikzpicture}[scale=0.4]
\filldraw (0,0) circle[radius=2pt];
\node[below left] at (0,0) {$O$};
\draw[color=red] (0,0) -- (5,5) node[above left] (B1) {$B1$};
\draw (0,0) -- (6,4) node[right] (B2) {$B2$};
\draw[color=blue] (0,0) -- (7,3) node[right] (B3) {$B3$};

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\item Choose an \emph{arbitrary} point $P$ along the middle bearing $B2$.
\item Draw lines which are along the headings $B1$ and $B3$ passing through $P$. Again, they are parallel to the other two headings but they intercept $P$ on $B2$. The line parallel to $B1$ is $B1'$ and the line parallel to $B2$ is $B2'$.


\item Find where $B1$ intersects $B2'$ and where $B2$ intercepts $B1'$ and mark them.
\item The target vessel will be traveling roughly parallel to the line that passes through these two marks.
\end{enumerate}

\begin{figure}[H]
\centering
\begin{tikzpicture}[scale=0.8]
\filldraw (0,0) circle[radius=2pt];
\node[below left] at (0,0) {$O$};
\draw[color=red] (0,0) -- (5,5) node[above left] (B1) {$B1$};
\draw (0,0) -- (6,4) node[right] (B2) {$B2$};
\draw[color=blue] (0,0) -- (7,3) node[right] (B3) {$B3$};
\filldraw (5,3.33333) circle[radius=2pt];
\node[below right] (P) at (5,3.33333) {$P$};
\draw[color=red]  (2,0.33333) node[below] {$B1'$} -- (6,4.33333);
\draw[color=blue]  (0,1.19) node[left] {$B2'$} -- (6,3.76);
\draw[color=orange,->] (0,4.155) node[left] {$C$} -- (4.172,0) ;
\filldraw(2.082,2.082) circle[radius=2pt];
\filldraw (2.917,1.25) circle[radius=2pt];
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\subsection{Four Bearing Method}
In reality a ship at sea is never truly stationary. We can develop a method for fixing target position from a moving vessel. For simplification of calculations we will assume bearing measurements are taken at equal intervals.
\begin{enumerate}
\item
\end{enumerate}
\section{Torpedo Firing Solutions}
\begin{figure}[H]
\centering
\includegraphics[scale=0.42]{firecontrol.jpg}
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To effectively intercept and destroy hostile ships that are underway from distances of 1-12km, the torpedo is equipped with an internal gyroscope and maneuvering fins that allow it to travel along trajectories that are not parallel to the submarine. This gyroscope is set prior to firing either manually or fed with data from the ships instruments such as the stadimeter and the periscope. You can gather all the data you need to manually configure the torpedo using the RAOBF. \\

Most torpedo attacks are made either directly to the port or starboard (left or right) side of the enemy vessel. The larger profile from the side provides a larger target, but you must compensate for it's speed. It will also be very difficult for the enemy to evade a torpedo attack from the side, and the torpedo will strike at a steep angle which is required for reliable detonation. \\

The data required to make a torpedo firing solution is as follows:
\begin{enumerate}
\item \textbf{Target Speed:} At range the target vessel may travel it's own length several times before the torpedo is able to intercept it.
\item \textbf{Range:} The farther a target vessel is from the U-Boat at the time of launch, the farther the torpedo will need to lead the target vessel to account for it's motion.
\item \textbf{Angle On Bow (AOB):} The Angle-On-Bow measurement tells you \textbf{your relative heading from the target's perspective.} This is will allow you to determine the target's course. You can tell what the target's relative heading using the periscope or hydrophone, but to find \textbf{your} relative heading you need to plot their course or use the RAOBF within visual range.
\end{enumerate}
\subsection{RAOBF Guide}
The \textbf{RAOBF} is an instrument that allows gathering all the data required for a firing solution just using optical measurements of the target vessel.
\begin{figure}[H]
\centering
\includegraphics[scale=.25]{RAOBF.jpg}
\end{figure}

\subsection{Speed Finding}
\begin{enumerate}
\item Measure the time it takes the vessel to cross the reticule from bow to stern in seconds using stopwatch.
\item Rotate the \textcolor{red}{middle wheel} until the number of seconds on the \textcolor{red}{outer guide of the middle wheel} aligns with the \textbf{reference vessel length} on the \textcolor{blue}{outer wheel}.
\item Read off the \emph{vessel's speed} on the 1:30 o' clock red marker line on the \textcolor{red}{inner guide of the middle wheel}.
\end{enumerate}


\subsection{Range Finding}
\begin{enumerate}
\item Measure the \textcolor{orange}{optical height} of the target vessel in number of reticule ticks.
\item Rotate the \textcolor{red}{middle wheel} of the RAOBF until the point on the \textcolor{red}{inner guide of the middle wheel} corresponding to the \textcolor{orange}{optical height} is aligned with the vertical red marker.
\item Find the mark on the \textcolor{blue}{outer wheel} that corresponds to the \textbf{reference mast height} of the target vessel. The mark on the \textcolor{red}{outer guide of the middle wheel} adjacent will provide you the \emph{target range in hundreds of meters}.
\end{enumerate}


\subsection{Angle on Bow (AOB) Finding}
\begin{enumerate}
\item Measure the \textcolor{orange}{optical length} of the target vessel in number of reticule ticks.
\item Align the \textcolor{red}{middle wheel} until the mark on the \textcolor{red}{outer guide of the middle wheel} corresponding to the target range that was previously found using the range-finding method points to the mark on the \textcolor{blue}{outer wheel} corresponding to the \textbf{ship reference length} (Now the outer guide corresponds to ship length in $m$, not mast height in $m$).
\item View Angle-on-Bow (AOB) from the point where the \textcolor{green}{inner wheel} meets the corresponding \textcolor{orange}{optical length} on the \textcolor{red}{inner guide of the middle wheel}.
\end{enumerate}


\section{Attack Disc}
\begin{figure}[h!]
\centering{
\includegraphics[scale=.6]{attackdisc.jpg}
}
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\begin{enumerate}
\item Use main switch to automatically align the middle wheel with your own vessel's heading.
\item Align bearing pointer (pointer with red/green scale) to the target direction on outermost wheel.
\item Use the scale on bearing pointer to align one-sided vessel pointer to the target's bearing using AOB measurements as deflection from target direction using the innermost wheel.
\item Align the two sided pointer perpendicular to the one-sided pointer to get the two 90 degree attack angles on the innermost wheel to find the two perpendicular attack directions on the outermost wheel.
\end{enumerate}


\section{Stadimeter}

A less accurate but faster way of measuring range, the stadimeter is a good way to make quick adjustments to range calculations before a 90 degree shot.
\begin{enumerate}
\item Ideally place reticule at the waterline.
\item Press stadimeter button to generate a ghost image of the target ship.
\item Align the ghost vessel so that it's waterline is at the top of the original ship's mast in the stadimeter image.
\item Read off the target range at this point.
\end{enumerate}
\section{Glossary}
\begin{itemize}
\item \textbf{Hydrophone:} The hydrophone is an underwater acoustic listening device. Sound waves travel much farther underwater vessels which are underway can be detected from a distance of many miles.
\item \textbf{Sonar:} Sonar is an \emph{active} underwater acoustic listening device that works in a manner similar to radar. A high power acoustic pulse is generated. By analyzing the change in frequency of the return pulse, distant objects can be detected.
\item \textbf{TDC (Torpedo Data Computer):}
\item \textbf{RAOBF (Real/Range Angle on Bow Finder):} The RAOBF allows finding range, speed, and angle on bow using optical measurements. Since you must first identify the target vessel and take accurate optical measurements, the RAOBF is only useful within visual range (<10km).
\item \textbf{Stadimeter:} Another instrument that uses optical measurements, you stack a ghost image of the vessel on top of it's mast within a movable image to estimate the range.
\item \textbf{Attack Disc:} The attack disc is a tool for determining the target vessel's bearing in relation to your own using the direction to the target and angle-on-bow measurements.
\item \textbf{Destroyer:} The smallest warship found in the open sea, the destroyer is a small, fast, and heavily armed vessel meant to screen large fleets. They are equipped to deal with submarines with sonar, hydrophones, and depth charges.
\item \textbf{Destroyer Escort:} The destroyer escort is smaller than the destroyer and more specifically designed for dealing with submarines. They feature longer ranges a greater emphasis on submarine detection and depth charging over guns for engaging other surface ships.
\item \textbf{Depth Charge: } The depth charge is an adjustable underwater bomb launched from both surface vessels and aircraft to destroy submerged submarines. During the war the British depth charges were only effective to around 100m while U-Boats could dive as far as 200m. Later launchers fired from the front and sides of the vessel and fired multiple charges at a single time, increasing their effectiveness.
\item \textbf{Three Bearing Method:}The three bearing method is a bearing-intercept technique for approximating the target's heading by taking three bearing measurements at equal intervals. While the Three Bearing Method gives you the target heading, it does not give you the target's distance. The distance to the line plotted using the Three Bearing Method is dependent on the parameter $P$ and is not equal to the target distance.
\item \textbf{Four Bearing Method:}
\end{itemize}
\end{document}