[Chromatix]

I suppose it fits the theme of the thread, since the diving controls are currently in the engine room. In fact I was already considering writing something on the subject. Let me have a stab at it:

Fresh water has a density of (almost exactly) 1kg per litre, or 1 metric tonne per cubic metre. In fact that was part of the original basis of the definition of metric units. Sea water density is usually a little higher, which means that a given object immersed in it will be a few percent more buoyant. In a submarine context this is potentially very significant. This is also why cargo ships have several different safe waterlines marked on the side, in case they plan to travel between areas of differing water density.

Baltic Sea water is a lot closer to "fresh" than ocean water, because it has several large rivers flowing into it (the catchment areas of most of Eastern Europe and almost all of Northern Europe) and only the narrow and shallow Øresund, Lillebælt and Storebælt straits as an outflow. This flow actually does reverse about twice a decade on average, when spring tides coincide with strong winds in the right direction, but almost all the time it flows outward, into the North Sea, to some degree. Since HMS Marulken is supposedly set (almost?) entirely in the Baltic, this implies buoyancy figures must be based on Baltic-specific figures rather than the usual oceanic ones.

Marulken's developers could reasonably assume that only one seawater density exists (that of the Baltic), but more ambitious developers might want to consider that water in ballast tanks might have a different density to the surrounding seawater, if the sub has moved into a different density since the tanks were flooded. This can easily occur during a dive, as density layers sometimes exist and were reported to act as sub-surface "support" depths which it was more difficult to dive past. It can also occur if entering a river outflow.

Once you know the density of the water and the location and volume of each ballast tank, the weight and balance contribution of the water in them is easy to calculate. Likewise the buoyancy contribution of the outer hull. Beware the "free surface effect" in partly-filled tanks; fortunately MBTs are almost always completely full or completely empty, so there is no free-surface effect in them. Flooded compartments however will very much be subject to it.

Ideally a dived submarine should have zero net buoyancy. Most of the difference between the strong positive buoyancy required to stay on the surface and this dived condition is achieved by completely flooding the main ballast tanks. This effectively reduces the buoyant volume to that of the pressure hull (assuming a double-hulled or saddle-tank boat, with the MBTs outside the pressure hull). This is still significantly more than required the balance the weight of the boat though, so the safety tank (if fitted) is also flooded and the trim tanks are partly flooded to fine-tune the buoyancy.

The trim tanks are located at the extreme ends of the boat and are used not only to obtain zero net buoyancy, but to achieve correct fore-and-aft balance as well. They are usually kept in their dive-adjusted condition even while surfaced, so that they don't need to be set up again for every dive. Sea water could be pumped into, out of, or between the trim tanks at will, but the pump used for this was often rather noisy and could potentially give away the sub's position. Using compressed air to "blow" the tank made less noise, but this was in limited supply.

It was normal practice to carry out a "trim dive" immediately after leaving port to perform this adjustment, since taking on fuel, ammunition, supplies and exchanging some of the men would have substantially changed the sub's overall weight and balance. This "trim dive" would be repeated at regular intervals thereafter if no other reason to dive was found, so that the sub would always be ready to dive safely if required. Such dives were also useful for training purposes.

Fuel was usually carried in large external tanks very like the MBTs, and as it was used, it was displaced by water from below. This mostly compensated for the change in submerged weight due to consumed fuel. When a fuel tank was completely drained, some of them could be converted into normal MBTs, improving surfaced buoyancy.

The centre of buoyancy must be somewhat above the centre of mass in order to keep the boat upright. This condition must be maintained both when surfaced and when dived, and for preference even having taken damage. The term "metacentric height" is key here, and there is much literature on the subject.

Blowing the MBTs using compressed air while submerged would only be done to effect a very rapid surfacing, either in an emergency or as part of a "battle surface" for a gun action. The consumption of compressed air would be very high, and it would be prudent to be sure of recharging this supply before needing to dive again.

For normal surfacing, the dive planes would be put on full rise and the safety tank would be blown, putting enough of the sub above water to run the engines and low-pressure compressors; this low-pressure air would be used to empty the MBTs.

To dive safely, it is absolutely vital that all openings in the pressure hull are sealed shut. As well as manual checks and automatic indicators, it was usual to let a little compressed air into the boat and observe on the barometer (and the crew's eardrums) whether it was held in. This indication was robust even in the face of failure of the other two checks, and gave much confidence when making a rapid dive under combat conditions.

To make a "crash dive", British and American subs had a "negative buoyancy" tank which was normally kept empty, but could be flooded and blown independently of the trim system. There was a particular "fill mark" corresponding to the empty state; some water was kept in it so that blowing it "to the mark" wouldn't leak too many bubbles which might be spotted. German U-boats didn't have such a tank, but instead had most of the men run through the boat into the forward torpedo room in order to quickly get a down-angle on the boat. Obviously they had to run back again when normal trim was again required.

So much for static buoyancy. As mentioned earlier, depth control was primarily by means of the dive planes, which on a WW2 sub were almost always provided both forward and aft. On the surface, the fore planes were usually folded. Obviously they had no effect when stopped, so the buoyancy tanks had to be used instead.

Japanese submarines often had an automatic trimming system for depth control while stopped, but it tended to "hunt" badly (ie. did not settle on a stable state) and, because it relied on the trim pumps, made a lot of noise. Manual control of the trim made much more economical use of the pumps, so was both quieter and more effective.

Dive planes were normally sized to be capable of providing several tons of up or down force at silent-running speeds. This was sufficient to correct a considerable degree of error in the trim, which was an important safety consideration when performing a trim dive or performance damage control. Obviously, greater dive plane forces were available at higher speeds, so if a large trim error was present, the dive officer could request (and usually got) a higher speed for purposes of depth control.

IIRC, the plane forces scale with the square of the speed, except that they also reverse sense (like the rudder) when moving astern. This latter effect (and others) can be accounted for by remembering that the angle of attack of the plane on the water flow is what matters, not the absolute angle setting of the planes. This also applies to the rudder and the propeller blades!

The stern planes primarily have the effect of changing the *angle* of the boat, in much the same way as the rudder does on course. Obviously when at an angle, the hull itself acts as a giant (if somewhat inefficient) dive plane, and the propellers' thrust angle also changes. Angle is normally shown on an inclinometer consisting of a curved, fluid-filled tube with a bubble in it; hence the term "bubble" used for angle in USN phraseology.

The fore planes obviously act primarily on the front half of the boat, but if the stern planesman is instructed to maintain a level angle (as he normally would when near periscope depth, to avoid broaching), he will naturally end up following the fore plane setting, making the fore planesman primarily in control of *depth* rather than angle.

There are normally three different types of depth gauge in the boat, duplicated wherever required. One gives a very precise reading of shallow depths (covering optimum periscope and listening depths), another is calibrated for the full test depth of the boat (and then some), and there are also direct readings of sea pressure, not calibrated for depth, which are provided in other compartments than the control room.

Compensation and impulse tanks were provided forward to assist with firing torpedoes, and to counter the sudden change in trim occasioned by the torpedo leaving the tube. The first submarines capable of deploying weapons discovered the need for this the hard way, as they tended to stand on their tails immediately after detaching them! The compensation tank was generally drained into the forward trim tank so that another torpedo could be fired using it. If aft tubes were fitted, the compensation and impulse tanks would be duplicated there for obvious reasons.