Propeller Shafting - A primer for Naval Architects & Marine Engineers : Part 3

The previous blogs have looked at how propellers work and the causes and effects of vibration. This blog is the third part of a trilogy, showing how this information can be used to select the appropriate shaft , gearing and machinery arrangements for a specific warship. Once a suitable hull form has been arrived at and the shaft horsepower needed to drive that hull at the specified speed calculated, the question becomes one of transforming that power into thrust with the maximum efficiency.

The first consideration is weight economy. The propeller, shaft and gearing all represent dead weight that is duplicated with multi-shaft arrangements. In addition, the curve of engine output power as compared to size and weight is not linear; two smaller engines together weigh substantially more than a single larger unit of the same output. It may, therefore, seem that an ideal arrangement will involve keeping such duplication, that is the number of shafts, down to a bare minimum. Provided the total power in question is below the maximum that can be absorbed by a single propeller, then a single shaft arrangement would seem to be the most efficient. If the installed power is greater than the maximum that can be absorbed by a propeller, then the most efficient arrangement would be that involving the fewest number of shafts; in most cases two. Another way of saying this is that the most efficient design for shafting is to load the propellers as highly (that is, to put as much power through) as possible.

For merchant ships this is indeed the case. Merchant ships are designed for economy of construction and use, not for the most efficient use of high power settings. In their case, the economic advantages of a single shaft outweigh any disadvantages from the layout. What this really proves is that merchant ship practice does not carry over into warship design. It is not possible to make arguments for a given configuration for a warship by quoting merchant ship practice. The demands of the two are so different that a comparison between, for example, a liner and a battleship are essentially meaningless.

A single centerline shaft turns out to be a very poor choice for a heavy warship. One problem that's immediately obvious is the dangers of damage or mechanical failure. If that shaft is damaged by, for example, mine or torpedo strikes, bearing failure or any of the other hazards of being a combatant warship, the ship is helpless until the damage is repaired. Experience has shown that accidents and mechanical failure are more of a problem than combat damage but the principle holds; a single shaft exposes the ship to appreciable risk. The same applies to machinery; if a ship is powered by a single engine, then she is held hostage to the reliability of that engine.

There are, however, more serious problems with a single shaft. One is that a ship so equipped cannot use her engines for steering. Below about 10 knots, a ship's rudders become ineffective. In this environment, a single shaft ship is uncontrollable and needs to have tug assistance for docking or other maneuvering requirements. This can be partially cured by using twin rudders that flank the single screw and direct the race from that screw. This reduces the minimum effective speed for rudder control but does not cure the problem completely. Multi-shaft ships can use differential power from their engines to bring about steering control, intrinsically a much safer and more satisfactory situation.

Another mechanical problem with single shaft layouts is the fact that the shaft has to be along the centerline of the ship, for most of its length above the keel. The problem here is that the keel is also the foundation for and primary support of the heavy gun turrets. This point became critical in the era just before WW1 when the weight of gun turrets increased rapidly as gun caliber moved inexorably upwards. One effect of this was to make wing turrets (which obviously could not use the keel as their primary support) less viable. Unless an all-forward armament solution is adopted, we have an immediate design conflict that is extremely difficult to resolve. The only way heavy gun turrets and a centerline shaft can be accommodated is to provide heavy carry-through structures that distribute the weight of the turrets (similar structures were used for wing turrets). These structures are heavy enough to completely eliminate any weight efficiency gains resulting from the use of a single shaft. To make matters worse, they act as a transfer medium by which shock and explosion damage can be carried through from the sides of the ship to the centerline, offsetting the added protection apparently afforded by burying a shaft deep in the hull structure (reports in Dubious and Ghastly of the damage suffered to the center shaft of Scharnhorst illustrate this).

Another serious problem with centerline shafts is vibration. The torsional vibration within the shaft itself cannot be cancelled and will be a constant factor afflicting the ship. The screw itself is operating in the turbulent wake of the hull structure, causing pulses of vibration as the blades hit the turbulence. To make matters worse, this screw is directly under the ship's keel so the vibration pulses strike the centerline of the hull and are immediately transmitted through keel and distributed throughout the ship's structure. Other vibration pulses, travelling down the centerline shaft pass through all the structural nodes of the ship, spreading them throughout the hull structure. The heavy carry-though members provide excellent vibration transmission paths and add to the problems. In merchant ships, these problems are not that serious; merchant ships do not usually use the power settings and use profiles that make vibration a serious concern although the single shaft on most merchant ships does give a characteristic and unpleasant thumping in the aft sections.

For warships, these vibration problems are of grave concern. Yet, they are not the prime problem for single shaft layouts. The main killer for these designs is that centerline propellers are grossly inefficient under the conditions prevailing in warships. For true efficiency, propellers have to act in smooth water yet a centerline prop is, by definition, surrounded by the turbulent wake from a ship's hull. The effect on the propeller's efficiency is devastating. Investigations quoted in the earlier posts have shown that between 15 and 45 percent of the energy supplied to a centerline propeller at high power loadings is lost in inducing vibration within that propeller and its surroundings. In contrast, the equivalent figures for wing propellers are between one and four percent. Related to this is a more fundamental point. As we have already seen, propellers work best when turning slowly, that is when lightly loaded. Their efficiency drops rapidly as loading increases. Therefore, two slow-turning, lightly loaded propellers use power more efficiently than a single faster-turning propeller of equal size.

The next question is, given the propulsive advantages of adopting twin screws over single shaft layouts for surface ships, does the configuration bring any specific disadvantages with it? The first is that a twin-shaft solution requires additional space in the rear end of the ship in order to ensure that there is enough space between the screws to prevent unfavorable interactions. The layout also means that the screws will be closer to the sides of the ship, a feature that will give problems in designing the torpedo protection system in this area. The vulnerability of the shafts is enhanced by the fact that the hulls lines aft mean that those shafts run outside the hull for a substantial proportion of their length. Although this is beneficial in that it reduces the level of vibration transmitted to the hull, it does add to vulnerability compared with a centerline shaft buried within the hull structure.

A factor related to damage control is the engine room design itself. A twin-screw ship will usually require a larger engine room (to accommodate the two engines required for its shafts) than that needed for a single shaft ship. If breached and subject to flooding, this larger volume represents a greater proportional danger to the ship. However, this point is often overstated. The most immediate danger resulting from damage to an engine room is not flooding but loss of power from the generators invariably co-located with the main engines. The time taken to switch from this power to emergency back-up generators can be critical. In this context the dimensions of the engine room are of little consequence. It could be argued that a twin-shaft layout actually has some advantages since it allows the installation of a centerline bulkhead that could restrict damage to one engine room and preserve the other, and its generators, from flooding. Centerline bulkheads are very controversial since they can also cause asymmetric flooding and foster capsizing. Japanese designers liked them; US designers abhorred them. The point is that the choice of shaft arrangements does not compel a decision one way or the other and this is a matter best left to the Instructions to Designers.

On balance, these considerations add up to a conclusion that the gains from using a twin-shaft layout greatly outweigh the weight inefficiency of doubling up on shaft, propeller and gearing. The only time when a single shaft is acceptable is where we have a mobilization design and the primary requirement is to keep the number of engineering bottleneck components to a minimum, the recent US FF and FFG classes being good examples. Here, the driving requirement was to keep the gear cutting to a minimum since this has historically been one of the main bottlenecks in ship production. Another case is where the ship's lines aft are so fine that doubling up on shafting is not practical. In this context, modern submarines, almost invariably single shaft designs, are a very special case due to their highly specialized hull lines.

The next question is; since using twin shafts as opposed to a single centerline shaft shows such great advantages; what happens if we double again and go to a four-shaft solution? Do we see further gains or does the law of diminishing returns apply?

The weight economy arguments against going from twin to a quadruple shaft layout are effectively a repeat of those against going from single to twins. The gearing, shaft and propeller are effectively deadweight while four small turbines weigh more than two larger ones of the same aggregate output. Much of the pro-argument follows along the same lines as well; assuming the screws are the same size, they can be much less heavily loaded and, therefore, operate more efficiently.

The big negative on quadruple screws is that they require a broad aft section; four shafts simply cannot be fitted into a finely tapered stern section without serious design problems. The screws have to be spaced out to prevent unfavorable interactions. In reality this means that the choice is often not between two and four screws of the same size but between two large and four smaller screws and the question now becomes one of the relative propulsive efficiencies for that particular design. However, there is one factor here that is interesting; with proper design, it is possible to arrange quadruple screws so that there is a small but appreciable benefit in propulsive efficiency from the races of the screws and their interaction with each other and the hull lines. This benefit is usually between two and four percent on propulsive efficiency; not a great amount but one worth having.

A major plus for quadruple screws is that the arrangement allows for effective active cancellation of torsional vibration in the shafts. In effect, the shafts on each side can be designed to cancel their torsional vibration and then the pairs on the opposed sides balanced to smooth out what's left.

A big advantage of quadruple screws is damage control. Engine steering in the event of rudder or stern damage is greatly eased. Internally, having four engines opens many possibilities with regard to dividing up the engine rooms and makes plausible the idea of controlling lists from engine room damage by counterflooding opposing areas while maintaining the watertight integrity of others. The important thing is that quadruple screw layouts do not, of themselves, force the designers to any particular solution for compartmentation of the engine room spaces; whether to install a centerline bulkhead remains an option of the designer as determined by the appropriate ItD. Put another way, the use of four smaller engines opens up options not available with different configurations.

So, if four screws is a desirable (but space consuming ) solution, can we gain anything by going a step further and installing six screws? Here, the evidence seems to be that we've hit a point of declining return and that the combination of a very wide hull forced by this arrangement, the dead weight of all the additional shafting etc and possible interactions between the screws means that the penalties outweigh the benefits. Or seem to; the only example I can find of a ship with six screws is the old Russian Popovka class river defense ships. These failed quite badly.

Heading the other way, if, on a given power output, four screws is efficient but space and weight consuming and two screws uses weight more effectively but shows less propulsive efficiency, would a triple screw layout offer a good compromise? A preliminary examination of the figures suggests that it might; a comparison of machinery weight per SHP output between ships using triple and quadruple shaft layouts does show an appreciable advantage to the former. However, as we have seen, this is not the whole story.

Firstly, we are comparing numbers between two ships from two different countries. This is always dangerous since no two countries measure such statistics the same way. There is a strong probability that one set of figures contains components that the others do not. Even if this is not the case, weight economy is only one part of the equation. Propulsive efficiency and vibration are of greater significance as is the effect of the arrangement on the ship as a whole.

Here, triple shafts combine all the worst problems of a single-shaft layout and a twin shaft system. About the only advantage of the triple shaft layout is that it eliminates the vulnerability of the single shaft layout to mechanical damage or accident. The design hydrodynamics is such that the effects of the centerline screw actual degrade the efficiency of the wing propellers. In his memoirs, Admiral Scheer made the following comments on his (triple shaft) battleships.

"The advantage of having three engines, as had each of these ships, was proved by the fact that two engines alone were able to keep up steam almost at full speed; at the same time, very faulty construction in the position of the engines was apparent, which unfortunately could not be rectified owing to limited space' Thus it happened that when a condenser went wrong it was impossible to conduct the steam from the engine with which it was connected to one of the other two condensers, and thus keep the engine itself working. It was an uncomfortable feeling to know that this weakness existed in the strongest unit at the disposal of the Fleet, and how easily a bad accident might result in leakages in two different condensers and thus incapacitate one vessel in the group."

This excerpt has two valuable insights. One is the confirmation that the German ships could maintain speed using their wing shafts only; an indication of the inefficiency and redundancy of the center shaft. The other is the suggestion that the center shaft itself was seen as being a reserve against mechanical failure and/or battle damage. The comments about condenser problems are also interesting but by no means unique. "Condenseritis" was a well-known and pervasive problem with all ships in WW1 and its prevalence in the German fleet should not be seen as unusual.

Triple shafts come into their own where there is a requirement for high output power in a hull with extremely fine lines aft. This was the motivation behind the use of the configuration on the Ark Royal and Illustrious class carriers (the combination of treaty limits restricting the length of the armored box, the need for beam and high installed power all conspired to give the designers heart failure). When the treaty limits were lifted, the British redesigned their carriers (Indefatigable and Implacable) with a conventional four shaft layout.

The final question is, would a five-shaft layout show any particular advantages or limitations? On purely theoretical grounds, it’s difficult to see why this would be adopted; it would simply share the problems of four-shaft and single shaft layouts. I don't think a five-shaft design has ever been seriously considered - if someone does know of such a design, could they please point me to it???

Summary

Single shaft: Advantages; good weight economy in power train components, shaft buried in hull for protection, economy in war-critical production bottleneck items. Disadvantages. Inefficient power utilization, high noise and vibration levels, no redundancy against mechanical or combat damage. No engine steering capability. Severe design problems with regard to other parts of ship

Double shaft: Advantages, relatively efficient with reduced noise and vibration, allows engine steering, and provides redundancy against damage. Disadvantages. Requires wider section aft. Preferred design for smaller warships - say up to light cruiser size.

Triple shaft: Advantages, allows increased power through narrow stern section. Disadvantages. Inefficient power utilization, high noise and vibration levels. Severe design problems with regard to interaction of power train configuration with other parts of ship.

Quadruple shaft: Advantages, very efficient due to favorable prop interactions with reduced noise and vibration, allows engine steering, and provides redundancy against damage. Also, allows flexible subdivision of machinery spaces. Disadvantages. Requires wider section aft. Preferred design for larger warships - from heavy cruiser to battleship size.

Ship Vibrations - A Primer for Naval Architects & Marine Engineers : Part 2

Vibration has been a matter of concern to ship designers since the end of the 19th century although its presence in ship characteristics was known long before that time and its importance has become much emphasized over the last half century. Some sailing warships, particularly the lightly-built frigates, suffered from serious vibration aft when driven hard, probably as a result of flow interaction while there are accounts of mast/sail combinations causing such severe vibration that crewmen were thrown from their feet or, worse, from their mast-top positions. However, for most of the history of the ship, the problem was not regarded as being of any great importance. The situation began to change with the introduction of steam propulsion. A French naval design book (Theorie de Navir) published in 1894, contains a discussion of ship vibration, written from the premise that the phenomenon was the result of the propeller. The slow-rotating props used at that time had relatively few blades per shaft, a combination that generated a long wave-length (low frequency) vibration that felt like the hull flexing in a heavy sea. This was not regarded as being anything out of the ordinary and probably explains why ship’s trials reports of the era contain so few mentions of vibration unless the situation was really unusual. There were, however, enough really unusual cases to start people thinking.

Vibration is defined as a relatively small amplitude oscillation around a rest position. It can be transverse (at right angles to the rest line), longitudinal (orientated along the rest line) or torsional (twisting around the rest line). Transverse vibration is the most commonly encountered, torsional is frequently present but its effects are subversive, longitudinal vibration is comparatively rare but can cause truly hellish problems. All hull components have “natural frequencies”; these are the frequencies at which the component will vibrate when struck. Another vital term is resonance. This is a state that occurs when the natural frequency of hull components matches that of an imposed vibration. The components act as amplifiers, the effect only being limited by system damping.

Looking at the sources of vibration in a ship, it is easiest to start from the front of the power train and work backwards. Its important to remember that vibration doesn’t really pass through air, it travels along things and the routes that it follows are as important as the vibrations themselves. The boilers of course generate their own series of vibrations but these are largely isolated from the power train proper (the steam lines absorb and damp vibration). The real problems start with the ship’s engines.

Reciprocating and diesel engines are universally bad news. They are not continuous action; they operate in a series of jerks, each of which adds a kick to the vibration patterns. I won’t bother with reciprocating engines since they were dying out by 1914 but diesels are very much of contemporary interest. The problem with diesels is that, for a given size, there is a fixed amount of power generated per cylinder. The only way to add power is to add cylinders (this assumes that engine room dimensions etc prevent the sheer size of the diesel increasing further but I understand there are nasty problems in designing big diesels. Trouble is, if cylinders are added, they lengthen the crankshaft. After a very limited number of additions, the lengthened crankshaft begins to flex and vibrate all on its own. This is torsional vibration at its most elemental and is, by the way, why big automobile engines with a straight line configuration (the so-called straight-8s and so on) got abandoned. On a ship, its a killer.

Steam and gas turbines, when new and/or in good repair, do not, by themselves generate excessive vibration. It’s possible to stand a dime on its edge on the casing of an LM-2500 running flat out (I’ve done it) and watch it stand for several seconds. That happy state will remain as long as the turbine blades continue to be perfect and rotate in a smooth gas flow. Eventually, though, this ceases to be the case. Microscopic defects in the metal of the steam/gas intake and blades eventually fail, causing small pits to appear in the surface of the intake and the blades. These set up eddies in the gas flow that have two bad effects. One is that a turbulent gas flow is much more erosive than a smooth flow so the progressive deterioration of the blade will accelerate. The hotter and higher pressure the intake, the more erosive the gas and the higher the standards of metallurgy required to resist those conditions. If the steam (temperature and pressure) conditions adopted exceed the ability of the metals use din the intake area and blades to resist their erosive effects, then the result will be a short-lived, very unreliable powerplant. With gas turbines, this is less of a problem since they are maintained by pulling the entire engine and replacing it. With steam turbines, deteriorated blades can be replaced but the trend in engine performance is ever-downwards until it reaches a point where performance loss and vibration reach unacceptable levels and the plant is worn out.

The other is that the blades themselves are no longer rotating in a smooth environment and start to shake. This sets up vibration which gets transmitted down the turbine shaft to the gears. Now, there is an interesting effect on a gearbox if it is placed directly between the compressive loads generated by drive shaft from the turbine and the compressive loads traveling up the shafts from the screws. The gearbox explodes. This is not good.

Gearing was impossible with the first generation of turbine driven ships (the direct-drive ships). Since screws work more effectively at slow speeds than at high and turbines work more effectively at high speed than low, there was a dichotomy that could not be resolved. Either the screws ran so fast they cavitated, shaking the ship the way a terrier shakes a rat or the turbines ran so slowly they guzzled fuel. This is when (a) people began to realize there was much more to this vibration business than they had thought and (b) screw design suddenly took several large leaps forward. The solution was a thing called a thrust block that took the compression loadings in the shafts and prevented them being transmitted to the gearbox. This meant geared turbines could be designed and the world got easier. Then somebody had a BLIFFO [Ed - BLInding Flash of the F***ing Obvious]. Mass damps (absorbs) vibration. Mass keeps gears nicely in line and prevents flexing. In ship’s gearing, mass is good. Lets have LOTS of it guys!!! As a result, the thrust blocks and main reduction gearing in a ship are about as over-engineered as it is possible to get. There is a price paid; all that metal takes some design accommodation and there are mechanical penalties in getting the bits moving but they’re nothing compared with the benefits.

The main reduction gearing generates vibration of its own (particularly if a resentful sailor tosses a wrench into it - usually good for a one-year to 18 month refit and repair). But, by and large, it is a vibration sump rather than a generator. What it tends to do is isolate the mechanical vibration forward from the hydrodynamic vibration aft to the great benefit of all. Well - mostly. The massive reduction gears cannot absorb torsional vibration from diesels which is why trying to gear diesels to a common shaft is an unhappy experience. It can be done but the designer usually does so while trying to work out what he did to deserve the punishment.
Coming out of the back end of the main reduction gearing are the shafts. These are important from two points of view. Firstly, they run the a substantial proportion of the length of the ship and carry vibration along that length, transmitting it to any vulnerable component. The shafts are the primary means by which vibration is transmitted into the ship which is why their design and layout is so essential to the success of the design. Secondly, they are important generators of vibration in their own right.

This vibration is both torsional and transverse. The shaft is a long steed rod being twisted at one end. At the other end is the resistance provided by the water against the effort to turn the screw in it. This means that the engine end of the shaft will turn before the screw end, setting up torsional stress in the shaft. When the screw starts to turn, this energy is released in making the screw turn a bit faster. It overruns the engine end so now there is torsional stress in the opposite direction - this is released by slowing the screw down. This happens in a series of cycles and quickly settles down into series of pulses - torsional vibration. There is a trick here. Every so often the gods look down on naval engineers struggling with slide rules in their tiny offices with green steam coming out of their ears and give us a break. The frequency of that torsional vibration is pretty fixed and is proportional to the length of the shaft. If one shaft is half that frequency longer than another, the torsional vibrations from them will cancel out, often almost completely. This is why twin-screw cruisers (for example) usually have asymmetric shaft lengths. With quad-screwed ships, the designer gets an even greater benefit since the shaft lengths on each side can be manipulated to provide cancelling torsional vibration frequencies on each side and then between side. The fact that this can’t be done with triple screws is as good a reason as any for not using the layout though there are many, many more.

Shafts can also generate transverse vibration by literally shaking in their tunnels. It is a lot to ask any foundry to produce a shaft 200 feet long that is perfectly dynamically balanced all the way down. Somewhere it won’t be and spinning at ship-applicable speeds, it’ll cause vibration. The next solution is to block the shaft at regular points and physically prevent the vibration from occurring. The blocks have to be resilient to absorb vibration or they will simply transfer it to the ship. Problem is, every block also absorbs power and the situation quickly develops where the resistance from the blocks is so high that the shaft won’t turn. The best solution to transverse shaft vibration is to keep the shaft as short as possible (this also reduces torsional vibration) and get it out of the hull as quickly as possible (there are, of course, many reasons why a designer might want to keep the shaft’s within the hull but that’s another matter). Which is why modern merchant ships have their machinery aft. I have always wondered if that consideration interested the designers of the British G-3 Battlecruiser? By putting the machinery aft, could they have had in mind (as a subsidiary benefit) cutting vibration??? By the way, this shows another problem with a centerline shaft - it has to be inside the hull for a lot of the way and also (nasties of nasties) runs right through the ship’s structural nodes - putting it in a perfect position to distribute vibration evenly throughout the aft section. Also, the gun turret supports are directly on top of it, wrapping the center shaft in a heavy carry-through structure that also serves to distribute the vibration (guns do not like being mounted on flexible supports).

Finally, we get to the end of the shaft and reach the witch’s cauldron - the screws. Hydrodynamically, the pressures on the screws change across the blade, along the length of the blade, following the contours of the blade and all of the above change in accordance with speed of rotation and the relative speed of the water impacting on the blades. For many years, people attempted to get a handle on this situation using uniformly continuous relational mathematics and failed. Today, the calculations use that are non-uniform and discrete. In general, each propeller blade has six components of displacement, three translations and three rotations and six corresponding force components at each nodal point. How many nodal points are there? As many as you want, friends, and the more you have the less inaccurate the answer. Scary isn’t it?

In general, the screws work best when the are rotating cleanly in smooth water. Thus vibration will be cut down if the water impacting on the screws is smooth - best achieved when it is faced with as few changes in direction as possible. The screws need to be far enough apart so that disturbance from one does not impact on another. They need to have large separation from the hull so that the water flow between the topmost tip on the screw and the hull plating is enough to permit smooth flow (very difficult on a centerline shaft and why merchant ships with single screws have that characteristic thumping feel on their fantails). Each blade of the screw has to be designed so it cuts the water cleanly, leaving it smooth for the next. As the blades get more numerous (essential to absorb power) they get less efficient. Each screw leaves a spiral race behind it - this causes vibration when it hits the hull and rudders (putting a rudder in a screw race does wonders for steering but there is a price to be paid for that in potential vibration.

Each prop generates its own resonance frequency. This is easy to calculate its the number of blades on the prop times the speed of rotation. Thus, a five-bladed prop turning at 300 rpm will generate vibration at 5x300=1,500 pulses per minute or 25 Hz. That’s easily detectable on passive sonar at long range. If the natural frequency of the hull component is 25 Hz, beware, trouble looms.

If there is a bar of turbulence in the water, every time a blade hits it, that blade will shake and transmit that shaking up the propshaft to the gearing from whence it will radiate forwards. This is called blade beat and is a bear. Nobody knew it existed until the 1950s when US submariners detected it and started to use it for ASW. It was crucially vital because, radiating forward, it revealed the position of a Russian submarine while it was approaching (most sonar-detectable noise radiates aft). The Russians didn't have a clue that blade beat even existed until the mid-1970s when the Walkers blew the secret. Scythe-shaped blades kill off blade beat very nicely since the curved edge of the blade hits the turbulence progressively (much as a curved sword slices flesh more efficiently than a straight edge).

There is a low pressure area on the edge of props that can be low enough to cause bubbles of water vapor to form. These expand and eventually collapse against the prop blade, striking it like a tiny hammer. There are thousands of them. They really start a propeller vibrating nicely. Cavitation can also form in the screw race. If the designers are really unlucky they get a thing called sheet cavitation where the blade generates a large bubble that envelopes the blade and part of the hub; this can rip of a blade without trouble. Sheet cavitation is a major design blunder. Small, fast running many-bladed props are much more prone to cavitation that slow-running, larger, fewer bladed ones.

Given all the possible sources of vibration, its no wonder that ships vibrate and sometimes that vibration exceeds acceptable limits. Those limits are much tighter now than they were 30 years ago because electronic equipment really does not like being thrown a few feet in the air a dozen times per second. If vibration is unacceptable, then the designers try new screws (hoping to change the natural vibration and get rid of resonance), add extra shaft blocks, brace things, change the water flow aft and swear that it is all the crew’s imagination (the latter never works but it might one day so is worth trying). Bad vibration can take years to correct - each item has to be checked and changed until the right combination is struck. Its called “running trials”.

Basics of Designing a Marine Propeller - A primer for Non Naval Architects : Part 1

Marine Propellers are usually described as pushing against water in order to propel a ship forward. In fact, this isn’t quite the case. What a propeller does is apply an acceleration to a mass of water. According to Newton’s Law of Action and Reaction, the action of increasing the velocity of a mass of water in a given direction generates an equal and opposite reaction in the propeller/shaft assembly. This is described as the thrust of the propeller and it is this thrust that drives the ship forward.

The basic theory of how a propeller works was put together by three eminent Victorians, Rankine, Greenhill and RE Froude (son of our old friend William Froude) between 1865 and 1889. They envisaged an idealized propeller called a Rankine Disk Actuator which imparts a sudden uniform acceleration to all the fluid passing through it, the flow being frictionless and the water being present in unlimited quantities and the Rankine Disk working with 100 percent efficiency. In this idealized system, the energy imparted to the water by the Rankine Disk Actuator is

E = 0.5 x M x (V1-V0)(p2)

Where E is the energy required for the acceleration, M is the mass of water accelerated, V1 is the final velocity of the water and V0 is the initial velocity of the water. Due to the limitations of the text system here I can’t use superscripts so (p2) indicates squares, (p3) indicated cubes etc., etc. This is, of course, a slightly modified standard kinetic energy equation. Unfortunately, that’s the last easy bit of mathematics. Because adding any energy into the system changes the values of both V1 and V0, the equation has to be integrated between zero and t seconds where t is the time taken for the system to come to equilibrium.

Now, (V1-V0), the increase in velocity of the water, is determined by the design of the screw. Each turn of the screw accelerates a package of water from V0 to V1. Increasing the rate of revolution increases the number of those packages that goes through the Rankine Disk but does not increase the speed at which they leave the disk. This is important; it doesn’t matter how fast the screw turns or how large it is, it the design of the screw and that design only that determines the acceleration of the water. A good comparison is a road with a 55 mph speed limit - improving the quality of the road or widening it to include more lanes will increase the volume of traffic the road can handle but the speed of the traffic will only be increased by raising the speed limit.

M, the mass of the water passing through the Rankine Disk Actuator, is equivalent to the density of water times the volume of water passed. Increasing the volume (and thus the mass) of the disk can be achieved by using a larger disk and/or increasing the revolutions per minute of the propeller. In mathematical terms, the water passing through the Rankine Disk is a cylinder, the diameter of which is the diameter of the disk and the length of which (the number of packages transiting the disk) is determined by the speed at which the disk is turning. From an energy point of view, it doesn’t matter very much whether the cylinder is long and thin (a small prop running at high speed) or short and fat (a large prop running at slow speed). As long as the two cylinders contain the same volume of water being accelerated the same amount, they’ll demand the same amount of energy and yield the same level of thrust. (Remember these cylinders are mathematical constructs not physical reality).

This treatment gives us one very important lesson which takes some complex mathematics to prove because it seems so outrageous. Since we are accelerating a cylinder of water through a disk, fully half the thrust developed by the acceleration of that cylinder is delivered before the water ever touches the disk! In short, we seem to get the thrust before the water gets the acceleration. This is outrageous, ridiculous, unbelievable and perfectly correct - it is a major consideration in designing underwater hull forms.

Unfortunately, when we leave the idealized world of the Rankine Disk Actuator and enter the real world, life starts to get complex. Firstly, the cylinder isn’t a cylinder. Before the water hits the propeller it is being drawn along at speed above that of water outside the cylinder. Bernoulli’s law dictates that water will be drawn into the cylinder from outside, causing the cylinder to bulge outwards. The other side of the prop, the fact that acceleration is constant by the volume of water being pushed through is increased as the revolving speed of the prop goes up causes increased pressure areas aft of the prop. This causes a high-pressure bulge here too. (A simple experiment illustrates this - take a garden hose and set it running full blast. Now put your thumb over the nozzle). Eventually, this high-pressure region reaches the proportions where it breaks the surface, giving the famous rooster-tail effect. (It can also have a forward vector that has a propulsive effect on the ship). These two factors mean that the propeller isn’t at the center of a cylinder but a complex shape rather like an hourglass with the propeller at the thin neck. Again, the equations have to be integrated in order to get the “volume” (i.e. the energy content) of the system. If we were following the maths in detail, we would now be dealing with several layers of integrated equations.

Another problem is induced rotation. In the Rankine Disk Actuator, no axial rotation is applied to the water flow. At low transiting volumes, this is almost true, but as volumes get larger and the ratio of prop diameter to speed of rotation reaches critical values, the water leaving the propeller (the race) becomes more and more spiral in shape. This is purely awful - every drop of energy that goes into rotating the water instead of accelerating it is wasted (in effect it shortens our mathematical-construct cylinder). In mathematical terms the pitch of the spiral shortens as speed of prop rotation increases and the loss of energy is proportional to the square of that pitch.

Increasing prop size and speed of rotation are both good in that they increase the volume of water the prop accelerates. However, there are limits on both. Propeller size has physical limitations (we really do not want the blade tips hitting the hull plating), material restrictions (having the prop fly apart from metal fatigue is usually quite depressing) and also hydrodynamic restrictions which we’ll come to later. If speed of rotation is pushed too high, the propeller starts to hit the axial rotation problem described above and also starts to cavitate. This is by way of being an upper limit - reductions in propeller efficiency from cavitation quickly get so high that adding extra power will actually slow the ship down.

The inefficiency of a small, fast running propeller is murderous. For example, if the efficiency of a prop was really that of a Rankine Disk Actuator, halving the diameter of a propeller could be compensated by increasing the speed of the propeller by a factor of four - the energy contents would be the same. In reality, the efficiency of the half-diameter quadruple-speed propeller would be only 61.8 percent of the full-size, slow speed version - it would provide less that 2/3 the thrust. So, mathematically, the Rankine Disk Actuator equations eventually show us that a large, slow-turning propeller is a better deal than a small, fast-turning one. As an insight into a science nobody had thought of a few years earlier, the Rankine Disk momentum theory isn’t bad for a group of Victorian gentlemen who had virtually nothing to work with except slide-rules and their own perceptive brilliance.

In effect we have a cycle by which the engines generate power, that power is used by the screws to accelerate water, the reaction to which is thrust which pushes the ship forward. Unfortunately, the limitations on prop size and speed of rotation plus the fact that the acceleration applied to the water by the props is fixed by the design of the props, means there is a limit to the energy the props can use (in mathematics, to the size of our hour-glass or cylinder depending on whether we are looking at reality or theory). Any extra power generated by the engines above that limit is so much deadweight. In reality, of course, this limit isn’t a sharp point but an area in which the efficiency by which the screws convert energy into thrust quickly drops to zero. Nonetheless, adding 500 tons of machinery to a ship that is already overpowered will not achieve anything at all.

We can’t do much about the density of water (well actually we can. The effects of pressure from depth are quite important - a propeller running at 45 feet will give measurably more thrust than the same prop at 15 feet due to water pressure. Also, the compressive effect of a heavy hull will have a beneficial effect on the effective mass of water going through the prop. These are, however, relatively minor effects in terms of the sort of gains we are looking for). If we are going to get a major gain in energy utilization out of the power train we have to improve the amount by which the propeller accelerates the water and design the prop so that cavitation is delayed as long as possible. Unfortunately, here the Rankine Disk ceases to be of help since the mechanism by which it accelerates the water is not considered. There are two theories that do deal with this, the Blade Element Theory (which evolved shortly after the pioneering work of Rankine, Greenhill and Froude) and the Circulation Theory (evolved by F.W. Lanchester for aircraft in 1907 and applied to ships by Betz and Prandtl some years later). Both involve mathematics of extreme complexity. The Circulation Theory in particular allows the acceleration applied to water by a blade of given shape to be calculated by a thing called the Kutta-Joukowski Equation. The fun question is, what is the ideal shape?

What makes this question difficult is the fact that the propeller works in the ship’s wake. What is normally called a wake isn’t; its a combination of the ship’s real wake and the race from the screws. Differentiating between the two is easy - the race travels backwards relative to the ship, the wake travels in the same direction as the ship but at a lower speed. The wake results from (a) the frictional drag of the hull which produces a following current, maximizing around the stern (b) the streamline flow past the hull causing increased pressure where the hull lines close also creating a following current and © the wave pattern formed by the ship on the surface in which the water packages have an orbital motion, the top being in the same direction as the movement of the ship and the bottom being in the opposite direction. The forward speed of the wake in proportion to that of the ship is called the Wake Fraction. This will significantly reduce the (V1-V0) value (by half for a wake fraction of 50 percent) with obvious effects on thrust. The three factors that create the wake give a hydrodynamic picture of unsurpassed complexity. Newton and Hadler did a whole series of studies back in 1960 on the performance of propellers using Fourier Analysis to create mathematical constructs of wakes using the computers then available. They produced a series of flow diagrams of single and twin-screw ships sections aft and of the props working in those flow conditions. These clearly showed that the twin-screw environment was much less chaotic than the single-screw situation. In a single centerline screw, the relative intensity of the wake/prop interaction (which should be constant for maximum efficiency) varied from 0.10 at the tip to 0.67 at the root of the blade. In a twin-screw, the same figures were 0.02 at the tip to 0.04 at the root. The study also showed that the effect on the wake form from a centerline screw was enough to badly disrupt the more favorable environment surrounding the wing screws. These experiments at last provided a reasonable explanation of why twin screws work better than single centerline props and lead to a concerted effort to relate hull design to wake characteristics.

In 1965, Van Manen produced a series of conclusions based on his extrapolation of Newton and Hadler’s work. These were that the wake pattern is largely a product of the aft body of the ship, that harmonic amplitudes (transverse vibration) are inherently more severe on ships with centerline screws, the finer the stern, the more efficient the props, that blade geometry has a significant effect on induced shaft vibration, that transom sterns are less prone to cavitation, that the rudder has little effect on the wake and that minor changes in speed, displacement, hull form and trim have major and completely unpredictable effects on the wake pattern and, therefore, screw performance. In 1972, Van Oossanen et al investigated these areas but failed to come up with meaningful answers as did Holden in 1980 (although he did have some success in predicting effects on wakes with low peak values). This whole area is still largely a mystery although Chaos Theory may provide some clues as to what is happening back there.

So, having gotten the theory out of the way, how do we design a prop to convert more power into thrust and, thus, to make bigger battleships possible? If the ship design isn’t pushing the limits of practical, it’s quite simple. We take the desired prop diameter from the hull design, take the desired speed of revolution from the machinery design people and put the two figures into a pre-calculated graphical projection that will give us the “optimum” prop design for those conditions. This optimum isn’t really that, its the best commercial approximation that can be mass produced for those conditions. If we want anything better, its has to be custom-designed for that specific ship.

This involves massive tank-testing of hull forms to determine the wake characteristics at a wide variety of ship speeds and then the incorporation of those figures into a computer model to determine how a propeller will behave in those conditions. The geometry of each blade can then be designed (and redesigned and redesigned and ... you get the message) to try and reduce wake/prop interaction and to equalize that effect across the blade. This involves, slow, patient changes to leading and trailing edge configuration and blade cross section at varying points along the length of the blade (i.e. from root to tip). Blade area should be maximized to eliminate cavitation and the number of blades selected to give optimum results (usually that means as many as possible consistent with keeping flow conditions smooth). Typical selections these days are four, five and seven bladed props with nine-bladed units beginning to make an appearance. For some unfathomable reason, six-bladed props are more prone to exhibiting unfavorable characteristics than other configurations so are usually avoided (this is not an absolute). These days, much of this work can be done by computer simulation with the results confirmed by tank testing. Today’s customized propellers have extremely complex blade shapes, involving high skew and rake levels and extreme radial pitch changes and radical differences in cross section at each stage along the tip to blade axis. Throughout the design process one thing has to be kept in the back of people’s minds - can this prop actually be built? There is no point in designing the perfect propeller if it can’t be built!