Fuel Consumption - Typical Values

Baker gives these figures as average consumptions, as installed, although it is unclear whether these Shaft Horsepower (SHP) figures are given before or after all the ancillary drives. I suspect the latter. The unfeasibly high-speed turbines were land based installations, but he was obviously aware that naval turbines still had a way to go in efficiency. I've included a modern truck diesel in the table to show where they were heading. It looks as though the diesel engines are far more efficient than the steam units, but part of that difference is due to the higher calorific value of oil, which is discussed more fully later on.

Engine type lbs/hr/SHP Fuel type
Triple expansion steam engine 1.54 coal (type unspecified)
Quad expansion steam engine 1.34 coal (type unspecified)
Turbine at low speeds 2.4 coal (type unspecified)
Turbine at high speeds 1.2 coal (type unspecified)
Turbine at unfeasibly high revs 1.0 coal (type unspecified)
Diesel 4 stroke 0.44 oil (type unspecified)
Diesel 2 stroke 0.47 lamp oil
modern turbo diesel at optimum efficiency 0.35 diesel

The turbines will usually need a speed reducing system of some sort if the losses in the prop itself are to be reduced to the same level as a reciprocating engine's. The two common alternatives were either an electrical 'transformer' (Baker's phrase -presumably a generator-motor set 88% efficient) or a gearbox (98% efficient). I'd add that once you have a speed reducer of whatever form you could end up with a better prop than the direct drive reciprocating engine. He later comments that the pulseless drive from a turbine tends to delay cavitation. These two factors might allow you to design a more radical, and so more efficient, prop for a given ship's speed, but he makes no mention of this.

On these numbers a turbine at high speed will always be more economical than a triple expansion reciprocating steam engine, whichever transmission system is used. At low speeds (typically less than 14 knots) then the reciprocating engine is better. I haven't found a quad expansion engine in naval use, but they would have been roughly as efficient as a triple at low speed, or slightly better, and as economical as a turbine with an electrical transformer at high speed. A turbine with a reducing gear would still have been about 10% better.

Another installation uses triple expansion engines on the outer shafts, with their exhaust steam going to a direct drive low-pressure turbine on the center shaft, and notes that the engine room was very long. He claims a 12% reduction in fuel consumption over a sister ship with just two shafts and two quad expansion steam engines, which is equivalent to 1.18 lbs coal per SHP hour - pretty impressive.

Mechanical Efficiency of Engines

In a separate discussion Baker gives the following values for SHP/IHP. This is the power in the shaft as a proportion of the measured gas cycle in the working chamber. Turbines don't have an IHP as such (in this book), and I can't find representative numbers in my other books.

Engine type Efficiency
Triple expansion at low power 0.80
Triple expansion at full power 0.88
Quad at full power 0.92
4 stroke Diesel 0.85
2 stroke Diesel 0.71

This drop in efficiency is due to friction, auxiliary plant, windage and some of the residual energy in the exhaust. On average quad engines were larger than triples, so the higher mechanical efficiency of the quad is probably because the parasitic auxiliaries tend to be a smaller percentage of the SHP.

Calorific Value of Fuels

Charles Braun found me the details of the coal, the kerosene figure comes from Rogers and Mayhew's "Engineering Thermodynamics, Work and Heat Transfer", which is almost as exciting as it sounds.

Fuel Calorific value
MJ/kg hp hours per lb lb per hp hour
Kerosene (diesel) 44 7.3 0.136
Welsh Admiralty coal 35 5.8 0.172

Approximate Relative Efficiency of Engines

Adding in the relative performance of each fuel gives an approximation to the overall efficiency of each engine, and steam plant, if applicable. I don't know that the coal used in the first table was necessarily Welsh Admiralty, so the following analysis is necessarily flaky. According to Mark's Engineering Handbook, the very best American coal is 33 MJ/kg, and the worst (other than lignite) is 20 MJ/kg, so Welsh Admiralty coal is very good indeed. A better calorific value worsens the efficiency I've calculated below. This is the proportion of the energy 'in' the fuel (it's more complicated than that, but the complexities don't make much difference) that actually gets into the crankshaft. Note that a proper analysis of this is much more complex, so these figures are approximate.

Engine type Efficiency
Triple expansion steam engine 11%
Quad expansion steam engine 13%
Turbine at low speeds 7%
Turbine at high speeds 14%
Turbine at unfeasibly high revs 17%
Diesel 4 stroke 31%
Diesel 2 stroke 29%
Modern turbo-Diesel 39%

The efficiencies of the steam plants are a little low compared with my expectations. Diesels, which at the time were limited to 2000 hp or so (as Baker says- at least 6000 hp was available by 1930), were obviously the first choice for efficiency. It is also obvious that developing reduction gears to handle the high speeds and high powers of efficient turbines should have been a priority. These numbers allow us to compare each installation independent of the fuel type, which, since they can all run on oil, is quite handy and separate from the coal vs. oil decision. I would expect all the coal fired numbers (all the steam engines) to improve slightly when run on oil, as it must be easier to design an efficient oil fired boiler than a coal fired one. Incidentally one of the reasons why the steam plants show a disappointingly low efficiency is that a boiler is around 88% efficient (source unknown), and the more of these efficiencies you string together in series, the less efficient the overall system is. These efficiencies bear little resemblance to the mechanical efficiencies in the previous section, since they include the thermodynamic efficiency of the steam cycle in the powerplant, and the boiler efficiency.

He also gives some more examples showing the relative performance of sister ships using different powerplants. Some of these were unsuccessful turbine installations. Here's the most detailed chart, showing nautical miles per ton of coal for two sister ships.

Speed (knots) Direct drive Turbine (miles/ton) Reciprocating steam engine (probably triple expansion) (miles/ton)
10 7.4 9.7
14 6.6 6.8
18 4.8 3.7
20 4.2 2.9

So, in this comparison the turbine was better at all speeds in excess of 14 knots, which bears out the argument above. I have not included other data, for ships where a direct drive turbine was less economical than a reciprocating engine. This certainly happened, as a direct drive turbine is relatively cheap, but getting the prop right can be somewhere between fairly difficult and impossible. An example of this is given later on.

He only has one comparison of plant weight, for two 520' 19000 ton sister ships:

Engine type Weight (tons) Speed (knots) Power
Turbine/generator/motor 156 14.8 6300 SHP
Two triple expansion steam engines 280 14.6 6700 IHP

It would be interesting to know the comparative installation size and weight of a diesel unit - obviously getting rid of the boilers and condensers would be a huge advantage.

Thrust Bearing Efficiencies

Once the power has been transmitted to the propeller shaft, after any reduction gearing, it still has to be transformed into useful work to push the boat along. To do this it needs to push against the boat, so it needs a thrust bearing. Rather worryingly Baker mentions casually that 'just' 2-4% is lost in the thrust bearing, but that a better pivoted block design drops this to 0.3% I am amazed that anyone would casually throw 1.7-3.7% away.

Propeller Design

The best efficiency that Baker shows for a three-blade prop is 0.75, and this would be for a very large slow revving prop in a small fast ship. To get an efficiency as high as this typically needs shaft speeds less than 60 rpm, which is possible, and screw diameters in excess of 28 feet, which is not practical for ships using normal harbors.

He includes a worked example for a twin-shafted ship with 16000 HP at the propellers. The operating speed is assumed to be 20.6 knots. Coincidentally this is roughly the power per prop and speed of the first generation Dreadnoughts. The optimum prop for a given shaft speed is as shown in the following table. He starts with a 0.5 Disc Area Ratio (DAR) (that is, the blades cover half the disc), which cavitates at 200 rpm. To suppress this he switches to a 0.8 DAR design, which is less efficient, but exerts a lower pressure on the water, and so tends to cavitate less.

Optimum prop at 0.5 Disc Area Ratio
Propshaft (RPM) Diameter (ft) Pitch (ft) Efficiency (%)
100 20.6 24.7 72
120 20.6 22.7 70
140 18.0 18.0 69
160 16.5 16.5 68
180 16.0 14.4 66
Optimum prop at 0.8 Disc Area Ratio
Propshaft (RPM) Diameter (ft) Pitch (ft) Efficiency (%)
180 15 15 62
200 14.1 14.1 59
220 13.4 13.4 58
240 12.8 12.8 56
260 12.0 10.8 55

Increasing the DAR lost about 4% and the efficiency drops by 3% for each 20% increase in speed. Not very surprisingly, the slower the prop, the bigger it is, and the longer the pitch. As this example reinforces, it is important to fit a large slow moving prop, if that is practical.

The methodology used to select propellers, in this book, is much less clear to me than the method proposed by Taylor based on the dimensionless groups Bp and delta. All the data is available in both methods, but Taylor's charts make selecting an optimal prop much easier.

Propulsive Efficiencies

The final section in Baker's book is a table showing the propulsive efficiency, EHP/IHP, of the transmission and propeller system for many different vessels fitted with reciprocating engines. This lumps together every source of inefficiency I have discussed above, for each ship. We can see from the figures in each section above that we can expect to see a maximum figure of perhaps:

Maximum efficiency = (mechanical, for a triple) * (thrust bearing) * (propeller)
= 0.88 * 0.98 * 0.72
= 62%
Worst case using the above figures would be
Worst efficiency = 0.88 * 0.96 * 0.55
= 46%
In practice he has one straggler at 33%, which actually had too large a prop fitted, reducing it by a couple of feet in both pitch and diameter gave it 2 more knots, and boosted the efficiency to a respectable 50%. The others range over 43% to 59%. That agrees suspiciously well with my estimate 46% to 62%.

The best we could hope for is rather better than that, with a quad we could see 66%. It is much more difficult to analyze the turbine, since the speed matching is so crucial to its efficiency. At best a direct drive turbine of precisely the right speed and power might hit the full 70%, although that is a proportion of SHP, not IHP. A geared turbine, in a large hull (making room for a large prop), might even achieve 73% efficiency.

He also gives an example of two sister ships, one fitted with two quad engines, running at 80 rpm, the other with three direct drive turbines at 175 rpm. This speed is very slow for such small turbines (1000-2500 rpm is much more typical), so we can expect a relatively high fuel consumption. If we assume that both ships were designed to be as efficient as possible then we can compare the relative efficiencies. From the table above we'd expect to lose around 10% prop efficiency as a direct result of speeding up the propeller from 80 rpm to 175 rpm. So the designer's other option would have been to fit a transformer, or a gearbox. This would have regained 2-8% of the difference. A crafty designer would have increased the speed of the turbines yet further, and geared them down even more, or fitted one larger turbine and geared it across two or three shafts. This would reduce his basic fuel consumption, and increase the prop efficiency. Not very surprisingly, in this case, as built, the direct drive turbine ship used more coal than the quad expansion ship.

Power Capacity of Primemovers and Transmission Elements in 1920

In 1920 the following sizes were the approximate practical power limits for each individual unit. The steam engine figures are from Jane's for ships built 1912-1916. These are not definitive, just the best figures I could find.

Engine type Power
Triple reciprocating 7000+ SHP (USS New York)
Quad reciprocating Not used in large naval ships
Diesel 2000 SHP
Turbine 28000+ SHP (HMS Repulse)
Reduction gear 15000 input
25000 output reductions up to 28:1 or 55:1 if two are ganged
Electric reduction 22000+ SHP reductions of at least 18:1 are possible

Although it is possible to use more than one engine or turbine per propeller shaft, this necessitates using a gear or electric drive, i.e., you cannot simply string a series of engines up and connect them end to end. It was common to put more than one engine onto a reducing gear, hence the different input/output limits on the reduction gear. From this table it is obvious that turbines offered significantly simpler installations for large fast ships.


By 1920 hydronamicists, engineers and physicists had gathered enough data to analyze and discuss the shapes of hulls, and propellers, quite well. Reciprocating steam plant had already been analyzed to death in the previous century. The steam turbine, particularly when geared down, was proving to be a more economical engine than the reciprocating engines, and in some installations the direct drive turbines were also efficient. By 1920 the design of three and four blade propellers in their own right was well understood. The difficulties came when trying to match them to hulls, and powerplants, in an efficient manner. The hull and the propeller interact in an extremely complex fashion - which even today can cause problems.

In 1920 it was obvious that to be efficient turbines had to be run at much higher speeds than the propellers could handle, for most ships. According to the figures given, gearing turbines looked like a better solution than using an electrical transformer, due primarily to the gearbox's higher efficiency, higher power-handling, and greater reduction ratio. Nonetheless the combination of a high-speed turbine and a transformer would still give better fuel consumption than a triple expansion engine, at high speeds.

The high efficiency of diesel engines had also been recognized, although their small size at that time militated against their use in large fast ships. The high powers available from a single turbine must have simplified the layout of these ships considerably.

Typical measured values of propulsive efficiency, from steam pressure at the piston's surface to overcoming resistance of the hull, of 43-59% have been shown to be in line with the product of the known efficiencies of each component in the system.

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26 April 2001