This is probably one of the best "posts" I've read about props over at the boatdesign forum, posted by Canada eember Jeff D.
I hope he will forgive me for shamelessly copying and pasting it here in the hope it may help others who get to read it.
quote:The question of diameter seems to raise its head every few weeks – is a large diameter more efficient than a small diameter? The real answer is sometimes and it all depends why the diameter is small in the first place.
Prof. Burrill – of Cavitation Diagram fame – once said that it was easy to design a marine propeller but difficult to design a good one! Therefore, if the answer to the riddle is always a resounding yes then the designs must be worse than even Burrill ever imagined.
First of all these notes only give a brief overview of propeller design as it applies to ordinary, run-of-the-mill types so forget about surface piercing, super-cavitation, vertical axis or any other special types. So although we are left with “ordinary” screw propellers there remain a few types and styles so a brief review, then down to basics.
Fixed pitch versus controllable pitch
The pitch may vary along the length of the blade to take some account of the varying wake pattern or it can be constant or constant for the outer 50% and reduce towards the hub. Whatever type it is then the blades for that particular propeller are constant shape and if the propeller is a one-piece casting then it is known as a fixed pitch propeller. Some propellers have blades that are bolted onto the hub and it is impracticable to remove the blades and change the angle so they are still fixed pitch. Even bolted blades that can be adjusted are fixed pitch in the sense of being fixed while in operation.
These propellers are designed to suit only one operating condition and their efficiency drops off when they operate at other conditions so the design could be a compromise. A tug is the best example; it could be stopped and trying to push or pull something many times its own size or it could be racing to an accident. These are the extremes so the propeller would usually be designed to be pulling something at a speed of about 7 knots absorbing full power. If the tug spent a majority of its time pushing something in a harbour the compromise would be biased to accommodate this.
Even so, the efficiency drops off and the owner may elect to pay the extra for a controllable pitch propeller. The blades on these rotate on the hub so the pitch changes during propeller operation and the efficiency improves over a wide range although the peak efficiency is a slightly less than the fixed pitch screw’s at its operating condition. They are becoming normal now on tugs and other stop and go vessels. Cross-river ferries or those on short trips can also benefit so too can vessels that have different seasonal modes of operation like full speed in summer and half speed in winter.
Blade form
Propeller blades in the beginning were very simple in shape for the simple reason that the science was still new and also because manufacturing facilities too crude. The science developed and blades took on a more complex, but more efficient shape, while engine plants got bigger, more powerful and eventually lighter.
It became apparent that despite the better efficiency of a highly complex shape it was often better to use a simpler shape if repairs were necessary on a regular basis. For example, this resulted in some Navies using simpler blades because they would be easier to fix in the event of some emergency when far from home. This is basically how the propeller used on small boats came into being; it is the Gawn-Burrill type that is much cheaper to make and repair and only a little less efficient than a typical Troost or Wageningen type.
With the advent of CAD-CAM and CNC the situation changed, the design being done on computer allowed more investigation and research so the designs became more efficient but computer shape definition and computer controlled machining allowed faster and more accurate manufacture. The cost of machining fell so that the complex shapes began to be used and some types now were justified on an economical basis.
Propellers for small boats still tend to be on the simple side but inroads are being made by some exotic designs, especially the out of the ordinary cases of extra high speed or exceedingly low draft. A major difference between large ship and small boat propellers is that the ship propeller is custom designed to suit but the small boat types are standard designs. If the first one doesn’t work then try another one until it does.
Number of blades
The fewest number that will do the job at an acceptable cost. Different vessels have different needs and what is sauce for the goose need not be sauce for the gander. Acceptance standards have changed also, the TITANIC had three bladed propellers, but nowadays it is not unusual to see five and six bladed versions or Azipods. The most efficient, in terms of the power out of the screw compared to the power delivered, is the least number of blades but it is easily unbalanced and can set up unacceptable vibration and noise.
In the old days on a passenger ship, it did not matter too much as long as it still worked because the problem area was where the steerage passengers were. As long as the clatter etc was only in their quarters and some of the lowest paid crew and did not bother the first class and the senior crew it was tolerated. The situation today is quite the opposite and word of mouth derogatory comments spread like wildfire and the occupancy rate drops – not good for business.
When a propeller turns, there is an effect something like a hammer pounding on the hull when a blade passes by. With only three blades compared to six blades the rate it happens is half but the pressure pulse is higher and so more clearance is needed to drop the effect to a suitable level. The Classification Societies such as the American Bureau of Shipping (ABS), Bureau Veritas (BV), Lloyds Register of Shipping (LR), Det Norske Veritas (DNV) etc have rules establishing the minimum clearance. These are all useful in the early stages and can be refined as the design develops. Minimum clearances are given from the propeller to the hull and to the rudder etc.
Each Society has its own standards and formulas and the easiest to apply is DNV whose formulas for the tip-hull clearance are simply;
Single screw Dia x (0.24 – 0.01 x Blade number) metres minimum
Twin screw Dia x (0.30 – 0.01 x Blade number) metres minimum
The next is probably BV whose formula for tip-hull clearance, three blades is;
Single or Twin screw Dia/(8xL) x 0.80 x (Cb x Power)^(2/3) metres, minimum 0.1 x Dia
These formulas are from the Ship rules and may be different for the Small Craft that can be classed nowadays; I don’t have them so I can’t comment.
All these formulas are metric with dimensions of diameter and ship length in metres and power in kW. Note that DNV gives only absolute minimum whereas BV gives a formula with a minimum 0.1 x Dia for a single screw, no one would use such a low value unless the blades were specially designed such as the swept blade forms now standard on passenger ships. These are the types where a blade looks a lot like a rounded boomerang and the pressure pulse gradually builds up on the outer half of the blade so there is no sudden effect. The typical rule of thumb is to use 0.15 x Dia on 4-blades and the DNV formula usually is the most onerous.
Another reason for more blades is balance, the more blades the better but the basic cost rises and the propeller efficiency falls. The effect of damage to a blade on a multi-blade screw is less than the same extent on a blade of a two or a three bladed screw. A multi-bladed propeller will usually tolerably operate at reduced rpm while the others can still cause serious damage.
Cavitation and ventilation
Used to be a most serious problem but nowadays it can be avoided fairly easily. The old method was simply to limit the blade tip speed to 12,000 ft/min and the total thrust loading on the propeller developed area to 0.75 tons/sq. ft. which is 11.667 lb/sq. in. This worked well until ship designs changed and the rules-of-thumb no longer applied. Nowadays it is usual to use the Burrill chart or something similar taking account of the loading but also the immersion and the water vapour pressure.
Other factors can also come into play such as the blade thickness and shape; masking caused by waterlines filling out at the top, propellers with no hull above, local eddies just ahead of the blades. Poor location and design can cause a propeller extensive damage in a short time, so bad that it is sometimes cheaper just to replace it.
Extremely low pressures on the blade cause cavitation and this causes vapour bubbles to appear that implode on the blade resulting in corrosion. Cavitation is the same effect as when water boils and the bubbles appear. It is due to the blades being too close to the surface in association with high thrust loadings. The solution is to increase the blade area with a greater BAR or Ae/Ao ratio.
Ventilation is air drawn from the surface down to the blades or exhaust from underwater exhausts. It has the same effect as cavitation and the first line of defence is a hull or tabs above the propeller.
Material
On ships, it is pretty much a choice between stainless steel and various bronze alloys.
More selection on boats with a wider strength range with more problems. Plastic, aluminum, stainless steel and bronze with some newer hi-tech alloys. If you run in fresh water with an outboard then plastic or aluminum are common and good enough. However, an inboard in salt or brackish water with sand or grit will call for stronger materials.
Standard Series
There are many standard designs that are available in a variety of number of blades, blade area, different pitch ratios and so on. The most widely known is probably the Wageningen series that was began in 1936(?) by Professor Troost from the model-testing establishment at Wageningen in Holland. It is a general commercial ship type but the advantage is design charts are available and a set of formulas that cover the entire range so they can be programmed. There are other series with published data but the Wageningen is the most comprehensive even though it is not a particularly good type for small boats. Another advantage is that it is the most common type on the net and a useful paper is posted by Prof. Journée on his site at
http://dutw189.wbmt.tudelft.nl/~johan/ it is called ProPol.zip and it is near the bottom about one screen above the Curriculum Vitae. The formula coefficients are difficult to read but this site
http://asdal.snu.ac.kr/korean/lectu...CH06/6_1_2.html has clearly legible values in Arabic numerals although the document is in Korean.
The Dutch site paper is a scanned version of the original paper by Oosterveld and van Oossanen entitled Further Computer-Analyzed Data of the Wageningen B-Screw Series published in July 1975 by International Shipbuilding Progress.
Later I will concentrate on this series but first some general notes on design diagrams.
Design diagrams
There is one diagram called the Kt~Kq diagram that can be used to solve any propeller design questions and it is also the most difficult to use. The coefficients are non-dimensional so the chart can be used with feet and pounds or metric units and you get the same answer. Kt deals with the thrust and is what you get out of the propeller while Kq is about torque or what you put into it. Kt divided by Kq is a function of the propeller efficiency. The problem is that each pitch ratio value is a different line on the chart so it is awkward; nowadays of course, it is simpler using the computer. Excel is handy and you can optimize the design using the SOLVER function, very useful.
There are other diagrams that are more useful if you want to work with charts rather than leave it entirely to the computer. To determine bollard pull the Sigma~Mu is useful but the most common of all the charts is the Bp~Delta, more later about that.
All these charts have one thing in common; they allow you to find the optimum propeller as well as off-optimum if you choose – optimum in the sense of maximum efficiency taking into account boat speed, propeller revs, diameter and pitch ratio with one chart per blade number and area ratio.
Some older design charts can still provide useful information such as the type developed by the Froudes, father and son. It was coincidental that older works on Naval Architecture in Britain were written by warship designers and both Froudes worked for the British Admiralty. The result was that the examples on propellers concentrated on warship types, for example, Theoretical Naval Architect by Attwood and Pengelly included design diagrams for three bladed, elliptical propellers with a disk area ratio of 0.45 based on Gawn’s early research. These resulted in the well known Gawn series and boat propellers are normally based on this type of flat faced, elliptical blade.
There are also some design Nomograms that give a close approximation like the one shown above here by Jeff. Each nomogram can only show one type, Jeff tells us it is 3-bladed but we do not know the design type nor the blade area ratio and P/D. What irritates me is that I have seen it before somewhere but I forget where. I’d be obliged if you could enlighten me Jeff. The same diagram turns up in the
www.bomon.com site but it’s obviously not a boat diagram as bomon only goes to 250 hp max but the diagram is up to 10,000. Notice the title is slightly different.
Another design nomogram is shown in the illustration below; it was used for British warships and shows half of the Gawn range of blade area ratio, the other half continues up to 1.1 BAR. Much more complex than Jeff’s diagram as it is based on Kt/J^2 which is Thrust/(rho x Dia^2 x Va^2) all in consistent units. Again, it is for the optimum condition and cannot show the off optimum results. It is always a case of making some basic assumptions plot a graph and read the value you need.
Rather than me re-inventing the wheel and making a big deal out of it, I did some searching trying to find sites where there is a good explanation of propeller design. I wanted something that erred on the side of simplicity and I could only find two sites. One deals with exclusively the Boston Whaler and covers the propeller selection quite well, the site is
http://continuouswave.com/whaler/ and it has the propeller calculator Applet that is in so many sites. This one has some explanation of what is going on and there are several articles that are also useful.
The other site is
http://www.realtrawlers.com/articles.html that is surprisingly good. It deals with larger small boats and small ships. The approach is the standard approach taken by all larger yards until computer programs became useful. It shows how the efficiency changes in the way it does and explains what goes on with the diameter. It misses a couple of things that I’ll explain but you should go to the site and print out the design chart that is their FIGURE 2 about half way down the page.
That chart is the standard Bp~Delta diagram that was initially developed by D.W. Taylor and is the usual one used to find the optimum diameter or revs and efficiency given the power and speed. There are some errors in the text due to the usual problem of the site showing text in a different manner to which it was prepared. I’lI write a DOC or PDF file later to explain the workings etc and I’ll stay with the example on the site. I sent an e-mail congratulating them on the presentation and pointed out the bloopers, if they repost before I complete my file I’ll just dump it and work with theirs.
But I imagine, Jeff, that you’ll find this most interesting – some formulas.
They are based on a method I developed in about 1970, I was fed up having to work out propeller sizes for new designs before stern apertures, propulsion systems etc were fully worked out. That was the era before computers and even with a very expensive electronic calculator that did square roots (it cost almost $2,400, a Litton or a Monroe) it took weeks to work out just one case. Now that work takes a few minutes on Excel.
It uses a simple equation of the form: value = coefficient x variable^number, I chose this because it is easy to manipulate and still give reasonable answers. Other types of equations give more accurate answers but they result in jaw-breaking expressions.
I have all the data for Wageningen propellers so what follows is for the B3-50 type which is three bladed aerofoil, area ratio 0.50 and they are slightly better than Gawn types but preferable for larger, working vessels, could I say professional instead of recreational?
Propeller design data is too complex to find a single formula to give good answers over the entire possible range for even one type. I have elected to give two sets – one for Bp values up to but less than 20 and the other from 20 to 50.
Bp is the Taylor power coefficient which is: N x P^0.5/Va^2.5 where
N is the propeller revs in rpm
P is the power delivered to the propeller ie BHP less bearings, gearbox and similar mechanical losses, less engine driven auxiliaries and the like, in US hp
Va is the propeller speed of advance through the water in knots. For planing boats, the boat speed can be used, for displacement boats and others in the early semi-planing mode Va is less than the boat speed and Va is boat speed x (1 – Taylor wake fraction).
The values for the formulas that follow are all of the form;
Y = constant x N^a x P^b/Va^c and the values of N, a, b, and c follow the formula name below
For Bp 5.25 to less than 20
Diameter 46.47684 -0.53356 0.233221 0.166105
Efficiency 0.91431 -0.1209 -0.06045 -0.30226
Pitch ratio P/D 2.094151 -0.34301 -0.1715 -0.85752
example: Dia in ft = 46.48 x N^-0.5335 x P^0.2332/Va^0.1661
For Bp 20 to 50
Diameter 51.7566 -0.57165 0.214175 0.070875
Efficiency 1.239311 -0.22431 -0.11215 -0.56077
Pitch ratio P/D 1.436779 -0.21238 -0.10619 -0.53094
Example;
1500 hp @ 450 rpm & 10 knots gives 76.9” - 50.4% - 0.61 where Bp is 55.1, the diagram Jeff posted gives about 74” dia so the formula seems about 4% high but if the speed is changed to 17.13 knots the values become 74” – 68% - 0.82
200 hp @ 1500 rpm & 25 knots gives 22.7” – 72.5% - 1.09 while the diagram gives 24.5” so now the formula seems almost 7% too low. Change the speed to about 14 knots and the values become 24.5” – 58.2% - 0.70
These demonstrate how the speed plays an important part and the posted diagram uses a varying speed but does not say what it is. If the speed were constant, the central scale would be a straight, vertical line.
But also don’t forget that the diagram is a Gawn type and the formulas are Wageningen so there is a difference because of that too.
Be careful not to use the formulas outside the Bp limits although up to Bp 75 or so you will still get reasonable answers but less than 5.25 the results are not too good because the required P/D would exceed 1.4, which is the limit for the Wageningen designs.
So do they help you in any way, Jeff?
Michael
Oh, by the way! Did anyone notice that in the first example the diameter was reduced but the efficiency increased? Kind of disproves the theory of bigger prop = higher efficiency, doesn’t it? Did the same on the second but efficiency increased! The answer’s on the Bp~Delta diagram.
Havent got a clue what it all means - but it sure looks good!
Cheers!
Prop Diameter question 
Boston Whaler, "MUMBLER", 24' Outrage, twin 175 HP Evinrude Ocean Pros. 
Snowball, the cat... 
