The first step was to determine the basic constraints that I want to put on the new engine.  I could simply put the largest diesel that will fit in the engine compartment into the boat.  That would probably be in the 80-100 h.p range.  However, I have a number of  factors to consider that limit my choice of engine both in terms of physical size and horsepower.

Given the outrageous cost of fuel, approaching $4 a gallon in February 2011, fuel consumption is now an important factor.  Naturally I would like to minimize fuel consumption while still maintaining good cruising speed.  Because of its plumb bow, the 32'9" LOA Tortuga has a waterline length of 32 feet.  Furthermore, Tortuga has a pure displacement hull.  Consequently, pushing Tortuga much faster than its hull speed will take a lot of power.  The hull speed is related to the waterline length by the relationship:

That works out to a hull speed of 7.58 knots.  So, I can run Tortuga at speeds up to about 7.5 knots with a relatively small engine and reasonable fuel economy.  If I want to go faster than that, I will need a considerably bigger engine and will use a lot more fuel.  The old gas engine was rated at about 110 h.p. and according to the previous owners could push Tortuga along at 12 knots or so with the throttle wide open.  However, it probably burned about 7-8 gallons of gas an hour to do that.  That wasn't a huge consideration when gas cost $1 a gallon or less, but now at $4.00 a gallon, that sort of fuel consumption adds up quickly.  So I have decided that I will be happy to cruise along at 6.5 to 7.5 knots with a bit of power in reserve for when it chops up a bit.

A second consideration is that I eliminated the engine box in the cockpit and the intrusion the engine makes into the cabin.  Getting rid of the engine box will really opens up the cockpit.

I have junked the engine box and replaced it with a new bit of sole.  The down side of replacing the engine box  is the vertical height constraint it places on the engine size.  I have measured the engine compartment carefully and the highest engine I can fit is 25".  Less than that is desirable so that I can get more sound insulation in over the top of the engine.

My third consideration is money.  Bigger engines cost major money.  I would like to spend as little as I can get by on.  The desire not to spend a lot of extra money also means that I would like to keep the existing prop and shaft.  The prop is a 20" diameter by 15" pitch three blade wheel.  I can have the prop repitched for considerably less than buying a new prop, but the limits ate +/- about 2" in pitch.  So I would like the new engine to be able to turn the existing prop.

So these are my constraints.   I want an engine that has enough power to push the boat at 7 to 7.5 knots with a bit of power in reserve.  The engine also needs enough torque (and displacement) to turn the existing 20x15 prop (possibly pitched down as far as 20x13).  Finally the engine needs to be small enough to fit under the cockpit platform.

The first step in picking the engine now that I have established my desires is to figure out how much horsepower I need to push the boat along at 7.5 knots.  Since I have been thinking about installing a new engine, I have found that there are lots of simple formulae for calculation power required for displacement power boats.  There are also several more complex methods.  As a scientist I tend to shy away from the simple, generalized formulae toward more specific approaches even if they are a little more complex.  Nevertheless I am going to summarize the various formulae I found with a few comments.  I have tried to give considerable detail about the various formulae used as well as the engines I am considering in the hope that the information may be useful to others.  I have also strived for accuracy in my discussions, but this is the internet, so remember that when you read my words.

The first formula I came across was the one in The Propeller Handbook by Dave Gerr published by International Marine.  The formula, like all those to follow, calculates power required at the propeller, which is called shaft horsepower (SHP), from waterline length in feet (LWL), displacement in pounds (Disp) and boat speed in knots (KTS).  The formula in Gerr's book actually gives boat speed as a function of power, displacement and LWL.  I have rearranged that and the following formulae to give required shaft horsepower.  Gerr's formula is:

In June 2008 Dave Gerr published a revised formula in the Westlawn Institute's publication The Masthead, vol. 2 No. 2.  (http://www.westlawn.edu/news/WestlawnMasthead06_June08.pdf).  That formula was cast in terms of the speed to length ratio and displacement.  I have recast the formula into the same terms used for his earlier formula.  It is:

In the same issue of The Masthead, Gerr also printed Wyman's relationship which I have also rearranged to solve for SHP.  Note that the Wyman formula includes a coefficient that depends on the speed to length ratio.  However, that coefficient is one for speed to length ratios (SL = KTS/(LWL^1/2)) less than two.  Since I don't expect to be pushing Tortuga above 11.3 knots (SL = 2 for Tortuga's 32' LWL), I have not explicitly stated the coefficient in the following rearrangement of Wyman's formula:

Gerr suggests that it is appropriate to use his newer relationship for SL ratios less than two and then use the Wyman relationship for larger SL ratios.  However, in a series of discussion presented in the on-line Boat Design forum, naval architect Eric Sponberg, argues that there is no reason to use anything other than the Wyman relationship.

The last formula I found is the Keith formula, which Sponberg also discusses in the Boat Design Forum and in a pdf file on his web page ( http://www.sponbergyachtdesign.com/THE%20DESIGN%20RATIOS.pdf):

These simple relationships can be used to estimate the power needed to drive a displacement hull at speeds up to about a speed to length ratio of approximately two.  For Tortuga with its 32' waterline length, that corresponds to about 11 knots as mentioned above.  However, to apply these formulae, I need to know the Tortuga's displacement.  The paper work I got with the boat listed values ranging from about 10,000 lbs to 20,000 lbs.  Naturally I need a much more precise estimate if I am going to make a reasonable estimate of the power required.

There is one other approach to calculating the power required to push Tortuga at any given speed.  That methods is discussed in some detail in Principles of Yacht Design by Larsson and Eliasson (1994).  That method calculates the resistance of the hull to movement as a function of speed.  The approach calculates resistance due to frictional/viscous forces, wave making forces, wind resistance and resistance due to sea waves.  The input parameters are displacement, LWL, waterline beam, canoe body depth, water plane area, wetted surface area, the longitudinal location of the center of buoyancy, the maximum cross sectional area of the hull below the waterline, the maximum cross sectional area of the boat above the waterline.  All of that information can be calculated or measured from a lines drawing for the hull.  Consequently, I decided to take the lines from Tortuga's hull.  The Larsson and Eliasson method is described more fully below.
 
 

From these lines and the observation that Tortuga's actual waterline was about 3" below the painted waterline, I calculated that the displacement was 11,100 lbs with the Chrysler crown engine and a normal fuel load.  The old engine weighed approximately 1,000 lbs with its reversing gear.  In addition, the shift linkage weighed about 50 lbs because it consisted of a eight feet of 1" bronze rod and a 25 lb lead counter weight.  So removing the engine reduced the weight of the boat by approximately 1,050 lbs.  During my work on the hull I have removed 975 lbs of lead trim ballast.  Most of that weight was in the bow and I don't intend to put it back.  About 350 lbs of the ballast was on the starboard side under the settees.  I think it was there due to the placement of a 35 gallon water tank under the port settee.  I removed that tank from the boat and replaced it with a 26 gallon bladder tank which weighs about 25 pounds less than the old stainless tank.  In addition, I removed all the old frames and sisters and put in new frames, that further lightened the boat.  Consequently, I am pretty confident that the hull without an engine now displaces approximately 9,000 lbs.  The diesels I am considering all weigh under 500 lbs, thus, I am using 10,000 lbs for all the calculations that follow to allow for the new engine installation and the weight of passengers, fuel and stores.

My first attempt at determining how much power Tortuga needs to cruise at various speed was done by applying the four formulae above.  The results are shown in the following diagram.

As you can see the four formulae give comparable results up to a speed to length ratio of about 1 then they start to diverge.  The Keith formula gives the lowest power requirement and the Wyman the highest up to an SL ratio of about 1.56 when the Gerr-2 formula suddenly goes to very high values inconsistent with the other relationships.  The table below lists the calculated power requirements given by the four formulae for a several different boat speeds.
 
 

Formula	SHP @ 5.5.knots	SHP @ 6.5 knots	SHP @ 7.5 knots	SHP @ 8.5 knots	SHP @ 10 knots
Gerr-1	5.69	12.5	19.21	27.95	45.53
Gerr-2	6.60	12.29	20.27	36.97	124.2
Wyman	6.90	15.17	23.30	33.92	55.24
Keith	5.36	8.86	13.61	19.81	32.26

As you can see from the table, the four formulae don't agree well at all.  Above 8.5 knots the Gerr-2 formula is clearly an outlier.  The Keith Formula also give consistently lower results than the other three formulae.  Clearly, if I was to use one of these relationships to determine the power requirements for Tortuga, the resulting engine choice would be quite different depending on which formula I chose.  The inconsistency of these relationships greatly decreases my confidence in their usefulness.  Furthermore, these formulae are all generalizations that don't include much information about the hull form.  Because of that I decided to go with the more complex approach described by Larsson and Eliasson (1994).  A more thorough description of that approach follows.

The methodology discussed in "Principles of Yacht Design" takes a much more fundamental approach to determining the power required to drive a boat through the water.  In summary, the method deals with calm conditions (no wind or waves), but also provides methods to add in the effects of waves and head winds.  The calm water case calculates resistance to motion due to friction/viscous forces that occur as the boat moves through the stationary water and resistance due to wave making by the hull as it moves through the water.  The rough water case includes added forces due to the presence of waves on the water that the boat much push through and wind resistance on the above water parts of the boat.  The input parameters used in these calculations include: velocity through the water, waterline length, displacement, longitudinal center of buoyancy, the prismatic coefficient, water plane area, wetted surface area, cross sectional area of the above water parts of the boat when viewed from directly ahead of the boat.  There are also a few other parameters that can be derived from the hull lines.

Rather than list the details of the equations involved in the calculation, I will briefly summarize the hull parameters and variables involved in each part of the calculation.  Anyone interested in the details should read "Principles of Yacht Design".

Computation of the friction/viscous resistance values is relatively simple.  The input parameters are the vessel speed, waterline length and the wetted surface area.  Waterline length and the wetted surface area are determined in the conventional way from the lines drawing.  The specific numbers I am using are LWL = 32' (9.75 m) and wetted surface = 265.5 sq. ft. (24.7 sq. m).  The LWL is used to calculate a Reynolds number, which is then used to derive a friction coefficient.  That coefficient, the vessel speed and the wetted surface area are then used to compute the frictional/viscous resistance as a function of vessel speed.

The next step is to compute the resistance due to wave making.  The calculations are done via two polynomials that were derived by multiple regression analysis of a large data set.  The two polynomials are used for low speeds up to a Froude number of 0.45 and high speeds (Froude numbers of 0.45 to 0.75), where the Froude number F_r is given by:

V is velocity in meters/sec, LWL is the waterline length in meters and g is the acceleration of gravity.  A Froude number of 0.45 corresponds to the maximum velocity that a pure displacement hull can achieve under normal circumstances and is analogous to the hull speed defined above, although the resulting velocities are not the same.  A Froude number of 0.45 corresponds to a speed of  8.57 knots for a 32' LWL vessel, while the conventional hull speed is 7.59 knots.

The low speed polynomial has ten coefficients that are themselves functions of the Froude number.  The first coefficient is a true constant and the others are multiplied by the input parameters.  Those parameters are: the prismatic coefficient (Cp), the longitudinal center of buoyancy (LCB) expressed as a percentage of the LWL and measured from the midships position with positive numbers forward of midships, the waterline beam (B_wl), the depth of the canoe body (T_c), the volume displacement and the waterline length.  Those parameters are combined in various ways to calculate the terms that are multiplied by the constants.  The high speed polynomial has 6 coefficients that depend on Froude number with the first being a constant in the equation and the other five being multiplied by combinations of the input parameters LWL, B_wl, waterplane area, volume displacement and LCB.

I have also added a third resistance term to determine the resistance due to moving the boat at various speeds through static air.  That resistance depends on the wind speed, the density of air and the athwartships cross sectional area of the boat above the waterline including the cabin house.  Finally, I have added a surface roughness correction to the friction/viscous resistance curve assuming typical surface roughness for a hull with unburnished bottom paint following the data presented by Larsson and Eliasson (1994) in their chapter 5.

I have shown the frictional/viscous resistance corrected for surface roughness (black line), air resistance due to apparent wind speed (green line), wave making resistance (red line) and the total of the three resistances (light blue line) in the diagram above.  These calculations assume no waves and still air and constitute the calm conditions case.  The various resistance curves illustrate several things about the power required to move the Tortuga.  First, the resistance due to pushing the boat through static air is small compared to the water based resistances at the speeds illustrated above.  Second, at speeds up to approximately 7.2 knots the skin friction/viscous resistance is the largest.  This suggests that Tortuga's hull will not make significant waves up to that speed.  Above 7.2 knots the wave making resistance becomes the dominant term and rapidly becomes the major resistance to motion as speed increases.  The total resistance curve increases relatively gradually up to about 6 knots boat speed.  At higher speeds the total resistance climbs very rapidly.  These results are consistent with relatively low power requirements at speeds where frictional/viscous resistance dominates (<7.2 knots) and rapidly increasing power requirements as speed increases above 7.2 knots where wave making resistance dominates.

The resistance numbers can be converted into shaft horse powers given propeller efficiency.  The diagram below shows calculated horsepower as a function of boat speed calculated assuming a propeller efficiency of 55%.  The results are superimposed on the power curve calculated from the Wyman formula to provide a comparison with the results from the simple formulations.

The diagram above shows power curves for three cases.     These power curves are engine power curves because I have accounted for a 4% power loss in the transmission and other bearings.  It must be noted that these power curves only illustrate trends because the actual power curve will depend on the efficiency of the installed propeller.  Nevertheless, these curves can be used to roughly calculate required engine horsepower.  The flat water case (black line) assumes no waves and still air although it does include wind resistance due to the movement of the boat through that still air.  The heavy weather (green line), case includes a head wind of 25 knots and worst case seas in terms of resistance to forward motion.  The wind resistance is calculated as described above.  The sea state resistance is calculated from a constant that is linearly related to the length to weight displacement ratio and the displacement of the boat.  The calculated term is based on studies of wave resistance at Delft University as reported by Larsson and Eliasson  The final case is what I term the average conditions case (red line).  In that case I have set the head wind to 10 knots and assumed that resistance due to seas is related to the heavy weather case by the square of the ratio of the wind speed to that used in the heavy weather case.

Comparing these results with the Wyman horsepower equation shows that the more complex model yields considerably lower power requirements that does the Lyman model at low speeds for the flat water cases and a higher power requirement for the rough water case.  The "average conditions" case is very comparable to the Lyman equation.

My overall feeling is that I trust the power curves calculated by the methods of Larsson and Eliasson (LE) more than I do any of the simplified power formulae.  Consequently, I have decided to use the results of the LE power curves for initial engine selection.  My first approach is to use the "flat water case" in combination with the heavy weather case to determine the approximate horse power requirements for the Tortuga.  I will then use available engine data and the Bp-delta method to determine suitable propeller/gear ratio combinations for each of the engines that meet the power requirements.

Considering the total resistance curve plotted above I drew an approximate tangent to the curve in the high power range and another approximate tangent to the curve in the low power range.  The intersection of the two tangents is approximately the transition between the high and low power ranges of the curve.  That intersection is at approximately 6.5 knots.  This suggests that a cruising speed around 6.5 knots is a good compromise between speed and fuel consumption.  Consequently I will use 6.5 knots as my cruising speed for the analyses that follow.  The calm, average and rough water cases for which I computed horsepower curves yield 10, 13.6 and 25 horsepower, respectively to achieve 6.5 knots.  If I assume that the cruising horse power should be about 75% of the rated engine horsepower, the resulting engine horse power for the "average conditions" case works out to be 18 hp.  However, if I consider the "rough weather" case, it is clear that 18 horse power would only permit a boat speed of 5.6 knots if the conditions deteriorated.  Ideally, I would like the boat to be able to maintain cruising speed in adverse conditions, which would require 25 horse power for a 6.5 knot cruising speed.  Similarly, the power required to maintain the Tortuga's nominal hull speed of 7.59 knots (1.34 times the square root of the LWL in feet) is 23.25 hp for the average weather case and 38 hp for the rough weather case.  Consequently, the analysis suggests that the engine should be at least 25 hp and while 38 hp would be required to maintain hull speed in poor conditions.  A 25 hp engine would be adequate for a minimally powered cruiser, but a larger engine would allow a higher cruising speed if desired.  Alternatively the power requirements to attain the velocity that corresponds to a Froude number of 0.45 (8.57 knots for Tortuga) are 35.5 and 51 hp for the average and rough weather cases, respectively.  These engine powers provide a guidline for choosing an engine.

The next question is which engine.  There are a bunch to choose from including  the kubota based engines Beta, Nanni and Universal; the mitsubishi based engines Vetus and Westerbeke as well as Volvo-Penta and Yanmar.  I have included an engine near the low end of the suggested power range and one that would allow the boat to maintain hull speed in rough weather from each of the manufacturers mentioned above.  In addition, I have included one higher horse power engine from Westerbeke largely because it is an engine that would let the boat come close to maintaining a velocity corresponding to a Froude number of 0.45 in rough weather conditions.  Those engines are summarized in the table below.  All of the engines listed below will fit in the engine compartment, although the Beta 38 would require an optional shallow pan, which is not reflected in the approximate cost.  The engine data I have tabulated come from engine data sheets I found on line, or calculated from the engine horsepower.
 

Engine	hp	rpm	Cyl	Disp (liters)	Speed  (kts) (note-3)	Weight (lbs) (note-4)	Alternator amps	Stop Manual (M) Electric (E)	Exhaust  (in)	Cost (Approx.) (note-1)	Gear Ratios (note-2)
Beta 30	30	3600	3	1.123	8.5/6.8	305/10.16	65	M?	2"	$8,500	2.45
Beta 38	38	3600	4	1.498	9.1/7.5	374/9.84	65	M?	2"	$9,400	2.45
Nanni N3.30	29	3600	3	1.0	8.5/6.8	320/11.03	100	E	2"	$7,800	2.33, 2.64
Nanni N4.38	37.5	3000	4	1.498	9.1/7.5	335/8.93	100	E	2"	$9,300	2.45, 2.29, 2.71
Universal M35B	35	3000	4	1.335	9.0/7.3	352/10.06	51	M	2"	$9,100	2.63
Vetus 4.15	33	3000	4	1.5	8.7/7.1	397/12.03	60	E	2"	~$9,500	2.47
Vetus 4.17	42	3000	4	1.758	9.3/7.8	408/9.71	60	E	2"	~$10,500	2.47
Vetus 4.55	52	3000	4	1.758	9.9/8.5	432/8.31	110	E	2"	~$11,200	2.47
Westerbeke 35E	28	3000	3	1.318	8.4/6.7	386/13.79	50	E	2"	$9,900	2.63, 2.71
Westerbeke 44C	38	3000	4	1.758	9.1/7.5	416/10.95	50	E	2"	$10,800	2.63, 2.71
Westerbeke 55D	48	2600	4	2.18	9.278.2	450/9.38	50	E	3"	$11,300	1.93, 2.29, 2.71
Volvo-Penta D1-30	28.4	3200	3	1.13	8.4/6.7	320/11.27	115	E	1.75	$9,100	2.63, 2.7
Volvo-Penta D2-40	39.6	3200	4	1.51	9.2/7.7	392/9.8	115	E	1.75	$9,700	2.14, 2.63
Yanmar 3YM30	29.1	3600	3	1.115	8.4/6.8	271/9.31	60	E	2"	~$8,800	2.21, 2.63, 3.22
Yanmar 3JH5E	38.5	3000	3	1.642	9.1/7.6	381/9.9	60	E	3"	~$10,900	2.33, 2.64

The information above is a large part of the choice of an engine.  There are a number of additional factors that need to be considered.  These include: availability of the engine including shipping costs, availability of local servicing, parts availability and cost and guaranty.  I will now address the various engine parameters.  Please note that some of my discussion is purely subjective in that it represents my personal preferences.  I feel that that subjectivity is acceptable since I am repowering "MY" boat.

So far I have been concentrating on engine horsepower alone.  However as the table above shows there are many other parameters that should be considered.  I will discuss each parameter separately.

Engine RPMs - Engine rpms have a couple of implicatiions.  First, operating at higher rpms is generally noisier.  Since I would like to minimize engine noise, I prefer to be able to operate at lower engine rpms for a given speed.  Second, a higher rpm engine will either require a higher gear ratio or a lower prop pitch to allow the boat to reach full engine rpms.  For example, consider two engines that both produce 30 hp, one does it at 3,000 rpms and the other does it at 3,600 rpms.  Lets assume that both engines are fitted with a ZF15MA transmission with a 2.63:1 ratio.  If I use the Bp-delta method to calculate the props required for both engines to achieve 8.6 knots at maximum engine rpms I get the following:

3000 rpm engine - 19.5" diameter, 13.45" pitch
3600 rpm engine - 17.6" diameter, 11.56" pitch

Similarly, if I want to get the same propeller result for the 3,600 rpm engine as I do for the 3,000 rpm engine, I need to raise the gear ratio to 3.16:1 from 2.63:1.  Unfortunately, my table above shows that such high gear ratios are not available for the transmissions available with any of the 3,600 rpm engines.  I do list a 3.22:1 ratio for the Yanmar 3YM30 engine, but that is not a down angle transmission and would make the engine clearances very small between the forward top of the engine and the underside of the deck hatch.  The result is that installing one of the 3,600 rpm engines would most likely also require that I install a new propeller which would cost approximately $700-$800.  Basically, using one of the 3,600 rpm engines would result in noisier operation because of the higher rpms required for cruise speed and would cost at least $700 more than installing a 3,000 rpm engine with a similar horsepower rating.

Engine Cylinders - This is one of the subjective criteriaa.  Basically I prefer a 4 cylinder engine to a 3 cylinder engine because I expect more cylinders to result in a smoother running and quieter engine.

Engine Displacement - This is another subjective criterion.&  My feeling, right or wrong, is that the higher displacement per horsepower engines will be working a bit less hard at any particular horsepower output and will have a longer life.

Weight - The weights of the engines above rangee from about 270 lbs to 450 lbs.  Considering that the new engine is replacing an approximately 1,000 lb engine, all of the engines above represent a substantial weight savings.  My subjective feeling about engine weight is that I prefer a bit higher weight per horsepower engine for durability reasons and because I expect a heavier engine to be a bit quieter.  However, that feeling is based on the extra weight being in the right places.  Unfortunately, I don't know where in the engine the extra weight is, so this feeling may be completely unsubstantiated.

Alternator Amps - Since Tortuga is a power boat and I wiill be installing a 50-60 watt solar panel to maintain battery charge while the boat hangs on its mooring, the size of the alternator isn't a huge consideration.  Furthermore, my plan is to install only an approximately 300 amp-hour house battery bank and a single 100 amp-hour starting battery.  The starting battery will not be drawn down significantly during normal use, so the size of the house bank is the determining factor as to the amount of charging capacity I will be able to use.  With a 300 amp-hr battery bank, the maximum charge acceptance rate for flooded batteries will be about 75 amps.  Only the high output alternators on the Nanni and Volvo-Penta engines will be able to provide that much amperage at cruising engine rpms (~2200-2400).  Consequently, the alternators on the Nanni and Volvo-Penta engines should be able to recharge a 50% depleted battery bank in about 3-4 hours of running time, while run times required to fully recharge the same level of battery depletion will be more like 5-6 hours with the engines that have 50-60 amp alternators.  Fortunately for me, the only electrical systems on Tortuga that will be run when the engine is off are the cabin and anchor lights and the pressure water pump.  So I doubt I will ever draw the batteries down by more than 20% so pretty much any engine run over two hours should be adequate to recharge the batteries for any of the engines above with their standard alternators, particularly since the solar panel should provide at least 6-8 amp-hours of charging power on all but the foggiest days.  Nevertheless, the larger output alternators should more or less guarantee that the batteries will be nearly fully charged after any engine run.

Manual versus Electric Stop - I have installed an automatic fire exttinguishing system in the engine room.  For that system to work properly the engine must be shut down if the fire extinguisher discharges.  The system is set up to automatically turn off an engine with electric stop when the extinguisher discharges, but I would have to rig up some sort of solenoid to pull the stop lever on a manual stop engine.  As far as I can tell from on-line data sources both of the Beta engines and the Universal M35B have manual stop.  Unless electric stop is available as an option, those engines are likely going to be dropped from my list.

Exhaust - Tortuga is currently set up with a 2.55" exhaust.  The includes hoses in good shape, a vernatone muffler and a bronze thru-transom fitting.  When I do the engine install I will add a vernalift waterlift muffler.  They are available with different size inlets and outlets, so I can buy a vernalift with a 1.75" of 2" inlet and a 2.5" outlet, which will allow engines with exhaust outlets to easily connect to the existing exhaust system.  However, the Westerbeke 55D and Yanmar 3JH5E have 3" exhaust outlets.  Thus, for those engines I would have to replace the existing exhaust system with a 3" system, which will add about $300-$400 to the cost of the engine installation.

Gear Ratios - In the table above I have listed gear ratios options with the down angle transmissions which are available with the various engines.  Gear ratio is one of the most important factors in determining the propeller diameter and pitch for a given engine.  For the smaller horsepower engines with 3,600 rpm ratings, high gear ratios are neccesary to get the shaft rpms down to reasonable levels and to allow enough torque at the propeller to turn a reasonably large propeller.

I have used the engine data above along with the calculated power curves for the various conditions to calculate approximate propeller requirements for each of the engines.  Propellers were calculated using the calm water power curve via the Bp-Delta method.  I have then summarized the cost of that engine taking into account the need to either repitch my existing propeller or buy a new propeller.  The estimated total cost for each engine includes the initial propeller expense.  The results are summarized below.
 
 

Engine	3 Blade Propeller (Dia x Pitch)	Base Cost (including shipping)	Propeller Adjustments	Total	Max rpms	Max speed (kts)	6.5 Knot rpms (note-1)	6.5 knot GPH (note-3)
Beta 30 30 hp, 3600 rpm, 2.45:1	18 x 11	$9,000.00	$700.00	$9,700.00	3605	8.5	2850	0.68
Beta 38 38 hp, 3,600 rpm, 2.45:1	18 x 12	$9,900.00	$700.00	$10,600.00	3555	9.1	2786	0.72
Nanni N3.30 29 hp, 3,600 rpm, 2.64:1	18 x 11	8,300.00	$700.00	$9,000.00	3555	8.5	2927	0.68
Nanni N4.38 37.5 hp, 3,000 rpm, 2.71:1	20 x 13	9,800.00	$300.00	$10,100.00	2991	9.1	2267	0.68
Universal M35B 35 hp, 3,000 rpm, 2.71:1	20 x 13	$9,100.00	$300.00	$9,400.00	2982	9.0	2300	0.68
Vetus 4.15 (note-2) 33 hp, 3,000 rpm, 2.47:1	20 x 12	$10,000.00	$300.00	$10,300.00	2980	8.7	2360	0.69
Vetus 4.17 (note-2) 42 hp, 3,000 rpm, 2.47:1	20 x 13	$11,000.00	$300.00	$11,300.00	2977	9.3	2290	0.68
Vetus 4.55 (note-2) 52 hp, 3,000 rpm, 2.47:1	20 x 13	$11,700.00	$300.00	$12,000.00	3000	9.9	2160	0.68
Westerbeke 35E 28 hp, 3,000 rpm, 2.71:1	20 x 14	$9,900.00	$300.00	$10,400.00	2965	8.4	2381	0.70
Westerbeke 44C 38 hp, 3000 rpm, 2.29:1	20 x 13	$10,800.00	$300.00	$11,300.00	2878	9.1	2217	0.72
Westerbeke 55D 48 hp, 2,600 rpm, 2.29:1	20 x 15	$11,300.00	0.00	$12,050.00	2421	9.7	1801	0.68
Volvo-Penta D1-30 28.4 hp, 3,200 rpm, 2.7:1	20 x 13	$9,100.00	$750.00	$10,550.00	3198	8.4	2540	0.71
Volvo-Penta D2-40 39.6 hp 3,200 rpm, 2.63:1	20 x 15	$9,700.00	$0.0	$10,600.00	3306	9.2	2508	0.68
Yanmar 3YM30 29.1 hp, 3600 rpm, 2.63:1	18 x 12	$9,300.00	$700.00	$10,000.00	3580	8.4	2940	0.71
Yanmar 3JH5E 38.5 hp, 3000 rpm, 2.64:1	20 x 13	$11,650.00	$300.00	$11,950.00	2866	9.1	2175	0.68

Note-1: The 6.5 knot rpm numbers are estimates only in that the prop slip numbers used in their calculation are approximations.

Note-2:  As of March 2011, the three Vetus diesel engines listed here are not available in the United States.  My understanding is that they are undergoing EPA recertification and that they should be available sometime during the summer of 2011.  Since these engines are based on the same Mitsubishi blocks used for Westerbeke engines, I expect the Vetus engine's horsepower ratings to be decreased to values similar to the equivalent Westerbeke engines.  It that respect, the Vetus 4.17 and 4.55 are based on the same block as the Westerbeke 44C.  The Vetus 4.55 achieves higher horsepower by virtue of being turbocharged while 4.17 and the Westerbeke 44C are naturally aspirated.

Note-3: Fuel consumption is calculated from the fuel curves for the individual engines based on calculated horsepower output at 6.5 knots.

Second, because the Vetus engines are not currently available (see note-2 on the table above), I am dropping them from consideration.  In addition, a recent call to Westerbeke told me that the Universal M35B is no longer available.

The deletions above leave six engines under consideration.  They are:

Nanni N4.38 - $10,100, 37.5 hp, 9.1 knots maximum speed and 2330 rpm cruise

Westerbeke 35E - $9,300, 28 hp, 8.4 knots maximum speed and 2430 rpm cruise

Westerbeke 44C - $11,600, 38 hp, 9.1 knots maximum speed and 2340 rpm cruise

Westerbeke 55D - $12,050, 48 hp, 9.7 knots maximum speed and 1965 rpm cruise

Volvo D2-40 - $11,100, 39.6 hp, 9.1 knots maximum speed and 2455 rpm cruise

Yanmar 3JH5E - $11,650, 38.5 hp, 9.1 knots maxmum speed and 2285 rpm cruise

The remaining engines have an approximately $2,650 price range from $9,400 to $12,050.  All of the remaining engines are four cylinder engines except the Yanmar 3JH5E and the Westerbeke 35E, which are three cylinder engines.  I am biased in that I think a four is smoother and quieter than a similarly sized three.  On the other hand, the low cruising rpms of the Westerbeke 55D make it very attractive.

March 10, 11 - After talking engine options over with my wife I have decided to drop the Nanni N4.38 and the Yanmar 3JH4E from consideration.  The reasons are parts and service availability for the Nanni and the tightness of the fit for both the Nanni and the Yanmar.  That leaves the three Westerbekes and the Volvo-Penta.  In the end I suspect it will come down to money, but you never know.

March 16, 11 - As of today I have narrowed my choices down to four engines: Volvo-Penta D1-30 and D2-40 and Westerbeke 35E and 44C.  So I decided to refine the propeller selections by doing a more comprehensive job of propeller selection.  The propeller selection method involves calculating various propeller-gear ratio combinations and plotting the results on the engine power diagram.  To do that I wrote a program that solves for the propeller thrust coefficient Kt and propeller torque coefficient Kq as a function of the advance coefficient J, propeller disk area ratio, propeller pitch ratio and number of propeller blades using the method of Oosurveld and van Oossanen (1975).  Those results are used with the resistances calculated as described above to calculate power curves for various propellers for both the calm and rough water resistance cases.  The calculations yield the boat speed, engine horsepower, propeller torque, propeller efficiency and engine rpms.

The program I wrote is actually quite simple in concept.  First the program uses the methods described by Larsson and Eliasson (1994) to compute resistance as a function of boat speed.  As described above the resistance calculation includes frictional/viscous resistance, wave making resistance, wind resistance due to boat motion through still air and surface roughness for what I refer to as the "Calm" case.  The calculation also includes a "Rough" case that includes additional terms for added wind resistance due to head winds and resistance due to existing waves.  The input parameters for this part of the program are a variety of hull data that can be either read directly from or derived from hull lines drawings.

The next part of the program uses the calculated resistance, which is assumed to be equal to thrust required to move the boat at the speed for whch the resistance was calculated, as one of the input parameters to calculate propeller power curves for the boat.  The other input parameters are the advance ratio (J), propeller diameter (D), pitch (P), disk area ratio (DAR) and number of blades (Z).  The program used the polynomials derived by Oosurveld and van Oossanen (1975) to calculate the propeller thrust and torque coefficients, K_t and K_q, respectively for Wageningen B-Screw Series propellers.  These propeller parameters are defined as follows:

The approach taken is to use the input parameters to calculate the ratio of K_t to J² from:

V_a can either be assumed to be the speed of the boat through the water, or it can be calculated from the block coefficient (C_b) as:

Once a value of K_t/J² has been calculated from input parametsrs, a value of K_t is calculated from the Oosurveld and van Oossanen (1975) polynomial expression using a seed value of J.  That result is used to calculate a first approximation of K_t/J².  The program then systematically varies the seed value of J until until the the calculated value of  K_t/J² converges with the input value.  The results are the calculation are values of K_t and J.  The derived value of J is then used as an input parameter to calculate K_q.  I am not going to present the polynomials for K_t and K_q here because they have 39 and 47 terms, respectively.

The derived values of K_t, K_q and J are then used to calculate propeller revolutions per second from:

The expression for Kq is solved for torque (Q) and the power at the prop is calculated from the relationship between torque and power.  The combined expression in which the torque term has been eliminated is:

Power in horsepower is given by:

The program output is P_hp over a range of speeds specified during input as well as engine rpms calculated from the input transmission gear ratio.  The program does the calculations for both the calm and rough water cases.  The results can then be plotted on engine power diagrams to determine the appropriateness of a given propeller.

References

Gerr, D (2001) Propeller handbook: The complete reference for choosing, installing and understanding boat propellers. International Marine, Camden, ME, 152p.

Larsson, L and Eliasson, R.E. (1994) Principles of Yacht Design. International Marine, Camden, ME, 302p.

Oosurveld, M.W.C. and van Oossanen, P. (1975) Further computer-analyzed dataof the Wageningen B-screw series. International Ship Building Progress,  Vol. 22, No. 151.

To test the program I calculated the resistance for my sailboat that I have owned for 15 years.  I then ran the program using the data for the transmission and prop on that boat.  The results were spot on for engine rpms versus boat speed on flat water.  Consequently I now have considerable confidence in using this program evaluate prop choices for the different engines in Tortuga.

This approach to calculating the power requirements for the boat is much more satisfying to me than using a simple formula such as those of Gerr, Wyman or Keith since the power calculated is specific to the boat being studied and the propeller used.  Furthermore there is no need for a generic "slip" term like that used in Crouch's propeller method.  Consequently, I have more confidence in these results, misguided as that confidence might be.

I have plotted the results for several propellers each for the Westerbeke 35E, Westerbeke 44C, Volvo-Penta D1-30 and Volvo-Penta D2-40 engines.  The diagrams show the engine power curves along with the calculated propeller power curves.  Note that the calculated propeller powers have been corrected to include losses in bearings and the transmission to yield engine horsepower.

The diagram above shows the power curve for the Westerbeke 35E (black line) as well as calculated propeller curves for 20x13 (red line) propeller for the calm conditions case.  The red dotted line shows the calculated curve for the propeller for the rough water case. The 20x13 propeller hits the power curve at 2995 rpms and 8.3 knots under calm conditions.  Under rough conditions the top speed drops to 7.3 knots at 2895 rpms under rough conditions.  Calculated propeller efficiency ranges about 63% at 6.5 knots to 56% at maximum speed.  This result means that I can use the existing prop after having it repitched down to 13", which the local prop shop says they can do.

The next case to consider is the Westerbeke 44C (38 hp at 3,000 rpms).

When I ran the calculations the existing 21x15 prop came out right on for the Westerbeke 44C for the calm case.  The rough case result predicts a top speed of 7.9 knots at about 2,900 rpms.  Top speed under calm conditions is 9 knots at almost exactly 3,000 rpms.  Calculated propeller efficiency ranges about 56% at 6.5 knots to 57% at maximum speed.    This is a very satisfting result since it means I can use the existing prop with no changes.

Now I will move on to the Volvo-Penta D2-40.

The results for the Volvo-Penta D2-40 engine are shown above.  The 20x13 prop results in the boat being slightly under propped in calm conditions but slightly over propped in rough conditions.  Calculated propeller efficiency ranges about 63% at 6.5 knots to 56% at maximum speed.    This is pretty much an ideal prop again.  Top speed in calm conditions is 9 knots, while in rough conditions it only drops to 8 knots.  Again the result indicates that the existing prop can be used after repitching down to 13" pitch.

After doing the calculations above, I decided to reconsider the Volvo D1-30 engine.  The engine diagram for it is below.

The result for the Volvo-Penta D1-30 shows is slightly over propped with a 20x12 propeller.  However, with this propeller the engine can reach approximately 98% or rated rpms in calm conditions and approximately 95% of rated rpms in rough conditions.  Under calm conditions the maximum speed is 8.35 knots at 3130 rpms.  That speed drops to 7.3 knots ar 3030 rpms under rough conditions.  Calculated propeller efficiency ranges about 60% at 6.5 knots to 55% at maximum speed.    Thus, a 20x12 prop is acceptable.  The prop shop tells me that taking 3" off the pitch is pretty much the maximum that they can do, so a smaller pitch would require a new prop.  If I was to buy a new prop for this engine I would most likely go with an 18x13 prop and change the transmission to a 2.63:1 ratio.

The table below summarizes the results for the four engines considered.  I have included revised costs based on the current propeller results.
 

Engine, gear ratio propeller	HP, max rpms	Cost	6.5 knot rpms fuel gph	7.5 knot rpms fuel gph	8.5 knot rpms fuel gph	Max speed  fuel gph	Comment
Westerbeke 35E 2.714:1, 20x13	28, 3000, 3 cyl	$10,200	1912, 0.42 gph	2460, 0.99 gph	8.4 kts 3000, 1.9 gph	8.4@3000 rpm 1.9 gph	repitch prop -2"
Westerbeke 44C 2.714:1, 20x15	38, 3000, 4 cyl	$10,800	1717, 0.45 gph	2219, 0.96 gph	2777, 1.95 gph	9.0@3000 rpm 2.5 gph	No prop work needed
Volvo D2-40 2.63:1, 20x13	39.6, 3200, 4 cyl	$10,000	1855, 0.39 gph	2386, 0.89 gph	2976, 1.84 gph	9.0@3200 rpm 2.5 gph	repitch prop -2"
Volvo D1-30 2.7:1, 20x12	28.4, 3200, 3 cyl	$9,400 $9,800	1971, 0.44 gph	2595, 0.98 gph	8.35 kts 3131, 1.85 gph	8.35@3131 rpm 1.85 gph	repitch prop -3" new 19x13 prop and 2.63:1 gear

These four diagrams illustrate that the power required to push Tortuga at speeds below the nominal hull speed is quite small as the resistance calculations suggested.  The differences in performance between the 28 hp engines and the 38-39 hp engines are at the top end where the larger engines will deliver about six tenths of a knot more boat speed at a significant cost in fuel consumption.  Furthermore, even the 28 hp engines have enough power to push Tortuga to 7.3 knots under rough conditions.  Although none of the engines will be working very hard at a 6.5-7.5 knot cruise speed, the 28 hp engines will be at a higher proportion of their maximum output at the rpms required to maintain a given speed than the larger engines, which will be better for the smaller engines.    The small table below shows the calculated percentage of available engine power at 6.5, 7.5 and 8.5 knots for each engine.

I have recalculated the fuel costs for an 8 hour run based on the power curves above.  The results for the four engines are shown in the next table.  Operating at 6.5 knots or less is very economical, but speeds up to 7.5 knots are not overly costly.  However, above 7.5 knots fuel costs increase rapidly.

Given the small differences in cruising rpms, top speeds and prices for 28 hp rngines and 39-40 hp engines, there seems to be little to choose between them.  One factor is how well do the various engines fit in the available space.

The diagram above shows the two engines in the engine room.  Both engines fit, but the Volvo has more top clearance and is about 1.5" shorter.  Based on physical size, the Volvo-Penta D1-30 is preferable.

Of the four engines the Westerbeke 35E is actually the tightest fit.  The Volvo-Penta D2-40 is tight on the bottom, but the engine can be slid forward an inch or so to provide a bit more bottom clearance.  That can be done by putting a drive saver flexible coupling between the transmisstin and the prop shaft, but that  adds about $300 to the cost for the engine, which makes makes the costs for the Westerbeke 44C and the Volvo-Penta D2-40 basically the same.

The major four engines stack up as follows:

Volvo-Penta D1-30 - 3 cylinder, maximum speed 8.35 knots, good fit, 115 amp alternator, likely will require a new prop, 1,910 rpms at 6.5 knots.

Weserbeke 35E - 3 cylinder, maximum speed 8.4 knots, tightest fit, 50 amp alternator, requires repitched prop, 1970 rpms at 6.5 knots.

Volvo-Penta D2-40 - 4 cylinder, maximum speed 9 knots, good fit but may require extra cost to move engine forward, 115 amp alternator, repitched prop 1850 rpms at 6.5 knots.

Westerbeke 44C - 4 cylinder, maximum speed 9 knots, good fit, 50 amp alternator, no change to prop, 1720 rpms at 6.5 knots.

Basically, at this point I have to decide which factors matter most to me.

March 30, 2011 - I just ordered a Volvo-Penta D2-40.  It came down to a combination of price and size of the engine.  The D2-40 turned out to be only about $200 more than the D1-30 when I factored in the need for a new prop with the D1-30, and the D2-40 came out nearly $1,000 cheaper than the Westerbeke 44C and a couple of hundred less than the Westerbeke 35E.

The D2-40 will give me a maximum speed between 8 and 9 knots and will allow me to cruise at 6.5 to 7.5 knots on 0.4 to 0.9 gallons per hour of diesel.  I expect to receive the engine the first week of June.

If you have any comments or question about anything above, please send me an e-mail at: tortuga@todddunnmicroyachts.com . I will answer as soon as possible.