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, which would push the boat at up to 12-14 knots.  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, 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 should have been able to push Tortuga along at 12 knots or so with the throttle wide open.  However, it probably burned about 5 gallons of gas an hour.  That wasn't a huge consideration when gas cost $1 a gallon or less, but now at $3-$4 a gallon, that sort of fuel consumption adds up quickly.  So I have decided that I will be happy to cruise along at 7 to 7.5 knots with a bit of power in reserve for when it chops up a bit.

A second consideration is that I would like to get rid of the engine box in the cockpit and the intrusion the engine makes into the cabin.  Getting rid of the engine box will really open up the cockpit.  It will also let me move the entry into the cabin from the starboard side to the center.  I want to move the entry because the present entry

goes down two small steps and ends on the start of the up-slope of the hull.  My wife doesn't like stepping onto the sloping cabin sole.  So the cabin entry has to be changed to allow the steps to end on a "flat" cabin sole.  Second, getting rid of the engine box will let me fill that area with a flush cockpit sole, or platform.  The down side of replacing the engine box with a bit more cockpit platform is the vertical height constraint it places on the engine size.

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.  Keeping that prop, means that the engine I install has to have enough torque to turn the 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.  Finally the engine needs to be small enough to fit under the cockpit platform so I can move the cabin entry to the center.

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.  There are a number of books that tell you how to figure this out.  I am using the formulae in "The Propeller Handbook" by Dave Gerr for the calculations.  As you will see, the calculations are all pretty simple.

According to Gerr, the power (shaft horsepower or SHP required to push a displacement hull at a given speed in knots (KTS) can be determined from the boat's displacement (D) in pounds and waterline length (WL) in feet by:

^{Tortuga's waterline length is 32', but the displacement is essentially unknown.  I have the listing from when I bought the boat, which gives the displacement as 10,000 lbs.  I also have a survey from 2002, which lists the displacement as 20,000 lbs.  That is a bit too much of a range for me, so I will calculate the displacement.  In order to calculate the displacement, I need the hull lines.  All I know about the boat is that it was built in 1936 by the Nunes Brothers Boatyard in Sausalito, CA.  I have spoken with the two previous owners and neither knew the name of the designer.  I searched the web for information on the Nunes Brothers, but couldn't find much to go on.  So I decided to take the lines off the boat.  I measured the hull at the transom and three other points and used that data, along with a few other measurements to draw the lines shown below.}

From those lines and the observation that Tortuga's actual waterline was about 3" below the painted waterline, I calculated that the displacement is 11,100 lbs.  That displacement is based on the waterline with the old engine which weighed just under 1,000 lbs.  No matter what new engine I choose, the new engine will weigh less than that, so 11,100 lbs seems like a safe upper limit displacement.  So I plugged that displacement and the 32' waterline length into the formula above and came up with this power curve.

The power curve shows that I will need about 21.2 horse power to push Tortuga at 7.5 knots.  At first glance this curve suggests that any engine with more than about 25 horse power will do the job.  However, it is not that simple.  The engine should generate the required power at 70-80% of its rated rpms.  Furthermore, it is desirable to have enough power to push the boat a knot or two faster than cruising speed should that be necessary.  The power curve shows that a speed of 9 knots will require about 37 h.p. and it will take 50 h.p. to push Tortuga at 10 knots.  Although, the curve doesn't show speeds above 10 knots, the formula yields a power requirement of 87 h.p. to go 12 knots and 170 h.p. to make 15 knots.  It is clear from this curve, that speeds above about 10 knots are going to need a lot of power and a correspondingly big engine.  So my decision to settle for a 7-7.5 knot cruise speed means that I can probably get away with 50 horse power or less. That is a relief to my wallet, since it means that I should be able to get the new engine for $12K or less.  The next question is which engine.  There are a bunch to choose from including Beta, Nanni, Universal, Vetus, Volvo, Westerbeke and Yanmar.  Each of those manufacturers makes 2-3 engines that might work.  The next step is to narrow down the choice.

Choosing the engine also involves picking an appropriate transmission rear ratio and determining if the these engines can turn the existing 20"x15" prop.  Naturally the two factors are not independent.  Basically, available torque at the prop shaft increases as the gear ratio increases.  So, pretty much any of the engines I am down should be able to turn the prop given a high enough gear ratio.  However, increasing the gear ratio means that the engine will have to run ar higher rpms to make my desired cruising speed.  So before I can decide on a gear ratio, I have to determine how many prop rpms will be required to maintain cruising speed.

Tortuga's prop has a 15" pitch, so in a perfect world, the prop would advance 15" for each revolution.  Unfortunately the world isn't perfect and props do not advance by their pitch per revolution due to prop slip.  Prop slip varies with boat speed and prop rpms.  Fortunately, Gerr gives a simplified formula for prop slip in terms of boat speed (KTS):

Given prop slip as a function of boat speed, the prop rpms (RPMp) can be calculated from the boat speed and the prop pitch (P) by:

For example, at 7.5 knots prop slip is (1.4/(7.5^0.56)) = 0.453 and the required prop speed is 883 rpms.  Engine rpms (RPM) can be calculated from prop speed simply by multiplying by the transmission gear ratio.  So, for a 2.64:1 ratio transmission, an engine speed of 2330 rpms will be required to push the boat at 7.5 knots.  Given this relationship between boat speed and required engine rpms, I plotted engine power curves for the engines mentioned above for different available transmission ratios.

The curves plotted above show propeller horsepower produced by the Westerbeke 44B and 55C with gear ratios of 2.273:1 and2.737:1 in the left panel.  The curves for the Yanmar 4JH4e (54 hp) and 3JH4E (40 hp) for a 2.64:1 gear ratio are shown in the right panel.  The red prop curve for the Westerbeke engines with the 2.273:1 gear ratio shows that neither engine would be able to run up to its full rated 3,000 rpms with that gear.  Furthermore, the calculations suggest that the biggest props that the engines could turn with this gear ratio are 18" and 19" for theWesterbeke 44B and 55C, respectively.  The blue curve in the left panel shows the results for a 2.737:1 gear ratio for the Westerbeke engines.  Both engines should be able to turn the 20" prop with the 44B topping out at just under 2,900 rpms at a speed of about 9.3 knots.  The Westerbeke 55C will be able to achieve its full 3,000 rpm rating with this gear ratio with about 5 hp to spare.  In fact, the 55C could haldle a 16" pitch prop and still get up to 3,000 rpms.  Maximum boat speed with the Westerbeke 55C should be just under 10 knots.  Both engines should be able to push the boat at 7.5 knots at about 2,400 rpms, which is 80% of rated rpms.  That leaves about 25% reserve power, relative to cruise rpms for the 55C and about 20% reserve power for the 44B.

Based on the results I got for the Westerbeke engines, I only plotted the results for the 2.64:1 gear ratio for the two Yanmar engines.  The results are very similar to those for the Westerbeke engines in terms of maximum achievable rpms and boat speeds.  Based on these curves alone, either engine would do the job.  However, the prop diameter calculations suggest that the biggest prop the 40 hp Yanmar 3JH4E can turn with this gear ratio is 19", while the 54 hp 4JH4E can turn a 21" prop.  Consequently, since the 2.64:1 gear ratio is the highest available for the 3JH4E, the calculations eliminate that engine from consideration.  The result for the 54 hp 4JH4E is almost ideal because the propeller and engine horsepower curves intersect almost exactly at the engine's rated 3,000 rpm.

The curves above strongly suggest that if I am going to stay with my existing prop, that I will be fine with either the Westerbeke 55C with the 2.737:1 gear or the Yanmar 4JH4E with the 2.64:1 gear.  The Westerbeke 44C, if I can get it with the 2.737:1 gear, will also work although it would reduce the maximum achievable speed by about half a knot.

As I mentioned above, a few quick measurements suggested that the Westerbeke 55C and Yanmar 4JH4E would fit under the cockpit platform.  However, I wanted to confirm that, so I went back to the boat and made a much more careful set of measurements and made a good drawing of the engine space.  I also scaled  engineering drawing of the two engines to the same scale as the engine space drawing.  The results are shown below.

Both engines fit nicely.  The Yanmar is fitted with a KM35A 7 degree down angle transmission and the Westerbeke with a ZF25M down offset transmission.  The gear ratios available for the Yanmar KM35A transmission go up to 2.64:1 while the ZF25M has 2.29:1 and 2.737:1 gear ratios available.  A downside of both engines is that the throttle and transmission connections are on the right side.  Since Tortuga's helm is on the port side of the boat, those connections will require the cables to be longer than would be the case with a starboard helm, which will impart a bit more friction, particularly in the throtle linkage.

The drawing above shows the Westerbeke 44B with the ZF25M transmission.  Like the other two engines the Westerbeke 44B has the transmission linkage on the starboard side, but the throtle connection is to port.

The fuel consumption for the various engines is also a factor in the decision.  Fuel consumption is determined by horsepower consumed at the horsepower required for a given speed.  The horse power required to maintain different speeds is given in the table below along with fuel consumption for the Westerbeke 44B, 55C and Yanmar 4JH4E.  The fuel consumption was calculated assuming a 3% of rated horsepower power loss in the transmission and 0.25 horsepower to run the alternator.  I made the calculations using the fuel consumption curves provided by the manufacturer based on engine rpms required to achieve each speed. I also adjusted the fuel consumption based on the required shaft horsepower and the brake horse power at each speed since the published fuel consumption curves are for brake horsepower.
 
 

Speed (kts)	Shaft Horsepower	Fuel Comsumption Westerbeke 44B (gal/hr)	Fuel Comsumption Westerbeke 55C (gal/hr)	Fuel Comsumption Yanmar 4JH4E (gal/hr)
5	6.32	0.24	0.42	0.48
6	10.92	0.42	0.65	0.75
7	17.34	0.61	1.01	1.12
7.5	21.33	0.77	1.25	1.35
8	25.88	0.92	1.53	1.62
9	36.81	1.24	2.25	2.26
Max	50.55	1.56 (9.4 kts)	3.0 (9.9 kts)	3.06 (10 kts)

Given the fuel consumption estimates above, I can calculate approximate costs to motor 100 nautical miles at different speeds assuming a given cost for diesel fuel.  I have done this for speeds of 7 and 7.5 knots assuming diesel costs $4.30 per gallon (the price in late August 2008).  The table below shows the results for the three engines

Fuel Cost for a 100 nm trip
 

These calculations are approximate, but serve to illustrate operating fuel consumption and cost.  The calculations suggest that the higher horsepower engines will cost approximately 65-70% more to operate than the 44 hp Westerbeke 44B, with the Westerbeke 55C being just a bit less expensive to operate than the Yanmar 4JH4E.

I can also use the fuel consumption estimates above to calculate the range for Tortuga with the different engines at different speeds.  The results for 6, 7 and 7.5 knots are shown below.  I base these calculations on the fact that Tortuga has two 45 gallon tanks, which contain about 80 gallons of useable fuel.
 
 

The differences in the engines are quite striking when considered in terms of boat range.  Based on operating cost and range considerations, the Westerbeke 44B looks very good relative to the higher horsepower engines, particularly considering that the only performance sacrifice is half a knot at the top end.