The following paper was prepared by our President, Mr. Paul Bezzi, several years ago. We hope you find it interesting and useful.

**Introduction.**

** **

I am writing this paper with the aim to help those deciding on which propulsion system to select for their particular application.

The majority of yachts and fast boats are targeting speeds in excess of 30 knots. For that purpose, engine manufacturers, boat-yards, and propulsion manufacturers are increasing power, behaviour at sea, and efficiency. Very shortly, problems appear due to the lack of know how; the true reason of failure of performance…

I propose to go step by step in the detail of a typical project.

**1-The hull**

There are several types of hull capable of performance, and the best hull will be the one that fulfils the owner’s needs.

In fact , most of the errors I observed during the past years were due to contradictions between what owners want, and what boat yards can offer. Most of the disputes could have been avoided just by putting some margins in the project. So,

**The length of the boat for a specific weight will be an important factor**.

Not the length Overall **( LOA**) but the length waterline(**LWL**).

A longer hull is always faster with a better behavior than a shorter one at the same weight. (that weight is also replaced by displacement or Greek symbol **Δ**)

In the end, the best hull will be the one with a minimum of resistance (**R) **and the final speed of the boat will be (**V) **when the propeller thrust (**T)** will be the same as** (R).**

** **

A simple method to determine the hull resistance is to use the Satvisky equations .

Or to proceed to tank tests .

Boats with waterline length of less than 40 meters and weight less than 120 tons, with hard chine hull and constant deadrise, are an acceptable compromise between speed and sea behaviour if the main parameters such as LWL , total power , gearbox ratio, and propulsion are in harmony. The picture below show a typical 25m LOA which successfully reached 36 knots with attached the table of resistance at the various speeds.

The hump is clearly visible at 33 knots. The resistance of the hull at that point is 0 maximum. It will be necessary to check the thrust of the propulsion at that working point to make sure to plane.

We can observe that the trim angle of the hull is also maximum at that point and decreases after reaching a top speed running angle of 4.2 degrees with trim tabs.

The trim angle as well as the resistance can be modified by using trim tabs (flaps) or moving the centre of gravity (**LCG**)forward. Attention must be paid to the fact that moving the **LCG** forward could increase the wetted area and by consequence add resistance.

A quick speed estimation is given by the following formula

**V = (SHP TOTAL ^ .551/ D^.466)* 2.6**

In our example V=32.29knots ( with 5 % losses for gears and shafting)

**PROPULSION SELECTION**

Once the resistance is known, the second step is to calculate an approximate propulsion thrust .

Because the high difference in efficiency between the different propulsion system, the propulsion system must be selected as a first step.

1- The conventional propeller will limit the performance above 35 Knots because of the unavoidable cavitation phenomenon and will generate a lift force equal to the sine angle of the shaft multiplied by the thrust force.

2- The CPP will limit the performance to 30 Knots with an additional drag and weight problem due to the size of the hub and 2 % less efficiency than conventional propeller

3- The waterjet limit is around 60 Knots if the diameter of the impeller is correctly sized

**Limits to be considered are:**

-weight of the unit and the water carried by the waterjet itself which must be added to the normal weigth

-The particular need of clean water flow face of the water-jet inlet

-The risk of cavitation if the impeller get air in the inlet instead of water almost with high values of deadrise angle ( in general above 15°)

4- The Surface drive has no theoretical speed limits. The limits are the mechanical properties of the material and excessive transom forces if used at high speed in rough seas.

Once selected the propulsion system, the calculation start by assuming for each system an acceptable efficiency comparing the final thrust with the resistance.

The various efficiencies can be obtained trough the propulsion manufacturers or an estimate can be made by using the table below.

PROPULSION TYPE |
AVERAGE EFFICIENCY |

CONVENTIONNAL PROPELLER | 0.66 |

CPP | 0.62 |

WATERJET | 0.68 |

SURFACE DRIVE | 0.71 |

Then the thrust can be estimated by using a formula.

**T= Power*efficiency/ speed**

To simplify the calculation and to use coherent factor the Thrust formula can be expressed

**T=(146.2 *P* eff)./ Va**

Where

Va = knots

P= power per unit in HP

Eff= see table above

Note:

The boat speed is not the flow speed at propeller. The flow speed at propeller is slower than the speed of the boat. A correction factor must be applied. This correction factor, called wake factor, is expressed as (**w)** factor, so:

Va = V( 1-**w**)

For a planning hull the **w** factor is assumed to be 0.02 for a twin engine installation

**Ence Va = V*.98**

For the above mentioned yacht the speed of water at propeller to be considered in the calculation will be:

**Va=33*.98= 32.34 knots**

Also

**P = power in horsepower**

The power to considered in the calculation is the net power resulting at propeller after deduction of all losses such as gearbox , additional PTO, shaft losses due to frictional on the bearings , stuffing boxes etc…

As preliminary calculations the values of losses can be assumed to be:

Gear box = 3%

Shaft line =5 %

Finding the necessary power to reach the targeted performance can be now calculated

by reversing the thrust formula.

**P=( T * Va) / (146.2 * eff**)

Note : the value of 146.2 is a constant added to the calculation to multiply values which are not coherent and must be divided by the number of engine.

A table of POWER SELECTION can be established.

CONVENTIONAL PROPELLER |
1133,72 |
HP |

CPP |
1206,86 |
HP |

WATERJET |
1100,38 |
HP |

SURFACE DRIVE |
1053,88 |
HP |

8 % losses must be added to these calculated power

Supposing that conventional propeller is the fist choice, the total power to be installed will be

**P total =1134 *1.08=1224 hp*2 engine=2450 SHP**

According to engines available on the market the selected engines are

**2 X 1300hp@ 2300 rpm**

### THE PRELIMINARY GEARBOX SELECTION

** **

The selection of the correct gearbox ratio is of premium importance.

The revolutions at propellers will determine the propeller diameter and the size of the propulsion to be used.

The thrust and by consequence the performance of the boat is a direct function of the gearbox ratio selection.

The gear ratio to select is based on the following parameters.

- The engine revolutions (rpm)
- The power/weight ratio (hp/tons)
- The speed of advance, or the
**Froude number ( V/ LWL**^{0.5})

For V/ LWL^{0.5 }> 1 and SHP > 100 the following formula can be used to start calculation.

- V= Boat speed in Knots=33
- LWL= length waterline in feet= 22/.3048=72.17 ft
- P = Total power on board = 2 x 1224 =2448 hp
- W= Weight of the boat full load (tons) =48 tons(metric)
- RPM = Engine revolutions per min. =2300 rpm

Optimum gear ratio

**GEAR RATIO =1.45 e ^{(0.0038*x)}**

Where

- x = rpm / (
**P**/**D**) = 45

**hence gear ratio = 1.77/1**

Checking with the gearbox manufacturer, the available gear ratio is the acceptable ratio of 1.77 / 1 is selected.

So , the propeller revolutions will be,

**Prop rpm = 2300 / 1.77=1299 rpm or 21.65 r/ sec**

**SELECTION OF THE CORRECT PROPELLER DIAMETER**

** **

** **There are many ways to selected a correct diameter

The first way is to use empiric formula, while the second way is to use the well accepted method of Kt , Kq ,efficiency curves based on cavitation tunnel test where :

Kt = thrust coefficient

Kq =torque coefficient

Eff= propeller efficiency

J= speed of advance coefficient

The relation between these coefficients is given by

**Kt = T / ( p*n^2*D^4)**

*Kq=Q/ (p *n^2*D^5)*

*J= Va/Nd*

*Eff =(J/2*Pi)*(Kt/Kq)*

* *

*where*

* *

*P= water density ( 1025 kg/ m3)=1025/9.81=104.5*

*J= speed of advance coefficient*

*n=propeller revolutions*

The optimum Kt being:

**0.14 for 3 blade propeller**

**0.17 for 4 blade propeller**

**0.19 for 5 blade propeller**

**0.20 for 6 blade propeller**

Turning the Kt formula in Diameter formula the diameter will be

**D= (T/p*n^2*Kt)^ 0.25**

As a first choice we select 4 blade

Hence

**D= ( (6.63/2)/.1045*21.65^2*0.17)^.25=0.80m and J=Va/nD=(33*0.98/1850)/(21.65*0.8)=0.98**

At this stage of project several points need to be checked.

The first is to check the **cavitation limits **and determine the Blade area ratio **B.A.R**

To run the calculation, the parameters needed for calculation are:

**Atmospheric pressure = 10100 kg/m²**

**The hydrostatic pressure due to propeller immersion(0.9m) =900 kg/ m²**

**The level of the wave above sea level(assumed 0.5m ) =500 kg//m²**

**Static pressure at propeller centre =11500 kg/m²**

**Radius at 0.7 r= .80 /2*.7 =0.28 m**

**Circumfrencial propeller speed at 0.7 r= U = 38.06 m/sec**

**U² =1449**

**Boat speed in m/sec=33*1852/3600= v =16.97 m/s**

**v² =288.02**

**V²= U²+v²=1449+288.02 =1437.02**

**½ pV² =0.5*104.5*V =75084.29**

** **

**Cavitation criteria = static pressure / ½ pv² = 0.153**

**Burrill coef. tc.=0.1575*Cc+0.0792 =0.1033**

**Fp=T/(tc*1/2*p*V²)=3315/(0.1033*75084.29) =0.427m²**

**J=as previous calculation =0.98**

**Pitch /Diameter ratio=0.9511*J+0.21 =1.142**

**Fa=Fp/ (1.067-(0.229*P/D)=0.427/(1.067-(0.229*1.142)=0.530**

**Disk area= D²*pi/4=.0.8²*3.14/4 =0.5 m²**

** **

**BAR=Fa/Da=0.530/0.5=1.06**

** **

The second is to check the propeller efficiency

We now estimate the diameter=0.8

The BAR=1.06

The pitch=0.931

The blade number=4

The speed of advance J=0.98

The Kt=0.17

We need to calculate the torque Q

Q= 716.2*Power/ rpm=716.2*(1300*.95)/(2300/1.77)=680.68 kg/m=6677N

Kq=Q/p*n²*D^5=0.0418

Kt/Kq=.17/.418=4.06

J/2pi=0.98/6.24=0.157

**Eff=4.06*0.157=0.63**

** **

The third is to check the final thrust

** **

T=146.2*(power *.95)*eff. / Va= 146.2*(1300*.95)*.63/ 32=3554* 2 engine=7109.43 kg=7.1 ton

The hull resistance is 6.63 which need margin 5% the total resistance is 6.91 tons

** ****THE PERFORMANCE OF 33 KNOTS CAN BE ACHIEVED**

The fourth concern is the circumferential speed of the screw, which sould not exceed 50 m/ sec

Revs at propeller =2300/1.77/60=21.65 rev/s

Circumference =.8*pi=2.51m

Circumferential speed= 2.51*21.65=54.38m/sec

This speed is 8% above the limit but can be acceptable if the clearance between hull and propeller is at 15 % of the diameter. If not, the gear ratio must be increased to slow down the rpm and reduce the risk of cavitation**.**

**The Propeller Design **

The propeller design can some time help to increase the efficiency , the manufacturing class also help to get optimized performances.

The new technologies CAD and CNC as well as Hydrodynamic programs help to optimize the performance by increasing the efficiency and behaviour of the propulsion , reducing noise and vibrations as well as reducing fuel consumption.

The propeller is working with a certain amount of thrust and torque . The design must guaranty the time life and the safety of crew. In many application the use of classification rules will solve

The safety aspect of the installation but applying those rules the losses in performance can be estimated to be not less than 10%.

It’s the shipyard’s responsibility to decide to go for one way or the other.

But if decision is made to go for performance first , it is impossible to change for safety after work , just because there is no way to increase the diameter of a shaft nor the thickness of a propeller blade.

So , manufacturers should always calculate the application with safety factor.

To do so, company internal sizing rules should never be less than factor 2 for safety.

The next page show the design of the propeller previously calculated.

At this stage of the project the propeller design helps to clarify the boat general arrangement drawing .

**Mass moment of inertia**.

The torsional and whirling calculation will require to the propeller manufacturer to calculate the mass moment of inertia in air and in water of the shaft line and propeller.

For propellers, the accurate calculation of weight help to do so with the mass polar moment of inertia defined as the product of the masses and the square of the radius of gyration of the screw.

* I mp=m*i²*

* *

*I mp* = The mass polar moment of inertia in kg cmsec²

*m* = the mass of the screw in kgcm^{-1}sec²

In general the value of PD² for the propeller is commonly used, i.e the product of the weight and the square of twice the radius of gyration. The PD² can be expressed in kgm²

**PD²= mass *(k*diameter)²= 65.7*(0.5*.8)²=10.5 kgm² in air**

** **

It is commonly admitted that a mass of water is dragged by a turning propeller the final PD² in water is:

PD² water=PD²air *1.25= 13.14 Kgm².

Where k = .47 < k> .53

**Propeller frequency**

** **

In some application vibrations could result of harmonics coming from resonances due to same frequecies between hull, engines,propellers.

To avoid such inconvenience, it’s necessary to check the natural frequency of each components in the various mode.

The propeller frequency can be easily determined by calculation.

RPM at prop =1299

Number of blade = 4

Frprop = 1229* 4/60=81.99 hertz

**VIBRATIONS**

** **** **

The causes of vibration are many.

When vibrations are observed at sea trial the method to solve the problem consist in isolating the various items of the shaft line .

Vibrometer tools can also help to determine the source of the vibrations.

This type of tools will measure the amplitude of the vibration , the acceleration of the vibration and then determine the frequency of the measured vibration.

The possible cause of vibration are:

**Propeller**

Unbalanced propeller

Angular difference between blade

Cavitation

**Shaft**

Misalignement of the shaft line

Wrong machining of the cone and / or bended shaft

Shaft diameter too small

Shaft bending when turning due to too important distance between bearings

Reaction on bearing due to whirling.

Engineering failure ( ex ; rigid shafting coupled to flexible mounted engine)

**Engine**

** **

Diesel Injection failure ( injector nozzle )

Distribution timing failure

Silent block too loose or too tight ( shore hardness error)

Bad matching between propeller pulse ( wake factor variation) and axial admitted thrust of the slient- block .

Failure of the gearbox gears or input thrust roller bearings.

**Hull**

Structural problem in the rear part of the boat

Natural horizontal and vertical frequency which generate harmonics

Insufficient panel sizing at high speed due to slaming forces ( g too high)

**Conclusion**

** **

This quick note does not pretend to cover all the aspects of engineering the propulsion of fast boats.

Many other matters should have been discussed such as surface drives and going deeper in the propeller design.

It simply shows that nothing is impossible to solve . So far ,all toolings are available and computers are a great help to manage a technical project if people who use them in the marine industry respect the proportional rules that common sense will bring to mind.