Today’s article is a document published a while back by Mr. Paul Bezzi of France Helices (WEBSITE), that gives a highly detailed description of how to properly match engines, gearbox, and propellers. This is often a tricky task, and we hope that this explanation helps MarineDiesel customers in obtaining optimum performance on their vessels. If you wish to contact France Helices on a project for a quote, follow the link above or give them a call at +33493476938.
A RATIONAL APPROACH TO ENGINE / PROPELLER MATCHING FOR HIGH SPEED AND FAST BOATS
Introduction.
I am writing this paper with the aim to help those who want decide 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, boatyards, propulsion manufacturers are increasing power, behaviour at sea and efficiency .Very shortly problems appears due to the lack of know how, and true reason of failure of performance…
I propose to go step by step in the detail of a typical project.
1The hull
There are several type of hull capable of performance, the best hull will be the one that fulfills 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)
At 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 .
For boats with waterline length of less than 40 meter, 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.
EXAMPLE OF CALCULATION
HULL DATA 


LOA 
25 
meters 
LWL 
22 
meters 
Bpx 
4,85 
meters 
Draft midship 
1,12 
meters 
draft transom 
1,12 
meters 
Deadrise angle midship 
17 
degrés 
dearise at transom 
17 
degés 



spray size 
0,18 
meters 
propeller position from transom 
1 
meters 
propeller immersion h2 
0,9 
meters 
engine centerline 
2,1 
meters 
side inclination 
1,1 
% 
water density 
1,025 
t/m3 
boat weigth 
48 
tons 
lcg 
8 
meters 
propeller diameter 
0,8 
m 
shaft angle 
6 
degres 
shaft length 
4 
m 
ENGINE DATA 

number of engine 
2 
power hp 
1300 
max revolutions 
2300 
gear ratio 
1,77 
SPEED 
0,00 
3,39 
6,78 
10,17 
13,56 
16,95 
20,34 
23,73 
27,12 
30,51 
33,90 
resistance 
2,06 
2,21 
2,50 
2,91 
3,45 
4,10 
4,82 
5,49 
6,02 
6,38 
6,63 
resistance with flaps 
1,86 
2,01 
2,28 
2,67 
3,18 
3,80 
4,48 
5,16 
5,74 
6,17 
6,51 
The hump is clearly visible at 33 knots. The resistance of the hull at that point is o maximum it will be necessary to check the thrust of the propulsion at that working point to make sure to get planning.
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/Δ^.466)* 2.6
In our example V=32.29knots ( with 5 % losses for gears and shafting)
PROPULSION SELECTION
Once we know the resistance, the second step is to calculate an approximate propulsion thrust .
Because the high difference of efficiency between the different propulsion systems, the propulsion system must be selected as a first step.
TABLE OF PROPULSION LIMITS
 The conventional propeller will limit the performance above 35 Knots because of the unavoidable cavitation phenomena and will generate a lift force equal to the sine angle of the shaft multiplied by the thrust force.
 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
 The waterjet limit is around 60 Knots if the diameter of the impeller is correctly sized
Waterjet limits to be considered are:
weight of the unit and the water carried by the waterjet itself which must be added to the normal weight.
The particular need of clean water flow face of the waterjet inlet
The risk of cavitation if the impeller gets air in the inlet instead of water almost with high values of deadrise angle (in general above 15°)
 The Surface drives has no theoretical speed limits, though the limits are mechanical properties of the material, and excessive transom forces if used at high speed in rough seas.
Once the propulsion system is selected, the calculations 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 
CONVENTIONAL 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 the 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( 1w)
For a planning hull the w factor is assumed to be 0.02 for a twin engine installation
Hence 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 the 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 engines.
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 the 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
X 1300hp@ 2300 rpm
THE PRELIMINARY GEARBOX SELECTION
The selection of the correct gearbox ratio is of premium importance. The revolutions at the 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
hence gear ratio = 1.77/1
Checking in the gearbox manufacturer the available gear ratio 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 ,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 known as
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
Circumferential 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 should 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, and also help to get optimized performance.
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 problem. 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 the 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 a safety factor.
To do so, company internal sizing rules should never be less than factor 2 for safety.
This is the design of the propeller previously calculated.
At this stage of the project the Propeller design helps to clarify the boat general arrangement drawing .
Checking the clearance with the hull , sizing the shaft, calculating the weight
DIAMETER 
800 
mm 
POWER 
1300 
CV 
956,8 
Kw 
PITCH 
931 
mm 
REVS 
2300 
tr/mn 
1,05 
BAR 
BLADE 
4 
3,4,5 
GEAR RATIO 
1,77 
/ 1 
65,70 
Weigth en kg 
BLADE RATIO 
1 

Leading edge 
2,5 
mm 
42.04 
PD² air 
SHAFT DIAMETER 
75 




52.55 
PD² water 
RAKE DEG, 
6 

Skew% 
0,7 


RADIUS 
PITCH DISTRIBUTION 
l section mm 
rake mm 
skew mm 
THICKNESS 
Pitch mm 
Pitch angle 
0.2R 
0,920 
244,968 
80 
18,039 
40,000 
856,603 
59,59558375 
0,25R 
0,920 
255,293 
100 
22,703 
34,400 
856,603 
53,73994693 
0,3R 
0,920 
270,628 
120 
26,503 
30,200 
856,603 
48,64575911 
0,4R 
0,956 
313,939 
160 
32,789 
24,000 
890,269 
41,52703181 
0,5R 
0,984 
366,084 
200 
36,644 
19,200 
916,453 
36,10290564 
0,6R 
1,001 
417,914 
240 
37,045 
15,200 
931,950 
31,71683384 
0,7R 
1,001 
462,853 
280 
32,789 
12,000 
931,950 
27,91151889 
0,8R 
0,986 
489,310 
320 
20,355 
9,200 
917,700 
24,53321431 
0,9R 
0,945 
450,650 
360 
5,505 
6,640 
879,795 
20,12607725 
0,95R 
0,890 
332,434 
380 
26,986 
5,600 
828,923 
19,14580542 
0,98R 
0,863 
205,432 
392 
46,222 
4,800 
803,486 
18,06743693 
R 
0,836 
0,000 
400 
66,436 
4,000 
778,050 
17,20128356 
Mass moment of inertia.
The torsional and whirling calculation will require 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 helps 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 in harmonics coming from resonance due to the same frequencies between hull, engines, and propellers.
To avoid such inconvenience, it’s necessary to check the natural frequency of each component in the various modes.
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 consists of isolating the various items of the shaft line .
Vibrometer tools can also help to determine the source of the vibrations.
These types 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 slamming 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 technical project if people who use them in the marine industry respect the proportion rules that common sense will bring to their mind.
Thanks to France Hélices engineering team for having provided time and efforts to help me with this document.