1. Published in Ingenieria Naval November 2009
FROM TVF PROPELLERS TO THE LAST GENERATION OF CLT PROPELLER
Evolution of the design process
Dr. Gonzalo Perez Gomez naval architect and retired profesor of ETSI Navales de Madrid.
† To the memory of Don Ramon Ruiz-Fornells doctor naval architect, whose tireless and
enthusiastic support made possible the realization of this tenacious research.
1. SUMMARY
The historical evolution of theoretical principles explaining the performance of this type of
propellers and allowing them to be designed, is described.
To make easier the understanding of the text, mathematical formulation any has-been omitted.
In reference list, all mathematical developments are included.
The link between existing analyze theoretical principles and propeller geometry has been standed
out.
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2. INDEX
CONTENTS Page
1. SUMMARY 1
2. INTRODUCTION 3
3. CORRELATION BETWEEN THE EFFICIENCY OF A PROPELLER AND THE MAGNITUDES 3
OF THE PROPELLER INDUCED VELOCITIES
4. PRESENTATION OF TVF PROPELLERS 4
5. LERBS LIFTING LINE THEORY AND TVF PROPELLERS 4
6. NEW MOMENTUM THEORY AND CLT PROPELLERS 6
7. RENEWED LIFTING LINE THEORY AND LATEST GENERATION OF CLT PROPELLER 9
8. REFERENCES 11
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3. 2. INTRODUCTION
References (1) and (2) are the theoretical principles of the most modern and advanced
procedure, which exists at present to project as accurately as any type of propeller and in particular
the most recent version of CLT propeller.
Its differences with the propeller project procedure which has been using so far are very
noticeable. For this reason it has been considered appropriate in the present study justify the
reasons for this development.
In my 70 years of age and due to my deep dedication to the University, I feel the need to make
available to the profession the knowledge learned during my self-didactic work in the field of
propellers. I was worried too, by de fact that in the future, merits of CLT propellers could be judged
using our theoretical developments published before 2004.
My expertise in this field of hydrodynamics was started around 1970, when Don Ramón Ruiz
Fornells (Technical Director) and I (Head of Section for Hydrodynamics) worked in AESA. In tose days
the design of the propellers were done by the model basins, and for AESA was critical the period of
time necessary to have fully defined the constructive drawings of the propeller of a new building.
It was completely normal that in any experimental program would need to be designed and
tested over two propellers, which, sometimes, for planning reasons became irremediable have to
launch the ship without propeller, placing in the stern bearing a blind flange.
As a result, Ramon decided that in AESA, besides making the design of hull form, we designed the
propeller, to save time and try to improve the quality of the designs.
The price of fuel was very high, and the ship owners in addition to seeking the best prices on
construction, highly valued that offers with a reduced fuel consumption. The shipyards competed in
the optimization of the ship design and in particular hull lines, and the ship propulsion.
The above facts allow the understanding that were initiate a very difficult specialization, which
was very exciting for me, because of my teaching at the University in the subject Resistance and
Ship Propulsion.
The effort to implement the service of propellers design give us the enough creativity to try to
improve the quality of future ship propellers.
3. CORRELATION BETWEEN THE EFFICIENCY OF A PROPELLER AND THE MAGNITUDES
OF THE PROPELLER INDUCED VELOCITIES
Let us consider a generic propeller blades anular section. The water falls on it at some angle with
the plane perpendicular to the shaft line. This angle is called the hydrodynamic pitch angle, and is a
consequence of the relative velocity of water relative to the propeller plan and of the induced
velocity.
The forces acting on the propeller blades annular section are: the lift force, which is
perpendicular to the direction of incoming water, and viscous resistance, which is opposite to the
velocity of incoming water.
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4. Projecting these forces in the direction of the shaft line and its perpendicular, it is concluded that
the net thrust exerted by the ring section increases as the hydrodynamic pitch angle decreases, or
what is the same, when the induced velocity components decrease.
The projection of these forces on the direction perpendicular to the axis decreases, when the
induced velocity decreases.
Clearly, therefore, can be concluded that the efficincy of the propeller blades annular sections
grows, when the components of the induced velocities decreases.
In paragraph 2.7.3.4 of ref. (12), these arguments are fully developed.
4. PRESENTATION OF THE TVF PROPELLERS
In ref. (3) it was proposed to improve the performance of the propellers by growing
monotonously geometric pitches of the tip sections, and placing a cylindrical tip plates at the ends
of the blades.
That conclusion was reached in seeking the type of circulation radial distribution that would
optimize the propulsive efficiency of the ship.
The used mathematical developments were at a rudimentary theory of propeller blades elements,
wich incorporated some additional errors to the criticism in ref. (1).
To test the feasibility of these ideas, was conducted in the El Pardo Model Basin a pilot program
using a stock propeller model of Kaplan type, whose geometrical pitches were increased
monotonically from the hub to the ends of the blades. At this propeller model were set forth
different types of tip plates and performed with it, propeller open water test.
Although not known at that time, the important effect of scale that affect the results of propeller
open wáter tests, findings obtained were enough stimulants like to go on developing the proposed
idea. Ramon's support was decisive.
I want to emphasize that since then it was fixed in our minds the wrong concept that the
geometrical pitched of TVF propellers end sections should be increased monotonically to improuve
the propeller efficiency.
5. LERBS LIFTING LINE THEORY AND TVF PROPELLERS
To prove the feasible to design conventional propellers of ships that were built in AESA, and in
order to design new TVF propellers I conduct a study on the state of the art of the procedures used
then by the model basin, to the design of propellers. Immediately concluded that the procedures
used by the model basins had an empirical nature, and had no publications in which fully describe
the sequence of calculations necessary for the project of a propeller.
At that time the six major factories of AESA were fully occupied, thus, the number of model test
programs that I had to manage was very high, and this forced us that in order to make our designs
for conventional and TVF propellers we had to make test orders in the main European model basins.
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5. This activity allowed and forced me to hold technical discussions with leading European experts in
hydrodynamics, leading to the conclusion that I had no other recourse that to develop our own
computer programs. Therefore, I decided that it was essential to study deeply the paper of Lerbs
quoted in ref. (8) of our ref. (1).
The effort to understand the paper of Lerbs allowed us to correct and generalize that theory to
make our designs of conventional and TVF propellers, ref. (5).
In order to define the three-dimensional geometry of the propellers, I develop a new theory of
cascades, which turned out to be remarkably accurate and valid for any type of propeller (see chap. 4
ref. (12)). It was also necessary that I developed an analytical procedure for checking the mechanical
strength of the blades of any type of propeller.
Once the computer program was ready we designed, with the aid of some chemical, conventional
and TVFpropellers. Many propellers were tested and built to full scale whose performance was
reasonably satisfactory.
In order to extrapolate at full-scale model test results, was necessary to assess the scale effect of
viscous resistance of the propeller blades. In paragraph 11.3.4.2. Ref. (12) describes the program
developed, and which was subsequently accepted as basic in the R + D + i described in ref. (13).
At this point, we should remember that Lerbs mathematical developments, based on the
assumption that the velocities induced on the propeller disc have values equal to half the
corresponding values at infinity downstream (hypothesis that the propeller is moderately loaded).
Our effort was aimed at getting that at the propeller disk the induced velocities were as small as
possible. It happens, however, that in accordance with Lerbs developments, the induced velocities at
infinity downstream would also be small, so that the thrust of the propeller would be too small and
the same would happen to the efficiency of the propeller.
This paradox was a result of not taking into account in the arguments the existence of radial
contraction of the liquid vein that passes through the propeller disk.
Although the omission of the influence of contraction of the vein did not invalidate completely
settled our developments, it was inevitable to have to try to introduce such influence on the
calculation of induced velocities. The procedure developed was a mixture tedious, of Lerbs analytical
solution, and an a iterative numerical integration program, which is to define the equilibrium
positions of free vortices, discretized then and calculate the induced velocities by applying the Biot-
Savart law. See ref. (6) or paragraph 3.5.13. Ref. (12).
It was obvious that they were exhausted the possibilities of application of Lerbs induction factors
in the design of TVF propellers.
Were published or presented at various conferences, many informative technical papers of the
brilliant successes had been achieved at full scale. In the design of TVF propellers theoretical
resources were used combined with the inevitable weightings of empirical nature (chemistry).
Since being introduced TVF propellers, we claimed always that excited vibration levels on the hull,
for these propellers, would be reduced due to the lack of blade tip-vortex. Obviously, the smaller
optimal diameter of TVF propellers was also working.
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6. Because of my activities at the University, I had begun serious study of the propeller momentum
theory by finding that it incorporated some mistakes, I set out to correct.
6. NEW MOMENTUM THEORY AND THE CLT PROPELLERS
Having become convinced that it was imperative to take into account in design calculations, the
influence of radial contraction of the liquid vein, it made sense to pass this influence in defining the
three-dimensional geometry of the propeller.
Premature and forced retirement of Ramon and other executives of AESA, was associated with
the onset of labor problems for those who had been his closest collaborators, so I decided to
continue my career out of AESA. In ref. (11) includes the text of my patent application of CLT
propellers. The CLT name attributed to this type of propeller, comes from the features claimed in the
patent application, "Contracted Loaded Tip Propeller."
Reference (4) corresponds to the publication that is designated for the first time, this type of
propeller with the name CLT
Once out of AESA, promoted the creation of Sistemar, among others, Don Ramon Ruiz-Fornells,
Don José María Rotaeche, Don Juan González-Adalid, and me. Later on joined us Don Alfonso Alfaro,
Don Javier Ferrer, and Don Gerardo Bonnin.
The momentum theory is characterized by modeling the action exerted by the propeller on the
surrounding water. In this theory the action of the propeller disk is modeled using an actuator disk
that causes in the wáter a discontinuity in the axial distribution of pressure field.
Upstream produces some depression edp, while downstream there is an excess of pression (1-e)
dp, where dp total magnitude of the jump of pressure, which is linearly related to the thrust exerted
by the propeller.
Applying Bernoulli's theorem, it is posible to relate the pressure field, with the field of the axial
components of water velocites.
In the original version of this theory, it was wrongly concluded that the magnitude of the axial
component of induced velocity in the disk of the propeller was equal to half the magnitude of this
component at the infinite downstream.
In ref. (8) I showed that this conclusion was wrong and I deduced the right expressions of the
axial components of the velocities induced in the actuator disk, dependent of coefficient e and, and
at infinite downstream, dependent only of the thrust of the propeller.
The energy balance, with which it was intended to calculate the angular components of the
induced velocities in the original momentum theory was totally wrong, and I correct it (ref. (7), from
the 1982 edition), ref. (9), ref. (10), ref. (12) (3.8)).
Corrections on the momentum theory encouraged me to call the new developments new
momentum theory.
In the case of conventional propellers, when one could accept the hypothesis were moderately
loaded, one could assume that the axial component of induced velocity in the disk of the propeller,
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7. had a value equal to half the corresponding value at infinite downstream, thereby circumventing the
need to attach a value to the factor e.
When it was not a conventional propeller moderately loaded, I found that e factor remained
almost constant at 0.4167.
We note with great satisfaction that with the procedure developed for the calculation of induced
velocities was achieved to predict the efficiency and the geometric pitches of conventional
propellers, without resort to any further empirical support. There is a copious list of references
justifing the excellent results obtained.
Analyzing the expression of the efficiency of a propeller blades annular section is concluded that
this increases as the factor e decreases. On the other hand when e decrease the pressure increases
in the pressure side of the propeller blades and the pressure decreases in the suction side of
propeller blades.
I found no valid analytical expression allows us to calculate the value of the factor e that should
be introduced in the calculations, when designing a CLT propeller for a given radial loading
distribution.
To design CLT propellers were available only the recommendation that the factor e should be as
small as possible, or what is the same, to be achieved, the pressure in the pressure side of the
propeller blades to be as large as possible.
In ref. (12) are include the most important developments that have been created to discern
whether a given value of the e coefficient it is admissible for some propeller blades anular section.
Speculative resources are also included to deduce the value of the most appropriate e coefficient
associated with a given radial loading distribution.
At this point, it is essential to establish, that to qualify a design procedure as consistent, it should
require at least that it be exempt from empirical calibrations, the design speed be achieved in reality,
and that geometrical pitches and the camber – chord ratios be appropriate.
In the present case, by a process of trial and error, to predict correctly the design speed, it was
concluded that an e factor should be used, ranging between 0.12 and 0.2, depending on the type of
ship. Under these conditions the geometric pitches were prohibitive.
To perform the detailed design of the propeller it was used a value of e factor close to 0.09. The
speed prediction was extremly optimistic and the propeller rpm was light.
To correct this inconvenient, when it was defined the geometry of the propeller blades annular
sections, the cambers-chords ratios were reduced and consequently the geometrical pitches were
increased. Thus the right revolutions of the propeller were obtained, but the propeller blades annular
sections work very far from the free-sock entrance conditions.
Having in mind the objective to get radial loading distributions with a significant excess of
pressure on the pressure side of propeller blades, still were using radial geometrical pitches
distributions which monotonically increased geometrical pitches toward the ends of the blades.
The resulting propeller efficiency depended on the value assigned to the e factor and if the
gradient of the radial distribution of geometrical pitches be adequate for design conditions of the
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8. propeller in question. A low gradient may not generate the necessary over pressure, and an excessive
gradient could lead to inadmissible flow separations in extreme annular sections, and increasing the
viscous resistance of the propeller blades in this región.
As regards the cavitación behavior of the propeller, apart from the boundary conditions, the
designs had to favor the lowest underpressure existing upstream, due to the low value of the factor
e, and against the flow separation produced in the tip sections of the propeller, as a consecuence of
the excessive angle of attack.
Besides the risk of vibration excitation, highest risk in relation to the cavitation behavior of the
propeller was due to the possibility that the separated flow existing in the tip sections could return
on the blades causing cloud cavitation, with the consequent erosion.
To successfully conduct the CLT propeller cavitation tests, it was necessary to develop the special
procedure described in ref. (13) to take into account the scale effect that affects to the viscous
resistance of the propeller blades in the model field and to the value of the a factor during the
cavitation test.
The number of CLT propellers built and designed with the help of the new momentum theory has
been very high. And there were also some results obtained at full scale, seemingly inexplicable, but
which can be justified taking into account the foregoing arguments.
I must place on record the great support received from Don Ramón López Diaz-Delgado Technical
Directorof Navantia who incorporated to us to a numerous research programs led brilliantly by Don
Mariano Perez Sobrino in which we cooperate with experts from Navantia of CEHIPAR, TSI and other
companies.
It has also been very important the support received from Don José Luis Cerezo Preysler and Don
Antonio Sanchez Jauregui, both from the Gerencia del Sector Naval, at the time.
In ref. (13) it is described the programs of R & D & i in Spain have helped establish the
experimental technique of CLT propellers.
The numerous cavitation tests carried out on programs of R + D + i that have been made with CLT
propellers have revealed that the tip sections of these propellers have important flow separation,
which can cause cloud cavitation.
In several CLT propellers that have been built, erosions have appeared in the tip sections of the
blades.
In order to try to avoid the risk of cloud cavitation, I proposed that in the future, the end sections
of the blades had a negative rake, in order to hinder, return on the propeller blade, of separated
cavitating flow.
Due to the evidence that, without doubt, the propellers designed using the procedure described
are too loaded at the tips of the blades, I since 2003, strongly recommend, unsuccessfully, to
Sistemar to modify the design procedure that it was being used.
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9. 7. RENEWED LIFTING LINE THEORY AND THE LAST GENERATION CLT PROPELLER
At University, during 2003-2004, in addition to being professor of Resistance of Ship Propulsion I
also was profesor of graduate course in Advanced Procedures to Design Ship Propellers.
I proposed to the students that we would do a small research project, once complete it would be
published in Ingenieria Naval. As at the time I was immersed in developing a new propeller design
procedure, I proposed then to perform the work described in ref. (1). I imposed the condition that
they should make their own computer program, in order that the effort to be done by then, would
result for them useful.
I looked to find an alternative and more accurate design procedure, to the new momentum
theory. The looked design procedure must connet the shape of radial loading distribution with the
propeller open water efficiency, and must allow to the designer to obtain geometrical pitches
distribution decresing towards the blade tips.
In ref. (1) emphasizes that the Goldstein theory had the attractive of working with an infinite
number of blades, and considering that the vortices are threaded into a cylinder of infinite length.
Due to this, the calculation of induced velocities is simplified significantly.
The influence of contraction of the liquid vein is automaticly taken into account, since the induced
velocities are calculated at the infinite downstream, once the free vortices adopt their equilibrium
positions on a cylinder.
The components of induced velocities correspondic to the propeller disck are calculated
respectively by applying the continuity equation and the conservation of angular momentum
between the the propeller disk and the infinite downstream.
In ref. (1) it was demostrated tha a new design procedure for conventional propellers had been
obtained correcting adequately the traditional Goldstein procedure. The asumption that it is posible
to replace a finite number of propeller blades by a infinite number of blades were pruved to be
correct. Also it was proved that the new procedure is compareble, in the case of conventional
propellers, to the new momentum theory.
In ref. (2) was presented the generalization of this procedure for the case of CLT propellers.
It is introduced as input the radial distribution of circulation. In the case of conventional
propellers, necessarily, such distribution ends in a null value at the tip of the blades.
The calculation process does not require the introduction of any empirical weighting, and
calculation results are excellent, and the prediction of the speed of project is very precise and
geometric pitchs are also successful.
The advantage of this project procedure (ref. (1) and ref. (2)), to be called the renewed lifting line
theory, over the new momentum theory lies in that in the case of conventional propellers, it must no
be assumed if the propeller is moderately loaded or not, when calculating the axial component
induced velocity. The importance of the load of the propeller it is automatically taken into account in
the results of the calculations.
To ensure that a propeller has a high efficiency, its induced velocities must be smaller than in the
case of a conventional propeller. In ref. (2) it is justified the hydrodynamic model of systen of radial
9

10. and free vortex that has to manage to get induced velocities only produced by a fraction of the
ordinates of the radial circulation distribution.
Also it is justified the need of having to install a tip plates on the ends of the propeller blades,
with the aim of reaching a non-zero circulation in the blades tips.
Naturally, as in the case of new momentum theory, the size of the tip plates must be appropriate
in order to reach the intended circulation at the ends of the blades.
I must correct the contents of ref. (2), with respect to the component of the radial distribution of
the circulation that ends with a nonzero value at the ends of the blades. This may also have a
nonzero value at the propeller hub, without the viscous resistance of the blades is seen unfavorably
affected.
I have found that making this component maintains a constant value radially from the hub to the
ends of the blades, the results of the calculations, besides being very precise, are very accurate.
The radial distribution of geometrical pitchs, which are obtained using this method of project is
very different from that obtained using the new momentum theory. The pitchs of the end sections of
the blades decrease monotonously to the ends of the blades.
The marked differences in their geometry show the birth of a new generation of CLT propellers.
From the appearance of the radial circulation distribution is easy to conclude that the end
sections of the blades are downloaded, as intended.
This procedure does not require empirical correction coefficients, and their results are excellent,
both as regards the prediction of the ship velocity, as the radial distribution of geometrical pitches.
The annular sections of the blades can operate in conditions as close as you want to the ones
corresponding to free shock entrance. From the point of view of excitation of vibrations on the hull
this procedure has the following advantages over the new momentum theory:
The end sections of the propeller blades are much more downloaded, thus the
excitation of vibrations caused by phenomena of flow separation are lower.
The station more loaded it is not the blade tip but another station close to 0.7, and
therefore farther from the hull.
The annular sections are operating in conditions closer to those of free- shock
entrance, and the camber-chord ratios are very close to the optimum, thereby decreasing
the extent of the sheet cavitation.
It is important to mention also that the quality of the preliminary design that are obtained by
combining the design procedure with the theory of Lerbs equivalent profile (ref. (2)) is excellent. The
results obtained are very close to those of the detailed design.
I must place on record that, I was able to make a design of a new generation CLT propeller, which
was tested and the results were excellent.
Its ship speed exceeded by 3.22% to the corresponding to a conventional propeller alternative.
The speed prediction was diferent from the one corresponding to the extrapolation of model test in
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11. a 0.77%, and the prediction of ship velocity obtained from the preliminary design disagree with the
one obtained from the extrapolation of model test in 0.22%.
Geometrical pitch corresponding to station 0.7 disagreed with the needed in 1.8%, and the
geometrical pitch predicted in the preliminary design disagreed with the required in 5%.
CLT propellers are becoming popular today. Reference (14) is an excellent example of the
approach to the study of their behavior with the aid of CFD. This work includes the discussion I had
with authors, courtesy of Don Antonio Sanchez-Caja.
He hoped that the new design resources that have been developed will be useful to the
profession, and I hope that in future the justification of the merits of CLT propellers are made taking
into account the content of this contribution.
8. REFERENCES
1. Pérez Gómez, G., Souto Iglesias, A., López Pavón, C., González Pastor, D., ¨Corrección y
recuperación de la teoría de Goldstein para el proyecto de hélices ¨. Ingeniería Naval. Nov. 2004.
2. Pérez Gómez, G., ¨Utilidad de la teoría renovada de las líneas sustentadoras para realizar el
diseño de hélices con carga en los extremos de las palas, y para estimar el rendimiento de cualquier
hélice al efectuar su anteproyecto ¨. Ingeniería Naval. Marzo 2007.
3. Pérez Gómez, G., ¨Una innovación en el proyecto de hélices ¨. Ingeniería Naval. 1976.
4. Pérez Gómez, G., González – Adalid, J. ¨Comportamiento del Sesermendi Barri dotado
alternativamente de una hélice convencional en tobera y de una hélice CLT ¨. Rotación ¨. Julio 1987.
5. Pérez Gómez., y Baquerizo Briones, I. ¨Análisis de las contribuciones de Lerbs, de Morgan y
de Wrench sobre la teoría de las líneas sustentadoras, enmiendas a sus resultados y
perfeccionamiento de las mismas¨. Ingeniería Naval, Mayo 1978.
6. Pérez Gómez, G., González Linares., and Baquerizo Briones,I., “Some Improvements of
Traditional Lifting Line Theory for Ship Propellers”. International Shipbuilding Progress, July 1980.
7. Pérez Gómez. G., “Conferencias sobre Teoría del Buque¨ ETSI Navales de Madrid. Sucesivas
ediciones desde 1973.
8. Pérez Gómez. G., ¨ Correcciones a la teoría clásica de la impulsión y habilitación de la misma
para el diseño de propulsores¨. Ingeniería Naval. Enero 1983.
9. Pérez Gómez. G., Pérez Gómez, G., Baquerizo Briones, I., González Adalid, j .,¨ Aplicaciones
de la nueva teoría de la impulsión al diseño de propulsores ¨ .ingeniería Naval. Julio 1983.
10. Pérez Gómez. G., Application of a New Momentum Theory to the Design of Highly Efficient
Propellers¨ WENT, Paris julio 1984.
11. Pérez Gómez. G., ¨ Solicitud de patente de invención referente a los propulsores de los
buques caracterizados por la incorporación en las secciones extremas de unas placas tangentes a la
11

12. superficie de revolución que encierra a la vena liquida que atraviesa al propulsor, con lo cual el radio
del extremo del borde de salida ha de ser menor que el radio correspondiente al borde de entrada.
Etc…¨. Registro de la Propiedad Industrial. 13 de Agosto de 1985.
12. Pérez Gómez. G., González Adalid, J. ¨ Detailed Design of Ship Propellers¨. Libro editado por
Fondo Editorial de Ingeniería Naval. Madrid 1998.
13. Pérez Gómez, G., Pérez Sobrino, M., González Adalid, J., García Gómez, A., Masip Hidalgo,
J., Quereda Laviña, R., Minguito Cardeña, E., Beltrán Palomo, P., ¨Un hito español en la propulsión
naval. Rentabilidad de un amplio programa de I+D+ i ¨´. Ingeniería Naval .Junio 2006.
14. Sánchez-Caja, A., Sipia, T.P., Pylkkanem, J.V., ¨Simulation of the Incompressible Flow around
an Enplate Propeller Using a RANSE Solver ¨, 26 Symposium on Naval Hydrodynamics, Roma 17-22
Sept. 2006.
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