II
I r
On the
verification of
a theory
for sculling propulsion
TECHNISCHE UNIVERSITEIT----r
Scheepshydramechanica
Archief
Mekelweg 2, 2628 CD Delft
Te1:015-786873/Fax:781836
aj
'4:11 4sk -1 041R.M.R. MULITJENS TECHNISCHE UNIVERSITEri Laboratorium voor Scheepshydromechanica Archief Mekelweg 2, 2628 CD Delft Tel.: 015 - 786873 - Fax: 015- 781838
On the
verification of a theory
for sculling propulsion
TECHNISCHE UNIVERSITEIT Laboratorium vox Scheepshydromechanica Archief Mekelweg 2, 2628 CD Delft Tel.: 015- 766873- Fax: 015 - 781838
On the
verification of a theory
for sculling propulsion
PROEFSCHR1FT
iter verkrijging van de grand van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof. dr. J.H. van Lint, voor een commissie aangewezen door het College van Dekanen
in het openbaar te verdedigen op dinsdag 3 november 1992 om 16.00 uur
door
RUDOLF MATHIAS ROSALIE MULITJENS geboren te Stein
Dit proefschrift is goedgekeurd door de promotoren
prof. dr. ir. W.M.J. SchlOsser
prof. dr. ir. M.W.J Schouten
en copromotor dr. ir. W.J.A.E.M. Post
Summary
The experimental verification 'of an optimization theory for sculling propulsion is described in this thesis. This research project was done under the supervision of Professor
Dr. Ir. W.M.J. Schltisser and sponsored by the Technology Foundation (STW)' in the Netherlands.
The optimization theory was developed by Dr. Ir. W. Potze under the guidance of Professor Dr. J.A. Sparenberg at the University of Groningen. This theory models the hydrodynamics of a specific class of sculling propellers. This propeller consists ofone wing or two wings moving side by side or one behind the other. An optimum motion to generate a certain prescribed mean thrust T with the highest possible hydrodynamic efficiencyti can be calculated with this model. The optimum motion consists of a periodic sideways motion of the wing superimposed by a periodic pitching motion. The forces and the moment as a function of time for the two dimensional wing(s) can be calculatedas well. The theoretical model reached a stage where a comparison with measurements was necessary.
The verification of the theory is divided into three parts, 'namely: - a short introduction in the theory of sculling propulsion; - an evaluation of the methods and assumptions used; - a comparison of theoretical and measured results.
First, the basic principle of sculling propulsion is explained and the theory of Potze is discussed.
In the second part, the calculation methods are applied to a defined sculling propeller. An evaluation shows that the forces and the pitching moment are calculated with sufficient accuracy for a two dimensional wing only. A comparison of the theoretical results with results of the steady state wing theory shows that the latter theory gives equivalent values, for the forces on the two dimensional wing. Within the limits of this evaluation, also relative accurate results for the mean thrust of the wings are obtained with the steady state wing theory. The conclusion of a sensitivity analysis is that the motion of the wing is to be realized with high accuracy for a verification.
A prototype, designed for measurements, is discussed in the third part. This prototype 'with its measuring equipment has to fulfill special needs when looking at the high dynamic
character of die sculling process. Therefore transmissions with high speed, high accuracy servo-systems are used. The angle is measured with high accuracy using an inductosyn. The position is measured with a sensor using two proximity switches. A special instrument to measure the force on the wing is developed. The pitching moment is measured via the required current of the servo-motor. A data acquisition system with a sample hold unit is used to digitize the analog signals of the measuring equipment. To further process the measured signals, a computer system is used. With this computer system, the quantities needed for the comparison with the theoretical' results are calculated.
The tests on die prototype were carried out in the towing tank of the University of Technology in Delft. The measurements show that the theory yields equivalent results for the mean thrust in several cases tested. Limitations in the performance of the wing were
Summary
-encountered in all cases measured. It is likely that laminar bubble separation of flow influences the performance of the wing.
A comparison with other propulsion systems cannot yet be performed due to the small
Contents
Summary Symbols
Preface 1
Sculling propulsion 3
2.1 Structure of a sculling propeller 3
2.2 Working principle of a sculling propeller 4
2.3 Optimization theory of Potze 6
2.3.1 The principles 7
2.3.2 The two dimensional theory 10
2.3.3 The three dimensional theory 13
2.4 Summary on sculling propulsion 18
Theoretical evaluation 19
3.1 Scope of the evaluation 19
3.2 Evalution of the different models 20
3.3 The calculated thrust Fx and pitching moment M 20
3.4 Comparable calculations 23
3.4.1 Method of calculation 23
3.4.2 Results of comparative calculations 25
3.5 Sensitivity analysis 27
3.6 Occuring maxima within the scope of the verification 29
3.7 Results and conclusions of the theoretical evaluation 32
The testbed and signal processing 33
4.1 Towing tank 33
4.2 Design of the prototype 33
4.3 Drive units 36
4.3.1 The rotary drive 36
4.3.2 The linear drive 39
4.4 Important parts of the assembly 41
4.4.1 The &wile 41
4.4.2 Design of the wing 42
4.4.3 The clutch 42
4.5 Measuring instruments 43
4.5.1 Measuring accuracy 44
4.5.2 Measuring of the angle 46
4.5.3 Measuring of the position 47
4.5.4 Force measurement 49
4.5.5 Measuring of the pitching moment 50
4.5.6 Accuracy of the chosen measuring methods 51
4.6 The data acquisition 52
4.7 Summary on the prototype 56
1.
2.
3.
Experimental verification 57
5.1 Measuring range 57
5.1.1 Principles of conformity and dimensionless numbers 57 5.1.2 Possible limitations within the measuring range 59
5.2 Test results 63
5.2.1 Measured versus theoretical signals 63
5.2.2 Results of the forces Fx and Fy 68
5.2.3 Results of the pitching moment M 79
5.2.4 Results of the mean thrust T 82
5.2.5 Results of the efficiency ri 84
5.2.6 Observations during tests 86
5.3 Remarks on the test results 87
5.4 Comparison with other propulsion systems 88
5.5 Summary on the experimental verification 89
Conclusions and recommendations, 91
6.1 Conclusions 911 6.2 Recommendations 93 References A -Samen vatting Nawoord D
Symbols:
a amplitude of the path [ml.
AR aspect ratio of the wing 1-1
Z
Amotion projected area of the wings, motion [m 1,
Awing wing area i[m2j,
chord length of the wing lm1;
Ca lift coefficient ILA
Ca,
lift coefficient for a wing with infinite span E*1Ca, 8 lift coefficient for a wing with finite span
.0
Cd, total drag coefficient 17.1
Cw viscous drag coefficient [-I
Cwi induced drag coefficient 1[-11
d maximum thickness of therwing,, i[ml
D drag IlNI1
Elm kinetic energy loss ,[Nm]
f frequency of the periodic motion [Hz]
f(x), path (-1
Fr Froude number RI
FLJ force in pull rod j of bearing ir
IN
Fir( force Fx of bearing i I[N]
Ft), force Fy of bearing i fls13
Fa, normal force as function of time 1[N]
Fr resistance force [N]j
Fa suction force as function of time [Nil
Fx thrust as function of time [NI
Fy side force as function of time [N]
g acceleration of gravitation, [ms-2]
I 'moment of inertia [kgin21
J advance coefficient I-]
k factor Fl
capillarity lkgm-1s-2]
KT [thrust coefficient [-I
Km torque coefficient Ill
I length [m]
lift [NI]
M pitching moment as function, of time [Nm]
N/2 number of pitches IF
pressure
[Null
vapour pressure [Nm-2]
p pitch in11
R radius hmi
Re Reynolds number [-II
s span of the wing
[th]
It time IsII i
mean thrust with respect to time IN]
forward velocity [tit
sJi
va induced voltage in conductor a [V]
Vb induced voltage in conductor b I[V]
velocity along the path
in st
voltage [V]
We Weber number Hi
x displacement l[m]
9 Sideways velocity IIm ily
Y position Elul
dux' angular acceleration [deg s-2.]
s
AIM angular velocity [deg -1]
ea tangent of the path, (deg]
atm total angle [deg]
angle of incidence [deg]
a
angle of the base motion [deg]P angle of the added motion [deg]
y 'surface tension INm-2]
8 correction factor [-]
8 error HI
I
a cavitation number [ii
cc critical cavitation number [-,1
op 'peek pressure cavitation number [-1i
8 angle [deg]
I-] kinematic viscosity [m2s-11 II
1 efficiency [-")
s-1
co 'rotational frequency [rad si]
I
P density [kg m-3]
T. 'time ,period (Si
V V
1. Preface.
A thrust is to be generated to propel a ship. This thrust is necessary to overcome the drag of the ship, when it moves with a certain velocity through the water. This thrust can be generated with a sculling propeller. A sculling propeller consists of one or more, flexible or rigid, vertical or horizontal wings. To generate a thrust, the wings have to move in a specific way in the water. This motion is mostly a periodic sideways motion back and forth superimposed by a periodic pitching motion.
Numerous designs were made to realize sculling propulsion (for example Meindersma 1929, 1933, Barnes 1964, Hovers 1967, Hertel 1973, Isshiki 1980). Along with the constructive work, several theories for sculling propulsion were developed (Burgers 1933, Lighthill 1960, Wu 1961, Hertel 1961, Chopra 1971, Katz and Weihs 1978, Isshiki 1985 and Sparenberg 1960, 1967, 1984).
Studies to model the hydrodynamics of sculling propulsion by mathematical means (de Graaf 1970, Potze 1984) were conducted under the supervision of Sparenberg. There is a main difference between the studies of Sparenberg c.s. and other researchers. With the theories of Sparenberg c.s., the optimum motion of a wing generating a certain mean thrust with the highest efficiency is calculated. A prescribed motion of the wing(s) is used in the studies of the other researchers. For such a prescribed motion, the forces of the wing(s) with the resulting efficiency are calculated.
Hovers (1967) made a prototype of a sculling propeller and did a feasibility study on sculling propulsion under the supervision of Schlosser. Experiments and preliminary modelling showed that sculling propulsion was a possible principle for ship propulsion. De Visscher (1983) worked on a design study under the guidance of Schlosser. In this study, the possibilities for a mechanical realization of sculling propulsion for real ships were examined. Contributions for the performance of sculling propulsion were made by Meijer (1983) in that study. Results from theoretical work under the guidance of Sparenberg (Potze 1984) were used as well. The main conclusion of de Visscher was that the
modelling was still incomplete. The major problem was the unknown optimum motion of the wing to generate the thrust with a high efficiency. A study on the optimum motion under the guidance of Sparenberg resulted in the theory of optimum sculling propulsion by Potze (1987). With Potze's theory, the optimum motion for the wing(s) of a sculling propeller and the resulting efficiency can be calculated. The wings generate thereby a prescribed mean thrust. The forces and the moment as a function of time for a two dimensional wing are also calculated. The research of Potze was sponsored by the Technology Foundation (STW) in the Netherlands. One of the results was that the theory should be verified with experiments.
In this thesis, the results of an experimental verification of Potze's theory are presented. In this verification, a sculling propeller with one vertical, rigid wing under supposed free streaming conditions is considered. This research project was also sponsored by the Technology Foundation in the Netherlands.
The thesis is divided into three parts. A short discussion of the principle of sculling propulsion and Potze's optimization theory is given, followed by a theoretical evaluation of some of the methods and assumptions used. Also he design of a prototype with its power transmissions and the measuring devices is presented. The results of measurements are shown. From these results, conclusions about the theory and the construction are drawn.
The basic principles and Potze's theory of the hydrodynamics for sculling propulsion are discussed in CHAPTER 2.
A theoretical evaluation of some methods and assumptions used is presented in CHAPTER 3. In this chapter, the calculation of the thrust as a function of time is evaluated. A comparison with results of the steady state wing theory is made and a sensitivity analysis is carried out. Finally conclusions about the measurements to be performed on the prototype are drawn from this evaluation.
The design of the prototype is shown in CHAPTER 4. Special attention is given to the servo-systems with their path control devices. These devices are necessary to realize the optimum motion of the wing with high speed and accuracy. Also the measuring equipment with data-acquisition system is described in this chapter.
In CHAPTER 5 a measuring range is defined and the results of measurements on the prototype are presented. The results are evaluated and differences between the measurements and the theory are elucidated.
Conclusions and recommendations about the theory and the design of a sculling propeller are drawn in CHAPTER 6.
Because the theory of Potze (1987) is the object of this verification, the same definitions and symbols for the different quantities as in Potzes work are used in this thesis.
Definitions and names for quantities which are not used by Potze, are taken from the steady state wing theory (Abbott Von Doenhoff 1959) or defined in this thesis.
2. Sculling propulsion.
In this thesis, the optimization theory of the hydrodynamic behavior for sculling propulsion of Potze (1987) is verified. An idea of the structure and working principle of sculling propulsion is given first in this chapter. Next the optimization theory of the hydrodynamic behavior for sculling propulsion is discussed briefly.
2.1 Structure of a sculling propeller.
A thrust can be generated with a sculling propeller consisting of one or more wings moving side by side or behind each other in a fluid. The motion of a wing is mostly a combination of a periodic translation and a periodic rotation. An example of such a motion
is shown in figure 2.1. A wing is described by a chord length c, a span s and a given wing section. The wing has an axis of rotation, being the pivotal line. The geometry of such a wing is shown in figure 2.1. The span of the wing can have a horizontal or vertical
orientation.
chord
xis of rotation
ivotol point
Figure 2.1 Structure of a sculling propeller with rotational and translational motion of a wing
The different quantities involved in the modelling of the hydrodynamics of sculling propulsion are defined in a Cartesian coordinate system XYZ. The X-direction of this coordinate system is defined as the forward direction of motion. The sideways direction is in the Y-direction, while the span of a wing is parallel to the Z-direction. Normally the
2. Sculling propulsion. 3
sculling propeller moves with a given velocity U in the X-direction. The pivotal line of the wing describes a periodic path y = f(x) in the fluid. Mostly a periodic pitching motion around the pivotal line is carried out, while moving along the path. An example of such a motion is shown in figure 2.2. The path y is periodic with a time periodT,an amplitude a and a projected length b on the X-axis of one period. The length b is defined as the length period of the motion. The time periodTis equal to the quotient of the length period b and
the velocity U. In the following, the wing makes a periodic sideways and a periodic pitching motion, while the sculling propeller moves with a constant velocity U in the
forward direction.
4 2. Sculling propulsion.
Figure 2.2 Motion of a wing with relevant parameters for sculling propulsion
2.2 Working principle of a sculling propeller.
The performance of sculling propulsion is mainly determined by the motion of the wing. The generated thrust and the resulting efficiency 1 are the most important parametersin this process. The motion is determined by the velocity V of thewing's pivotal line and by the pitching motion around this line. The pitching motion is described by the total angle amt. This angle aioi is defined as the angle between the chordline of the wing and the X-axis. The different quantities are shown in figure 2.2. With this motionof the wing, a thrust Fx is to be generated.
The generation of thrust Fx is based on the existence of lift on a wing. LiftL is produced by a wing when moving with a certain velocity in the fluid. A lift Lonly exists when a
finite, non-zero angle of incidence p with respect to the direction of the "undisturbed" main stream of the viscous fluid flow exists. Along with this lift, a force D and a moment M on We wing exist. The forces L and D and moment M on the wing are defined in figure 2.3.
Figure 2.3 Definition of the forces L and() and moment M on a wing
In sculling propulsion, forces L and D and moment M are a result of the periodic motion of the wing. The periodic pitching motion is such that a finite angle of incidence p with respect to the direction of the "undisturbed" main stream exists (see figure 2.2).
It is known that the defined forces L and D and momentIM under the unsteady flow condition of sculling propulsion can differ from those forces and moment under steady state conditions. In literature, an explicit definition of the forces Land Dona wing in unsteady flow is not yet given. Still the definitions of the steady state wing theory are used to clarify the basic principle of the generation of the forces in sculling propulsion.
The normal force Fn on the wing is calculated by resolving the forces L and D in the normal direction of the chord line. A force F, in the direction of the chord is calculated by resolving the forces Land Dinthis direction. These two forces are calculated via:
Fn = L * cos l3 + D * sin 13 (1)
Fr = L * sin [3 + D * cos 13 (2)
as is also shown in figure 2.4.
The thrust Fx and the side force Fy are determined by resolving the normal force Fn and the force Fr in X- and Y-direction via:
Figure 2.4 Calculation of the normal Fr, and resistance force Fr
Fx = Fn * sin atot - Fr * COS atOt (3)
Fy Fn * cos atot + Fr * sin atot (4)
These forces are shown in figure 2.5.
With the forgoing modelling, an idea of the principle of generating thrust Fx with sculling propulsion is given. The motion of the wing in a sculling propeller determines for the most part the generation of thrust Fx and the resulting efficiency 1. The emphasis in modelling the hydrodynamics of sculling propulsion should therefore lie on the calculation of an optimum motion of the wing. Such a motion can be calculated with the condition that for example a given mean thrust T with high efficiency 11 is realized.
2.3 Optimization theory of Potze.
The optimization theory of Potze (1987) is one of the theories modelling the
hydrodynamic behavior for sculling propulsion. This theory consists of a two and a three dimensional part. In the two dimensional part, an optimum motion of a wing for generating a given mean thrust T with respect to time with the highest possible hydrodynamic
efficiency is calculated. This optimum motion and the resulting efficiency ri are calculated for a given geometry of the sculling propeller (Potze 1987 page 13). Also the forces Fx and Fy and pitching moment M on the wing as a function of time are calculated in the two dimensional part.
With the three dimensional model, the influence of the wing shape and the viscous resistance of the fluid on the mean value of thrust and on the value of the efficiency is calculated. The motion of the wing can be chosen freely in this three dimensional model.
6 2. Sculling propulsion.
Figure 2.5 Calculation of thethrust Faand side force Fy
Inutile following, the principles of Potze's theory are explained. Also the essential calculation methods in the model of Potze are described. Results of calculations are shown as well.
2.3.1 The principles
As already mentioned, the theory consists of a two and a three dimensional model. In the two dimensional model, a wing is modelled as a flat plate with no thickness d, with an infinite span s and a chord length c. The influence of the viscosity is not taken into account in this model. In the three dimensional model, the wing has a chord length c, a thickness distribution over the chord length (wing section) and a finite span s. The influence of the viscous resistance of the fluid is also taken into account in the latter model. The geometry of a two and a three dimensional wing is shown in figure 2.6.
Three different geometries of a sculling propeller can be analyzed with the model of Potze, namely (see figure 2.7):
- one wing moving along a periodic path y = f(x);
- two wings moving side by side with non-intersecting periodic paths y = f(x) and y = g(x);
- two wings, one moving behind the other with intersecting periodic paths y = f(x) and y = h(x).
The span of the wing can have a horizontal or a vertical orientation.
In this research, the two dimensional model is linked with the three dimensional model via the optimum motion. This motion is calculated for a two dimensional wing to generate a given mean thrust T with the least possible energy loss or in other words the highest
single path 2 dimensional wing infinite span no wing section chord c 8 2. Sculling propulsion.
Figure 2.6 Geometry eta two and a three dimensional wing
non-intersecting paths dimensional wing span s chord c wing section (symmetric)! intersecting paths
Figure 2.7 Different geometries of a sculling propeller
hydrodynamic efficiency. This hydrodynamic efficiency ri is defined as (Pine 1987 page 13):
T U
= (5)
T * U + Eioss
Thereby T is the mean thrust, U is the forward velocity andNoss is the hydrodynamic
energy loss due to the motion of the wing.
An optimum motion for a three dimensional wing cannot yet be calculated. Therefore a motion based upon the calculated optimum motion is applied to the three dimensional wing (Potze 1987, page 116). The optimum motion is adjusted to compensate the losses in thrust for a three dimensional wing. Thus the same mean thrust T for both the two and three dimensional wing is generated (see section 2.3.3). The link between the two models is also explained in figure 2.8.
Input: confidtration data
2D-model with wing: infinite Wan fiat plate nonVISCOUS 2D vorticity distribution Optimum motion Ii
3D-rrodel with wing:
finite span
thickness distribution viscous drag
3D vorticity distribution
ii
Forces
Forces and
pitching moment
loss calculation
Figure 2.8 Link between the two and three dimensional model
It was hoped by Potze (Potze 1987 page 65) that the energy losses will be small when a three dimensional wing is moving in the given way. The resulting mean thrust T and efficiency ri of this adjusted optimum motion are calculated with Potze's three
dimensional model. In this three dimensional model, the influence of the finite span, the
2. Sculling propulsion. 9
*
-thickness distribution of the wing and the viscous resistance of the fluid is considered. The efficiencies calculated by Potze show that the difference in energy loss between a two and a three dimensional wing is small for a given situation. The forces Fx and side force Fy as a function of time on a three dimensional wing are not calculated by Potze.
The theoryofPotze (1987) is examined through the results presented in this thesis. A geometry of a sculling propeller with one wing having a vertical orientation is considered. The wing moves according to a motion based upon the optimum motion. The optimum motion is calculated with the two dimensional model. The resulting mean thrust and the efficiency are calculated with the two dimensional and the three dimensional model. The forcesFxand Fy as a functionof time can be calculated accurately with the two
dimensional model only. The graphs and figures in the following discussion of the two and three dimensional model are the resultofcalculations for cases to be verified. These results are such that they can justifiably be considered to be reliable.
2.3.2 The two dimensional theory.
With the two dimensional model of Porze, the optimum total angle am, of a two dimensional wing to generate a given mean thrust T with the highest efficiency is
calculated. The pivotal line of the wing moves thereby along a given path y with a constant forward velocity U. Several approximations and assumptions to formulate the problem are made by Potze. These are:
- the fluid is incompressible and inviscous; - the wins are rigid;
- the span s is large in comparison to the chord length c and the length b of the path y; - the inflow is homogenous;
- the wings are not heavily loaded.
10 2. Sculling propulsion.
In first instance, a cosine function for the path y is chosen (Potze 1987, page 11) being:
y = a * cos 2*Tr*f*t (6)
where a is the amplitude, f is the frequency of motion and t is the time.
For the solution of the optimization problem, the motion of the wing is divided in a base motion and an added motion (Potze 1987, page 9). The total angleaimconsists of the tangent angle at, the angle a of the base motion and the angle 13 of the added motion. These angles are shown in figure 2.9. The angle al is equal to the tangent of the path y=f(x) of the wing. The angle a of the base motion is defined as that angle whereby no kinetic energy is left behind in the fluid. Hence, no free vorticity is shed into the fluid. As a result, no mean thrust T with respect to the time is generated. This angle a is superimposed on the tangent angle at.
The angle a of the base motion is calculated with the help of the vorticity distribution on the wing. This motion is calculated with the condition that the circulation around the wing is constant. An example of the calculated angle a along the path is given in figure 2.10.
15 se 3 3 9
15
0.00 0.17 0.35 0.52 0.70 time failFigure 2.10 Calculated angle cc of a base motion
0.87
Situation with:
cosine path y=f(x)
amplitude a: 0.5 m frequency f: 1.15 Hz velocity U: 2.5 m/s mean thrust T: 89 N efficiencyn:0.888 wing: s = 0.4 m c = 0.1 m
The angle p of the added motion is that angle with which a given mean thrust T is gemirated. This mean thrust T should be generated with the least possible loss of kinetic energy. The angle p is superimposed on the angle at plus a. To deliver a thrust, free vorticity is to be shed into the fluid by the wing. This vorticity is assumed to be shed at the trailing edge of the wing. This vorticity is then carried away with fluid particles passing this trailing edge (Potze 1987, page 11). Shedding free vorticity means loss of kinetic energy. This loss of kinetic energy is minimized under the condition that a given mean thrust T is generated. The optimum angle 3 of the added motion is determined with the calculated optimum vorticity. An example of an angle p along the path is shown in figure 2.11.
1 5 9 3 th
3
9
ii /5
Situation with: cosine path y amplitude a:0.5m frequency f: 1.15 Hz velocity U: 2.5m/s mean thrustT: 89 N efficiency11: 0.888 wing: s = 0.4m C =0.1 m 12 2. Sculling propulsion.Figure 2.12 Calculation of the thrust Fx and side force Fy
0.00 0.17 0.35 0.52 0.70 0.87
time DO
Figure 2.11 Calculated angle°tan added motion
The total optimum motion of the wing along the path is determined when knowing the angles a and 13 as a function of time. The mean thrust I is given in the calculation. The resulting hydrodynamic efficiency ri is calculated with the use of the calculated
hydrodynamic energy loss. Out of the calculated vorticity distribution, the resulting normal force F. suction force Fs and pitching moment M as a function of time are determined. For this calculation, Bernoulli's law for unsteady flow is used. The thrust Fx and side force Fy are calculated from the normal force Fn. the suction force Fs and the total angle atot as shown in figure 2.12.
300 180 60
60
180
300
0.00 yzt(x) Fx 20 total motion Fy 20 0.17 0.35 0.52 0.70 off* lei Situation with: cosine path y amplitude a: 0.5 m frequency f: 1.15 Hz velocity U: 2.5 m/s mean thrust T: 89 N efficiency 0.888 wing: s = 0.4 m C= 0.1 m 0.87 10 6 26
10
0.00 0.17 0.35 0.52 rmets.1Figure 2.13 The optimum motion, the thrust Fx, side force Fy and pitching moment M
The optimum motion, the thrust F5, side force Fy and pitching moment M along the path for a specific situation are shown in figure 2.13.
2.3.3. The three dimensional theory.
With the three dimensional model, the resulting mean thrust T and efficiency r) for a given motion of a wing can be calculated. These two quantities can be calculated on the basis of the chosen free vortex layers. Several assumptions and approximations for the solution of the three dimensional problem are made by Potze, namely:
the fluid is incompressible;
- the fluid is at "rest" infinitely far in front and at the sides of the wing; - the wing is modelled as being rigid.
In the theory:
- the influence of the thickness of the wing is linearized;
0.70 0.87
- the wing is symmetrical with respect to the planform and midspan;
- the efficiency of three different geometries for the planform of a wing as shown in figure 2.14, can be calculated;
- the fluid surface is modelled as being rigid or as being free.
The calculation results presented next are legitimate for a rigid fluid surface and a rectangular planform of a wing.
rectangular
elliptic
Different wing types
Figure 2.14 Three different shapes of the wing
The solution to the problem is obtained by representing the flow around the wing by vortex layers on the planform and on the wake and by source layers on the planfomi of the wing. With this representation, the three dimensional velocity potential can be determined. The mean thrust T is calculated with the balance of momentum induced by the shed
vorticity far behind the wing over one time period in the X-direction. This mean thrust is corrected with the X-component of the total viscous force. This viscous force acts in the opposite direction of the mean thrust. The viscous force Fv is determined by equalizing the three dimensional lift L to the calculated normal force Fr, on the wing. This normal force Fn along the path is calculated from the velocity potential with the use of Bernoulli's law for unsteadyflow.From the lift L, the lift coefficient Ca is calculated with the use of the velocity V of the pivotal line. Then, the viscous force Fv is approximated with the help of the Ca/Cd characteristic for the wing section under steady flow condition (Abbot, von Doenhoff 1959). The total viscous drag is calculated by adding the components of the viscous force Fy in the X-direction for every time step over one time period of the motion. The mean thrust T is corrected with this total viscous drag. This process of calculating the viscous force is visualized in figure 2.15. The influence of the viscosity is thus modelled with this quasi-stationary method.
As already mentioned, a motion based upon the calculated optimum motion of the two dimensional model is used to calculate the efficiency ri and the mean thrust T for a three
14 2. Sculling propulsion.
Figure 2.15 Calculation of the thrust Fx
dimensional wing. The calculated optimum motion is adjusted to maintain a given mean thrust T for both the two and the three dimensional wing. The mean thrust T forathree dimensional wing is in general lower than for a two dimensional wing for the same motion due to the extra losses. The optimum motion is adjusted via:
awl = at + a + k *13 (7)
where k is a correction factor and k> 1.
The mean thrust T is calculated from the balance of momentum induced by the shed vorticity far behind the wings over one time period in the X-direction. The forces Fx and Fy for a three dimensional wing as a function of time are not calculated by Potze. The used methods in his three dimensional model do not give accurate results for the suction force
Fs as a function of time. The overall influence of the suction force Fs is however taken into account in the calculation of the mean thrust T.
In the verification, the forces Fx and Fy as a function of time are approximated by using only the normal force Fn and the total angle awl (see figure 2.15). The calculated thrust Fx
is corrected with the component of viscous force 17,, in X-direction. An example of the thrustFxas a function of time calculated in this way is shown in figure 2.16.
Calculation results of this three dimensional model for a case
tote
verified are presented in figure 2.17a. These results are the total angle atot along the path, the mean thrust T and the hydrodynamic efficiency ii. The thrust Fx and side forceFyas a function of timepresented in figure 2.17b are approximate results obtained from the normal force Fri only. This force Fn is used to calculated the viscous force in Potze's theory.
The results for the mean thrust T, the efficiency ti and partly for the forces Fx and Fy for a three dimensional wing willbe used for a comparison of the theory with measurements.
300
220 140 6020
100
0.00 0.17 0.35 0.52 0.70 0.87 t I map to)Figure 2.16 The approximated thrust Fx as a function of time
60
60
0.00 0.17 0.35 0.52 0.70 0.87
time. NO
Figure 2.17a Result for the total angle snotof the three dimensional theory.
16 2. Sculling propulsion. Situation with: cosine path y amplitude a: 0.5 ay frequency f: 1.15 Hz velocity U: 2.5 m/s mean thrust T: 89 N efficiencyn: 0.888 wing: s = 0.4 m c = 0.1 m wingsection: NAGA 0015 Situation with: cosine path y amplitude a: 0.5 m frequency f: 1.15 Hz velocity U: 2.5 m/s mean thrust T: 89NI efficiency n: 0.888 wing: sso0.4 m C =0.1 m wingsection: NACA 0015 36
1
1212
2. Sculling propul 17 8 st 300 180 BO
60
180
300
Fat 30 Fie 30 ""14\ 0.00 0.17 0.36 0.52 0.70 0.87 time (s12.4 Summary on sculling propulsion.
In this chapter, an idea of the structure and the working principle of sculling propulsion is given.
The theory of Potze consists of two models, namely a two and a three dimensional model. A motion based upon the optimum motion calculated for a two dimensional wing is applied to a three dimensional wing. This motion for a three dimensional wing is analyzed with the three dimensional model.
The optimum motion of a wing is defined as that motion whereby a given mean thrust T is generated with the least possible kinetic energy loss. This optimum motion is calculated for a given geometry of a sculling propeller. With the two dimensional model, also the resulting efficiency, the forces and pitching moment as a function of time for a wing with infinite span without thickness are calculated. The mean thrust T is given in the
calculation. The influence of the viscous resistance of the fluid is not taken into account in this model.
In the three dimensional model, the resulting mean thrust and efficiency of a three dimensional wing moving according to a motion based upon the optimum motion are calculated. The influence of a finite span and a thickness distribution of the wing on value of the mean thrust and of the efficiency are taken into account in this model. Also the influence of the viscous resistance of the fluid is considered.
In both the two and the three dimensional theory, the mean thrust T is calculated from the balance of momentum induced by the shed vorticity far behind the wing over one time period in the X-direction. The thrust Fx and side force Fy as a function of time are calculated in the two dimensional, but not in the three dimensional model of Potze.
The pitching moment M for a two dimensional wing is calculated while the pitching moment for a three dimensional wing is not calculated in the model of Potze.
3. Theoretical evaluation.
The theory of Potze (1987), as reviewed in the previous chapter is the subject of the following evaluation. In this evaluation, the methods of that theory will be applied to a sculling propeller. The results of calculations with the theory will be examined.
The evaluation toke place within given limits. For this purpose, a basic geometry of a sculling propeller is defined. The methods used in the theory of Potze are applied to this geometry. Some results of the theory for sculling propulsion are compared with results of a
steady state wing theory. A sensitivity analysis is carried out to give an insight into accuracy demands. Conclusions for measurements are drawn from the results of this evaluation.
3.1 Scope of the evaluation.
In the evaluation, a basic geometry of a sculling propeller with the following properties is used:
- the sculling propeller consists of one wing; - the span of the wing has a vertical orientation; - the dimensions of the wing are:
chord c = 0.1 m; span s = 0.4 m;
- the wing section is a NACA 0015;
- the motion of the wing is based upon the optimum motion of a two dimensional wing; - the velocity U has a maximum of 5.0 m/s;
- the amplitude a of the cosine path has a maximum of 0.5 m; - the frequency f of the periodic motion has a maximum of 2.5 Hz; - the wing generates a mean thrust T of maximal I(X) N.
pivotal line (axis of rotation) cr0 1 anti-ventilation plate wing section
i0
015m pivotal point NACA 0015Figure 3.1 Geometry of the wing
The planform of the wing is rectangular. The tip of the wing is rounded with a varying radius along the chord. This geometry of the wing is shown in figure 3.1.
A prototype has to have the same dimensions as this theoretical sculling propeller. In this defined geometry, the limitations of the towing tank of the University of Technology in Delft are considered. The towing tank has the following dimensions:
- length: 90 m; - depth : 1.25 m; - width : 2.5 m.
Calculations with the theory of Potze give the following maximum values for the different quantities:
the maximum total angle atoi . 600;
- the maximum angle a of the base motion 150;
the maximum angle [3 of the added motion 90; the maximum normal force F,, on the wing : 250 N; the maximum suction force Fs on the wing
(for a two dimensional wing only) : 100 N; - the maximum thrust Fx produced by the wing : 250 N; - the maximum side force Fy produced by the wing : 250 N;
- the maximum pitching moment Mon the wing : 15 Nm.
The evaluation toke place within these set limits.
3.2 Evaluation of the different models.
Assumptions and approximations are made in the theory of Potze. Some of the assumptions and approximations are evaluated in this section. The results of this evaluation give valuable information for the measurements to be done. The examined
points are:
the calculated thrust Fx and pitching moment M for a three dimensional wing;
a comparison of results of the two and three dimensional model with comparable results of the steady suite wing theory;
- the sensitivity of the results for variations in the motion of the wing.
3.3 The calculated thrust Fx and pitching moment M.
In an experimental verification, the quantities as a function of time are essential quantities, because these quantities are measurable. It is therefore necessary that quantities as a function of time are calculated with sufficient accuracy. Then a direct comparison with measured quantities is possible. Mean values of measured quantities can be calculated from the measured quantities as a function of time. In this way, a comparison of mean values is possible. The accuracy of these mean values is dependent on the measuring accuracy. Such a comparison normally takes place at a lower accuracy level than the accuracy level of measured quantities as a function of time.
20 3. Theoreticalevaluation. : -- :
-Thrust F. without and with the suction force Fs.
Figure 3.2 Influence of the suction force F. on the thrust Fs and side force Fy
The thrust Fx and side force Fy as a function of time are only calculated accurately for a two dimensional wing. These forces can however not be used to compare the theory with the measurements due to the absence of relevant influences in the two dimensional case.
In the three dimensional model of Potze (1987), the mean thrust T is calculated from the balance of momentum induced by the shed vorticity infinitely far behind the wing in the X-direction over one time period (Potze 1987 page 51). In this mean thrust, the overall influence of the suction force is included. The suction force Fs as a function of time cannot yet be calculated with sufficient accuracy in the three dimensional model of Potze. The thrust Fx and the side force Fy as a function of time can therefore not be calculated accurately by Potze.
In this evaluation of the three dimensional model, the thrustFx and side force Fy are approximated by using the component of the normal force SI in the X- and the Y-direction
rust Fx Trust Fx with Fs without Fs -25 0.00 0.40 0.80 120 160 2.00 Situation with: cosine path y amplitude: 0.5 m frequency: 0.5 Hz velocity U: 2.5 m/s mean thrust: 32.3 NI efficiency: 0.861 wing: c = 0.1 m S = 0.4 m time Eel
Figure 3.3 The thrust Fs with and without the suction force Fs for a 2 dimensional wing
3.Theoreticalevaluation. 21 100 75 50 8 -§ 25
respectively. This force Fn is calculated in Potze (1987) and used in the calculation of the viscous force. In figure 3.2, the possible influence of the suction force on the thrust Fx and side force Fy is shown. The influence of the suction force Fx on the thrust Fx and side force Fy can be calculated for a two dimensional wing with the theory of Potze. In this
verification, calculations within the limits of the parameters involved are done, showing differences of 10 to 25 % in the maximum amplitude of the thrust F. An example of the result of such a calculation is shown in figure 3.3. It is assumed here that this difference in maximum amplitude of the thrust Fx will not be significantly lower for a three dimensional wing.
In the three dimensional theory, the pitching moment M as a function of time is not calculated in contrast to the two dimensional theory of Potze. The pitching moment for a two dimensional wing is calculated from the pressure distribution around the wing. This pressure distribution is also used for the calculation of the normal force Fn on a two and a three dimensional wing. An idea of the magnitude of the resulting pitching moment M of a three dimensional wing can be obtained by comparing the normal force Fn for a two and a three dimensional wing. In this evaluation, it is assumed that the pressure distribution for a two and a three dimensional wing mainly differ; in magnitude.
Frc 2D Fre 30 300 180 60
60
180
300
0.00 DOFigure 3.4 Normal force Fn of a two (2D) and a three dimensional (3D) wing
An example of the normal force Fn along the path according to the two and three dimensional calculations is shown in figure 3.4. The maximum magnitude of the normal force Fn for the three dimensional wing is about 15 % lower than for the two dimensional wing. On the basis of this result, it is expected that the maximum magnitude of the pitching moment M for the three dimensional wing will also be about 15% lower than for the two dimensional wing.
22 3. Theoretical evaluation. Situation with: cosine path y amplitude: 0.5 m frequency: 1.15 Hz velocity U: 2.5 m/s mean thrust: 99.7 iN efficiency: 0.884 wing: c = 0.1 m S = 0.4 m
wingsectionNAGA 0015
0.17 0.35 0.52 0.70 0.87
The conclusion is that the calculation of the suction force Fs and the pitching moment M as a function of the time should be added to the three dimensional theory of Potze. This will lead to more accurate results of the forces Fx and Fy for a three dimensional wing as the here calculated approximations of these forces. Also the results of pitching moment M for a three dimensional wing will be more accurate. More accurate results will lead to a better comparison of the theory and the measurements. Another method for the solution of Potze's model will probably be necessary. Because it is not the purpose of this verification to improve the model, such a research is not performed here.
3.4 Comparable calculations.
With the two dimensional model of Potze, an optimum motion for the two dimensional wing is calculated (see section 2.3.2). It was hoped by Potze that a motion based upon this optimum motion would possibly lead to low energy losses for a three dimensional wing. A comparison of results of the efficiency done by Potze (Potze 1987, page 71) shows that the difference in the maximum hydrodynamic efficiency and the efficiency of a motion based upon the optimum motion is small. This also means that the kinetic energy loss of this calculated optimum motion is small. In literature, no other theories for calculating an optimum motion of a wing are found. A comparison of calculated optimum motions therefore cannot be performed. In the available literature on possibly "optimum" sculling propulsion (DeLaurier, Harris 1982), the performance of prescribed motions of wings is calculated. The angle mot as a function of time is mostly a sine function. The pivotal line of the wing moves sideways, also according to a sine function but with various phase shifts. The main stream of the fluid has a constant velocity. Measurements by Wu (1961), Hertel (1961), and Chopra (1971) showed that a sine function for the pitching motion and a cosine function for the sideways motion of the wing should lead to the "highest"
efficiency. This ''highest" efficiency is not further specified. However, the motion with the "highest" efficiency comes reasonably close to the optimum motion calculated with Potze's theory.
In the following, a comparison of the calculated thrust Fx and mean thrust T for the two and the three dimensional model with results of the steady state wing theory (Abbot, Von Doenhoff 1959) is carried out. The point of view in this comparison is that the unsteady flow conditions of sculling propulsion are such that the steady state wing theory still gives accurate results (Beddoes 1984, Coene 1989). The results of the steady state wing theory can be qualified as reliable, because this theory is verified with experimental claw. From this comparative calculations, conclusions about the results of Potze's model are drawn. 3.4.1 Method of calculation.
Calculation methods for lift and drag were drafted on the basis of theoretical and experimental results of wing sections in steady flow (Abbot, Von Doenhoff 1959). It is possible to calculate the lift, the loss of lift due to a thickness distribution and finite span. Also the drag due to the finite span and the viscous flow of a wing can be calculated. Comparable calculations are made with the use of the angle p of the added motion. This angle p is mainly responsible for generating thrust in sculling propulsion.
The method of calculation is discussed briefly next.
The lift coefficient for a two-dimensional wing is (Houghton. Carruthers 1982):
Cap. =0.1 *o Ks)
The lift coefficient for a wing with an infinite span and a NACA 0015 wing section lit (Abbott, Von Doenhoff 1959, see also figure 3.5):
'Ca.& = 0.0967 * p (9)
The lift coefficient for a wing with a finite span and the given wing section is (Prandt1,, Tietjens 1957):
7r* AR * Ca,s
Ca <0.095*13 (loy
Ca,8 + it * AR * ip
in which AR is the aspect ratio of the wing. The Ca in (9) is equal to the lift coefficient in (8). The lift L is calculated with:
L =0.5 * p Ca * V2 * Awing
where Awing is the area of the planform of the wing and V is the velocity of the pivot of the wing along the path y = f(x) (see figure 2.6).
24 3. Theoreticatvaluation.
.z
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Figure 3.5Polardiagram of a INACAr0015 wing sectionr
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3. Theoretical evaluation. 25
The drag due to the tip vortices is calculated with:
ca2
Cy/. *(14-43)< 0.0075 (12)
* AR
where Ca is the lift coefficient (9). This drag is called the induced drag (Abbott, von Doenhoff 1959). The factor 8 in (11) is a correction for a non-elliptic pressure distribution on a wing area. For a rectangular wing shape, this factor 8 is equal to 0.04.
The total drag coefficient Ca is equal to the induced drag coefficient Cwi plus the viscous drag coefficient C. The viscous drag coefficient Cw is determined with the use of the polar diagram of figure 3.5.
The total drag D is:
D = 0.5 * p * Cd * V2 * Awing (13)
The thrustFx bra two and a three dimensional wing is calculated from the lift L and drag D and the tangent angle at via:
Fx = L * cos at - D * sin at
This thrust Fx is compared with the approximated thrust Fx for a three dimensional wing. The thrust Fx without the drag component is compared with the thrust Fx of Potze's model for a two dimensional wing. The mean thrust T for the two theories is compared as well.
In these calculations, limitations in the performance of the wing due to possible separation of flow are not considered. These limitations are also not modelled in Potze's theory. It is however known that limitations due to laminar bubble separation (Selig, Fraser, Donovan
1989) can occur for flow conditions with a Reynolds number below300.000.This separation of flow can result in a lower maximum lift coefficient than used in the
calculations. It is unknown to which extent the performance of the wing is limited by these phenomena. Accurate models of these phenomena are not yet available. The theory of Potze and the steady state wing theory only give reliable results when these phenomena do not limit the performance of the wing.
3.4.2 Results of comparative calculations.
Calculation were done within the limits of the parameters involved. The result fora situation to be verified is shown in figure3.6.In this figure, the thrust Fx for a two and a three dimensional wing according to the steady state wing theory and according to Potze's theory are presented. Only a qualitative comparison for the thrust Fx as a function of time for a three dimensional wing is done (see section 3.3).
A comparison of the calculation results leads to the following results:
- the difference in thrustFxbetween the two theories for a two dimensional wing is small; - the differences in thrust Fx between the two models for a two dimensional and a three dimensional wing are small for frequencies of motion below 1 Hz as the calculation 1
results showed;
- the calculation results show that the difference in thrust Fx between the two models increases with increasing frequency of motion for a three dimensional wing.
- the resulting mean thrust T for a three dimensional wing in the steady state wing theory is about 2 to 10 % higher than in the theory of Potze;
- a time shift between the occurrence of the maximum thrust as calculated with the steady state wing theory and as calculated with the theory of Potze exists;
- a comparison of viscous drag is not included, because the method used in Potze's theory is the same as in the steady state wing theory.
The thrust Fx for a three dimensional wing is expected to be higher than given in these results (see section 3.3). The differences in the thrust Fx for a three dimensional wing of both theories will probably be less than found in these results.
The calculation results show that the theory of Potze and the steady state wing theory lead to a thrust Fx of the same magnitude for a two dimensional wing. Differences in the thrust Fx for a three dimensional wing are found between the two models. These differences increase with increasing frequencies of motion.
The difference in the mean thrust T between the two theories is not as high as found in the thrust F. This is partly due to the fact that in the calculation of the mean thrust in Potze's three dimensional theory, the overall influence of the suction force is taken into account.
300 220 140 "-(f) 60 -20 -100 26 3. Theoretical evuluution. Situtaion with: cosine path y amplitude:0.5 m frequency: 1.15 Hz velocityU: 2.5 m/s mean thrust:99.7 N efficiency:0.884 wing:c = 0.1 mr s = 0.4 m
wing sectionNACA 0015
Explanation:
stat: stationarytheory
Pots:theoryof Pots
0.00 0.17 0.35 0.52 0.70 0.87
time Is)
Figure 3.6 Thrust Fx of a two (2D) and three (3D) dimensional wing according to the two theories
Conclusion is that the energy loss of the calculated optimum motion is small. With the steady state wing theory, relative accurate results of the thrust Fx for a two dimensional wing and for the mean thrust T for a two and a three dimensional wing can be calculated
Fl2D
Pout
POD Fm2D F. 3D Potze stat. stat.
within the limits of this comparison. The difference in thrust and in mean thrust between the two models is within 10 %.
3.5 Sensitivity analysis.
In this section, the sensitivity of the thrust and the efficiency of a three dimensional wing for variations in the calculated angle a + p is examined. This analysis will give valuable information for the accuracy with which the motion is to be realized. Also information about the accuracy for measuring the different quantities will be obtained.
In this sensitivity analysis, two cases are examined. In the first case only the angle p of the added motion is varied. Thereby the same angle a of the base motion is used with the different angles The angle a +13 is varied in the second case. An estimate of the effect of the base motion on the efficiency can be made by comparing the results of both cases. Both cases are examined, although a separation of these two angles a and p in the three dimensional case is not realistic (Potze 1987, page 64).
The chosen functions for the approximation of the angle p of the added motion are: - a sine function;
- a trapezium-like function; - a triangular-like function.
These functions are shown in figure 3.7.
triangular sine trapezium optimum
time steo
Figure 3.7 Chosen angles 13 of the comparison
The sharp turns in the trapezium-like and the triangular-like functions are smoothed to avoid infinite acceleration. These functions are chosen, because of the low angular acceleration occurring in large parts of the motion.
Situation with: wing: c = 0.1 m
s = 0.4 m
wing section NACA-0015
3. Theoretical evaluation. 27
6
2
I-1
For a comparison, the efficiency is the essential parameter. The resulting efficiencies ri are:
angle : optimum sine trapezium triangle
0.890 0.883 0.882 0.880
for the situation characterized by: - a forward velocity U of 2 m/s, - a frequency f of motion of 0.5 Hz and - an amplitude a of 0.5 m.
- a resulting mean thrust T of 25.4 N.
The efficiencies of the three comparative angles atom are lower than the efficiency of the optimum angle atm The differences in the efficiencies are below 1.2 %.
In the second case, the angle a + p is varied. Only the results of the optimum angle a + [3 and a sine approximation of this angle are presented. Here also two possibilities are examined. First the optimum angle a + p is approximated as closely as possible by the sine function (1). Second an equal mean thrust T is to be generated for both the case with the optimum angle a + p as with the approximated angle (2). Result of the calculations is:
function : optimum (1) (2)
: 88.9 N 92.3 N (+3.8 %) 88.9 N (-)
: 0.888 0.856 (-3.5 %) 0.859 (-3 %).
for the situation characterized by: - a forward velocity U of 2.5 m/s, - a frequency f of 1.15 Hz and - an amplitude a of 0.5 in.
As the results show, the differences are small. The efficiency is about 3 % lower for the sine function in relation to the optimum angle for an equal mean thrust T. A good fit of the angle a +13 with the sine function leads to a mean thrust T which is about 3.8 % higher
than the mean thrust for the optimum angle. In the latter case, the efficiency for the sine function is about 3.5 % lower than for the optimum angle.
From this analysis follows that different. well chosen functions for the angle 13 do not influence the efficiency much, while maintaining the same mean thrust T.
If the optimum angle a + [3 is approximated by a sine function, the mean thrust T will be about 4 % higher while the efficiency is about 3.5 % lower. The efficiency for the case where the angle a + p is nearly approximated by a sine function will be about 4 % lower as for the optimum case, while both cases have the same value of mean thrust T.
A comparison of both the results of the variation of the angles shows that the influence of the base motion on the performance of a sculling propeller is also small. The results above are legitimate within the limits of the parameters involved.
28 3. Theoretical evaluation.
divided into two main groups: design parameters with a high manipulative ability and constant value parameters with a low ability. The value of a design parameter is either
determined by one or a set of mathematical expressions, or must be provided by the
designer. The value of a constant cannot be influenced, typical examples of parameters
with a low manipulative ability are physical properties or predictors in regression
models [Sen. 1990].
Mathematical relationshipsdescribe the dependency between the parameters. Using this
definition, the '=' sign in mathematics codifies a dependency among the design
parameters. This definition is important as a dependency defines a direction in the relationship, which can either be valid in one direction or in both directions.Frequently more than one alternative (empirically or physically based) relationship exist for predicting a design characteristic. When comparing these alternatives, the following statement is followed [maeCallum. 1990]: "Itis in the nature of the design process that increasing accuracy (for predicting a design characteristic) can be modelled with increasing availability of detail
(read: 'parameters with high discriminative and
manipulative abilities")"
The designer should however be aware that this statement is only valid when the design
problem requires examining the influence of those design parameters which are not included in the models with less detail. Motivated by the above given statement, the
codification of mathematical models starts with a selection of relevant design
parameters. Which design parameters are relevant and which are not, depends on the design problem at hand. For example. when calculating the submerged endurance athoovering speed the propulsion power can almost be neglected compared to the
required hotel load while at burst speed the opposite effect occurs.Conditional expressions describe the conditions and ranges of validity beyond which
the model is not valid. Specifically, relationships based on empirical knowledge, have
a limited validity, dependent on the context in which the relationship is derived. But
also the selection or inter- and extrapolations from a table of values can be limited by conditional expressions.
Coding geometric knowledge
Thegeometrical knowledge is codified by the size and shape of the space required for
or provided by components in the boat. The geometrical knowledge about the required
space is defined by the object properties: height. length. width, area and volume. The geometrical knowledge about the available space is defined by the properties of the space boundaries. Figure 5.1 shows examples of the object properties. Note that the
required height for the console is smaller than the overall height. Typically, the shape
of a console is different for each submarine and depends on the size and shape of the
available space. The correct volume and area requirements must ensure that sufficient
Figure 5.1 Transverse and longitudinal cross section of control centre in a pressure hull
Coding topological knowledge
The topological knowledge is codified by the relative location of components from
which a unique design is assembled. This knowledge expresses the characteristics of the spatial layout or also called arrangement. The spatial layout contains the spatial layout of spaces and the spatial layout of components. In literature several methods can be found for codifying the topological knowledge.
Coding spatial layout of spaces
In literature two different methods are presented for defining the spatial layout of spaces: the first method proceeds from structural elements to spaces, and the other
method proceeds the reverse way. The structural elements are the boundaries ofthe spaces, which can either be made from real materials or from nothing. The last type of boundary is called imaginary. Examples of structural elements in a ship are bulkheads
and decks.
From structural elements to spaces starts with defining and sizing structural elements
followed by the determination of enclosed spaces. This method is analogous tothe representation of graphical objects by surface boundaries as used in computer graphics [Foley, 1994]. Several references use this method in ship design Ken, 1987][-tills. 1989][Lee, 19911[Laansina. 1992]. These references show two main advantages of the method: structural elements can be defined at an arbitrary location, thereby generating
every requested spatial layout. and each structural element can be given a meaning. However this method has also some drawbacks: changes in the layout can only be achieved by changes made at the structural element level, and moving a space to
another location is impossible because only structural elements can be moved. From spaces to structural elements starts with defining and sizing spaces followed by
the determination of the structural elements. This method is analogous to the
representation of graphical objects by volumetric solids as used in computergraphics [Foley. 1994]. The main advantages of this method are that the shape and size of the space can be defined with a limited amountof data. and changes in the spatial layout.like adding, moving or deleting, are relatively uncomplicated. The main limitation of this method is the required re-definition of the structural elements when spatial changes
During conceptual design uncomplicated adding, moving or deleting of spaces supports
the exploration of possible solutions more than uncomplicated adding. moving or deleting meaningful structural elements. Thus, the method from spaces to structural
elements is more efficient for coding the topology of spaces. The hierarchy of available
spaces is shown in figure 5.2. The hull at the top level is divided along its length (by bulkheads) into one or more compartments. At the second level each compartment is
divided along its height (by decks) into one or more cells. At the lowest level each cell
can be divided along its length (by separation walls) into one or more rooms.
Compartment Cell
Structural elements
Figure 5.2 Definition of compartments, cells and structural elements for a surface ship
Coding spatial layoutofcomponents
In literature two different methods arc presented for defining the spatial layout of
components: locating the components at a specific location or locating the components at a non-specific location.
Coding the locations of components at a specific location can be achieved by a
drawing, a grid [Andre, 1986], or a nodal figure [Con, 1987]. The location of each component can accurately be specified. However, the designer is confronted withspecifying a large amount of topological information, often with an accuracy unsuitable
to the conceptual stage of design.
Alternatively, the location of components can be given non-specifically. Coding
topological knowledge about locating components non-specifically can be achieved by
an allocation-sequence of components to a space. A limited amount of topological knowledge can be coded. For example topological knowledge such as adjacency or
separation can not be represented. As a consequence, allocating objects non-specifically does not involve checking that a viable layout of objects within that space is achieved.
During conceptual design uncomplicated specification of the location of components supports the exploration of possible solutions more than accurately specifying the
location of components. Thus, non-specific component allocation is more efficient for
coding the topology of components. The allocation sequence of components is coded
by a list of objects, in which the top represents the first and the bottom the last
5.2
Conclusions
Design knowledge acquisition contains three tasks: data collection, analysing data and
coding the design knowledge. Five sources of submarine design knowledge are
distinguished: literature search, interviews, existing design programs, history of previous designs and design standards. An important source of information is the historical data
of previous designs. Utilisation of this data source is limited, due to the few number of existing designs. To overcome this limitation, more general applicable knowledge sources should be used. If possible. deep knowledge should be used instead of shallow knowledge, as deep knowledge enables the designer to diverge from the conventional
modes of thinking without affecting the correctness of the results. The deep and
shallow knowledge should be codified into numerical, geometrical and/or topological forms.
6
THE SUBMARINE DESIGN
MODEL
Ifdesign means anything, it must have a,
senseofhuman rightness DJ. Andrews
'this chapter discusses the application of various design models for predicting the size and' performance
of components and the boat as a whole. This chapter reviews the existing and newly developed knowledge about design models for sizing, balancing and calculating the performance of submarines. The importance of evaluating existing knowledge in the design process is illustrated by Weisberg's statement [Weisberg, 1986]:
"This might mean, perhaps paradoxically, that in order to produce something new, one should first become as knowledgeable as possible about the old"
The first paragraph of this chapter starts with an introduction to the submarine design knowledge. no
determine the most relevant problem areas. The following paragraphs describe the acquired models. The level of detail is dependent on the level of novelty. For example, much attention is given to ani
uncommon space balancing model. The models are presented using the framework of eight main submarine functions as introduced in chapter three.
6.1
Submarine design models
To solve the problems which are specified in the previous paragraph, 'submarine design
knowledge has to be acquired. This paragraph shows the current available knowledge for solving those problems. The first question which arises when acquiring knowledge is: 'what is the required scope, precision and level of detail for the acquired knowledge
to solve the top-level problem?' The required precision and level of detail, for predicting the object properties 'is different for each defined object as well as for each
