RA - Scientific Journals of the Maritime University of Szczecin

Transkrypt

Scientific Journals
Zeszyty Naukowe
Maritime University of Szczecin
Akademia Morska w Szczecinie
2014, 38(110) pp. 131–135
ISSN 1733-8670
2014, 38(110) s. 131–135
Approximate method of calculation of the wind action
on a bulk carrier
Katarzyna Żelazny
West Pomeranian University of Technology, Faculty of Maritime Technology and Transport
71-065 Szczecin, al. Piastów 41, e-mail: [email protected]
Key words: bulk carrier, approximate method of wind action, approximation of surface and resistance
Abstract
While a ship is sailing, wind is acting upon the ship hull above water. As a result, additional resistance,
as well as transfer drift force and drift moment emerge. The article presents an approximate method of calculating these forces for bulk carriers, in the form useful at preliminary ship design, when only basis ship
dimensions are known.
Introduction
Wind action on a sailing vessel
While a transport vessel sails on a given shipping route in real life conditions, its service speed is
affected by numerous factors, wind action among
others. If the wind is acting upon a vessel from bow
sectors, then additional resistance, as well as transfer drift force, as well as a drift moment appear (in
order to keep the vessel on a present shipping route,
this moment has to be counterbalanced by a rudder
plane and resulting carrying helm. Knowledge of
wind action on a vessel is important not only in
anticipating its speed, but also its steering. There
are various method of calculation of wind action on
the ship part above water, available in the literature
on the subject matter, most often, however, they
require the knowledge of aerodynamic resistance
coefficients, which depend – among others – the
shape of the ship part above water including superstructures.
During preliminary ship design, when the shape
of the ship part above water is not known yet,
models based on basic geometrical ship hull parameters are highly useful. The article presents an
approximate method of calculating wind action
forces on a sailing vessel (bulk carrier) useful at
preliminary ship design.
Mean wind action forces on a sailing ship can be
calculated from the formulas:
1
2
R xA    A S xVRA
C Ax  RA 
2
1
2
(1)
R yA   A S yVRA
C Ay  RA 
2
1
2
M zA   A S y LV RA
C Am  RA 
2
where:
ρA  air density;
Sx, Sy  projections of vessel surface above water
(from bow and lateral respectively) onto
midship plane and plane of symmetry;
L  ship length;
VRA  relative wind speed (Fig. 1);
CAx, CAy, CAm(βRA)  aerodynamic resistance coefficients of the ship part above water, dependent on relative wind direction (βRA);
βRA  relative wind direction (Fig. 1).
Zeszyty Naukowe 38(110)
2
2
VRA  VRAx
 VRAy
VRAx  VA cos  A  V
VRAy  VA sin  A
131
(2)
(3)
Katarzyna Żelazny
 A   A   180
The coefficients CAx, CAy and CAm are mostly determined during the model tests [1] above-water
part of the ship in the aerodynamic tunnel or can be
calculated from the approximate formulas [2, 3].
These coefficients for a specific type of a ship, e.g.
bulk carriers, depend on a ship size to a small degree. Coefficients CAx, CAy and CAm measured in
aerodynamic tunnel for a bulk carrier [1] have been
approximated by a polynomial dependent only on
relative wind direction βRA, (Fig. 1). Obtained relationships have the following form:
(4)
βA  wind action against the vessel (βA = 0 wind
from the stern, βA = 90 wind at the bow);
 RA  arctan
 VRAy
(5)
VRAx
VA  wind speed;
γA  geographical wind direction, (γA = 0 – north
wind, γA = 90 – east wind);
V  ship speed;
ψ  geographical course of a ship.
In equations (1) drift angle β of a ship has been
neglected, since it will only have small value and
influence the relative wind direction βRA and hence
wind action only to a minimal degree.
Force RxA, in equations (1), is an additional resistance resulting from wind action, while moment
MzA can cause drift and change in a vessel course,
to counterbalance which steering devices have to be
used.
C ax (  RA )  0.4770  0.01528 RA 
2
3
 3.202  10 4  RA
 1.060  106  RA
R 2  0.989
C ay (  RA )  0.01529 0.01529 RA 
2
 8.710  105  RA
R  0.981
C am (  RA )  0.01815 4.752  103  RA 
2
3
 5.868 105  RA
 1.783 107  RA
xo
A
VRA
xo
MzA
G
R 2  0.964
x
RA
V
(6)
2
while exactness of approximation against aerodynamic tunnel measurements has been shown in
figure 2.
A
Cax [–]
VA
1
RyA
0.5
RxA
RA []
0
y
-0.5

0
60
120
180
-1
00
-1.5
yo
Cax
Fig. 1. Coordinates, forces, velocities, as well as directions of
ship and wind
Wielob. (Cax)
Cay [–]
0.8
In equations (1) as well as in figure 1 it has been
assumed, that if a ship sails upwind, then wind action is additional resistance, however, with wind
from the stern, then wind action causes total resistance to decrease.
0.6
0.4
0.2
0
0
60
Cay
Approximation of ship additional resistance
from wind action
120
RA []
Cam [–]
0
Forces RxA, RyA, as well as MzA moment of wind
action on the ship part above water depend among
other on the resistance of the ship shape above water (given by coefficients CAx, CAy and CAm in equation (1)), as well as the surface of the ship part
above water Sx, Sy. As a result, quantities CAx, CAy,
CAm, Sx and Sy for selected types of ships will be
approximated here.
0
RA [] 180
Wielob. (Cay)
60
120
Cam
Wielob. (Cam)
180
-0.05
-0.1
-0.15
Fig. 2. Characteristics CAx, CAy, CAm from aerodynamic tunnel
[1] and those obtained from approximation (6)
132
Scientific Journals 38(110)
Approximate method of calculation of the wind action on a bulk carrier
Sx [m2]
Surfaces Sx i Sy for bulk carriers have been calculated for 33 ships, and then with the help of linear
regression, an appropriate polynomial including
only basic ship parameters (bulk carrier) has been
searched. Examples of such polynomials are given
in figures 3–12, while the degree of adjustment of
these models depending on ship parameters in tables 1 and 2 respectively.
Sx [m2]
Sx(BT)
1200
1000
800
600
400
y = 350.28ln(x) - 1381.6
R² = 0.8475
200
0
Sx(Lpp)
0
1200
200
400
600
800
Sx
1000
1000
Log. (Sx)
1200
BT [m]
Fig. 6. Approximation of projection of the ship part above
water from the bow Sx dependent on the product of the ship
breadth B and draught T
800
600
Sx [m2]
400
y=
200
+ 6.3616x - 301.65
R² = 0.7841
1000
0
100
150
200
Sx
250
300
800
350
Lpp [m]
Wielob. (Sx)
600
400
water from the bow Sx dependent on ship length between perpendiculars LPP
2
Sx [m ]
Sx(B(H-T))
1200
-0.007x2
y = 405.34ln(x) - 1453.2
R² = 0.8484
200
0
0
Sx(B)
100
200
300
400
Sx
1200
500
600
700
B(H-T) [m2]
Log. (Sx)
water from the bow Sx dependent on of the product of the ship
breadth B draught T and the ship lateral height H
1000
800
600
Table 1. The adjustment degree of a model for the approximation of the projection of the ship part above water from the bow
Sx in relation to other ship parameters
400
y = 596.35ln(x) - 1365.3
R² = 0.7799
200
Sx=f(Lpp) Sx=f(B) Sx=f(DISV) Sx=f(BT)
0
10
20
30
Sx
40
50
60
70
R2 – the
degree of
adjustment
of a model
B [m]
Log. (Sx)
water from the bow Sx dependent on ship breadth B
Sx [m2]
Sx(DISV)
800
600
400
y = 233.71ln(x) - 1879.3
R² = 0.8408
0
50000
Sx
Log. (Sx)
 [m ]
0.848
200
250
300
Wielob. (Sy)
350
LPP [m]
Fig. 8. Approximation of projection of the ship lateral part
above water Sy dependent on length between perpendiculars
LPP
water from the bow Sx dependent on ship displacement 
150
Sy
3
0.848
y = -0.0108x2 + 18.313x - 943.02
R² = 0.8252
100
100000 150000 200000 250000 300000
0.841
Sy(Lpp)
4500
4000
3500
3000
2500
2000
1500
1000
500
0
1000
0
0.780
Sy [m2]
1200
200
0.784
Sx=
f(B(H–T))
133
Katarzyna Żelazny
Sy [m2]
Sy [m2]
Sy(B)
4500
4500
4000
4000
3500
3500
3000
3000
2500
2500
2000
2000
1500
1500
y = 2078.8ln(x) - 4773.6
R² = 0.6385
1000
Sy(L(H-T))
y = 1361.1ln(x) - 7258
R² = 0.833
1000
500
500
0
10
20
30
40
50
Sy
60
0
70
0
B [m]
Log. (Sy)
1000
1500
Sy
2000
2500
3000
Sy(DISV)
Table 2. The adjustment degree of models for the approximation of the projection of the ship lateral part above water Sy
dependent on to ship parameters
4500
4000
3500
Sy=f(Lpp) Sy=f(B) Sy=f(DISV) Sy=f(LT)
3000
R2 – the
degree of
adjustment
of a model
2500
2000
1500
500
50000
100000 150000 200000 250000 300000
Sy
Log. (Sy)
 [m3]
0.802
0.814
0.833
1
2
RxA    A  233.71 ln( )  1879.3  VRA

2
2
 0.4770  0,01528  RA  3.202  104   RA

above water Sy dependent on ship displacement 
Sy [m2]
0.639
Having carried approximation for coefficients
CAx, CAy, CAm, as well as surfaces Sx, Sy equations
(1) for bulk carriers take e.g. the form:
0
0
0.825
Sy=
f(L(H–T))
Verification of a model and final
conclusions
y = 895.47ln(x) - 7472.4
R² = 0.802
1000
3500
2
Log. (Sy) L(H–T) [m ]
above water from Sy dependent on the ship length, draught T
and the ship lateral height H
above water Sy dependent on ship breadth B
Sy [m2]
500

Sy(LT)
3
 1.060  106   RA
4500

1
2
 A  895.4  ln( )  7472.4   VRA

2
  0.01529 0.01529  RA 
4000
R yA 
3500
3000
5
 8.710  10  
2500
2
RA
(7)

1
2
 A  895.4  ln( )  7472.4   L  VRA

2
  0.01815 4.752  103   RA 
2000
M zA 
1500
1000

y = 1407.5ln(x) - 8559
R² = 0.8142
500
2
3
 5.868 105   RA
 1.783 107   RA
0
0
1000
2000
3000
Sy
4000
5000
Log. (Sy)
6000

where  – ship displacement.
In these equations only basic ship and wind parameters are known, hence they can be used already
at preliminary ship design stage. The exactness of
calculated forces RxA and RyA, as well as moment
7000
LT [m2]
above water Sy dependent on the product of the ship length L
and draught T
134
Scientific Journals 38(110)
Approximate method of calculation of the wind action on a bulk carrier
MzA
[Nm]
MzA from wind is shown on figures 13–15. On these
graphs, points mark the value of forces and moment
calculated according to equation (1) on the basis of
measurements in aerodynamic tunnel [1], as well as
measured surfaces, while a solid line represents the
values for a chosen approximation (7) for different
wind speeds and directions.
Additional resistance from wind action RxA in
total ship resistance constitute around 30% [4] depending on the ship size and wind speed on head
wave. Taking this into account, it can be concluded,
that the obtained exactness of approximation is on
the sufficient level to determine wind action on the
ship required at preliminary ship design.
Mz M1
RA []
0
0
30
60
90
120
150
180
-2000
-4000
-6000
-8000
-10000
-12000
-14000
RxA [kN]
5a
5w
Rx M1
200
10a
10w
15a
15w
20a
20w
Fig. 15. Moment MzA from wind calculated on the basis of
measurements in aerodynamic tunnel [1] and measured surfaces obtained from approximation (7) for different wind
speeds and directions
150
100
50
References
0
0
30
60
90
120
-50
150
1. BLENDERMANN W.: Manoeuvring Technical Manual. Shiff
und Hafen, Heft 3/1990, Heft 4/1991.
2. ISHERWOOD M.R.: Wind resistance of merchant ships.
The Royal Institution of Naval Architects, Vol. 115, 1973,
327–338.
3. VORABJEW Y.L., GULIEV Y.M.: Application of aerodynamics test results in ships and floating structures at sea problems. SMSSH ’88, The Proceedings of the 17th Session,
Varna, Vol. 1, 17–22 October 1988, 32-1–32-7.
4. DUDZIAK J.: Teoria okrętu. Fundacja Promocji Przemysłu
Okrętowego i Gospodarki Morskiej, Gdańsk 2008.
180
RA []
-100
-150
5a
5w
10a
10w
15a
15w
20a
20w
Fig. 13. Force RxA – additional resistance from wind calculated
on the basis of measurements in aerodynamic tunnel [1] and
measured surfaces obtained from approximation (7) for different wind speeds and directions
RyA [kN]
Other
5. RALSTON A.: Wstęp do analizy numerycznej. Państwowe
Wydawnictwo Naukowe, Warszawa 1971.
Ry M1
400
350
300
250
200
150
100
50
0
0
30
5a
5w
60
10a
10w
90
120
15a
15w
150
180
20a RA []
20w
Fig. 14. Wind force RyA calculated on the basis of measurements in aerodynamic tunnel [1] and measured surfaces obtained from approximation (7) for different wind speeds and
directions
135

RA - Scientific Journals of the Maritime University of Szczecin

Transkrypt

Podobne dokumenty

Application Form