"""Ship resistance accoring to :cite:`holtropStatisticalReAnalysisResistance1984`.
Definitions to calculate ships ressitance according to Holtrop."""
from __future__ import annotations
# Standard libraries.
import math
# Third party libraries.
from astropy import units as u # type: ignore
from . import ship, hydro
__date__ = "2024/08/01 21:28:53 hoel"
__author__ = "Berthold Höllmann"
__copyright__ = "Copyright © 2019 by Berthold Höllmann"
__credits__ = ["Berthold Höllmann"]
__maintainer__ = "Berthold Höllmann"
__email__ = "berhoel@gmail.com"
[docs]
class Holtrop(ship.Ship):
"Calculate ship resistance for merchant ships acc. to :cite:`holtropStatisticalReAnalysisResistance1984`."
[docs]
def __init__(self, *args, **kw):
super().__init__(*args, **kw)
# According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
#
# .. math::
#
# d = -0.9
self.d = -0.9
@property
def L_R(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 272:
.. math::
L_R = L \left( 1 - C_P + \frac{0.06 C_P \text{lcb}}{4 C_P - 1}\right)
"""
return self.L * (
1.0 - self.C_P + 0.06 * self.C_P * self.lcb / (4.0 * self.C_P - 1.0)
)
@property
def k_1(self):
r"""Calculates (1+k_1) according to Holtrop:cite:`holtropStatisticalReAnalysisResistance1984`, page 272:
.. math::
1 + k_1 = 0.93 + 0.487118 c_{14} \left( \frac B L \right)^{1.06806} \left(
\frac T L \right)^{0.46106} \left( \frac L{L_R} \right)^{0.121563}
\left( \frac{L^3}∇ \right)^{0.36486} \left(1 - C_P
\right)^{-0.604247}
"""
return 0.93 + 0.487118 * self.c_14 * math.pow(
self.B / self.L,
1.06806,
) * math.pow(self.T / self.L, 0.46106) * math.pow(
self.L / self.L_R,
0.121563,
) * math.pow(
pow(self.L, 3) / self.Nab,
0.36486,
) * math.pow(
1.0 - self.C_P,
-0.604247,
)
@property
def c_14(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 272
.. table:: :math:`C_\text{Stern}` according to table: (see :cite:`holtropStatisticalReAnalysisResistance1984`, p. 272):
=================================== ========================
Afterbody form :math:`C_{\text{Stern}}`
=================================== ========================
Pram with gondola -25
V-shaped section -10
Normal section shape 0
U-shaped sections with Hogner stern 10
=================================== ========================
.. math::
c_{14} = 1 + 0.011 C_{\text{Stern}}
"""
return 1.0 + 0.011 * self.C_Stern
@property
def C_A(self):
if super().C_A is None:
return self.C_A_calc()
return super().C_A
@C_A.setter
def C_A(self, value):
super.C_A = value
[docs]
def C_A_calc(self):
r"""Correlation allowance coefficient according to :cite:`holtrop1982approximate`, p. 168:
Correlation allowance coefficient see :cite:`holtrop1982approximate`, p. 168:
.. math::
C_A = 0.006 (L + 100)^{-0.16} - 0.00205 + 0.003 \sqrt{\frac L{7.5}} C_B^4
c_2 (0.04 - c_4)
"""
return (
0.006 * math.pow((self.L.value + 100.0), -0.16)
- 0.00205
+ 0.003
* math.pow(self.L.value / 7.5, 0.5)
* math.pow(self.C_B, 4)
* self.c_2
* (0.04 - self.c_4)
).value
@property
def c_2(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_2 = \exp\left(-1.89 \sqrt{c_3} \right)
"""
return math.exp(-1.89 * math.sqrt(self.c_3))
@property
def c_3(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_3 = \frac{0.56 A_{BT}^{1.5}}{B T \left(0.31 \sqrt{A_BT} + T_F - h_B\right)}
"""
return (
0.56
* math.pow(self.A_BT.value, 1.5)
/ (
self.B
* self.T
* (0.31 * math.sqrt(self.A_BT.value) + self.T_F.value - self.h_b.value)
)
).value
@property
def c_4(self):
r"""According to :cite:`holtrop1982approximate`, p. 168:
.. math::
c_4 = \left\{
\begin{array}{lll}
\frac{T_F}L & \text{when} & \frac{T_F}L ≤ 0.04\\
0.04 & \text{when} & \frac{T_F}L > 0.04
\end{array}
\right.
"""
return max(self.T_F / self.L, 0.04)
@property
def c_17(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 272:
.. math::
c_17 = 6919.3 C_M^{-1.3346} \left( \frac∇{L^3}\right)^{2.00977}
\left( \frac L B - 2 \right)^{1.40692}
"""
return (
6919.3
* math.pow(self.C_M, -1.3346)
* math.pow((self.Nab / pow(self.L, 3)), 2.00977)
* math.pow((self.L / self.B) - 2.0, 1.40692)
)
@property
def m_3(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 272:
.. math::
m_3 = -7.2035 \left( \frac B L \right)^{0.326869} \left( \frac T B
\right)^{0.605375}
"""
return (
-7.2035
* math.pow(self.B / self.L, 0.326869)
* math.pow(self.T / self.B, 0.605375)
)
@property
def c_1(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_1 = 2223105 c_7^{3.78613} \left( \frac T B \right)^{1.07961} 90 -
i_E)^{-1.37565}
"""
return (
2223105.0
* math.pow(self.c_7, 3.78613)
* math.pow((self.T / self.B), 1.07961)
* math.pow((90.0 - self.i_E.value), -1.37565)
)
@property
def c_5(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_5 = 1 - 0.8 \frac{A_T}{B T C_M}
"""
return (1.0 - 0.8 * self.A_T / (self.B * self.T * self.C_M)).value
@property
def λ(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
λ = \left\{
\begin{array}{lll}
1.446 C_P - 0.03 \frac L B& \text{when} & \frac L B < 12\\
1.446 C_P - 0.36 & \text{when} & \frac L B > 12
\end{array}
\right.
"""
if (self.L / self.B) < 12.0:
return (1.446 * self.C_P - 0.03 * (self.L / self.B)).value
return (1.446 * self.C_P - 0.36).value
[docs]
def c_6(self, speed):
r"""According to :cite:`holtrop1982approximate`, p. 168:
.. math::
c_6 = \left\{
\begin{array}{lll}
0.2 (1 - 0.2 F_{nT}) & \text{when} & F_{nT} < 5\\
0 & \text{when} & F_{nT} ≥ 5
\end{array}
\right.
"""
if self.F_nT(speed) < 5.0:
return 0.2 * (1.0 - 0.2 * self.F_nT(speed))
return 0
@property
def c_7(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_7 = \left\{
\begin{array}{lll}
0.229577\left(\frac B L \right)^{0.33333} & \text{when} & \frac B L < 0.11\\
\frac B L & \text{when} & 0.11 < \frac B L <
0.25\\
0.5 - 0.0625 \frac B L & \text{when} & \frac B L > 0.25
\end{array}
\right.
"""
if (self.B / self.L) < 0.11:
return 0.229577 * math.pow((self.B / self.L), 0.33333)
elif (self.B / self.L) < 0.25:
return self.B / self.L
return 0.5 - 0.0625 * (self.L / self.B)
@property
def c_15(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_{15} = \left\{
\begin{array}{lll}
-1.69385 & \text{when} & \frac{L^3}∇ < 512\\
-1.69385 + \frac{\left(\frac L{∇^⅓} - 8\right)}{2.36}
& \text{when} & 512 < \frac{L^3}∇ < 1726.91\\
0 & \text{when} & \frac{L^3}∇ > 1726.91
\end{array}
\right.
"""
if (pow(self.L, 3) / self.Nab) < 512:
return -1.69385
elif (pow(self.L, 3) / self.Nab) < 1726.91:
return -1.69385 + ((self.L / pow(self.Nab, 1.0 / 3.0)) - 8.0) / 2.36
return 0.0
@property
def c_16(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_{16} = \left\{
\begin{array}{lll}
8.07981 C_P - 13.8673 C_P^2 + 6.984388 C_P^3& \text{when} & C_P < 0.8\\
1.73014 - 0.7067 C_P & \text{when} & C_P > 0.8
\end{array}
\right.
"""
if self.C_P < 0.8:
return (
8.07981 * self.C_P
- 13.8673 * math.pow(self.C_P, 2.0)
+ 6.984388 * math.pow(self.C_P, 3.0)
)
return 1.73014 - 0.7067 * self.C_P
@property
def calc_i_E(self):
r"""Angle if the waterline at the bow in degrees with referende to the
centre Plane but neglecting the local shape at the stem. Formula
according to :cite:`holtrop1982approximate`, pp. 167.
.. math::
i_E = 1 + 89 \exp \left( -\left(\frac L B \right)^{0.80856} \left( 1 - C_{WP}
\right)^{0.30484} \left(1 - C_P - 0.0225 \text{lcb} \right)^{0.6367} \left(
\frac{L_R}B \right)^{0.34574} \left( \frac{100 ∇}{L^3}
\right)^{0.16302} \right)
"""
return (
1.0
+ 89.0
* math.exp(
-math.pow((self.L / self.B), 0.80856)
* math.pow((1 - self.C_WP), 0.30484)
* math.pow((1 - self.C_P - 0.0225 * self.lcb), 0.6367)
* math.pow((self.L_R / self.B), 0.34574)
* pow((100.0 * self.Nab / pow(self.L, 3)), 0.16302),
)
) * u.degree
@property
def m_1(self):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
m_1 = 0.0140407 \frac L T - 1.75254 \frac{∇^{\frac13}}L - 4.79323
\frac B L - c_{16}
"""
return (
0.0140407 * (self.L / self.T)
- 1.75254 * pow(self.Nab, (1.0 / 3.0)) / self.L
- 4.79323 * self.B / self.L
- self.c_16
)
[docs]
def m_4(self, speed):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_{15} = 0.4 \exp \left( -0.034 F_n^{-3.29} \right)
"""
return (
self.c_15
* 0.4
* math.exp(-0.034 * math.pow(hydro.F_n(speed, self.L), -3.29))
)
[docs]
def R_W(self, speed):
r"""Wave ressistance formula according to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
R_W = \left\{
\begin{array}{lll}
R_{W-A} & \text{when} & F_n < 0.40\\
R_{W-A_{0.4}} + \left(10
F_n - 4\right) \frac{
\left(R_{W-B_{0.55}} -
R_{W-A_{0.4}} \right)}
{0.5} & \text{when} & 0.40 < F_n < 0.55\\
R_{W-B} & \text{when} & F_n > 0.55
\end{array}
\right.
Here $R_{W-A_{0.4}}$ is the wave resistance prediction for $F_n =
0.40$ and $R_{W-B_{0.55}}$ is the wave resistance prediction for
$F_n = 055$ according to the respective formulae.
"""
F = hydro.F_n(speed, self.L)
if F < 0.4:
return self.R_WA(speed, F)
elif F < 0.55:
return (
self.R_WA(speed, 0.4)
+ (10.0 * F - 4)
* (self.R_WB(speed, 0.55) - self.R_WA(speed, 0.4))
/ 1.5
)
return self.R_WB(speed, F)
[docs]
def R_WA(self, speed, F_n):
r"""Wave ressistance formula for speed range F_n < 0.4 according
to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
R_{W-A} = c_1 c_2 c_5 ∇ ρ g \exp\left(m_1 F_n^d + m_4 \cos \left(
\lambda F_n^{-2}\right)\right)
"""
return (
self.c_1
* self.c_2
* self.c_5
* self.Nab
* hydro.rho
* hydro.g
* math.exp(
self.m_1 * math.pow(F_n, self.d)
+ self.m_4(speed) * math.cos(self.λ * math.pow(F_n, -2.0)),
)
)
[docs]
def R_WB(self, speed, F_n):
r"""Wave ressistance formula for speed range F_n > 0.55 according
to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 272:
.. math::
R_{W-B} = c_{17} c_2 c_5 ∇ ρ g \exp\left(m_3 F_n^d + m_4 \cos \left(
\lambda F_n^{-2}\right)\right)
"""
return (
self.c_17
* self.c_2
* self.c_5
* self.Nab
* hydro.rho
* hydro.g
* math.exp(
self.m_3 * math.pow(F_n, self.d)
+ self.m_4(speed) * math.cos(self.λ * math.pow(F_n, -2.0)),
)
)
[docs]
def R_app(self, speed):
r"""Appedage resistance according to :cite:`holtrop1982approximate`, p. 167:
.. math::
R_{APP} = 0.5 ρ V^2 S_{APP} \left( 1 + k_2 \right)_{eq} C_F
"""
def calc_k_2_eq(App):
r"""Calculation of equivalent 1 + k_2 value for a combination of
appendages:
.. math::
\left(1 + k_2\right) = \frac{\Sum \left(1 + k_2 \right)
S_{APP}}{\Sum S_{APP}}
"""
S_Sum = 0.0 * u.m**2
k_2_Sum = 0.0 * u.m**2
for S_app, k_2 in App:
S_Sum = S_Sum + S_app
k_2_Sum = k_2_Sum + (S_app * k_2)
if S_Sum.value > 0.0:
return (S_Sum, (k_2_Sum / S_Sum))
return (0.0 * u.m**2, 0.0)
(S_app, k_2_eq) = calc_k_2_eq(self.App)
return (
0.5 * hydro.rho * pow(speed, 2) * S_app * k_2_eq * hydro.C_F(speed, self.L)
)
[docs]
def R_B(self, speed):
r"""Additional resistance due to the presence of a bulbous bow near
the surface, according to :cite:`holtrop1982approximate`, p. 168:
.. math::
R_B = 0.11 \exp \left(-3 P_B^{-2} \right) \frac{F_{ni}^3 A{BT}^{1.5} ρ g}
{1 + F_{ni}^2}
"""
if self.A_BT.value > 0:
return (
0.11
* math.exp(-3.0 * pow(P_B(self), -2))
* math.pow(self.F_ni(speed), 3.0)
* (self.A_BT * pow(self.A_BT, 0.5))
* hydro.rho
* hydro.g
/ (1.0 + pow(self.F_ni(speed), 2))
)
return 0 * u.N
# resistance calculation:
[docs]
def R(self, speed):
r"""Calculating of resistance of merchant ships according to the
statistical method of J. Holtrop, :cite:`holtropStatisticalReAnalysisResistance1984`, p. 272:
.. math::
R_{\text{Total}} = hydro.R_F(1+K_1)+R_{APP}+R_W+R_B+R_{TR}+R_A
"""
R_total = (
self.R_F(speed) * self.k_1
+ self.R_app(speed)
+ self.R_W(speed)
+ self.R_B(speed)
+ self.R_TR(speed)
+ self.R_A(speed)
)
return R_total
[docs]
def R_TR(self, speed):
r"""Additional pressure resistance due to immersed transom, according
to :cite:`holtrop1982approximate`, p.~168:
.. math::
R{TR} = 0.5 ρ V^2 A_T c_6
"""
return 0.5 * hydro.rho * pow(speed, 2) * self.A_T * self.c_6(speed)
[docs]
def R_A(self, speed):
r"""Model-ship correlation resistance according to :cite:`holtrop1982approximate`, p. 168:
.. math::
R_A = 0.5 ρ V^2 S C_A
"""
return 0.5 * hydro.rho * pow(speed, 2) * self.S * self.C_A
[docs]
def F_nT(self, speed):
r"""Froude number based on the transom immersion, according to :cite:`holtrop1982approximate`, p.
168:
.. math::
F_{nT} = \frac V{\sqrt{\frac{2 g A_T}{B + B C_{WP}}}}
"""
return speed / pow(
2.0 * hydro.g * self.A_T / (self.B + self.B * self.C_WP),
0.5,
)
[docs]
def C_A_ITTC78(L, k_s):
r"""Correlation allowance coefficient increase according to :cite:`holtrop1982approximate`, p.
168:
.. math::
C_A = \frac{0.105 k_s^{\frac 1 3} - 0.005579}{L^{\frac 1 3}}
"""
return (0.105 * math.pow(k_s, (1.0 / 3.0)) - 0.005579) / pow(L, (1.0 / 3.0))
[docs]
def C_V(speed, ship):
r"""Viscous resistance coefficient according to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 274:
.. math::
C_V = (1 + k) C_F + C_A
"""
return ship.k_1() * hydro.C_F(speed, ship.L()) + ship.C_A()
[docs]
def c_1(ship):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_1 = 2223105 c_7^{3.78613} \left( \frac T B \right)^{1.07961} 90 -
i_E)^{-1.37565}
"""
return (
2223105.0
* math.pow(c_7(ship), 3.78613)
* math.pow((ship.T() / ship.B()), 1.07961)
* math.pow((90.0 - ship.i_E().value), -1.37565)
)
[docs]
def c_7(ship):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_7 = \left\{
\begin{array}{lll}
0.229577\left(\frac B L \right)^{0.33333} & \text{when} & \frac B L < 0.11\\
\frac B L & \text{when} & 0.11 < \frac B L <
0.25\\
0.5 - 0.0625 \frac B L & \text{when} & \frac B L > 0.25
\end{array}
\right.
"""
if (ship.B() / ship.L()) < 0.11:
return 0.229577 * math.pow((ship.B() / ship.L()), 0.33333)
elif (ship.B() / ship.L()) < 0.25:
return ship.B() / ship.L()
return 0.5 - 0.0625 * (ship.L() / ship.B())
[docs]
def c_8(ship):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_8 = \left\{
\begin{array}{lll}
\frac{B S}{L D T_A} & \text{when} & \frac B{T_A} < 5\\
\frac{S7\frac B{T_A} - 25}
{LD \left(\frac B{T_A} - 3 \right)} & \text{when} & \frac B{T_A} > 5
\end{array}
\right.
"""
if (ship.B() / ship.T_A()) < 5.0:
return ship.B() * ship.S() / (ship.L() * ship.D() * ship.T_A())
return (
ship.S()
* (7.0 * (ship.B() / ship.T_A()) - 25.0)
/ (ship.L() * ship.D() * ((ship.B() / ship.T_A()) - 3.0))
)
[docs]
def c_9(ship):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_9 = \left\{
\begin{array}{lll}
c_8 & \text{when} & c_8 < 28\\
32 - \frac{16}{c_8 - 24} & \text{when} & c_8 > 28
\end{array}
\right.
"""
C_8 = c_8(ship)
if C_8 < 28:
return C_8
return 32.0 - 16.0 / (C_8 - 24)
[docs]
def c_11(ship):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
c_{11} = \left\{
\begin{array}{lll}
\frac{T_A}D & \text{when} & \frac{T_A}D < 2\\
0.0833333 \left( \frac{T_A}D \right)^3 + 1.33333
& \text{when} & \frac{T_A}D > 2
\end{array}
\right.
"""
val = ship.T_A() / ship.D()
if val < 2.0:
return val
return 0.0833333 * math.pow(val, 3.0) + 1.33333
[docs]
def c_19(ship):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273-274:
.. math::
c_{19} = \left\{
\begin{array}{lll}
\frac{0.12997}{0.95 - C_B} -
\frac{0.11056}{0.95 - C_P} & \text{when}& C_P < 0.7\\
\frac{ 0.18567}{1.3571 - C_M} -
0.71276 + 0.38648 C_P & \text{when}& C_P > 0.7
\end{array}
\right.
"""
if ship.C_P() < 0.7:
return 0.12997 / (0.95 - ship.C_B()) - 0.11056 / (0.95 - ship.C_P())
return 0.18567 / (1.3571 - ship.C_M) - 0.71276 + 0.38648 * ship.C_P()
[docs]
def c_20(ship):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 274:
.. math::
c_{20} = 1 + 0.015 C_{\text{Stern}}
"""
return 1.0 + 0.015 * ship.C_Stern()
[docs]
def C_P1(ship):
r"""According to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 274:
.. math::
C_{P1} = 1.45 C_P - 0.315 - 0.0225 \text{lcb}
"""
return 1.45 * ship.C_P() - 0.315 - 0.0225 * ship.lcb()
[docs]
def P_B(ship):
r"""A measure for the emergence of the bow, according to :cite:`holtrop1982approximate`, p. 168:
.. math::
P_B = \frac{0.56 \sqrt{A_{BT}}}{T_F - 1.5 h_B}
\end{equation}
"""
return 0.56 * ship.A_BT() ** (1 / 2) / (ship.T_F() - 1.5 * ship.h_b())
[docs]
def F_ni(speed, ship):
r"""Froude number based on the immersion, according to :cite:`holtrop1982approximate`, p. 168:
.. math::
\frac V{\sqrt{g \left( T_F - h_B - 0.25 \sqrt{A_{BT}} \right) + 0.15 V^2}}
"""
return speed / pow(
hydro.g * (ship.T_F() - ship.h_b() - 0.25 * pow(ship.A_BT(), 0.5))
+ 0.15 * pow(speed, 2),
0.5,
)
# prediction of delivered power:
[docs]
def w_single(speed, ship):
r"""Wake prediction for single screw ships according to :cite:`holtropStatisticalReAnalysisResistance1984`, p. 273:
.. math::
w = c_9 c{20} C_V \frac L{T_A} \left( 0.050776 + 0.93405 c_{11} \frac{C_V}
{\left(1 - C_{P1} \right)} \right) + 0.27915 c_{20} \sqrt{\frac B{L\left(
1 - C_{P1} \right)}} c_{19} c_{20}
"""
return (
c_9(ship)
* c_20(ship)
* C_V(speed, ship)
* (ship.L() / ship.T_A())
* (0.050776 + 0.93405 * c_11(ship) * (C_V(speed, ship) / (1 - C_P1(ship))))
) + (
0.27915 * c_20(ship) * math.sqrt(ship.B() / (ship.L() * (1 - C_P1(ship))))
+ c_19(ship) * c_20(ship)
)
[docs]
def t_single(ship):
r"""Thrust decuction prediction for single screw ships according to
:cite:`holtropStatisticalReAnalysisResistance1984`, p. 274:
.. math::
t = \frac{0.25014 \left(\frac B L \right)^{0.28956} \left( \frac{\sqrt{B T}}D
\right)^{0.2624}}
{\left(1 - C_P + 0.0225 \text{lcb}\right)^{0.01762}} +
0.0015 C_{\text{stern}}
"""
return (
0.25014
* math.pow(ship.B() / ship.L(), 0.28956)
* math.pow(math.sqrt((ship.B() * ship.T()).value) / ship.D().value, 0.2624)
/ math.pow(1 - ship.C_P() + 0.0225 * ship.lcb(), 0.01762)
+ 0.0015 * ship.C_Stern()
)
[docs]
def eta_R_single(ship):
r"""The relatigve-rotative efficiency prediction for single screw
ships according according to :cite:`holtrop1982approximate`, pp. 168:
.. math::
η_R = 0.9922 - 0.05908 \frac{A_E}{A_O} +
0.07424 \left( C_P - 0.0225 \text{lcb} \right)
"""
return (
0.9922
- 0.05908 * ship.A_E() / ship.A_O()
+ 0.07424 * (ship.C_P() - 0.0225 * ship.lcb())
)
[docs]
def w_single_open_stern(speed, ship):
r"""Wake prediction for single screw ships with open stern (as
sometimes applied on slender, fast sailing ships) according to
:cite:`holtrop1982approximate`, p. 169:
.. math::
w = 0.3 C_B + 10 C_V C_B - 0.23 \frac{D}{\sqrt{B T}}
"""
return (
0.3 * ship.C_B()
+ 10.0 * C_V(speed, ship) * ship.C_B()
- 0.23 * ship.D() / math.sqrt(ship.B() * ship.T)
)
[docs]
def t_single_open_stern(speed, ship):
r"""Thrust decuction prediction for single screw ships with open stern
(as sometimes applied on slender, fast sailing ships) according to
:cite:`holtrop1982approximate`, p. 169:
.. math::
t = 0.10
"""
return 0.1
[docs]
def eta_R_single_open_stern(ship):
r"""The relatigve-rotative efficiency prediction for single screw
ships with open stern (as sometimes applied on slender, fast
sailing ships) according according to :cite:`holtrop1982approximate`, pp. 168:
.. math::
η_R = 0.98
"""
return 0.98
[docs]
def w_twin(speed, ship):
r"""Wake prediction for twin screw ships according to :cite:`holtrop1982approximate`, p. 169:
.. math::
w = 0.3095 C_B + 10 C_V C_B - 0.23 \frac D{\sqrt{B T}}
"""
return (
0.3095 * ship.C_B()
+ 10.0 * C_V(speed, ship) * ship.C_B()
- 0.23 * ship.D() / math.sqrt(ship.B() * ship.T())
)
[docs]
def t_twin(ship):
r"""Thrust decuction prediction for twin screw ships according to :cite:`holtrop1982approximate`,
p. 169:
.. math::
t = 0.325 C_B - 0.1885 \frac D {\sqrt{B T}}
"""
return 0.325 * ship.C_B() - 0.1885 * ship.D() / math.sqrt(ship.B() * ship.T())
[docs]
def eta_R_twin(ship):
r"""The relatigve-rotative efficiency prediction for twin screw ships
according according to :cite:`holtrop1982approximate`, pp. 168:
.. math::
η_R = 0.9737 + 0.111 \left( C_P - 0.0225 \text{lcb} \right) + 0.06325 \frac P D
"""
return (
0.9737
+ 0.111 * (ship.C_P() - 0.0225 * ship.lcb())
+ 0.06325 * ship.P() / ship.D()
)
