The functions in this module are not specific to any of the ITTC appendices
As many of the functions in this library require SI units it can be helpful to have a knots-m/s converter and vice-versa.
knots_to_ms (knots:float)
convert knots to m/s
| Type | Details | |
|---|---|---|
| knots | float | the speed in knots |
| Returns | float | speed in m/s |
ms_to_knots (ms:float)
convert knots to m/s
| Type | Details | |
|---|---|---|
| ms | float | the speed in m/s |
| Returns | float | speed in knots |
Using these simple functions we can easily convert between knots and m/s
#convert knots to m/s
meters_per_second = knots_to_ms(5)
print('speed converted to meters per second '+str(meters_per_second))
#convert back to knots
knots = ms_to_knots(meters_per_second)
print('speed converted back into knots '+str(knots))speed converted to meters per second 2.572222873852017
speed converted back into knots 5.0Find the shaft power in ideal conditions considering an external (environmental) force acting on the ship. \[P_{Did} = \frac{1}{2} \left(P_{Dms} - \frac{\Delta RV_s}{\eta_{Did}} + \sqrt{ \left(P_{Dms} - \frac{\Delta RV_s}{\eta_{Did}} \right)^2 + 4P_{Dms} \frac{\Delta RV_s}{\eta_{Did}} \xi_P} \right)\] where:
\(P_{Did}\) is the shaft power in ideal conditions [W],
\(P_{Dms}\) is the measured shaft power [W],
\(\Delta R\) is the resistance increase due to wind, waves and temperature deviations [N]
\(V_S\) is the ship’s speed through water [m/s],
\(\eta_{Did}\) is the propulsion efficiency coefficient in ideal conditions, from the model test,
\(\xi_P\) is the overload factor derived from load variation model test,
ITTC equations: 5
power_correction (pd_meas:float, delta_R:float, stw:float, etaD_id:float, shaft_power_overload:float)
| Type | Details | |
|---|---|---|
| pd_meas | float | measured shaft power [W] |
| delta_R | float | increase of resistance due to wind, waves and temperature deviation [N] |
| stw | float | speed through water [m/s] |
| etaD_id | float | propulsion efficiency coefficienct in ideal conditions (from model test) [-] |
| shaft_power_overload | float | overload factor from load variation model test [-] |
| Returns | float | shaft power in ideal conditions [W] |
What is the ideal power given the following inputs:
measured power = 30,000 kW
delta R = 100000 N
STW = 8 m/s
etaD id = 0.75
shaft power overload factor = -0.1
power_correction(pd_meas = 30000000, #measured shaft power [W]
delta_R = 100000, #increase of resistance due to wind, waves and temperature deviation [N]
stw = 8, #speed through water [m/s]
etaD_id = 0.75, #propulsion efficiency coefficienct in ideal conditions (from model test) [-]
shaft_power_overload = -0.1 #overload factor from load variation model test [-]
)28822308.221276633Find the propeller revolution frequency in ideal conditions considering the measured and ideal shaft power.
\[n_{id} = \frac{n_{ms}}{\xi_n \frac{P_{Dms}-P_{Did}}{P_{Did}}+1}\]
Where
\(n_{id}\) is the propeller shaft revolution frequency in ideal conditions [1/s],
\(n_{ms}\) is the measured propeller shaft revolution frequency [1/s],
\(\xi_n\) is the overload factor derived from load variation model test [-],
\(P_{Dms}\) is the measured shaft power [W],
\(P_{Did}\) is the shaft power in ideal conditions [W],
ITTC equations: 6
shaft_speed_correction (n_ms:float, shaft_speed_overload:float, pd_meas:float, pd_id:float)
| Type | Details | |
|---|---|---|
| n_ms | float | measured propeller shaft revolution frequency [1/s] |
| shaft_speed_overload | float | overload factor derived from load variation model test [-] |
| pd_meas | float | measured shaft power [W] |
| pd_id | float | shaft power in ideal conditions [W] |
| Returns | float | propeller shaft revolution frequency in ideal condition [1/s] |
What is the ideal propeller shaft revolution frequency given the following inputs:
measured propeller shaft revolution frequency = 1.1 1/s
overload factor = 0.3
measured shaft power = 30,000 kW
ideal shaft power = 28,822 kW
shaft_speed_correction(n_ms = 1.1, #measured propeller shaft revolution frequency [1/s]
shaft_speed_overload = 0.3, #overload factor derived from load variation model test [-]
pd_meas = 30000000, #measured shaft power [W]
pd_id = 28822000#shaft power in ideal conditions [W]
)1.0866757610863946The resistance experienced by the ship as a result of passing through air.
\[R_{AA} = \frac{1}{2} \rho_A A_{XV} \left ( C_{DA}(\psi_{WREF}) V_{WREF}^2 - C_{DA}(0) V_{G}^2 \right),\] where \(\rho_A\) is the density of air, \(C_{DA}\) is the wind resistance coefficient, \(A_{XV}\) is the area of maximum transverse section exposed to the wind, \(\psi_{WREF}\) relative direction of the wind, \(V_{WREF}\) relative wind speed, and \(V_G\) is the speed over ground.
The formula calculates resistance experienced by the ship when there is no wind and all resistance comes from the movement of the ship itself. This value is then subtracted from the wind resistance experienced by the ship during the trial. Put this way it is clear that the equation finds the difference between the wind resistance on a still day and on the day of the trial.
The ITTC manual notes that values of \(C_{DA}(x)\) from the tables in load_wind_coefficients need to be reversed when enetering into the wind resistance formula, that is \(C_{DA}= -C_x\). For consistancy the same must be done here
ITTC equations: 9
wind_resistance (air_density:float, wind_resistance_coef_rel:float, wind_resistance_coef_zero:float, area:float, relative_wind_speed:float, sog:float)
Calculates the air resistance. N.B. SI units must be used. Do not use knots
| Type | Details | |
|---|---|---|
| air_density | float | Air density [kg/\(m\^3\)] |
| wind_resistance_coef_rel | float | the coefficient of wind resistance using the relative angle of the wind |
| wind_resistance_coef_zero | float | the coefficient of wind resistance using angle 0 radians |
| area | float | The maximum transverse area of the ship exposed to the wind [m^2] |
| relative_wind_speed | float | Relative wind speed [m/s] |
| sog | float | speed over ground [m/s] |
| Returns | float | Air resistance [N] |
What is the air resistance experienced by a cruise ferry with a tranverse area of 500\(m^2\) travelling at 20 knots with a relative wind of 10 knots and a relative wind angle of \(45^\circ\)
sog_ms = knots_to_ms(20)
wind_speed_ms = knots_to_ms(10)
wind_resistance(1.2, 0.34, 0.69, 500, wind_speed_ms, sog_ms)-19213.8238090769The temperature and salt content of the water affect its density. As such, they also affect the ship resistance.
\[R_{AS} = R_{T0} \left( \frac{\rho_S}{\rho_0} -1 \right) - R_F \left( \frac{C_{F0} + \Delta C_{F0}}{C_{F} + \Delta C_{F}} -1\right)\]
and
$R_F = _S S V_S^2 (C_F + C_F) $
$R_{F0} = 0 S V_S^2 (C{F0} + C_{F0}) $
$R_{T0} = 0 S V_S^2 C{T0} $
The below function taken from section 10.3.3 of the ITTC corrects the sea water temperature, and salt content to be that of the appropriate reference values.
| variable | reference value |
|---|---|
| temperature | \(15^\circ \text{C}\) |
| Density | 1026\(kg/m^3\) |
The coefficients of roughness used in the function are derived from ITTC Recommended Procedures 7.5-02-03-01.4
The values of CF and CF0 can be obtained using the CF_fn function. The values of delta_CF and delta_CF0 and be found using the roughness_allowance_fn
ITTC equations: 14 to 17
temp_salinity_water_resistance (CF:float, CF0:float, delta_CF:float, delta_CF0:float, CT0:float, S:float, stw:float, rho_S:float, rho_0:float=1026)
Resistance due to water temperature and salinity corrected relative to the reference values
| Type | Default | Details | |
|---|---|---|---|
| CF | float | frictional resistance coefficient for actual water temperature and salinity | |
| CF0 | float | frictional resistance coefficient for reference water temperature and salinity | |
| delta_CF | float | roughness allowance associated with Reynolds number for actual water temperature and salinity | |
| delta_CF0 | float | roughness allowance associated with Reynolds number for reference water temperature and salinity | |
| CT0 | float | total resistance coefficient for reference water temperature and salinity | |
| S | float | wetted surface area [m2] | |
| stw | float | ship’s speed through the water [m/s] | |
| rho_S | float | water density for actual water temperature and salt content [kg/m3 ] | |
| rho_0 | float | 1026 | water density for reference water temperature and salt content |
| Returns | float | resistance increase due to deviation of water temperature and water density [N] |
I have absolutely no idea what sensible values should look like, so this function will need to wait for beta testing, before the documentation can be complete
Also this function will probably need to point to some other functions for calculating the roughness coefficents.
temp_salinity_water_resistance(CF = 1.501e-3, CF0 = 1.5e-3, delta_CF = 2.12e-4, delta_CF0 = 2.1e-4,
CT0 = 1.4e-3, S = 8000, stw = 10, rho_S = 1025, rho_0 = 1026)669.9999999998915During Sea trials, vessels are usually in Ballast condition and not the laden condition for which they are built. Such a change reduces the amount of power required to propel the vessel. If the vessel displacement during the trial is outside pre-defined limits then the power can be adjusted using the below equation based on the Admiralty formula.
\[P_2 = P_1 \left( \frac{\nabla_2}{\nabla_1} \right)^{2/3}\]
Where \(P_2\) is the corrected power, \(P_1\) is the ideal power during the trial, \(\nabla_1\) is the displacement during the trial, and \(\nabla_2\) is the displacement during tank tests.
displacement_correction (power:float, trial_displacement:float, reference_displacement:float)
Corrects the power needed by the vessel when trial displacement differs from reference displacement
| Type | Details | |
|---|---|---|
| power | float | The total ideal power during the trial [kWh], |
| trial_displacement | float | diplacement of the ship during the trial [m^3] |
| reference_displacement | float | diplacement of the ship during the tank test [m^3] |
| Returns | float | The power corrected for the difference in displacement between the trial and the tank test |
An example of the correction can be seen below
trial_power = 10000.0
trial_displacement = 12000.0
# Displacement of the ship during the tank test [m^3]
reference_displacement = 15000.0
# Calculate the corrected power
corrected_power = displacement_correction(trial_power, trial_displacement, reference_displacement)
print("Corrected power:", corrected_power)Corrected power: 11603.972084031948There are some example datasets included in this library to help with understanding the process of evaluating seatrials. Loading the data uses the following function
load_datasets (dataset:str)
Load example datasets to try out the pyseatrials functions
| Type | Details | |
|---|---|---|
| dataset | str | The name of the dataset to load |
The propeller advance dataset contains the propeller advance curve for the coefficient of torque and the coefficient of thrust coefficient for an imaginary ship
propeller_advance_df = load_datasets("propeller_advance_lookup")
propeller_advance_df| J | K_T | K_Q | |
|---|---|---|---|
| 0 | 0.30 | 0.300 | 0.038 |
| 1 | 0.35 | 0.270 | 0.036 |
| 2 | 0.40 | 0.260 | 0.034 |
| 3 | 0.45 | 0.240 | 0.032 |
| 4 | 0.50 | 0.210 | 0.030 |
| 5 | 0.55 | 0.200 | 0.028 |
| 6 | 0.60 | 0.195 | 0.026 |
| 7 | 0.65 | 0.170 | 0.023 |
| 8 | 0.70 | 0.150 | 0.021 |
| 9 | 0.75 | 0.130 | 0.020 |
| 10 | 0.80 | 0.090 | 0.016 |
| 11 | 0.85 | 0.080 | 0.013 |
Plotting the dataset reveals a simple line from experimental data
import matplotlib.pyplot as pltplt.plot(propeller_advance_df['J'], propeller_advance_df['K_T'],'b-', lw=1, label='Linear')