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# Early-stage ship powering prediction (see DDS 051-1, MAY 1982) #
# Code written by Jay Borthen, April 2013 #
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# A: Section area
# A_fins: Area of fin centerplane times the number of fins
# ATTC: American Towing Tank Conference
# A_v: Ship above-water transverse area
# A_x: Section area at Station of Maximum Area
# A_0: Section area at Station 0
# A_20: Section area at Station 20
# BWL: Maximum beam of waterline at a particular draft
# B_x: Beam at Design Waterline and at Station of Maximum Area
# B_20: Beam at Design Waterline and at Station 20
# C_A: Correlation-allowance coefficient. This is a function of bottom paint and
# the condition of the bottom (e.g. roughness, fouling, etc.)
# C_AA: Air drag coefficient based on ship frontal area
# C_D: Drag coefficient
# C_D_Ap: Appendage drag coefficient. Because the formula herein for P_EAp is not non-dimensional, the values
# of C_DAp which is used to compute P_EAp are applicable for English-unit computations only.
# C_DBTD: Drag coefficient for bow thruster duct openings
# C_DFin: Drag coefficient for stabilizer fins
# C_F: Frictional resistance coefficient. Tabulated values given in "Coefficients
# for International Towing Tank Conference 1957 Model Ship Correlation Line"
# authored by Hadler, J.B., April 1958
# C_P: Longitudinal prismatic coefficient
# C_R: Residuary resistance coefficient
# CRPP: Controllable-reversible-pitch propeller
# C_RTSS: Residuary resistance coefficient for TSS hull forms
# C_S: Wetted surface coefficient. C_S = (S / (Nabla*LWL)^0.5) or alternatively determined from Figure 2 in DDS 051-1.
# C_STSS: Wetted surface coefficient for TSS hull forms
# C_WP: Waterplane area coefficient at Design Waterline
# C_StillAir: Still-air drag coefficient
# C_x: Section coefficient at station of maximum area (i.e. Midship coefficient)
# C_Nabla: Volumetric coefficient
# Delta: Ship displacement
# D_BTD: Diameter of bow thruster duct openings
# D_P: Propeller diameter
# DWL: Design waterline
# EAR: Propeller Expanded-Area Ratio
# FPP: Fixed-Pitch propeller
# ITTC: International Towing Tank Conference
# i_E: Design waterline entrance half-angle in degrees
# J: Propeller advance coefficient
# K_T: Propeller thrust coefficient
# K_l: Constant required to convert to standard units of power
# L: Ship length (usually LBP)
# L_PP: Length between perpendiculars
# LWL: Length on waterline at Design Waterline
# PD: Propeller pitch-to-diameter ratio
# P_E: Effective power
# P_EAA: Effective power due to still-air drag
# P_EAP: Effective power due to appendages.
# P_EBH: Bare hull effective power
# P_EBTD: Effective power due to bow thruster duct openings
# P_EFin: Effective power due to stabilizer fins
# P_EMisc: Effective power due to miscellaneous appendage items, hull openings, etc.
# P_ETot: Ship total effective power, inclusive of effective power added by still-air drag and by power margin
# PMF: Power margin factor. This "shall be applied to effective power, over the
# entire speed range" (perr DDS 051-1).
# P_S: Shaft power
# R_AA: Resistance due to still air
# R_AP: Resistance of appendages
# R_BH: Bare hull resistance
# R_F: Ship frictional resistance
# Rn: Reynolds number
# R_R: Residuary resistance
# R_RShip: Ship residuary resistance for a specific hull form
# R_RTSS: Residuary resistance of equivalent Taylor Standard Series hull form
# R_RPerTon: Residuary resistance per ton of displacement, R_RPerTon = R_R / Delta
# R_T: Total resistance, R_T = R_BH + R_AP + R_AA
# rps: revolutions per second
# S: Wetted surface
# S_Ship: Wetted surface of specific ship
# S_TSS: Wetted surface of equivalent TSS hull form. Determined from Figure
# 2 in DDS 051-1 (MAY 1984). The figure included in DDS 051-1 is from
# "Systematic Resistance Experiments with Taylor Models Having a Beam-
# Draft Ratio of 4.50" authored by Hahnel, G. et al., July 1966
# SWSF: Ship wetted surface factor (i.e. S_Ship/S_TSS). This is a function
# of general ship type, bow bulb or dome, transom size and skeg size.
# The bow dome and skeg wetted surface is typically included in SWSF.
# SWSF_alt: Alternate ship wetted surface factor (e.g. S/((Delta*LWL)^0.5) where S is in ft^2, Delta is in
# long tons, and LWL is in ft). This is typically a function of C_p, C_x, Delta/((LWL/100)^3),
# B/T, general ship type, bow bulb, and transom size. Use Figure 3 from DDS 051-1 to assess
# effects of C_x and B/T.
# t: Thrust-deduction fraction, t = (Thrust - R_T) / Thrust
# T_Mean: Ship mean draft
# TSS: Taylor Standard Series
# T_x: Ship draft on design waterline at station of maximum area
# TWL: Ship draft to a particular waterline
# V_A: Propeller speed of advance
# V_S: Ship speed
# WCF: Worm curve factor. Function of speed range.
# w: Taylor wake fraction, w = (V_S - V_A) / V_S
# Delta_App: Displacement of appendages
# Delta_BareHull: Bare hull displacement to Design Waterline
# Delta_Total: Displacement of fully-appended hull to Design Waterline
# Nabla: Ship submerged volume
# Nabla_BareHull: Bare hull volume to Design Waterline
# eta_D: Propulsive coefficient
# eta_O: Propeller Open-water efficiency
# eta_R: Propeller relative-rotative efficiency
# lambda: Ship model linear scale ratio
# nu: Kinematic viscosity of salt water at specified temperature and 3.5% salinity
# rho: Sea water mass density, 1.9905 slugs/ft^2 (to convert from Table 4 in DDS 051-1 values to g/cm^3,
# multiply by 0.01602 and then by 32.174)
# rho_A: Mass density of air
# designStage:
#
# Stage 1: During Feasibility and Preliminary Design, prior to development of
# a preliminary body plan, appendage configuration, etc.
# Stage 2: During Preliminary and Contract Design, prior to conduct of self-
# propelled model tests
# Stage 3: During Preliminary and Contract Design, after self-propelled model
# tests with the stock propeller have been conducted.
# Stage 4: During the final stages of Contract Design, after self-propelled
# model tests with the design propeller have been conducted.
# hullCondition: For U.S. Navy ships having the Navy vinyl paint system applied
# over sandblasted bottom plating, and having been out of drydock
# for only a short time, hullCondition=0. For estimating the
# resistance of U.S. Navy ships two years after the initial
# drydocking, hullCondition=1.
# KinematicViscosityTable: Table of salt water kinematic viscosity values at
# different temperatures.
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# Initialize variables
C_A<-0
# =====================
# Ship Characteristics:
# =====================
ShipType<-3 # 1 = Aircraft Carriers, 2 = Destroyer-Type Ships, 3 = Naval Auxiliaries
LWL<-465.88 # in ft
B_x<-62.00 # in ft
T_x<-20.00 # in ft
Delta_BareHull<-8400 # in long tons
Delta_App<-100 # in long tons
Delta_Total<-Delta_BareHull+Delta_App
C_x<-0.825
C_p<-0.610
BT<-B_x/T_x # Beam to draft ratio
Nabla_BareHull<-294000 # in ft^3
C_Nabla_BareHull<-0.002908
D_P<-17 # in ft
S<-31849 # in ft^2 <-- if "S" is unknown, approximate via S = 1.025*Lpp*(C_B*B+1.7*T) = 1.025*((Nabla_BareHull/T_x)+1.7*Lpp*T_x)
A_v<-4030 # in ft^2
# ================================
# Constraints, Ratios, and Factors:
# ================================
Temp_SW<-59 # in degrees F
rho<-1.9905 # in (lb)*(sec^2)*(ft^4)
nu<-0.000012817 # in (ft^2)/(sec)
# C_A_1 is calculated via formula from "Prediction of Resistance and Propulsion Power of Ships" (Kristensen, et al, 2012)
C_A_1<-(0.5*log10(Delta_Total*1.01605)-0.1*(log10(Delta_Total*1.01605))^2)/1000 # 1.01605 is conversion factor from long tons to tonnes
C_A<-0.0004 <-- Typical default value
# if (LWL>=190 & LWL<=960){
# C_A<-(0.008289/(LWL^(1/3)))-0.00064
# }else if (LWL<190){
# C_A<-0.0008
# }else{
# C_A<-0.0002
# }
# if (hullCondition==1){
# C_A<-C_A+0.0007
# }
C_S_TSS<-2.54 # Visually estimated from DDS 051-1 Figure 2
C_S_Ship = (S/((Nabla_BareHull*LWL)^0.5))
(C_S_Ship/C_S_TSS)
(S/((Delta_Total*LWL)^0.5))
PropNum<-2 # shafts assumed to be strut-supported
if (PropNum==2){
C_D_AP<-((0.000004*LWL^2)-(0.0066*LWL)+5.0053)*10^(-5)
}else if (PropNum==1){
# TBD
}else{
paste("Number of props is outside bounds.")
}
if (ShipType==1){
C_AA<-0.45
}else if (ShipType==2){
C_AA<-0.70
}else if (ShipType==3){
C_AA<-0.75
}else{
paste("Ship type unknown.")
}
hullCondition<-0
designStage<-1
VL<-seq(0.60,1.3,by=0.1) # EXAMPLE
V_knots<-VL*(LWL^0.5) # EXAMPLE
WCF<-c(3.45,3.22,2.20,1.54,1.09,0.92,0.83,0.80) # EXAMPLE
#VL<-seq(0.50,0.95,by=0.05) # VL: Speed-to-Length^(1/2) ratio
#V_knots<-VL*(LWL^0.5)
#WCF_AO177<-c(0.89,0.87,0.91,0.92,0.88,0.80,0.73,0.81,0.95,1.03)
Fn<-0.2976*V_knots/sqrt(LWL) # V_knots in knots, LWL in ft, and g in ft/sec^2. 0.2976 = (1.68781 ft/sec/knot)/sqrt(32.174 ft/sec^2)
if (designStage==0){
margin<-10
}else if (designStage==1){
margin<-8
}else if (designStage==2){
margin<-6
}else if (designStage==3){
margin<-4
}
PMF<-(1+(margin/100))
# Calculate Reynold's number:
#KinematicViscosityTable<-read.table("SaltWaterKinematicViscosityTable.csv",sep=",",header=TRUE)
#nu<-KinematicViscosityTable[which(((KinematicViscosityTable[,1])==waterTemp)),2] # in (m^2/s)*10^6
Rn<-(V_knots*1.68781*LWL)/nu # 1.68781 is the conversion factor from knots to ft/sec
# Determine frictional resistance coefficient:
C_F<-0.075/((log10(Rn)-2)^2) # Utilizes ITTC Line
# Calculate ship frictional resistance:
#WaterDensityTable<-read.table("WaterDensityTable.csv",sep=",",header=TRUE)
#rho<-WaterDensityTable[which(((WaterDensityTable[,1])==waterTemp)),2] # in (g/m^3)
#rho<-rho*0.01602*32.174
R_F<-(rho/2)*S*((V_knots*1.68781)^2)*(C_F+C_A) # 1.68781 is the conversion factor from knots to ft/sec
S_TSS<-C_S_TSS*(Nabla_BareHull*LWL)^0.5
LNabla<-round(LWL/(Nabla_BareHull^(1/3)),1) # LNabla: Length-to-Volume^(1/3) ratio
# The following C_R equation is from Kristensen, et al.
C_R<-(40733.90490*(Fn^5)-36751.17452*(Fn^4)+13395.20097*(Fn^3)-2415.43170*(Fn^2)+215.01129*(Fn)-7.26)/1000
# At the same value of V/sqrt(LWL), R_RTSS/Delta_TSS = R_RShip/Delta_Ship
# R_RTSS_to_Delta<- rho*S_TSS*(V_knots^2)*C_R/(2*Delta)
R_R_TSS<- rho*S_TSS*(V_knots^2)*C_R/2
R_R_Ship<-R_R_TSS*WCF
R_T<-R_F+R_R
C_D_Ap<-(-1.862*10^-09)*LWL^3+(4.615*10^-6)*LWL^2-(4.306*10^-3)*LWL+3.536 # Equation from MNVDET
EHP<-(C_T*rho*S*V_knots^3)/(2*550) # 550 ft-lb/sec