TrainRun.jl/src/formulary.jl

223 lines
9.0 KiB
Julia

#!/usr/bin/env julia
# -*- coding: UTF-8 -*-
# __author__ = "Max Kannenberg"
# __copyright__ = "2022"
# __license__ = "ISC"
#########################
## literature the driving dynamics equations are based on:
##
## @incollection{Bruenger:2014, % Chapter 4
## author = {Brünger, Olaf and Dahlhaus, Elias},
## year = {2014},
## title = {Running Time Estimation},
## pages = {65--90},
## booktitle = {Railway Timetabling \& Operations.},
## editora = {Hansen, Ingo A.},
## editorb = {Pachl, Jörn},
## isbn = {978-3-777-10462-1},
## publisher = {Eurailpress DVV Media Group},
## }
## @Book{Wende:2003,
## author = {Wende, Dietrich},
## date = {2003},
## title = {Fahrdynamik des Schienenverkehrs},
## isbn = {978-3-322-82961-0},
## publisher = {Springer-Verlag},
## }
#########################
#approxLevel = 6
v00 = 100/3.6 # velocity factor (in m/s)
## calculate forces
#TODO: replace the ? ? ?
"""
calcTractionUnitResistance(v, train)
Calculate the vehicle resistance for the traction unit of the `train` dependend on the velocity `v`.
...
# Arguments
- `v::AbstractFloat`: the current velocity in m/s.
- `train::Train`: ? ? ?
...
# Examples
```julia-repl
julia> calcTractionUnitResistance(30.0, ? ? ?)
? ? ?
```
"""
function calcTractionUnitResistance(v::AbstractFloat, train::Train)
# equation is based on [Wende:2003, page 151]
f_Rtd0 = train.f_Rtd0 # coefficient for basic resistance due to the traction units driving axles (in ‰)
f_Rtc0 = train.f_Rtc0 # coefficient for basic resistance due to the traction units carring axles (in ‰)
f_Rt2 = train.f_Rt2 # coefficient for air resistance of the traction unit (in ‰)
m_td = train.m_td # mass on the traction unit's driving axles (in kg)
m_tc = train.m_tc # mass on the traction unit's carrying axles (in kg)
F_R_tractionUnit = f_Rtd0/1000 * m_td * g + f_Rtc0/1000 * m_tc * g + f_Rt2/1000 * (m_td+m_tc) * g * ((v + Δv_air) /v00)^2 # vehicle resistance of the traction unit (in N) # /1000 because of the unit ‰
# TODO: use calcForceFromCoefficient? F_R_tractionUnit = calcForceFromCoefficient(f_Rtd0, m_td) + calcForceFromCoefficient(f_Rtc0, m_tc) + calcForceFromCoefficient(f_Rt2, m_td+m_tc) * ((v + Δv_air) /v00)^2 # vehicle resistance of the traction unit (in N)
return F_R_tractionUnit
#TODO: same variable name like in the rest of TrainRuns? return R_traction
end #function calcTractionUnitResistance
"""
TODO
calculate and return the freight wagons' vehicle resistance dependend on the velocity
"""
function calcFreightWagonsResistance(v::AbstractFloat, train::Train)
# equation is based on a combination of the equations of Strahl and Sauthoff [Wende:2003, page 153]
f_Rw0 = train.f_Rw0 # coefficient for basic resistance of the set of wagons (consist) (in ‰)
f_Rw2 = train.f_Rw2 # coefficient fo the consistsr air resistance (in ‰)
m_w = train.m_w # mass of the set of wagons (consist) (in kg)
F_R_wagons = m_w *g *(f_Rw0/1000 + f_Rw2/1000 * (v /v00)^2) # vehicle resistance of freight wagons (in N) with Strahl # /1000 because of the unit ‰
# TODO: use calcForceFromCoefficient? F_R_wagons = calcForceFromCoefficient(f_Rw0, m_w) + ...
return F_R_wagons
end #function calcWagonsResistance
"""
TODO
calculate and return the passenger wagons' vehicle resistance dependend on the velocity
"""
function calcPassengerWagonsResistance(v::AbstractFloat, train::Train)
# equation is based on the equations of Sauthoff [Wende:2003, page 153]
f_Rw0 = train.f_Rw0 # coefficient for basic resistance of the set of wagons (consist) (in ‰)
f_Rw1 = train.f_Rw1 # coefficient for the consists resistance to rolling (in ‰)
f_Rw2 = train.f_Rw2 # coefficient fo the consistsr air resistance (in ‰)
m_w = train.m_w # mass of the set of wagons (consist) (in kg)
F_R_wagons = m_w *g *(f_Rw0/1000 + f_Rw1/1000 *v /v00 + f_Rw2/1000 * ((v + Δv_air) /v00)^2) # vehicle resistance of passenger wagons (in N) with Sauthoff # /1000 because of the unit ‰
# TODO: use calcForceFromCoefficient? F_R_wagons = calcForceFromCoefficient(f_Rw0, m_w) + ...
return F_R_wagons
end #function calcWagonsResistance
function calcForceFromCoefficient(f_R::Real, m::Real)
# equation is based on [Wende:2003, page 8]
# f_R: specific resistance (in ‰)
# m: vehicle's mass (in kg)
F_R = f_R /1000 *m *g # Resisting Force (in N) # /1000 because of the unit ‰
return F_R
end #function calcForceFromCoefficient
function calcAcceleration(F_T::Real, F_R::Real, m_train::Real, ξ_train::Real)
# equation is based on [Bruenger:2014, page 72] with a=dv/dt
# F_T: tractive effort (in N)
# F_R: resisting forces (in N)
# m_train: train's mass (in kg)
# ξ_train: train's rotation mass factor (without unit)
a = (F_T - F_R) /m_train /ξ_train # acceleration (in m/s)
return a
end #function calcAcceleration
function calc_Δs_with_Δt(Δt::Real, a_prev::Real, v_prev::Real)
# equation is based on [Wende:2003, page 37]
# Δt: time step (in s)
# a_prev: acceleration from previous data point
# v_prev: velocitiy from previous data point
Δs = Δt * (2*v_prev + Δt*a_prev) /2 # step size (in m)
return Δs
end #function calc_Δs_with_Δt
function calc_Δs_with_Δv(Δv::Real, a_prev::Real, v_prev::Real)
# equation is based on [Wende:2003, page 37]
# Δv: velocity step (in m/s)
# a_prev: acceleration from previous data point
# v_prev: velocitiy from previous data point
Δs = ((v_prev + Δv)^2 - v_prev^2)/2/a_prev # step size (in m)
return Δs
end #function calc_Δs_with_Δv
function calc_Δt_with_Δs(Δs::Real, a_prev::Real, v_prev::Real)
# equation is based on [Wende:2003, page 37]
# Δs: distance step (in m)
# a_prev: acceleration from previous data point
# v_prev: velocitiy from previous data point
Δt = sign(a_prev) *sqrt((v_prev /a_prev)^2 + 2 *Δs /a_prev) - v_prev /a_prev # step size (in m/s)
return Δt
end #function calc_Δt_with_Δs
function calc_Δt_with_Δv(Δv::Real, a_prev::Real)
# equation is based on [Wende:2003, page 37]
# Δv: velocity step (in m/s)
# a_prev: acceleration from previous data point
Δt = Δv /a_prev # step size (in s)
return Δt
end #function calc_Δt_with_Δv
function calc_Δt_with_constant_v(Δs::Real, v::Real)
# equation is based on [Wende:2003, page 37]
# Δs: distance step (in m)
# v: constant velocity (in m/s)
Δt = Δs /v # step size (in s)
return Δt
end #function calc_Δt_with_constant_v
function calc_Δv_with_Δs(Δs::Real, a_prev::Real, v_prev::Real)
# equation is based on [Wende:2003, page 37]
# Δs: distance step (in m)
# a_prev: acceleration from previous data point
# v_prev: velocitiy from previous data point
Δv = sqrt(v_prev^2 + 2*Δs*a_prev) - v_prev # step size (in m/s)
return Δv
end #function calc_Δv_with_Δs
function calc_Δv_with_Δt(Δt::Real, a_prev::Real)
# equation is based on [Wende:2003, page 37]
# Δt: time step (in s)
# a_prev: acceleration from previous data point
Δv = Δt * a_prev # step size (in m/s)
return Δv
end #function calc_Δv_with_Δt
function calcBrakingDistance(v_start::Real, v_end::Real, a_braking::Real, approxLevel::Integer)
# equation is based on [Wende:2003, page 37]
# v_start: velocity at the start of braking (in m/s)
# v_end: target velocity at the end of braking (in m/s)
# a_braking: constant braking acceleration (in m/s^2)
s_braking = (v_end^2 - v_start^2) /2 /a_braking # braking distance (in m)
# TODO: also possible: calc_Δs_with_Δv(v_end-v_start, a_braking, v_start)
# return max(0.0, ceil(s_braking, digits=approxLevel)) # ceil is used to be sure that the train stops at s_exit in spite of rounding errors
return max(0.0, ceil(s_braking, digits= approxLevel +1)) # ceil is used to be sure that the train stops at s_exit in spite of rounding errors
end #function calcBrakingDistance
function calcBrakingStartVelocity(v_end::Real, a_braking::Real, s_braking::Real, approxLevel::Integer)
# equation is based on [Wende:2003, page 37]
# v_end: target velocity at the end of braking (in m/s)
# a_braking: constant braking acceleration (in m/s^2)
# s_braking: braking distance (in Ws)
v_start = sqrt(v_end^2 - 2*a_braking *s_braking) # braking start velocity (in m/s)
# return floor(v_start, digits= approxLevel)
return floor(v_start, digits= approxLevel +1)
end #function calcBrakingStartVelocity
function calcBrakingAcceleration(v_start::Real, v_end::Real, s_braking::Real)
# equation is based on [Wende:2003, page 37]
# v_start: braking start velocity (in m/s)
# v_end: target velocity at the end of braking (in m/s)
# s_braking: braking distance (in Ws)
a_braking = (v_end^2 - v_start^2) /2 /s_braking # constant braking acceleration (in m/s^2)
return a_braking
end #function calcBrakingAcceleration