#!/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 ? ? ? """ tractionUnitResistance(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> tractionUnitResistance(30.0, ? ? ?) ? ? ? ``` """ function tractionUnitResistance(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 forceFromCoefficient? F_R_tractionUnit = forceFromCoefficient(f_Rtd0, m_td) + forceFromCoefficient(f_Rtc0, m_tc) + forceFromCoefficient(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 tractionUnitResistance """ TODO calculate and return the freight wagons' vehicle resistance dependend on the velocity """ function freightWagonsResistance(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 forceFromCoefficient? F_R_wagons = forceFromCoefficient(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 passengerWagonsResistance(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 forceFromCoefficient? F_R_wagons = forceFromCoefficient(f_Rw0, m_w) + ... return F_R_wagons end #function calcWagonsResistance function forceFromCoefficient(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 forceFromCoefficient function acceleration(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 acceleration function 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 support point # v_prev: velocitiy from previous support point Δs = Δt * (2*v_prev + Δt*a_prev) /2 # step size (in m) return Δs end #function Δs_with_Δt function 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 support point # v_prev: velocitiy from previous support point Δs = ((v_prev + Δv)^2 - v_prev^2)/2/a_prev # step size (in m) return Δs end #function Δs_with_Δv function 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 support point # v_prev: velocitiy from previous support 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 Δt_with_Δs function 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 support point Δt = Δv /a_prev # step size (in s) return Δt end #function Δt_with_Δv function 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 Δt_with_constant_v function 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 support point # v_prev: velocitiy from previous support point Δv = sqrt(v_prev^2 + 2*Δs*a_prev) - v_prev # step size (in m/s) return Δv end #function Δv_with_Δs function 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 support point Δv = Δt * a_prev # step size (in m/s) return Δv end #function Δv_with_Δt function brakingDistance(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: 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 brakingDistance function brakingStartVelocity(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 brakingStartVelocity function brakingAcceleration(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 brakingAcceleration