Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

Notation

a Parameter in Davis equation (N)

a_B Ballast acceleration (m/s²)

a_T Train deceleration (m/s²)

A Reference area of train (m²)

A_B Ballast area (m²)

A_eq Equivalent leakage area (m²)

A_TU Tunnel area (m²)

b Parameter in Davis equation (Nsm⁻¹)

b₁ Parameter in Davis equation (Nsm⁻¹)

b₂ Parameter in Davis equation (Nsm⁻¹)

B Train cross-sectional area to tunnel cross-sectional blockage ratio

c Parameter in Davis equation (Ns²m⁻²)

c_a Speed of sound in air (ms⁻¹)

C_D Drag coefficient

C_DB Ballast drag coefficient

C_DBO Drag coefficient of bogies

C_DNT Drag coefficient of train nose and tail

C_DW Contact wire drag coefficient

C_D(ψ) Drag coefficient at yaw angle ψ

C_Df(ψ) Drag coefficient increment at yaw angle ψ due to increased wheel/rail friction

C_D(0) Drag coefficient at ψ = 0

C_f Friction coefficient

C_Fi Force coefficient in direction i

C_LB Ballast lift force coefficient

C_LW Overhead wire lift coefficient

C_Mi Moment coefficient about axis i

C_MxL Crosswind lee rail rolling moment coefficient

C_p Pressure coefficient

\frac{p - p_{r}}{0.5 ϱ v^{2}}

$\frac{p - p_{r}}{0.5 ϱ v^{2}}$

C_p1 Pressure coefficient on vertical surface

C_p2 Pressure coefficient on horizontal surface

C_S Smagorinsky coefficient

C_sp Specific heat at constant pressure (Jkg⁻¹K⁻¹)

C_sv Specific heat at constant volume (Jkg⁻¹K⁻¹)

C_ui Air velocity coefficient u_i/v

C_uiB Ballast velocity coefficient u_iB/v

C_uh Horizontal air velocity coefficient u_h/v

C_uh 95 95th percentile of horizontal gust velocity coefficient u_h95/v

C_ux0 Coefficient of velocity close to ballast bed u_x0/v

C_ux2 Square of air velocity coefficient (u_x/v)²

C_μ Constant in k – ε model

d Dispersion of extreme value distribution (m/s)

d_B Ballast size (m)

d_W Contact wire diameter (m)

E Internal energy (J)

f_a Admittance factor

f_c Curvature factor

f_r Track roughness factor

f_s1 Suspension factor – body roll

f_s2 Suspension factor – suspended mass movement

f_s3 Suspension factor – other effects

F (\bar{u})

$F (\bar{u})$

Cumulative distribution function of mean speed

F (\hat{u})

$F (\hat{u})$

Cumulative distribution function of wind gust speed

F_CWP Total contact force between a pantograph and the contact wire (N)

F_HAB Horizontal aerodynamic force on ballast (N)

F_HMB Horizontal mechanical force on ballast (N)

F_i Crosswind aerodynamic force in direction i (i = x,y,z) (N)

F_R Total train resistance (N)

F_RC Train resistance due to track curvature (N)

F_RG Train resistance due to gravity (N)

F_VAB Vertical aerodynamic force on ballast (N)

F_VMB Vertical mechanical force on ballast (N)

F_VAWP Vertical aerodynamic force between pantograph and contact wire (N)

F_VIWP Dynamic inertial force between pantograph and contact wire (N)

F_VSWP Static vertical force between pantograph and contact wire (N)

F_W Contact wire drag or lift force (N)

g Acceleration due to gravity (m/s²)

g_i Body force per unit mass in Navier–Stokes equations (m/s²)

G Gust factor

G (\vec{x}, r)

$G (\vec{x}, r)$

Large eddy simulation filter function

h Reference height (m)

h_Fi Weighting function for crosswind force component i(i = x,y,z)

h_u Under body gap height (m)

H Boundary layer form parameter

H_Fy Longitudinal point of action of side force

H_Fz Longitudinal point of action of lift force (m)

i Track gradient

I_i ith component of turbulence intensity

σ_{u i} / \bar{u_{x}}

$σ_{u i} / \bar{u_{x}}$

(i = x,y,z)

I_R Turbulence intensity relative to the train

k Turbulent kinetic energy

k_i Factor in resistance equations

k_loss Pressure loss coefficient

k_nose Coefficient showing the effect of the train nose

k_R Factor on mass for rotating masses

k_sim Factor used to correct Δp_sim

k_s1 Sand grain roughness of track (m)

k_s2 Sand grain roughness of train under body (m)

k_VK Von Kármán constant

k_i Factors used in drag coefficient equations in Chapter 7 (k = 1–7)

K Constant in Eq. (2.13)

K_B Bulk modulus of air (Pa)

K₁ Factor in Eq. (7.14)

K₂ Factor in Eq. (7.14)

K_W1 Factor in Eq. (7.8)

K_W2 Factor in Eq. (7.8)

l_i Integral turbulence length scale (m)

l_K Kolmogorov dissipation length scale (m)

l_mix Mixing length (m)

l_S Smagorinsky length scale

L Train length (m)

L’ Adjusted train length (m)

L_c Length of container (m)

L_g Length of gaps between containers (m)

L_i Length of intercar gap (m)

L_W Overhead wire length (m)

L_ui Integral length scale of velocity fluctuations (i = x,y,z) (m)

L_{u x}^{'}

$L_{u x}^{'}$

Integral length scale relative to train (m)

m Mode of extreme value distribution (ms⁻¹)

m_W Mass per unit length of catenary wire (kgm⁻¹)

M Train mass (kg)

M_B Ballast stone mass (kg)

M_i Crosswind aerodynamic moments about axis i (i = x,y,z) (Nm)

M_p Primary suspended mass (kg)

M_s Secondary suspended mass (kg)

M_xL Crosswind rolling moment about leeward rail (Nm)

Ma Mach number

n Frequency (Hz)

n_f Reynolds number friction exponent

n_g Characteristic gust frequency in Eq. (11.7) (Hz)

n_W Natural frequency of catenary wire (Hz)

n₁ Crosswind force coefficient parameterisation constant

n₂ Crosswind force coefficient parameterisation constant

N_B Number of bogies

N_P Number of power cars

N_p Number of pantographs

N_T Number of trailing cars

P Pressure (Pa)

p_ext Train external pressure (Pa)

p_int Train internal pressure (Pa)

p_loss Stagnation pressure loss (Pa)

p_max Maximum pressure (Pa)

p_min Minimum pressure (Pa)

p_MPW Peak value of the micropressure wave at a distance r_MPW from the tunnel portal (Pa)

p_o Reference pressure outside tunnel portal (Pa)

p_r Reference pressure (Pa)

p₁ Pressure on vertical structure (Pa)

p₂ Pressure on horizontal structure (Pa)

P (\bar{u})

$P (\bar{u})$

Extreme value probability of mean wind speed

q Centre of gravity height (m)

Q Heat transfer per unit length of tunnel (Js⁻¹m⁻¹)

Q_ij Residual stresses

r Radial coordinate (m)

r_MPW Distance between exit portal and point where micropressure wave is measured (m)

r_TR Track curve radius (m)

R_g Gas constant (J mole⁻¹K⁻¹)

R_B Ballast vertical reaction force (N)

R_S Velocity shear relative to the train

R_T Track radius of curvature (m)

R_TU Hydraulic radius of tunnel (m)

R_ui(τ) Autocorrelation function of velocity component i

R_MxL Ratio of rolling moment coefficients at 90 and 30°yaw

Re Reynolds number

Re_li Reynolds number based on integral length scale

s Streamline coordinate

S Suspension coefficient

Sc Scruton number

\bar{S_{i j}}

$\bar{S_{i j}}$

Mean strain rate tensor

S_Fi(n) Spectral density for force component i (N²s) (i = x,y,z)

S_ui(n) Spectral density of air velocity in i direction (m²s⁻¹)

S_V(n) Spectral density for V (m²s⁻¹)

S_m Shields parameter for ballast roll

S_x Shields parameter for ballast slide

S_{x}^{'}

$S_{x}^{'}$

Shields parameter using friction velocity

S_z Shields parameter for ballast lift

SS_E Sum of the squared approximation errors (Eq. 4.25)

SS_R Sum of the squared approximation variation from mean (Eq. 4.27)

SS_T Sum of the squared true response variation from mean (Eq. 4.26)

t Time (s)

Ta Tachikawa number

T_abs Absolute temperature (K)

T_ui Integral timescale of velocity component I (s)

T_W Wire tension (N)

u(x,t) Wind velocity at point x and time t (ms⁻¹)

u(z,t) Wind velocity at height z and time t (ms⁻¹)

u(h) Wind velocity at height h above ground (ms⁻¹)

\hat{u}

$\hat{u}$

Wind gust velocity (ms⁻¹)

u_c Characteristic wind speed (ms⁻¹)

u_i ith component of air velocity (i = x,y,z) (ms⁻¹)

u_iB ith component of ballast velocity (i = x,y,z) (ms⁻¹)

u_h Horizontal component of velocity (ms⁻¹)

u_h 95 95% confidence limit of ensemble of one-second gust values of u_h(ms⁻¹)

u_{h average} Average value of ensemble of one-second gust values of u_h (ms⁻¹)

u_{h gust} One-second gust value of u_h (ms⁻¹)

u_{h sd} Standard deviation of ensemble of one-second gust values of u_h (ms⁻¹)

u_r Velocity in radial direction (ms⁻¹)

u_x0 Velocity close to ballast bed (ms⁻¹)

u_xr Representative air speed inside tunnel portal (ms⁻¹)

u_{x, z=δ} Velocity at edge of boundary layer (ms⁻¹)

u_θ Velocity in angular direction (ms⁻¹)

u_τ Shear velocity

\sqrt{τ_{w} / ρ}

$\sqrt{τ_{w} / ρ}$

(ms⁻¹)

u⁺ u_x/u_τ

u₁ Lower velocity limit in cumulative probability distribution for human stability (ms⁻¹)

u₂ Upper velocity limit in cumulative probability distribution for human stability (ms⁻¹)

{\hat{u}}_{50}

${\hat{u}}_{50}$

Once in 50-year gust speed (ms⁻¹)

u(ε) Wind speed at an incident angle ε to contact wire (ms⁻¹)

u(90) Wind speed at 90°to contact wire (ms⁻¹)

v Train speed (ms⁻¹)

v_b Balancing train speed (ms⁻¹)

V Wind velocity relative to train (ms⁻¹)

V(t) Wind velocity relative to train at time t (ms⁻¹)

V(x,t) Wind velocity relative to train at point x and time t (ms⁻¹)

V(h) Wind velocity relative to train at height h above ground (ms⁻¹)

V_N Velocity normal to train surface in panel method calculation (ms⁻¹)

V_∞ Free stream velocity relative to train in panel method calculation (ms⁻¹)

V_FY Vertical point of action of side force (m)

w Contact wire weight/unit length (kg/m)

x Distance in train direction of travel, measured from train nose (m)

x_i x coordinate of panel i

x_r x coordinate of end of train

X_W Longitudinal distance along contact wire span, measured from span centre (m)

X_{F i}^{2}

$X_{F i}^{2}$

Aerodynamic admittance for force component i

y Lateral distance from the centre of the track (m)

y_i y coordinate of panel i

y_p Primary bump stop displacement distance (m)

y_s Secondary bump stop displacement distance (m)

y_TR Semitrack width (m)

Y Lateral distance of vertical structure from the centre of the track (m)

Y_W Maximum contact wire lateral displacement under wind loading (m)

z Vertical distance from the top of the rail (m)

Z Vertical distance of horizontal structure from the top of the rail (m)

Z_W Vertical distance of contact wire from support points (m)

z_d Velocity profile displacement height (m)

z₁ z at the bottom of train (m)

z₂ z at the top of train (m)

z₀ Surface roughness length (m)

z₀₁ Surface roughness of sleepers and ballast (m)

z₀₂ Surface roughness of train under body (m)

z⁺ zu_τ/ν

α Parameter in definition of characteristic velocity

α₀ Wheel unloading factor

β Wind direction relative to track (degrees or radians)

β_i Angle of panel i to the flow direction (degrees or radians)

γ Ratio of specific heats

δ Boundary layer thickness (m)

δ_d Boundary layer displacement thickness (m)

δ_m Boundary layer momentum thickness (m)

Δ Size of computation cell

ΔC_p Peak-to-peak pressure coefficient

ΔC_pB Pressure coefficient across ballast particle

Δp Peak-to-peak pressure (Pa)

Δp₉₅ 95% confidence limit of Δp (Pa)

Δp_average Ensemble average of Δp (Pa)

Δp_sd Ensemble standard deviation of Δp (Pa)

Δp_sim Numerically simulated value of Δp (Pa)

Δp_fr Pressure change due to friction effects due to the entry of the main part of the train into the tunnel (Pa)

Δp_HP Pressure change in a tunnel due to the passing of a train nose (Pa)

Δp_N Pressure change due to the passing of the train nose, also initial pressure rise (Pa)

Δp_T Pressure change due to the entry of the train tail (Pa)

Δt Computational time step (s)

Δt_p Characteristic time interval for the initial pressure rise

= \frac{2 k_{n o s e} R_{T U}}{v}

$= \frac{2 k_{n o s e} R_{T U}}{v}$

Δx Distance between computational nodes (m)

ε Turbulence dissipation rate or overhead wire incident angle

ζ Train wetted perimeter (m)

η Wheel/rail friction coefficient

θ Angular coordinate

ϑ Parameter in Eqs. (3.5) and (3.6)

κ Weibull distribution shape factor

κ^′ Modified Weibull distribution shape factor

λ Weibull distribution scale factor (ms⁻¹)

λ^′ Modified Weibull distribution scale factor (ms⁻¹)

μ Dynamic viscosity of air (kgm⁻¹s⁻¹)

μ′ Second viscosity of air (kgm⁻¹s⁻¹)

μ_B Ballast friction coefficient

μ_t Turbulent eddy dynamic viscosity (kgm⁻¹s⁻¹)

ν Kinematic viscosity of air (m²s⁻¹)

ν_t Turbulent eddy kinematic viscosity (m²s⁻¹)

ξ_W Mechanical damping ratio of catenary wire

π₁ Parameter in cumulative distribution function in Eq. (8.14)

π₂ Parameter in cumulative distribution function in Eq. (8.14)

ϱ Density of air (kgm⁻³)

ϱ_B Density of ballast (kgm⁻³)

ϱ₀ Reference density of air outside tunnel portal (kgm⁻³)

σ_ui Component of turbulence in direction i (i = x,y,z) (m/s)

τ Time (s)

τ_K Kolmogorov time scale (s)

τ_dyn Pressure tightness time (s)

τ_w Boundary shear stress (Pa)

ϕ Velocity potential (s⁻¹)

φ Stream function (s⁻¹)

ψ Yaw angle (degrees or radians)

ω Vorticity (s⁻¹)

Ω_r Accident risk cumulative density function in Eq. (8.9)

Ω_s Pedestrian stability CDF in Eq. (8.12)

Ω Solid angle associated with micropressure wave emission

Λ Source volume flow rate per unit length from point source

Λ^′ Source volume flow rate per unit length from panel

e

$e$

Error in optimisation regression analysis

k_{i}

$k_{i}$

Regression coefficients in optimisation regression analysis

ℝ² Coefficient of determination in optimisation regression analysis

ℝ_{a d}^{2}

$ℝ_{a d}^{2}$

Adjusted coefficient of determination in optimisation regression analysis

x_{i}

$x_{i}$

Function variable in optimisation regression analysis

y_{i}

$y_{i}$

Function variable in optimisation regression analysis

¯ Time average, mean or filtered value

′ Fluctuating value

″ Subgrid component

ˆ Extreme or gust value

˜ Normalisation of velocities with characteristic wind speed

→ Vector

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.

Table of Contents for Notation

Create new playlist

Sign In

Sign Up

Notation

Table of Contents for
Notation