Chapter 7: Train Movement and Energy Consumption

Example 7.1, Page 203

In [4]:
import matplotlib.pyplot as plt
%matplotlib inline

#Variable declaration
a=5.;#aceleration in kmphps
t1=30.;#in seconds
vm=a*t1;#maximum speed in kmph
tfr=10.;#time for free running in mins
b=5.;#retardation in kmphps

#Calculations&Results
ts=vm/b;#time for retardation in seconds
dta=((vm*t1)/(2*3600));#distance travelled during acceleration period
dtfr=((vm*tfr*60)/(3600));#distance travelled during retardation period
dtbp=dta;#distance travelled during breaking period
td=dta+dtfr+dtbp;#total distance between stations
print "\npart (a) "
print "total distance between station is %.1f km"%td
T=[0,t1,(t1+(tfr*60)),(t1+(t1+(tfr*60)))];#
V=[0,vm,vm,0];#
plt.plot(T,V)
plt.xlabel("Time in seconds ")
plt.ylabel("Spped in Km per Hour")
va=(td*3600)/(t1+(tfr*60)+ts);#average speed in kmph
print "part (b) "
print "average speed is %.2f kmph"%va
tst=5;#stop time in mins
vs=(td*3600)/(t1+(tfr*60)+ts+(tst*60));#sheduled speed in kmph
print "part (c) "
print "sheduled speed is %.2f kmph"%vs
part (a) 
total distance between station is 26.2 km
part (b) 
average speed is 143.18 kmph
part (c) 
sheduled speed is 98.44 kmph

Example 7.2, Page 204

In [5]:
import math
import matplotlib.pyplot as plt
%matplotlib inline

#Variable declaration
a=1.7;#aceleration in kmphps
b=3.3;#kmphps
s=1400;#m
va=42;#kmph

#Calculations&Results
tr=((s*10**-3)/va)*3600;#secomds
k=((1./(2*a)))+((1./(2*b)));#
vm=((tr/(2*k))-math.sqrt(((tr**2)/(4*k**2))-((3600*s*10**-3)/k)));#in kmph
t1=vm/a;#seconds
t3=vm/b;#seconds
t2=tr-(t1+t3);#seconds
T=[0,(t1),(t1+t2),(t1+t2+t3)];
V=[0,vm,vm,0];
plt.plot(T,V);
plt.xlabel("Time in seconds ")
plt.ylabel("Spped in Km per Hour")
Out[5]:
<matplotlib.text.Text at 0xb129fe6c>

Example 7.3, Page 204

In [35]:
import math

#Variable declaration
a=2.4;#aceleration in kmphps
b=3.2;#retardation in kmphps
s=1.5;#in km
vs=45;#shedule speed in kmph

#Calculations
ts=(s*3600)/vs;#shedule time in seconds
tst=20;#stop time
tr=ts-tst;#actual time for run in seconds
k=((1/(2*a))+(1/(2*b)));#constant
vm=((tr/(2*k))-math.sqrt(((tr**2)/(4*k**2))-((3600*s)/k)));#in kmph

#Result
print "maximum speed is %.f kmph"%vm
maximum speed is 74 kmph

Example 7.4, Page 205

In [36]:
import math

#Variable declaration
s=1.5;#in Km
a=0.8;#aceleration in kmphps
tsr=26;#time for stop in seconds
rm=1.3;#ratio
b=3.2;#retardation in kmphps

#Calculations
k=((1/(2*a))+(1/(2*b)));#constant
T=1;#assume
va1=(3600*s)/T;#average spped
vm1=(va1*rm);#maximum speed
vm=math.sqrt((vm1-va1)/k);#maximum speed in kmph
va=vm/1.3;#actua speed in kmpj
ta=(3600*s)/va;#actual time in seconds
ts=ta+tsr;#shedule time
vs=(s*3600)/ts;#shedule speed in kmph

#Result
print "schedule speed is %.f kmph"%vs
schedule speed is 30 kmph

Example 7.5, Page 205

In [40]:
#Variable declaration
S=1.;# in km
Vs=30.;# in km/h
Ts=(S*3600)/Vs; # in sec
D=20;# duration of stop in sec

#Calculations
T=Ts-D;# in sec
Va=(S*3600)/T;# Average speed in km/h
Vm=1.25*Va;# Maximum speed in km/h
beta1=3;# braking retardation in km/h/sec
A=((Vm*T)-(S*3600))/Vm**2;
B=1./(2*beta1);
alfa=1./(2*(A-B));

#Result
print "The Acceleration,alfa is (km/h/sec) = %.1f "%alfa
The Acceleration,alfa is (km/h/sec) = 1.8 

Example 7.6, Page 206

In [44]:
#Variable declaration
S=4;# in km
Vs=45;# in km/h
Ts=(S*3600)/Vs; # in sec
D=30;# duration of stop in sec

#Calculations
T=Ts-D;# in sec
Vm=70.;# Maximum speed in km/h
alfa=1.5;# in km/h/sec
A=((Vm*T)-(S*3600))/Vm**2;
B=1./(2*alfa);
Beta=1./(2*(A-B));

#Result
print "Retardation(km/h/sec) = %.3f"%Beta
Retardation(km/h/sec) = 0.574

Example 7.7, Page 206

In [45]:
#Variable declaration
S=1.6;# in km
Va=40;# in km/h
V1=64;# in km/h
alfa=2.0;#in km/p/sec
Beta_c=0.16;# in km/h/sec
Beta=3.2;# in km/h/sec

#Calculations&Results
t1=V1/alfa;# in sec
print "Duration of Acceleration,t1(sec) = %.f"%t1
T=(S*3600)/Va;# in sec
# Formula: T=(V1/alfa)+((V1-V2)/Beta_c)+(V2/Beta)
V2=(t1+(V1/Beta_c)-T)/((1/Beta_c)-(1/Beta));
t2=(V1-V2)/Beta_c;
print "Duration of coasting,t2(sec) = %.2f"%t2
t3=V2/Beta;
print "Duration of braking,t3(sec) = %.2f"%t3
Duration of Acceleration,t1(sec) = 32
Duration of coasting,t2(sec) = 96.84
Duration of braking,t3(sec) = 15.16

Example 7.8, Page 209

In [48]:
#Variable declaration
W=200;# weight of train in tonnes
D=0.9;# diameter in m
G=(1./200)*100;#percentage gradient
r=50;# in N/tonne
gama=4;# gear ratio
eta=0.80;# gearing efficiency
We=1.10*W;# in tonne
Vm=48.;# maximum speed in km/h
t1=30;# in sec

#Calculations
alfa=Vm/t1;# in km/h/sec
Ft=(277.8*We*alfa)+(98.1*W*G)+(W*r);# tractive effect required in N
T1=(Ft*D)/(eta*2*gama);# in N-m
T=round(T1/8);

#Result
print"Torque developed by each motor,T(N-m) = %.f"%T
Torque developed by each motor,T(N-m) = 2067

Example 7.9, Page 210

In [49]:
#Variable declaration
V=3000.;# line voltage in volts
W=200.;# weight of train in tonnes
D=0.9;# diameter in m
G=(30./1000)*100;#percentage gradient
r=50;# in N/tonne
gama=4.;# gear ratio
Vm=50.;#in km/h
eta=0.9;# gearing efficiency

#Calculations&Results
We=1.10*W;# in tonne
T=4*6000;# in N-m
eta_m=85./100;# efficiency of motor
Ft=(eta*T*2*gama)/D;
A=(98.1*W*G)+(W*r);
B=Ft-A;
alfa=B/(277.8*We);# tractive effect required in N
t=Vm/alfa;
print "Time taken ,t(sec) = %.2f"%t
Po=(Ft*Vm)/3600;# in kw
Pi=Po/eta_m;
It=(Pi*1000)/V;# in A
I=It/4
print "Current drawn per motor,I(A) = %.1f"%I
Time taken ,t(sec) = 24.82
Current drawn per motor,I(A) = 261.4

Example 7.10, Page 211

In [50]:
V=36;# speed in km/h
W=120;# in tonne
G=2;# in per cent

#Calculations
r=2*9.81;# in N/tonne
Ft=(98.1*W*G)+(W*r);
e=88./100; # efficiency of motors and gear
VL=1500;#line voltage in volts
Po=(Ft*V)/3600;
Pi=Po/e;
I=(Pi*1000)/VL;
bc=((98.1*(2+(0.1*2)))/(277.8*1.1));#in kmphps
tt=V/bc;#in seconds

#Results
print "current required in amperes is %.1f"%I
print "time taken to come to rest in seconds is %.f"%tt
current required in amperes is 196.2
time taken to come to rest in seconds is 51

Example 7.11, Page 211

In [51]:
#Variable declaration
t1=24;#in sec
t2=69;# in sec
t3=11;# in sec
V1=48.;# in km/h

#Calculations&Results
alfa=V1/t1;
print "part (a)"
print "Acceleration(km/h/sec) = %.f"%alfa
r=58;# in N/tonne
G=0;
Beta=r/(277.8*1.1);
print "part (b)"
print "Retardation(kmphps) = %.2f"%Beta
V2=V1-(Beta*t2);
S=round(((V1*t1)/7200)+(((V1+V2)*t2)/7200)+((V2*t3)/7200));
D=20;# duration of stop in sec
Ts=t1+t2+t3+D;
Vs=round((S*3600)/Ts);
print "part (c)"
print "Schedule time,Vs(kmph) = %.f"%Vs
D1=15;#when the duration of stop in sec
Ts_dash=t1+t2+t3+D1;
Vs_dash=(S*3600)/Ts_dash;
print "Schedule speed,VS_dash(kmph) = %.2f"%Vs_dash
part (a)
Acceleration(km/h/sec) = 2
part (b)
Retardation(kmphps) = 0.19
part (c)
Schedule time,Vs(kmph) = 29
Schedule speed,VS_dash(kmph) = 30.25

Example 7.12, Page 212

In [53]:
#Variable declaration
t1=30.;#in sec
t2=50.;# in sec
t3=20.;# in sec
alpha=2.;#kmphps

#Calculations
V1=alpha*(t1);# in km/h
r=40;# in N/tonne
G=1;
bc=((98.1+r))/(277.8*1.1);#in kmphps
V2=V1-(bc*t2);#km/hr
S=(((V1*t1)/7200)+(((V1+V2)*t2)/7200)+((V2*t3)/7200));
D=30;# duration of stop in sec
Ts=t1+t2+t3+D;
Vs=((S*3600)/Ts);

#Result
print "Schedule time,Vs(kmph) = %.2f"%Vs
Schedule time,Vs(kmph) = 28.53

Example 7.13, Page 212

In [56]:
#Variable declaration
w=250.;#in tonnes
we=(1+(10./100))*w;#efective weight in tonnes
r=5*9.81;#in N/tonne
G=1.;#
t1=30.;#in sec
t2=70.;# in sec
alpha=2.;#kmphps

#Calculations
V1=alpha*(t1);# in km/h
ft=(277.8*we*alpha)+(98.1*G*w)+(w*r);#in newtons
po=((ft*V1)/3600);#maximum power output in kW
n=0.97;#efficiency
pi=po/n;#in kW
bc=((98.1+r))/(277.8*1.1);#in kmphps
V2=V1-(bc*t2);#km/hr
beta1=3;#retardation
t3=V2/beta1;#in seconds
S=(((V1*t1)/7200)+(((V1+V2)*t2)/7200)+((V2*t3)/7200));

#Results
print "maximum power developed by traction motor is %.f (kW)"%pi
print "total distance travelled by train in km is %.2f"%S
maximum power developed by traction motor is 3257 (kW)
total distance travelled by train in km is 1.12

Example 7.14, Page 216

In [58]:
#Variable declaration
Vm=52.; #max speed in kmph
t3=15.8;#duration of braking in sec

#Calculations
D=(1./2)*Vm*(t3/3600);
S=1400;#in m
S1=(S*10**-3)-D;
r=50;#in N/tonne
WeBY_W=1.1;
Ec=((0.01072*Vm**2*WeBY_W)/(S*10**-3))+(0.2778*r*(S1/(S*10**-3)));

#Result
print "energy consumption in Wh is %.3f"%Ec
energy consumption in Wh is 35.533

Example 7.15, Page 217

In [62]:
#Variable declaration
w=1;#in tonnes
we=(1+(10./100))*w;#efective weight in tonnes
S=1525;#in meters
r=52.6/1000;#in N/kg
alpha=0.366;#m/s^2
V1=12.2;# in m/s

#Calculations
t1=V1/alpha;#in seconds
ft=we*alpha+r;#in newtons
ter=((1./2)*ft*V1*t1)/3600;#in watt-hours
seo=ter/(w*S);# in Wh/kg-m
n=0.65;#efficiency
sec1=seo/n#in Wh/kg-m

#Result
print "specific energy onsumption is %.2e Wh/kg-m"%sec1
specific energy onsumption is 2.59e-05 Wh/kg-m

Example 7.16, Page 217

In [64]:
#Variable declaration
t1=30.;#in sec
t2=50.;# in sec
t3=20.;# in sec
alpha=2;#kmphps
V1=alpha*(t1);# in km/h
r=40;# in N/tonne
G=1;

#Calculations&Results
bc=((98.1+r))/(277.8*1.1);#in kmphps
V2=V1-(bc*t2);#km/hr
S=(((V1*t1)/7200)+(((V1+V2)*t2)/7200)+((V2*t3)/7200));
D=15;# duration of stop in sec
Ts=t1+t2+t3+D;
Vs=((S*3600)/Ts);
print "Schedule speed,Vs(kmph) = %.2f"%Vs
S1=(V1*t1)/7200;#in meters
r=50.;#in N/tonne
WeBY_W=1.1;
Ec=((0.01072*V1**2*WeBY_W)/(S))+(0.2778*(98.1*G+r)*((S1)/(S)));
N=0.75;#
Sec=Ec/0.75;#
print "Specific energy consumption in Wh/tonne-km is %.2f"%Sec
Schedule speed,Vs(kmph) = 32.25
Specific energy consumption in Wh/tonne-km is 68.25

Example 7.17, Page 218

In [66]:
#Variable declaration
t1=30.;#in sec
t2=50.;# in sec
t3=20.;# in sec
alpha=2;#kmphps
V1=alpha*(t1);# in km/h
r=40;# in N/tonne
G=-1;

#Calculations&Results
bc=((-98.1+r))/(277.8*1.1);#in kmphps
V2=V1-(bc*t2);#km/hr
S=(((V1*t1)/7200)+(((V1+V2)*t2)/7200)+((V2*t3)/7200));
D=15;# duration of stop in sec
Ts=t1+t2+t3+D;
Vs=((S*3600)/Ts);
print "Schedule speed,Vs(kmph) = %.f"%Vs
S1=(V1*t1)/7200;#in meters
r=50;#in N/tonne
WeBY_W=1.1;
Ec=((0.01072*V1**2*WeBY_W)/(S))+(0.2778*(98.1*G+r)*((S1)/(S)));
N=0.75;#
Sec=Ec/0.75;#
print "Specific energy consumption in Wh/tonne-km is %.2f"%Sec
Schedule speed,Vs(kmph) = 42
Specific energy consumption in Wh/tonne-km is 38.85

Example 7.18, Page 219

In [68]:
import math

#Variable declaration
W=100.;#in tonne
We=1.1*W;# in tonne
S=2.5;# distance in km
Va=50.;#Average speed in kmph
Dr=(3600*S)/Va;
alfa=1.;# in km/h/sec
Beta=2.;# in km/h/sec
T=180.;
r=40.;#in N/tonne
G=1;

#Calculations&results
K=(1./(2*alfa))+(1/(2*Beta));
Vm=round((T/(2*K))-math.sqrt((T/(2*K))**2-((3600*S)/K)));# maximum speed
t1=Vm/alfa;# acceleration period
t3=Vm/Beta;# braking period
t2=T-(t1+t3);# in sec
Ft=(277.8*We*alfa)+(98.1*W*G)+(W*r);
P_max=round((Ft*Vm)/3600);
print "part (a)"
print "Maximum power,(kWh) = %.f"%P_max
e=60./100;# efficiency
Ft=(277.8*We*alfa)+(98.1*W*G)+(W*r);
Ft_dash=(98.1*W*G)+(W*r);
P_max=round((Ft*Vm)/3600);
Et=((1./2)*Ft)*(Vm/3600)*(t1/3600)+((Ft_dash*Vm)/3600)*(t2/3600);
Ec=Et/e;
print "part (b) "
print "Total Energy Consumption,Ec(kWh) = %.2f"%Ec
Sec=(Ec*1000)/(W*S);
print "part (c) "
print "Specific Energy Consumption,(Wh/tonne-km) = %.1f"%Sec
part (a)
Maximum power,(kWh) = 875
part (b) 
Total Energy Consumption,Ec(kWh) = 23.65
part (c) 
Specific Energy Consumption,(Wh/tonne-km) = 94.6

Example 7.19, Page 220

In [69]:
#Variable declaration
W=203;#in tonne
We=1.1*W;# in tonne
r=44;# N/tonne
G=(1./500)*100;# gradient
Vm=45.;# maximum speed in kmph
t1=30.;# in sec

#Calculations&Results
alfa=Vm/t1;# in kmph
Ft=(277.8*We*alfa)+(98.1*W*G)+(W*r);# in N
Po=(Ft*Vm)/3600;
print "part (a)"
print "The maximum power output,(kW) = %.2f"%Po
e=60./100;# efficiency
Et=(1./2)*((Ft*Vm)/3600)*(t1/3600);
E=(Et/e);
print " part (b) "
print "The energy taken(kWh) = %.1f"%E
part (a)
The maximum power output,(kW) = 1324.55
 part (b) 
The energy taken(kWh) = 9.2

Example 7.20, Page 220

In [71]:
import math

#Variable declaration
W=16.;#in tonne
We=1.1*W;# in tonne
Vs=45.;#in kmph
r=40.;# in N/tonne
S=2.8;# in km
Ts=(S*3600)/Vs;
Td=30.;# in sec

#Calculations&Results
T=Ts-Td;
alfa=2.;#in kmphps
Beta=3.2;# in kmphps
K=(1./(2*alfa))+(1/(2*Beta));
Vm=round((T/(2*K))-math.sqrt((T/(2*K))**2-((3600*S)/K)));# maximum speed
t1=Vm/alfa;# acceleration time
t3=Vm/Beta;# duration of braking
t2=T-(t1+t3);# time f free run in sec
Ft=(277.8*We*alfa)+(W*r);
P_max=(Ft*Vm)/3600;
print "part (a)"
print "Maximum power output,(kW) = %.3f"%P_max
# answer is wrong in book
Va=50;#Average speed in kmph
Dr=(3600*S)/Va;
T=180;
G=1;
e=80./100;#efficiency
Dt=(1./2)*((Vm*t3)/3600);# distance travelled during braking period in km
S1=S-Dt;# distance travelled with power in km
So=(((0.01072*Vm**2)/S)*(We/W))+((0.2778*r*S1)/S);
Sec=So/e;
print "part (b)"
print "Specific energy consumption,(Wh/tonne-km) = %.1f"%Sec
# answer is wrong in book
part (a)
Maximum power output,(kW) = 170.749
part (b)
Specific energy consumption,(Wh/tonne-km) = 31.5

Example 7.21, Page 221

In [73]:
#Variable declaration
t1=30.;#in sec
t2=40.;# in sec
t3=30.;# in sec
alpha=2;#kmphps
V1=alpha*(t1);# in km/h
r=40;# in N/tonne
G=1;

#Calculations&Results
bc=((98.1+r))/(277.8*1.1);#in kmphps
V2=V1-(bc*t3);#km/hr
Beta=2.5;#retardation
t4=V2/Beta;#in seconds
S=(((V1*t1)/7200)+((V1*t2)/3600)+(((V1+V2)*t3)/7200)+((V2*t4)/7200));
D=15;# duration of stop in sec
Ts=t1+t2+t3+t4+D;
Vs=((S*3600)/Ts);
print "part (a)"
print "Schedule time,Vs(kmph) = %.2f"%Vs
print "part (b)"
S1=((V1*t1)/7200)+((V1*t2)/3600);#in km
WeBY_W=1.1;
G=1;#
Ec=((0.01072*V1**2*WeBY_W)/(S))+(0.2778*(98.1*G+r)*((S1)/(S)));
N=0.75;#
Sec=Ec/0.75;#
print "Specific energy consumption in Wh/tonne-km is %.2f"%Sec
print "part (c)"
W=200;#
tec=(Sec*W*S);#
print "total energy consumption is %.1f kWh"%(tec*10**-3)
print "part (d)"
print "total distance travelled in Km is %.2f"%S
part (a)
Schedule time,Vs(kmph) = 39.89
part (b)
Specific energy consumption in Wh/tonne-km is 69.93
part (c)
total energy consumption is 20.7 kWh
part (d)
total distance travelled in Km is 1.48

Example 7.22, Page 222

In [88]:
#Variable declaration
W=500.;#
t1=60.;#in sec
t2=5*60.;# in sec
t3=3*60.;# in sec
alpha=2.5;#kmphps
V1=alpha*(t1);# in km/h
r=25.;# in N/tonne
G=1.;

#Calculations
bc=(((98.1*(8./1000)*100)+r))/(277.8*1.1);#in kmphps
V2=V1-(bc*t3);#km/hr
Beta=3.;#retardation
t4=V2/Beta;#in seconds
S=(((V1*t1)/7200)+((V1*t2)/3600)+(((V1+V2)*t3)/7200)+((V2*t4)/7200));
D=15.;# duration of stop in sec
Ts=t1+t2+t3+t4+D;
Vs=((S*3600)/Ts);
S1=((V1*t1)/7200)+((V1*t2)/3600);#in km
WeBY_W=1.1;
Ec=((0.01072*V1**2*WeBY_W)/(S))+(0.2778*((98.1*(8/1000)*100)+r)*((S1)/(S)));
N=0.80;#
Sec=Ec/N;#

#Result
print "Specific energy consumption in Wh/tonne-km is %f"%Sec
#incorrect answer in textbook
Specific energy consumption in Wh/tonne-km is 22.446222

Example 7.23, Page 223

In [89]:
#Variable declaration
Wl=1;#
W1=400;#
G=2;#in percentage
mu=0.2;#
alpha=1;#
r=40;#

#Calculations
x=(277.8*1.1*alpha+98.1*G+r)/(9.81*1000);#
wlo=(x*W1)/(mu-x);#in tonnes
al=22;#allowable load in tonnes
na=wlo/al;#

#Results
print "weight of the locomotive in tonnes %.1f"%wlo
print "number of axles required = %.f"%na
weight of the locomotive in tonnes 152.6
number of axles required = 7

Example 7.24, Page 224

In [91]:
#Variable declaration
W=12*30;#tonnes
we=1.04*360;#tonnes
r=5*9.81;#
G=1;#in percentage
mu=0.2;#
alpha=0.8;#
x=13.882;#
y=0.041;#

#Calculations
wlo=(x)/(mu-y);#in tonnes
al=20.;#allowable load in tonnes
na=wlo/al;#

#Results
print "weight of the locomotive in tonnes = %.1f"%wlo
print "number of axles required = %.f"%na
weight of the locomotive in tonnes = 87.3
number of axles required = 4

Example 7.25, Page 225

In [92]:
#Variable declaration
w1=100;#tonnes
w=w1+500;#tonnes
we=1.1*w;#effective weight
alpha=1;#
G=1;#
r=45;#

#Calculations&Results
ft=((277.8*we*alpha)+(98.1*w*G)+(w*r));#in newtons
ad=0.7;#adehsive percent
mu=(ft)/(100*10**3*9.81*ad);#
w2=130;#tonnes
ad2=w2*G;#
tadw=w1*ad+ad2;#tonnes
tted=mu*tadw*9.81*1000;#newtones
W=tted/(277.8*1.1*alpha+98.1*alpha+r);#in tonnes
trlw=W-(ad2+w1);#
print "part (a)"
print "trailig weight in tonnes is %.f"%trlw
w2=w1+500+ad2;#
G1=((tted/w2)-(277.8*1.1+r))*(1/98.1);#
print "part (b)"
print "maximum gradiant in percentage is %.3f"%G1
part (a)
trailig weight in tonnes is 1484
part (b)
maximum gradiant in percentage is 7.167

Example 7.26, Page 226

In [93]:
#Variable declaration
w1=100;#tonnes
w=w1+500;#tonnes
we=1.1*w;#effective weight
alpha=1;#
G=1;#
r=45;#

#Calculations
ft=((277.8*we*alpha)+(98.1*w*G)+(w*r));#in newtons
ad=0.7;#adehsive percent
mu=(ft)/(100*10**3*9.81*ad);#
w2=130;#tonnes
ad2=w2*G;#
tadw=w1*ad+ad2;#tonnes
tted=mu*tadw*9.81*1000;#newtones
W=tted/(277.8*1.1*alpha+98.1*alpha+r);#in tonnes
trlw=W-(ad2+w1);#
w2=w1+500+ad2;#
acc=((tted/w2)-(98.1+r))*(1/(277.8*1.1));#in kmphps

#Result
print "acceleration in kmphps is %.2f"%acc
acceleration in kmphps is 2.98

Example 7.27, Page 226

In [94]:
#Variable declaration
N=4;# number of motor
W=250;#in tonne
D=.95;# diameter in m
G=1;# percentage gradient
r=40;# in N/tonne
eta=95./100;# gear efficiency
gama=3;# gear ratio
We=1.1*W;
Vm=40;# kmph
t1=20;# in seconds

#Calculations&Results
alfa=Vm/t1;
Ft=((277.8*We*alfa)+(98.1*W*G)+(W*r));
T=(Ft*D)/(eta*2*gama);
Td=round(T/N);
print "Torque developed by each motor,Td(Nm) = %.f"%Td
mu=0.25;# adhesive coefficient
WL=(Ft/(9.81*1000))/mu;
Dw=round(WL/.75);
print "Dead weight of locomotive,(tonnes) = %.f"%Dw
Torque developed by each motor,Td(Nm) = 7805
Dead weight of locomotive,(tonnes) = 102