Utilization of Electrical Energy and Traction_J. B. Gupta, R. Manglik and R. Manglik
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Scilab Textbook Companion for Utilization of Electrical Energy and Traction by J. B. Gupta, R. Manglik and R. Manglik1 Created by Nitin Kumar B.TECH Electronics Engineering UTTARAKHAND TECHNICAL UNIVERSITY DEHRADUN College Teacher Arshad Khan Cross-Checked by K. V. P. Pradeep May 8, 2014
1 Funded
by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in
Book Description Title: Utilization of Electrical Energy and Traction Author: J. B. Gupta, R. Manglik and R. Manglik Publisher: S. K. Kataria & Sons, New Delhi Edition: 1 Year: 2012 ISBN: 978-93-5014-222-6
1
Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.
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Contents List of Scilab Codes
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1 Electric heating
8
3 Electrolytic processes
20
4 Illumination
26
5 Refrigeration and Air conditioning
45
7 Train Movement and Energy Consumption
47
8 Electric Traction Motors
70
9 Control of Traction Motors
77
10 Braking Mechanical Consideration and Control Equipment
83
11 Power supply for electric traction
88
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List of Scilab Codes Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 4.1 4.2 4.3 4.4
power drawm . . . . . . . . . . . . . diameter and length of wire . . . . . design the heating element . . . . . efficiency . . . . . . . . . . . . . . . average kW and kVA and pf . . . . average kW and kVA and pf . . . . rating . . . . . . . . . . . . . . . . . efficiency . . . . . . . . . . . . . . . power absorbed and power factor . . height . . . . . . . . . . . . . . . . . frequency . . . . . . . . . . . . . . . power required . . . . . . . . . . . . voltage and current . . . . . . . . . voltage and current . . . . . . . . . ampere hours . . . . . . . . . . . . . amount of copper . . . . . . . . . . weight of copper . . . . . . . . . . . thickness . . . . . . . . . . . . . . . thickness . . . . . . . . . . . . . . . current . . . . . . . . . . . . . . . . energy consumption . . . . . . . . . voltage . . . . . . . . . . . . . . . . WEIGHT OF ALUMINIUM . . . . quantity of electricity and ime taken MSCP . . . . . . . . . . . . . . . . . lumens per watt and MSCP . . . . . average luminance . . . . . . . . . . Illumination . . . . . . . . . . . . . 4
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8 9 9 10 11 12 13 14 15 16 16 17 18 18 20 20 21 21 22 22 23 24 24 25 26 26 27 27
Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa
4.5 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 4.29 4.30 4.31 5.1 5.2 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10
average intensity of Illumination . . . . . . . . . . . Illumination and lamp efficiency . . . . . . . . . . . height and Illumination . . . . . . . . . . . . . . . . candle power . . . . . . . . . . . . . . . . . . . . . . distance . . . . . . . . . . . . . . . . . . . . . . . . . total light flux and average Illumination . . . . . . . maximum and minimum Illumination . . . . . . . . Illumination . . . . . . . . . . . . . . . . . . . . . . Illumination . . . . . . . . . . . . . . . . . . . . . . Illumination . . . . . . . . . . . . . . . . . . . . . . Illumination . . . . . . . . . . . . . . . . . . . . . . spacing . . . . . . . . . . . . . . . . . . . . . . . . . wattage . . . . . . . . . . . . . . . . . . . . . . . . . candle power . . . . . . . . . . . . . . . . . . . . . . capacitance . . . . . . . . . . . . . . . . . . . . . . . compare diameter and length . . . . . . . . . . . . . constants and change of candle power per volt . . . . average Illumination . . . . . . . . . . . . . . . . . . number location and wattage . . . . . . . . . . . . . number rating and dipsotion of lamps . . . . . . . . number rating and dipsotion of lamps . . . . . . . . number and wattage . . . . . . . . . . . . . . . . . . number spacing height and totl wattge . . . . . . . . space height ratio . . . . . . . . . . . . . . . . . . . Illumination . . . . . . . . . . . . . . . . . . . . . . number and size . . . . . . . . . . . . . . . . . . . . power . . . . . . . . . . . . . . . . . . . . . . . . . . rating of heater . . . . . . . . . . . . . . . . . . . . . distance average speed and scheduled speed . . . . . plot the curve . . . . . . . . . . . . . . . . . . . . . . speed . . . . . . . . . . . . . . . . . . . . . . . . . . sceduled speed . . . . . . . . . . . . . . . . . . . . . acceleration . . . . . . . . . . . . . . . . . . . . . . . retardation . . . . . . . . . . . . . . . . . . . . . . . duration of acceleration coasting and braking periods torque . . . . . . . . . . . . . . . . . . . . . . . . . . time taken and current . . . . . . . . . . . . . . . . time taken and current . . . . . . . . . . . . . . . . 5
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28 28 29 30 30 31 31 32 33 33 34 34 35 35 36 37 37 38 39 39 40 41 41 42 43 44 45 46 47 48 49 49 50 51 51 52 52 53
Exa Exa Exa Exa Exa Exa Exa Exa
7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18
Exa 7.19 Exa 7.20 Exa 7.21 Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa
7.22 7.23 7.24 7.25 7.26 7.27 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 9.1 9.2 9.3 9.4 9.5 9.6 10.1 10.2 10.3
acceleration coasting retardation and scheduled speed sceduled speed . . . . . . . . . . . . . . . . . . . . . . maximum power and distance travelled . . . . . . . . energy consumption . . . . . . . . . . . . . . . . . . . specific energy consumption . . . . . . . . . . . . . . . sceduled speed and specific energy consumption . . . . sceduled speed and specific energy consumption . . . . maximum power total energy consumption and specific energy consumption . . . . . . . . . . . . . . . . . . . maximum power and energy taken . . . . . . . . . . . maximum power and specific energy consumption . . . Schedule speed specific energy consumption total energy consumption and distance . . . . . . . . . . . . . . . . specific energy consumption . . . . . . . . . . . . . . . weight and number of axles . . . . . . . . . . . . . . . weight and number of axles . . . . . . . . . . . . . . . trailing weight and maximum gradiant . . . . . . . . . acceleration . . . . . . . . . . . . . . . . . . . . . . . . torque and weight . . . . . . . . . . . . . . . . . . . . speed armature current characterstic . . . . . . . . . . speed torque curve . . . . . . . . . . . . . . . . . . . . motor speed and current . . . . . . . . . . . . . . . . . speed and voltage . . . . . . . . . . . . . . . . . . . . current . . . . . . . . . . . . . . . . . . . . . . . . . . power delivered . . . . . . . . . . . . . . . . . . . . . . new characterstics . . . . . . . . . . . . . . . . . . . . motor speed . . . . . . . . . . . . . . . . . . . . . . . power input and tractive efforts . . . . . . . . . . . . . linear synchronous and vehicle speed . . . . . . . . . . energy lost and total energy . . . . . . . . . . . . . . . rheostatic losses and train speed . . . . . . . . . . . . efficiency and speed . . . . . . . . . . . . . . . . . . . time duration speed and rheostatic losses . . . . . . . diverter resistance . . . . . . . . . . . . . . . . . . . . speed and drawbar pull . . . . . . . . . . . . . . . . . braking torque . . . . . . . . . . . . . . . . . . . . . . resistance . . . . . . . . . . . . . . . . . . . . . . . . . electrical energy and average power . . . . . . . . . . . 6
54 55 56 57 57 58 59 60 61 62 63 64 65 66 66 67 68 70 71 71 72 72 73 74 74 75 76 77 78 79 79 81 81 83 84 84
Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa
10.4 10.5 10.6 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9
energy returned . . power . . . . . . . . power . . . . . . . . total length . . . . . sag . . . . . . . . . sag . . . . . . . . . current . . . . . . . potential . . . . . . current . . . . . . . voltage and kW . . rating of the booster voltage . . . . . . .
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Chapter 1 Electric heating
Scilab code Exa 1.1 power drawm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
// Example 1 . 1 power drawn clc ; clear ; close ; format ( ’ v ’ ,6) r1 =100; // i n ohms r2 = r1 ; // i n ohms V =250; // a c s u p p l y i n v o l t s rp =((1) /((1/ r1 ) +(1/ r2 ) ) ) ; // e q u i v a l e n t r e s i s t a n c e i n ohms pp =(( V ^2) / rp ) ; // power drawn i n w a t t s disp ( ” p a r t ( a ) ” ) disp ( pp , ” power drawn when e l e m e n t s a r e i n p a r a l l e l , ( W)=” ) rs = r1 + r2 ; // e q u i v a l e n t r e s i s t a n c e i n ohms ps =(( V ^2) / rs ) ; // power drawn i n w a t t s disp ( ” p a r t ( b ) ” ) disp ( ps , ” power drawn when e l e m e n t s a r e i n s e r i e s , (W )=” )
8
Scilab code Exa 1.2 diameter and length of wire 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
// Example 1 . 2 // d i a m e t e r and l e n g t h clc ; clear ; close ; format ( ’ v ’ ,6) P =2.5; // power i n kW V =240; // i n v o l t s K =1; // r a d i a t i n g e f f i c i e n c y e =0.9; // e m i s s i v i t y p =42.5*10^ -6; // r e s i s t i v i t y i n ohm−cm T1 =1500; // i n d g r e e c e l s i u s T2 =450; // i n d e g r e e c e l s i u s x =(( %pi * V ^2) /(4*( p *10^ -2) * P *10^3) ) ; // H =((5.72* K * e ) *((( T1 +273) /100) ^4 -(( T2 +273) /100) ^4) ) ; // z =(( P *10^3) /( %pi * H ) ) ^2; // l =( z * x ) ^(1/3) ; // l e n g t h i n m e t e r d =(( sqrt ( z ) ) / l ) *10^3; // d i a m e t e r i n mm disp (l , ” l e n g t h i n m e t e r ” ) disp (d , ” d i a m e t e r i n mm” )
Scilab code Exa 1.3 design the heating element 1 // Example 1 . 3 // d e s i g n h e a t i n g e l e m e n t 2 clc ; 3 clear ; 4 close ; 5 format ( ’ v ’ ,7) 6 V =440; // v o l t s 7 P =20; // i n kW
9
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
T1 =1200; // i n d e g r e e c e l s i u s T2 =700; // i n d e g r e e c e l s i u s K =0.6; // r a d i a t i n g e f f i c i e n c y e =0.9; // e m i s s i v i t y t =0.025; // t h i c k n e s s i n mm p =1.05*10^ -6; // r e s i s i t i v i t y i n ohm − m e t e r Pp =( round ( P *10^3) ) /3; // power p e r p h a s e i n w a t t s Pv = ( V / sqrt (3) ) ; // p h a s e v o l t a g e R = Pv ^2/ Pp ; // r e s i s t a n c e o f s t r i p i n ohms x =(( R * t *10^ -3) /( p ) ) ; // H =((5.72* K * e ) *((( T1 +273) /100) ^4 -(( T2 +273) /100) ^4) ) ; // i n W/mˆ2 y =(( Pp ) /( H *2) ) ; // i n mˆ2 w = sqrt ( y / x ) *10^3; // w i d t h i n mm l = x * w *10^ -3; // l e n g t h o f s t r i p i n m e t e r disp (w , ” w i d t h i n mm” ) disp (l , ” l e n g t h o f s t r i p i n m e t e r ” )
Scilab code Exa 1.4 efficiency 1 2 3 4 5 6 7 8 9 10 11 12 13
// Example 1 . 4 // l o a d i n g i n kW and e f f i c i e n c y o f t h e tank clc ; clear ; close ; format ( ’ v ’ ,5) a =6; // a r e a i n mˆ2 l = a /6; // one s i d e o f t a n k i n m e t e r V = l * l * l ; // volume i n mˆ2 e =90/100; // c a p a c i t y wh =6* e *1000; // w a t e r t o be h e a t e d d a i l y i n kg s =4200; // s p e c i f i c h e a t o f w a t e r i n J /Kg/ d e g r e e celsius t1 =65; // i n d e g r e e c e l s i u s t2 =20; // i n d e g r e e c e l s i u s 10
14 hr = wh * s *( t1 - t2 ) *10^ -6; // h e a t r e q u i r e d t o
r a i s e the
temperture of water 15 hr1 = hr /3.6; // h e a t r e q u i r e d i n kWh 16 d =6.3; // d i f f e r e n c e i n w a t t s 17 l =(( d * a *( t1 - t2 ) *24) /1000) ; // l o s s e s from t h e s u r f a c e 18 19 20 21 22
o f t h e t a n k i n kWh es = hr1 + l ; // e n e r g y s u p p l i e d i n kWh lk = es /24; // l o a d i n g i n kW ef =( hr1 / es ) *100; // e f f i c i e n c y o f t h e t a n k i n percentage disp ( lk , ” l o a d i n g i n kW” ) disp ( ef , ” e f f i c i e n c y o f t h e t a n k i n p e r c e n t a g e ” )
Scilab code Exa 1.5 average kW and kVA and pf 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
// Example 1 . 5 // a v e r a g e kW ,KVA i n p u t , a r c v o l t a g e , a r c r e s i s t a n c e and p f o f t h e c u r r e n t drawn clc ; clear ; close ; format ( ’ v ’ ,7) sh =444; // s p e c i f i c h e a t o f s t e e l i n J /Kg/ C lh =37.25; // l a t e n t h e a t i n kJ / kg mp =1370; // m e l t i n g p o i n t o f s t e e l C t1 =19.1; // i n i t i a l t e m p e r t u r e i n C e =0.5; // o v e r a l l e f f i c i e n c y ip =5700; // i n p u t c u r r e n t i n a m p e r e s rs =0.008; // r e s i s t a n c e o f t r a n s f o r m e r r e f e r r e d t o s e c o n d a r y i n ohms rr =0.014; // r e c a t a n c e i n ohms m =4.3; // s t e e l i n t o n n e s ers =(( m *10^3*(( sh *( mp - t1 ) ) + lh *10^3) ) ) ; // e n e r g y required in j ou l es ersh = ers /(3.6*10^6) ; // e n e r g y r e q u i r e d i n kWh ata =1; // t i m e t a k e n t o m e l t s t e e l i n h o u r s 11
18 ao = ersh / ata ; // a v e r a g e o u t p u t i n kW 19 ai = ao / e ; // a v e r a g e i n p u t i n kW 20 vdr = ip * rs ; // v o l t a g e d r o p due t o r e s i s t a n c e 21 22 23 24 25 26 27 28 29 30 31
of
furnace leads vdr1 = ip * rr ; // v o l t a g e d r o p due t o r e a c t a n c e o f furnace leads va =(( ai *10^3) /(3* ip ) ) -( vdr ) ; // v o l t a g e r e s i s t i v e i n nature rac = va / ip ; // a r c r e s i s t a n c e i n oppv = sqrt (( va + vdr ) ^2+ vdr1 ^2) ; // open c i r c u i t p h a s e voltage in volts kvas =3* ip * oppv *10^ -3; // t o t a l kVA drawn pf =(( va + vdr ) / oppv ) ; // power f a c t o r disp ( ai , ” a v e r a g e i n p u t i n kW” ) disp ( va , ” a r c v o l t a g e i n v o l t s ” ) disp ( rac , ” a r c r e s i s t a n c e i n ”) disp ( pf , ” p f o f t h e c u r r e n t drawn from t h e s u p p l y ( l a g g i n g ) ”) disp ( kvas , ” t o t a l kVA drawn i n kVA” )
Scilab code Exa 1.6 average kW and kVA and pf 1 2 3 4 5 6 7 8 9 10 11 12
// Example 1 . 6 // a v e r a g e kW ,KVA i n p u t , a r c v o l t a g e , a r c r e s i s t a n c e and p f o f t h e c u r r e n t drawn clc ; clear ; close ; format ( ’ v ’ ,7) sh =0.12; // s p e c i f i c h e a t o f s t e e l i n k c a l /Kg/ C lh =8.89; // l a t e n t h e a t i n k c a l / kg mp =1370; // m e l t i n g p o i n t o f s t e e l C t1 =19.1; // i n i t i a l t e m p e r t u r e i n C e =0.5; // o v e r a l l e f f i c i e n c y ip =5700; // i n p u t c u r r e n t i n a m p e r e s rs =0.008; // r e s i s t a n c e o f t r a n s f o r m e r r e f e r r e d t o 12
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
s e c o n d a r y i n ohms rr =0.014; // r e c a t a n c e i n ohms m =4.3; // s t e e l i n t o n n e s ers =(( m *10^3*(( sh *( mp - t1 ) ) + lh ) ) ) ; // e n e r g y r e q u i r e d in jo u le s ersh = ers /(860) ; // e n e r g y r e q u i r e d i n kWh ata =1; // t i m e t a k e n t o m e l t s t e e l i n h o u r s ao = ersh / ata ; // a v e r a g e o u t p u t i n kW ai = ao / e ; // a v e r a g e i n p u t i n kW vdr = ip * rs ; // v o l t a g e d r o p due t o r e s i s t a n c e o f furnace leads vdr1 = ip * rr ; // v o l t a g e d r o p due t o r e a c t a n c e o f furnace leads va =(( ai *10^3) /(3* ip ) ) -( vdr ) ; // v o l t a g e r e s i s t i v e i n nature rac = va / ip ; // a r c r e s i s t a n c e i n oppv = sqrt (( va + vdr ) ^2+ vdr1 ^2) ; // open c i r c u i t p h a s e voltage in volts kvas =3* ip * oppv *10^ -3; // t o t a l kVA drawn pf =(( va + vdr ) / oppv ) ; // power f a c t o r disp ( ai , ” a v e r a g e i n p u t i n kW” ) disp ( va , ” a r c v o l t a g e i n v o l t s ” ) disp ( rac , ” a r c r e s i s t a n c e i n ”) disp ( pf , ” p f o f t h e c u r r e n t drawn from t h e s u p p l y ( l a g g i n g ) ”) disp ( kvas , ” t o t a l kVA drawn i n kVA” )
Scilab code Exa 1.7 rating 1 // Example 1 . 7 // r a t i n g o f f u r n a n c e 2 clc ; 3 clear ; 4 close ; 5 format ( ’ v ’ ,6) 6 sh =0.1; // s p e c i f i c h e a t o f s t e e l i n k c a l /Kg/
13
C
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
lh =26.67; // l a t e n t h e a t i n k c a l / kg mp =555; // m e l t i n g p o i n t o f s t e e l C t1 =35; // i n i t i a l t e m p e r t u r e i n C e =0.8; // o v e r a l l e f f i c i e n c y ip =5700; // i n p u t c u r r e n t i n a m p e r e s rs =0.008; // r e s i s t a n c e o f t r a n s f o r m e r r e f e r r e d t o s e c o n d a r y i n ohms rr =0.014; // r e c a t a n c e i n ohms m =2; // s t e e l i n t o n n e s ers =(( m *10^3*(( sh *( mp - t1 ) ) + lh ) ) ) ; // e n e r g y r e q u i r e d in j o u le s ersh = ers /(860) ; // e n e r g y r e q u i r e d i n kWh ata =1; // t i m e t a k e n t o m e l t s t e e l i n h o u r s ao = ersh / ata ; // a v e r a g e o u t p u t i n kW ai = ao / e ; // a v e r a g e i n p u t i n kW vdr = ip * rs ; // v o l t a g e d r o p due t o r e s i s t a n c e o f furnace leads vdr1 = ip * rr ; // v o l t a g e d r o p due t o r e a c t a n c e o f furnace leads va =(( ai *10^3) /(3* ip ) ) -( vdr ) ; // v o l t a g e r e s i s t i v e i n nature rac = va / ip ; // a r c r e s i s t a n c e i n oppv = sqrt (( va + vdr ) ^2+ vdr1 ^2) ; // open c i r c u i t p h a s e voltage in volts kvas =3* ip * oppv *10^ -3; // t o t a l kVA drawn pf =(( va + vdr ) / oppv ) ; // power f a c t o r rf = ai / ata ; // i n kW disp ( rf , ” r a t i n g o f f u r n a n c e i n kW” )
Scilab code Exa 1.8 efficiency 1 // Example 1 . 8 // e f f i c i e n c y 2 clc ; 3 clear ; 4 close ;
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of furnance
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
format ( ’ v ’ ,3) sh =880; // s p e c i f i c h e a t o f s t e e l i n J /Kg/ C lh =32000; // l a t e n t h e a t i n J / kg mp =660; // m e l t i n g p o i n t o f s t e e l C t1 =15; // i n i t i a l t e m p e r t u r e i n C ip =5700; // i n p u t c u r r e n t i n a m p e r e s rs =0.008; // r e s i s t a n c e o f t r a n s f o r m e r r e f e r r e d t o s e c o n d a r y i n ohms rr =0.014; // r e c a t a n c e i n ohms m =1.8; // IN KG ers =(( m *(( sh *( mp - t1 ) ) + lh ) ) ) ; // e n e r g y r e q u i r e d i n joules ersh = ers /(3.6*10^6) ; // e n e r g y r e q u i r e d i n kWh TM =10; //TIME TO MELT IN MINS ip =5; // i n p u t o f t h e f u r n a n c e i n kW ei =( ip ) *( TM /60) ; // e n e r g y i n p u t i n kWh n =( ersh / ei ) *100; // e f f i c i e n c y o f f u r n a n c e i n percentage disp (n , ” e f f i c i e n c y o f f u r n a n c e i n p e r c e n t a g e ” )
Scilab code Exa 1.9 power absorbed and power factor 1 2 3 4 5 6 7 8 9 10 11 12
// Example 1 . 9 // power a b s o r b e d and power f a c t o r clc ; clear ; close ; format ( ’ v ’ ,8) vs =10; // s e c o n d a r y v o l t a g e i n v o l t s p =500; // power drawn i n kW pf =0.5; // is =( p *10^3) / pf ; // s e c o n d a r y c u r r e n t i n a m p e r e s zs = vs / is ; // i m p e d e n c e o f s e c o n d a r y c i r c u i t i n ohms rs = zs * pf ; // r e s i s t a n c e o f s e c o n d a r y c i r c u i t i n ohms res = zs *( sqrt (1 - pf ^2) ) ; // r e c t a n c e t a n c e o f s e c o n d a r y c i r c u i t i n ohms 15
13 rs1 =2* rs ; // r e s i s t a c n e when h e a r t h i s f u l l i n 14 res1 = res ; // r e a c t a n c e when h e a r t h i s f u l l i n 15 zs1 =( sqrt ( rs1 ^2+ res1 ^2) ) ; // i m p e d a n c e o f s e c o n d a r y
c i r c u i t in 16 pf1 = rs1 / zs1 ; // power f a c t o r 17 is1 = vs / zs1 ; // s e c o n d a r y c u r r e n t i n a m p e r e s 18 pd = is1 ^2* rs1 *10^ -4; // power drawn i n kW 19 disp ( pf1 , ” power f a c t o r i s ” ) 20 disp ( pd , ” power drawn i n kW” )
Scilab code Exa 1.10 height // Example 1 . 1 0 // h e i g h t clc ; clear ; close ; format ( ’ v ’ ,8) vs =10; // s e c o n d a r y v o l t a g e i n v o l t s p =400; // power drawn i n kW pf =0.6; // is =( p *10^3) / pf ; // s e c o n d a r y c u r r e n t i n a m p e r e s zs = vs / is ; // i m p e d e n c e o f s e c o n d a r y c i r c u i t i n ohms rs = zs * pf ; // r e s i s t a n c e o f s e c o n d a r y c i r c u i t i n ohms res = zs *( sqrt (1 - pf ^2) ) ; // r e c t a n c e t a n c e o f s e c o n d a r y c i r c u i t i n ohms 13 x =( rs ) / res ; // h e i g h t 14 disp (x , ”maximum h e a t w i l l be o b t a i n e d w i t h t h e h e i g h t o f c h a r g e a s 3/4 o f h e i g h t o f h e a r t h ” ) 1 2 3 4 5 6 7 8 9 10 11 12
Scilab code Exa 1.11 frequency 1 // Example 1 . 1 1 // f r e q u e n c y 2 clc ;
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3 4 5 6 7 8 9
clear ; close ; format ( ’ v ’ ,5) p =5*10^ -7; // s p e c i f i c r e s i s t a n c e i n −m rp =1; // r e l a t i v e p e r m e a b i l i t y dp =0.0015; // d e p t h o f p e n e t r a t i o n i n mter f =(( p *10^7) /(( rp *( dp ) ^2) *4*( %pi ) ^2) ) *10^ -3; // f r e q u e n c y i n kHz 10 disp (f , ” f r e q u e n c y i n kHz ” )
Scilab code Exa 1.12 power required // Example 1 . 1 2 // power r e q u i r e d clc ; clear ; close ; format ( ’ v ’ ,10) l =0.5; // l e n g t h i n m e t e r b =0.25; // b r e a d h i n m e t e r h =0.02; // i n m e t e r t1 =25; // t e m p e r t u r e C t2 =125; // t e m p e r t u r e C t =10; // t i m e i n m i n u t e s f =30; // f r e q u e n c y i n 30 MHz w =600; // w e i g h t o f t h e wood i n kg /mˆ3 sh =1500; // s p e c i f i c h e a t i n J /Kg/ C e =50; // e f f i c i e n c y vp = l * b * h ; // volume i n mˆ3 wp = vp * w ; // w e i g h t o f plywood i n kg hr = sh * wp *( t2 - t1 ) ; // h e a t r e q u i r e d i n j o u l e s hrt =( hr /(3600) ) ; // h e a t r e q u i r e d t o r a i s e t h e t e m p e r t u r e o f plywood i n Wh 20 pu = hrt /(1/6) ; // power u t i l i z e d i n w a t t s 21 pi =( pu / e ) *100; // power i n p u t r e q u i r e d i n p e r c e n t a g e 22 disp ( pi , ” power i n p u t r e q u i r e d , (W)=” )
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
17
Scilab code Exa 1.13 voltage and current 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
// Example 1 . 1 3 // v o l t a g e , c u r r e n t and f r e q u e n c y clc ; clear ; close ; format ( ’ v ’ ,5) vl =600; // i n v o l t s p =200; // power a b s o r b e d i n w a t t s pf =0.05; // power f a c t o r f =30*10^6; // f r e q u e n c y i n Hz ep =8.854*10^ -12; // c o n s t a n t er =5; // a =150; // i n cmˆ2 t =0.02; // i n m e t e r c =(( ep * er * a *10^ -4) / t ) ; // c a p a c i t a n c e i n f a r a d s vr =( sqrt ( p /(2* %pi * f * c * pf ) ) ) ; // v o l t a g e i s r e q u i r e d i n volts i = p /( vr * pf ) ; // c u r r e n t i n a m p e r e s f2 =(( f *( vr / vl ) ^2) ) *10^ -6; // f r e q u e n c y i n Mhz disp ( ceil ( vr ) ,” v o l t a g e i n v o l t s ” ) disp ( round ( i ) ,” c u r r e n t i n a m p e r e s ” ) disp ( f2 , ” f r e q u e n c y i n MHz” )
Scilab code Exa 1.14 voltage and current // Example 1 . 1 4 / / v o l t a g e a c r o s s e l e c t r o d e s and current 2 clc ; 3 clear ; 4 close ; 1
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5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
format ( ’ v ’ ,6) pf =0.04; // power f a c t o r p =1000; // i n w a t t s f =10*10^6; // i n MHz a1 =.004; // a r e a i n mˆ2 a2 =0.001; // a r e a i n mˆ2 t =0.02; // t h i c k n e s s i n m e t e r t1 =.01; // t h i c k n e s s i n m e t e r t2 =t - t1 ; // t h i c k n e s s i n m e t e r ep =8.854*10^ -12; // c o n s t a n t i n F/m er =5; // r e l a t i v e p e r m i t t i v i t y o f plywood er1 =1; // r e l a t i v e p e r m i t t i v i t y i n a i r c =( ep *((( a1 * er1 ) / t ) +( a2 /(( t1 / er ) +( t2 / er1 ) ) ) ) ) ; // capacitance in farads vr =( sqrt ( p /(2* %pi * f * c * pf ) ) ) ; // v o l t a g e i s r e q u i r e d i n volts disp ( ” p a r t ( a ) ” ) disp ( round ( vr ) ,” v o l t a g e a c r o s s t h e e l e c t r o d e s i n v o l t s ”) i = p /( vr * pf ) ; // c u r r e n t i n a m p e r e s disp ( ” p a r t ( b ) ” ) disp (i , ” c u r e e n t i n a m p e r e s i s ” )
19
Chapter 3 Electrolytic processes
Scilab code Exa 3.1 ampere hours 1 2 3 4 5 6 7 8 9 10 11 12 13
// Example 3 . 1 // ampere h o u r r e q u i r e d clc ; clear ; close ; // g i v e n d a t a : r =5; // i n cm S =4* %pi * r ^2; t =0.005; // i n mm d =10.5; m = S * t * d *10^ -3; Z =(0.001118*3600) /1000; Amr = m / Z ; disp ( Amr , ” ampere h o u r r e q u i r e d , ( Ampere−h o u r )= ” )
Scilab code Exa 3.2 amount of copper 1 // Example 3 . 2 // mass o f c o p p e r d e p o s i t e d 2 clc ;
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3 4 5 6 7 8 9 10 11 12 13 14 15 16
clear ; close ; // g i v e n d a t a : m =20; // i n gm I =120; // i n A t =10*60; // i n s e c t1 =5*60; // i n s e c I1 =100; // i n A Cec =63.18/2; Cen =58.6/2; Z = m /( I * t ) ; Z1 =( Z *( Cec / Cen ) ) *10^ -3; m1 = Z1 * I1 * t1 ; disp ( ” mass o f c o p p e r d e p s o i t e d i s ” + string ( m1 ) + ” kg o r ” + string ( round ( m1 *10^3) ) + ”gm” )
Scilab code Exa 3.3 weight of copper 1 2 3 4 5 6 7 8 9 10
// Example 3 . 3 // mass o f c o p p e r d e p o s i t e d clc ; clear ; close ; // g i v e n d a t a : Z =1.044*10^ -8; // i n kg /C I =40; // i n A t =1*60*60; // i n s e c o n d s m1 = Z * I * t ; disp ( ” mass o f c o p p e r d e p s o i t e d i s ” + string ( m1 ) + ” kg o r ” + string (( m1 *10^3) ) + ”gm” )
Scilab code Exa 3.4 thickness 1
// Example 3 . 4 // t h i c k n e s s o f c o p p e r d e p o s i t e d 21
2 3 4 5 6 7 8 9 10 11 12 13 14
clc ; clear ; close ; // g i v e n d a t a : A =0.00025; // i n mˆ2 D =8900; // i n kg /mˆ3 Z =32.95*10^ -8; // i n kg /C I =1; // i n A t =100*60; // i n s e c o n d s m = Z * I * t ; // i n kg v=m/D; T =( v / A ) *10^3; disp (T , ” t h i c k n e s s o f c o p p e r d e p o s i t e d , T(mm) = ” )
Scilab code Exa 3.5 thickness 1 2 3 4 5 6 7 8 9 10 11 12 13 14
// Example 3 . 5 // t h i c k n e s s o f c o p p e r d e p o s i t e d clc ; clear ; close ; // g i v e n d a t a : A =0.00025; // i n mˆ2 D =8900; // i n kg /mˆ3 Z =32.95*10^ -8; // i n kg /C I =1.5; // i n A t =60*60; // i n s e c o n d s m = Z * I * t ; // i n kg v=m/D; T =( v / A ) ; disp ( ” T h i c k n e s s o f c o p p e r d e p o s i t e d i s ” + string ( T ) + ” m o r ” + string ( T *10^3) + ”mm” )
Scilab code Exa 3.6 current 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
// Example 3 . 6 // c u r r e n t clc ; clear ; close ; // g i v e n d a t a : m =50; // i n gm t =2*60*60; // i n s e c ECE_silver =111.8*10^ -8; // i n kg Cˆ−1 atomic_weight1 =108; // f o r s i l v e r atomic_weight2 =63.5; // f o r c o p p e r valency =1; // f o r s i l v e r Ces = atomic_weight1 / valency ; // c h e m i c a l e q u i v a l e n t o f silver Cec = atomic_weight2 /2; // c h e m i c a l e q u i v a l e n t o f copper Z = ECE_silver *( Cec / Ces ) ; I =( m *10^ -3) /( Z * t ) ; disp (I , ” c u r r e n t , I (A) = ” )
Scilab code Exa 3.7 energy consumption // Example 3 . 7 // e n e r g y c o n s u m p t i o n clc ; clear ; close ; // g i v e n d a t a : a =500; // e l e c t r o l y t i c c e l l s I =6000; // i n A t =40; // i n h o u r / week Z =32.81*10^ -8*3600; // i n kg /A−h V =0.25; // i n v o l t s Ah = a * I *( t *52) ; // t o t a l number o f ampere h o u r p e r annum 12 Ao = Z * Ah *10^ -3; // a n n u a l o u t p u t i n t o n n e s 13 Ea = Ah * V *10^ -3; // e n e r g y consumed p e r annum i n kWh 1 2 3 4 5 6 7 8 9 10 11
23
14 Et = Ea / Ao ; 15 disp ( Et , ” e n e r g y c o n s u m p t i o n , Et (kWh/ t o n n e ) = ” )
Scilab code Exa 3.8 voltage 1 // Example 3 . 8 // v o l t a g e 2 clc ; 3 clear ; 4 close ; 5 // g i v e n d a t a : 6 Z =1.0384*10^ -8; // i n kg /C 7 VbyZ =14.212*10^7; // i n j o u l e s 8 V = VbyZ * Z ; 9 disp (V , ” v o l t a g e , V( v o l t s ) = ” )
Scilab code Exa 3.9 WEIGHT OF ALUMINIUM 1 2 3 4 5 6 7 8 9 10 11 12 13 14
// Example 3 . 9 // mass o f aluminium clc ; clear ; close ; // g i v e n d a t a : ECE_silver =111*10^ -8; // i n kg /C Cew_silver =107.98; // c h e m i c a l e q u i v a l e n t o f s i l v e r Cew_al =27/3; // c h e m i c a l e q u i v a l e n t o f aluminium Z =( ECE_silver * Cew_al ) / Cew_silver ; C_efficiency =0.92; I =3000; // i n A t =24*60*60; // i n s e c o n d s m = Z * I * t * C_efficiency ; disp (m , ” mass o f aluminium , ,m( kg ) = ” )
24
Scilab code Exa 3.10 quantity of electricity and ime taken 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
// Example 3 . 1 0 // q u a n t i t y o f e l e c t r i c i t y and t i m e taken clc ; clear ; close ; // g i v e n d a t a : d =0.1; // i n m l =.25; // i n m Tc =2; // t h i c k n e s s o f c o a t i n g i n mm D =8.9; // d e n s i t y o f m e t a l i n gm/CC C_density =160; // i n A/ s q I_efficiency =0.9; S = %pi * d * l ; m = S * Tc *10^ -3* D *10^3; Z =30.43*10^ -8; // i n kg /C Q =( m / Z ) /3600; // i n A−h Q_dash = Q / I_efficiency ; disp ( Q_dash , ” q u a n t i t y o f e l e c t r i c i t y , Q dash (A−h ) = ” ) I = C_density * S ; t = Q_dash / I ; disp (t , ” t i m e r e q u i r e d , t ( h o u r s ) = ” )
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Chapter 4 Illumination
Scilab code Exa 4.1 MSCP 1 // Example 4 . 1 //MSCP 2 clc ; 3 clear ; 4 close ; 5 format ( ’ v ’ ,3) 6 F =1000; // i n t e n s i t y i n l u m e n s 7 MSCP = F /(4* %pi ) ; // MSCP o f t h e lamps 8 disp ( MSCP , ”MSCP o f t h e lamp i s ” )
Scilab code Exa 4.2 lumens per watt and MSCP 1 // Example 4 . 2 //LUMES PER WATT AND MSCP 2 clc ; 3 clear ; 4 close ; 5 format ( ’ v ’ ,4) 6 V =250; // i n v o l t s 7 I =0.8; // i n a m p e r e s
26
8 9 10 11 12 13 14
F =3000; // i n t e n s i t y i n l u m e n s wl = V * I ; // w a t t a g e o f lapms i n s w a t t s lpw = F / wl ; // l u m e n s p e r w a t t s i s MSCP = F /(4* %pi ) ; // MSCP o f t h e lamps MW = MSCP / wl ; //MSCP p e r w a t t s disp ( lpw , ” l u m e n s p e r w a t t i s ” ) disp ( MW , ”MSCP p e r w a t t o f t h e lamp i s ” )
Scilab code Exa 4.3 average luminance // Example 4 . 3 // a v e r a g e l u m i n a n e o f t h e s p h e r e clc ; clear ; close ; format ( ’ v ’ ,6) d =0.4; // d i a m t e r i n m e t e r p =0.20; // i n p e r c e n t a g e a b s o r p t i o n F =4850; // l u m e n s Fe =(1 - p ) * F ; // f l u x e m i t t e d by t h e g l o b e i n l u m e n s sa =4* %pi *( d /2) ^2; // s u r f a c e a r e a i n mˆ2 als = Fe / sa ; // a v e r a g e l u m n i n a n c e o f s p h e r e i n l u m e n s /m ˆ2 12 disp ( als , ” a v e r a g e l u m n i n a n c e o f s p h e r e i n l u m e n s /mˆ2 ”)
1 2 3 4 5 6 7 8 9 10 11
Scilab code Exa 4.4 Illumination 1 // Example 4 . 4 // i l l u m i n a t i o n 2 clc ; 3 clear ; 4 close ; 5 format ( ’ v ’ ,7) 6 P =20; // f i l a m e n t power i n w a t t s
27
h =5; // h e i g h t i n m e t e r s d =4; // d i a m t e r i n m e t e r p =0.50; // i n p e r c e n t a g e a b s o r p t i o n ef =0.89; // e f f i c i e n c y i n w a t t s cpl = P / ef ; // c a n d l e power o f lamp i n CP Lop =4* %pi * cpl ; // l u , i n o u s o u t p u t i n l u m e n s Fe =(1 - p ) * Lop ; // f l u x e m i t t e d by t h e g l o b e i n l u m e n s sa = %pi *( d /2) ^2; // s u r f a c e a r e a i n mˆ2 als = Fe / sa ; // a v e r a g e l u m n i n a n c e o f s p h e r e i n l u m e n s /m ˆ2 16 disp ( als , ” a v e r a g e l u m n i n a n c e o f s p h e r e i n l u m e n s /mˆ2 ”) 7 8 9 10 11 12 13 14 15
Scilab code Exa 4.5 average intensity of Illumination // Example 4 . 5 //AVERAGE INTENSITY clc ; clear ; close ; format ( ’ v ’ ,6) cpl =100; // h =5; // i n m e t e r th =60; // i n d e g r e e F =1000; // i n t e n s i t y i n l u m e n s MSCP = F /(4* %pi ) ; // MSCP o f t h e lamps ai =(( cpl / h ^2) * cosd (90 - th ) ) ; // a v e r a g e i n t e n s i t y o f illumination 12 disp ( round ( MSCP ) ,”MSCP o f a lamp i s ,= ” ) 13 disp ( ai , ” a v e r a g e i n t e n s i t y o f i l l u m i n a t i o n i s l u x ” ) 1 2 3 4 5 6 7 8 9 10 11
Scilab code Exa 4.7 Illumination and lamp efficiency 1
// Example 4 . 7 // lamp e f f i c i e n c y and i l l u m i n a t i o n 28
2 3 4 5 6 7 8 9 10 11 12
13 14 15
clc ; clear ; close ; format ( ’ v ’ ,7) p =500; // lamp power i n w a t t s mscp =1250; // h =2.7; // i n m e t e r s ea =( mscp ) /( h ) ^2; // i l l u m i n a t i o n d i r e c t l y b e l o w lamp in lux le =(4* %pi * mscp ) / p ; // lamp e f f i c i e n c y i n l u m e n s / w a t t s h1 =3; // m e t e r s eb =(( mscp ) /( h ^2) *(2.7^3/( h1 ^2+ h ^2) ^(3/2) ) ) ; // i l l u m n i n a t i o n a t a p o i n t 3 m e t e r s away on t h e h o r i z o n t a l p l a n e v e r t i c a l l y b e l o w t h e lamp i n l u x disp ( ea , ” i l l u m i n a t i o n d i r e c t l y b e l o w lamp i n l u x ” ) disp ( le , ” lamp e f f i c i e n c y i n l u m e n s /W” ) disp ( eb , ” i l l u m n i n a t i o n a t a p o i n t 3 m e t e r s away on t h e h o r i z o n t a l p l a n e v e r t i c a l l y b e l o w t h e lamp i n lux ”)
Scilab code Exa 4.8 height and Illumination 1 // Example 4 . 8 / / h e i g h t and i l l u m i n a t i o n 2 clc ; 3 clear ; 4 close ; 5 format ( ’ v ’ ,7) 6 l =100; // i l l u m i n a t i o n a t a p o i n t d i r e c t l y 7 8 9 10 11 12
below the
lamp i n l u m e n s /mˆ3 cp =256; // h1 =1.2; // i n m e t e r s h = sqrt ( cp / l ) ; // h e i g h t i n m e t e r s x = sqrt ( h ^2+ h1 ^2) ; // x1 = h / x ; // eb =(( cp ) /( h ^2) ) *( x1 ) ^3; // i l l u m n i n a t i o n a t a p o i n t 29
1 . 2 m e t e r s away on t h e h o r i z o n t a l p l a n e v e r t i c a l l y b e l o w t h e lamp i n l u x 13 disp (h , ” h e i g h t i n m e t e r s i s ” ) 14 disp ( eb , ” i l l u m n i n a t i o n a t a p o i n t 1 . 2 m e t e r s away on t h e h o r i z o n t a l p l a n e v e r t i c a l l y b e l o w t h e lamp in lux ”)
Scilab code Exa 4.9 candle power 1 2 3 4 5 6 7 8 9 10 11 12
// Example 4 . 9 / / c a n d l e power o f lamp clc ; clear ; close ; format ( ’ v ’ ,7) L1 =500; // c a n d l e power h1 =9; // i n m e t e r s d =2; // d i s t a n c e i n m e t e r s I2 =20; // i l l u m i n a t i o n i n Lux x = sqrt ( h1 ^2+ d ^2) ; // from p y t h a g o r a s theoram Cpx =(( I2 -( L1 / h1 ^2) ) * h1 ^2) /(( h1 / x ) ^3) ; // c a n d l e power disp ( Cpx , ” c a n d l e power o f lamp two i n CP” )
Scilab code Exa 4.10 distance 1 2 3 4 5 6 7 8 9
// Example 4 . 1 0 / / d i s t a n c e clc ; clear ; close ; format ( ’ v ’ ,5) h1 =10; // i n m e t e r s eL =1; //ASSUME Ea =1/(10) ^2; // X =(((10^3) * eL ) /10^2) *10*(1/ Ea ) ; 30
10 x =( X ) ^(2/3) ; // 11 y = sqrt (x -100) ; // 12 disp (y , ” d i s t a n c e i n m e t e r s
i s ”)
Scilab code Exa 4.11 total light flux and average Illumination 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
// Example 4 . 1 1 // t o t a l f l u x and a v e r a g e l u m i n a n e o f the sphere clc ; clear ; close ; format ( ’ v ’ ,6) th =15; // i n d e g r e e l =400; // c a n d e l a d =8; // m e t e r p =0.80; // i n p e r c e n t a g e a b s o r p t i o n Fe = p *4* %pi * l ; // f l u x e m i t t e d by t h e g l o b e i n l u m e n s dA = d * tand ( th /2) ; // d i a m e t e r i n d e g r e e sa = %pi *( dA ) ^2; // s u r f a c e a r e a i n mˆ2 als = Fe / sa ; // a v e r a g e l u m n i n a n c e o f s p h e r e i n l u x disp ( Fe , ” t o t a l f l u x i n l u m e n s ” ) disp ( als , ” a v e r a g e l u m n i n a n c e o f s p h e r e i n l u x ” )
Scilab code Exa 4.12 maximum and minimum Illumination 1 2 3 4 5 6 7 8
// Example 4 . 1 2 //maximum and minimum i l l u m i n a t i o n clc ; clear ; close ; format ( ’ v ’ ,5 ) CP =1000; // h =12; // i n m e t e r d =24; // d i a m t e r i n m e t e r 31
9 mil = CP /( h ) ^2; //maximum i l l u m i n a t i o n i n l u x 10 mal = mil *(12/ sqrt (12^2+12^2) ) ^3; // minimum
i l l u m i n a t i o n in lux 11 disp ( mil , ”maximum i l l u m i n a t i o n i n l u x ” ) 12 disp ( mal , ”minimum i l l u m i n a t i o n i n l u x ” )
Scilab code Exa 4.13 Illumination 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
// Example 4 . 1 3 / / i l l u m i n a t i o n clc ; clear ; close ; format ( ’ v ’ ,5 ) p =60; // CP =200; // h =6; // i n m e t e r d =10; // d i a m t e r i n m e t e r mil = CP /( h ) ^2; //maximum i l l u m i n a t i o n i n l u x disp ( ” p a r t ( a ) . ” ) disp ( mil , ” i l l u m i n a t i o n a t t h e c e n t r e o f t h e a r e a without r e f l e c t o r in lux ”) mal = mil *( h / sqrt ( h ^2+( d /2) ^2) ) ^3; // minimum i l l u m i n a t i o n in lux tl =4* %pi * CP ; // t o t a l l u m e n s ts =( p /100) * tl ; // t o t a l l u m e n s r e a c h i n g t h e s u r f a c e A = %pi *( d /2) ^2; // t o t a l s u r f a c e a r e a i n mˆ2 alf = ts / A ; // a v e r a g e i l l u m i n a t i o n w i t h r e f l e c t o r x = sqrt ( h ^2+( d /2) ^2) ; // y = h / x ; // om =2* %pi *(1 - y ) ; // i n s t e r a d i a n s tfr = CP * om ; // t o t a l f l u x r e a c h i n g t h e s u r f a c e alwr = tfr / A ; // a v e r a g e i l l u m i n a t i o n w i t h o u t r e f l e c t o r disp ( ” p a r t ( b ) . ” ) disp ( mal , ” i l l u m i n a t i o n a t t h e e d g e o f t h e a r e a without r e f l e c t o r in lux ”) 32
disp ( alf , ” a v e r a g e i l l u m i n a t i o n w i t h r e f l e c t o r i n l u x ”) 26 disp ( alwr , ” a v e r a g e i l l u m i n a t i o n w i t h o u t r e f l e l c t o r in lux ”) 27 // w i t h t h e r e f l e c t o r t h e i l l u m i n t a i o n a t t h e e d g e and a t t h e end w i l l be t h e same s i n c e t h e r e f l e c t i o n d i r e c t s t h e l i g h t u n i f o r m i t y on t h e surface 25
Scilab code Exa 4.14 Illumination 1 2 3 4 5 6 7 8 9 10 11 12 13
// Example 4 . 1 4 // i l l u m i n a t i o n u n d e r e a c h lamp and midway b e t w e e n lamps clc ; clear ; close ; format ( ’ v ’ ,5 ) CP =100; // h =6; // i n m e t e r d =16; // m e t e r x = sqrt ( h ^2+ d ^2) ; // em =2*(( CP / h ^2) *( h /( d - h ) ) ^3) ; // i l l u m i n a t i o n i n t h e middle in lux ee =(( CP / h ^2) *(1+( h / x ) ^3) ) ; // i l l u m i n a t i o n i u n d e r e a c h lamp i n l u x disp ( ee , ” i l l u m i n a t i o n u n d e r e a c h lamp i n l u x ” ) disp ( em , ” i l l u m i n a t i o n i n t h e m i d d l e i n l u x ” )
Scilab code Exa 4.15 Illumination // Example 4 . 1 5 // i l l u m i n a t i o n u n d e r e a c h lamp and midway b e t w e e n lamps 2 clc ; 1
33
3 4 5 6 7 8 9 10 11
clear ; close ; format ( ’ v ’ ,7 ) CP =800; // h =10; // i n m e t e r d =12; // m e t e r x = sqrt ( h ^2+ d ^2) ; // x1 = sqrt ( h ^2+( d /2) ^2) ; // em =(( CP / h ^2) *(1+( h / x ) ^3+( h / x ) ^3) ) ; // i l l u m i n a t i o n i u n d e r e a c h lamp i n l u x 12 ee =2*(( CP / h ^2) *( h / x1 ) ^3) ; // i l l u m i n a t i o n a t t h e centrelamp in lux 13 disp ( em , ” i l l u m i n a t i o n u n d e r e a c h lamp i n l u x ” ) 14 disp ( ee , ” i l l u m i n a t i o n i n t h e m i d d l e i n l u x ” )
Scilab code Exa 4.16 Illumination // Example 4 . 1 6 // i l l u m i n a t i o n midway b e t w e e n lamps clc ; clear ; close ; format ( ’ v ’ ,5 ) CP =400; // h =10; // i n m e t e r d =20; // m e t e r x = sqrt ( d ^2 - h ^2) ; // ee =4*(( CP / h ^2) *( h / x ) ^3) ; // i l l u m i n a t i o n a t t h e centrelamp in lux 11 disp ( ee , ” i l l u m i n a t i o n i n t h e m i d d l e i n l u x ” )
1 2 3 4 5 6 7 8 9 10
Scilab code Exa 4.17 spacing 1
// Example 4 . 1 7 / / d i s t a n c e 34
2 3 4 5 6 7 8 9 10 11 12 13 14
clc ; clear ; close ; format ( ’ v ’ ,5) cp =500; // cp h =4; // i n m e t e r x =((2* cp * h ^3) / h ^2) ; // y =(( cp * h ^3) / h ^2) ; // y1 = cp / h ^2; // y2 = y /2; // y21 = y1 /2; // d = sqrt (((( x - y2 ) / y21 ) ^(2/3) ) -h ^2) *2.29; // disp (d , ” d i s t a n c e i s , (m)=” )
Scilab code Exa 4.18 wattage 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
// Example 4 . 1 8 / / w a t t a g e o f lamp clc ; clear ; close ; format ( ’ v ’ ,6) d =6; // i n m e t e r h =4; // i n m e t e r ef =20; // l u m e n s p e r w a t t uc =0.5; // u t i l i z a t i o n c o e f f i c i e n t il =750; // i n l u x a =( %pi /4) *( d ) ^2; // F = a * il ; // i n l u m e n s tf = F / uc ; // t o t a l f l u x e m i t t e d by t h e lamp watt = tf / ef ; // w a t t a g e o f lamp disp ( watt , ” w a t t a g e o f lamp i n w a t t s ” )
Scilab code Exa 4.19 candle power 35
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
// Example 4 . 1 9 / / c a n d l e power clc ; clear ; close ; vl =220; // v o l t a g e o f lamp wl =60; // w a t t a g e o f lamp wl1 =75; // i n w a t t s v2 =440; // i n v o l t s r1 =(( vl ^2) / wl ) ; // i n ohms r2 =(( vl ^2) / wl1 ) ; // i n ohms i =( v2 /( r1 + r2 ) ) ; // i n a m p e r e s v1 = i * r1 ; // v o l t s v12 = i * r2 ; // i n v o l t s cp6 =( ceil ( v1 ) / vl ) ^4 *(100) ; // c a n d l e power cp7 =( v12 / vl ) ^4*(100) ; // c a n d l e power disp ( ceil ( cp6 ) ,” p o t e n t i a l d r o p a c r o s s 60 w a t t lamps in v o l t s ”) disp ( v12 , ” p o t e n t i a l d r o p a c r o s s 75 w a t t lamps i n v o l t s ”) disp ( round ( cp6 ) ,” c a n d l e power o f 60 w a t t s lampe i n percentage ”) disp ( cp7 , ” c a n d l e power o f 75 w a t t s lampe i n percentage ”) // a n s w e r i s wrong i n t h e book
Scilab code Exa 4.20 capacitance 1 2 3 4 5 6 7 8
// Example 4 . 2 0 / / c a p a c i t a n c e clc ; clear ; close ; w =84; // w a t t s pf =0.7; // power f a c t o r v =240; // i n v o l t s i =( w ) /( v * pf ) ; // i n a m p e r e s 36
9 10 11 12 13 14
rva = v * i * sqrt (1 - pf ^2) ; // r e l a t i v e v o l t −a m p e r e s cpf =1; // c o r r e c t e d power f a c t o r rvas = v * i * sqrt (1 - cpf ^2) ; // f =50; // i n h e r t z c =(( rva ) /(2* %pi * f *( v ) ^2) ) ; // i n f a r a d s disp ( c *10^6 , ” c a p a c i t a n c e i n ( micro −F ) i s ” )
Scilab code Exa 4.21 compare diameter and length 1 2 3 4 5 6 7 8 9 10 11 12 13 14
// Example 4 . 2 1 / / compare d i a m e t e r and l e n g t h clc ; clear ; close ; format ( ’ v ’ ,6) v1 =110; // i n v o l t s cp1 =16; // i n cp cp2 =25; // i n cp v2 =220; // i n v o l t s ri =(( cp1 / cp2 ) *( v2 / v1 ) ) ; // r a t i o o f c u r e n t s dr =( ri ) ^(2/3) ; // r a t i o o f d i a m e t e r s di =( cp1 / cp2 ) *(1/ dr ) ; // r a t i o o f l e n g t h s disp ( dr , ” r a t i o o f d i a m e t e r i s ” ) disp ( di , ” r a t i o o f l e n g t h i s ” )
Scilab code Exa 4.22 constants and change of candle power per volt 1 2 3 4 5 6
// Example 4 . 2 2 / / c o n s t a n t s and c h a n g e o f c a n d l e power per v o l t clc ; clear ; close ; format ( ’ v ’ ,9) c1 =71.5; // c a n d e l power 37
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
v1 =260; // i n v o l t s c2 =50; // c a n d e l power v2 =240; // i n v o l t s b = log ( c1 / c2 ) /( log ( v1 / v2 ) ) ; // a = c2 /( v2 ) ^(4.5) ; // disp ( ” p a r t ( a ) . ” ) disp ( ” c o n s t a n t s a r e ” + string ( a ) + ” and ” + string ( b ) + ” ”) v =250; // i n v o l t s p =4; // c h a n g e i n p e r c e n t a g e dvc = a * b *(( v ) ^( b -1) ) ; // i n c a n d l e p e r v o l t s dc =(1+( p /100) ) ^ b ; // when v o l t a g e i n c r e a s e by 4% pcp =(( dc -1) ) *100; // p e r c e n t a g e c h a n g e i n c a n d l e power dc1 =(1 -( p /100) ) ^ b ; // when v o l t a g e f a l l s by 4% pcp1 =(( dc1 -1) ) *100; // p e r c e n t a g e c h a n g e i n c a n d l e power disp ( ” p a r t ( b ) . ” ) disp ( dvc , ” c h a n g e o f c a n d l e power p e r v o l t s ” ) // c h a g e i n c a n d l e power p e r v o l t i s c a l c u l a t e d wrong i n t h e book disp ( pcp , ” p e r c e n t a g e c h a n g e i n c a n d l e power when v o l t a g e i n c r e a s e by 4%” ) disp ( pcp1 , ” p e r c e n t a g e c h a n g e i n c a n d l e power when v o l t a g e f a l l s by 4%” )
Scilab code Exa 4.23 average Illumination 1 2 3 4 5 6 7 8
// Example 4 . 2 3 / / a v e r a g e i l l u m i n a t i o n clc ; clear ; close ; format ( ’ v ’ ,5) dp =1.2; // d e p r e c i a t i o n f a c t o r uf =0.6; // u t i l i a z a t i o n f a c t o r l =15; // i n m e t e r s 38
b =6; // i n m e t e r s n =20; // no . o f lamps lw =250; // mscp i n w a t t s a = l * b ; // a r e a n i n mˆ2 tl = n * lw *4* %pi ; // / t o t a l l u m e n s lwp =(( tl * uf ) / dp ) ; // l u m e n s r e a c h i n g on t h e w o r k i n g plane 15 e = lwp / a ; // i l l u m i n a t i o n on w o r k i n g p l a n e i n l u x 16 disp (e , ” i l l u m i n a t i o n on w o r k i n g p l a n e i n l u x ” ) 9 10 11 12 13 14
Scilab code Exa 4.24 number location and wattage // Example 4 . 2 4 / / number , l o a c t i o n and w a t t a g e clc ; clear ; close ; format ( ’ v ’ ,5) ef =40; // e f f i c i e n c y i n l u m e n s / w a t t mil =80; // minimum i l l u m i n a t i o n i n l u m e n s /mˆ2 dp =0.8; // d e p r e c i a t i o n f a c t o r uf =0.4; // u t i l i a z a t i o n f a c t o r l =100; // i n m e t e r s b =10; // i n m e t e r s a = l * b ; // a r e a n i n mˆ2 tl = a * mil ; // / t o t a l l u m e n s glr = tl /( uf * dp ) ; // g r o s s i l l u m i n a t i o n r e q u i r e d twr = glr / ef ; // t o t a l w a t t a g e r e q u i r e d disp (42 , ” number o f lamps o f 150 w a t t r a t i n g i n 2 r o w s ”) 17 disp ( twr , ” t o t a l w a t t a g e i n w a t t s ” ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Scilab code Exa 4.25 number rating and dipsotion of lamps 39
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
// Example 4 . 2 5 / / number , r a t i n g and d i s p o s i t i o n o f lamps clc ; clear ; close ; format ( ’ v ’ ,6) h =4; // i n m e t e r s wp =75; // i n l u x ef =14; // e f f i c i e n c y i n l u m e n s / w a t t dp =0.2; // d e p r e c i a t i o n f a c t o r uf =0.5; // u t i l i a z a t i o n f a c t o r l =72; // i n m e t e r s b =15; // i n m e t e r s a = l * b ; // a r e a n i n mˆ2 mf =1 - dp ; // m a i n t e n a n c e f a c t o r glr =( a * wp ) /( uf * mf ) ; // g r o s s i l l u m i n a t i o n r e q u i r e d twr = glr / ef ; // t o t a l w a t t a g e r e q u i r e d wec = twr /80; // w a t t a g e o f e a c h lamps disp (80 , ” number o f lamps o f 150 w a t t r a t i n g i n 2 r o w s ”) disp ( ” w a t t a g e o f e a c h lamp ” + string ( wec ) + ” w a t t s e q u i v a l e n t t o 200 w a t t s ” )
Scilab code Exa 4.26 number rating and dipsotion of lamps 1 2 3 4 5 6 7 8 9
// Example 4 . 2 6 / / number , r a t i n g and d i s p o s i t i o n o f lamps clc ; clear ; close ; a =30*30; // e =75; // uf =0.5; // df =1 -0.2; // le =15; // e f f i c i e n c y 40
10 11 12 13 14 15
ph =( a * e ) /( uf * df ) ; // W = ph / le ; // ew =300; //W N = W / ew ; // disp (N , ” t o t a l number o f lamps i s ,= ( s a y 4 2 ) ” ) disp (W , ” w a t t a g e o f lamps i s , (W)=” )
Scilab code Exa 4.27 number and wattage // Example 4 . 2 7 / / number and w a t t a g e clc ; clear ; close ; format ( ’ v ’ ,6) h =5; // i n m e t e r s el =100; // i n l u x ef =16; // e f f i c i e n c y i n l u m e n s / w a t t dp =0.2; // d e p r e c i a t i o n f a c t o r uf =0.4; // u t i l i a z a t i o n f a c t o r l =60; // i n m e t e r s b =15; // i n m e t e r s a = l * b ; // a r e a n i n mˆ2 glr =( a * el ) /( uf *(1 - dp ) ) ; // g r o s s i l l u m i n a t i o n r e q u i r e d n =12*3; // t o t a l no . o f twr = glr / ef ; // t o t a l w a t t a g e r e q u i r e d wec = twr / n ; // w a t t a g e o f e a c h lamp disp (n , ” number o f lamps o f 150 w a t t r a t i n g i n 2 r o w s ” ) 19 disp ( ” w a t t a g e o f e a c h lamp ” + string ( wec ) + ” w a t t s e q u i v a l e n t t o 500 w a t t s ” )
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Scilab code Exa 4.28 number spacing height and totl wattge 41
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
// Example 4 . 2 8 / / number , s p a c i n g , mounting h e i g h t and total wattafe clc ; clear ; close ; format ( ’ v ’ ,6) h =5; // i n m e t e r s el =120; // i n l u x ef =40; // e f f i c i e n c y i n l u m e n s / w a t t tw =80; // i n w a t t s df =1.4; // d e p r e c i a t i o n f a c t o r uf =0.5; // u t i l i a z a t i o n f a c t o r l =30; // i n m e t e r s b =15; // i n m e t e r s a = l * b ; // a r e a n i n mˆ2 glr =( a * el * df ) /( uf ) ; // g r o s s l u m e n s r e q u i r e d twr = glr / ef ; // t o t a l w a t t a g e r e q u i r e d nt = twr / tw ; // no . o f t u b e s r e q u i r e d disp ( twr , ” t o t a l w a t t a g e r e q u i r e d i n w a t t s ” ) disp ( ” number o f t u b e s r e q u i r e d i s ” + string ( nt ) + ” e q u i v a l e n t t o 48 t u b e s ” )
Scilab code Exa 4.29 space height ratio 1 2 3 4 5 6 7 8 9 10 11
// Example 4 . 2 9 / / number o f lamps clc ; clear ; close ; format ( ’ v ’ ,6) el =50; // i n l u x df =1.3; // d e p r e c i a t i o n f a c t o r uf =0.5; // u t i l i a z a t i o n f a c t o r l =30; // i n m e t e r s b =12; // i n m e t e r s a = l * b ; // a r e a n i n mˆ2 42
12 glr =( a * el * df ) /( uf ) ; // g r o s s l u m e n s r e q u i r e d 13 watt =[100 ,200 ,300 ,500 ,1000]; 14 lum =[1615 ,3650 ,4700 ,9950 ,21500]; // 15 for i =1:5 16 n ( i ) = glr /( lum ( i ) ) ; // 17 disp ( ” i f ” + string ( watt ( i ) ) + ” w a t t lamps a r e u s e d
t h e n number o f lamps r e q u i r e d i s ” + string ( round ( n ( i ) ) ) + ” ” ) 18 19 end
Scilab code Exa 4.30 Illumination // Example 4 . 3 0 / / i l l u m i n a t i o n on s u r f a c e clc ; clear ; close ; format ( ’ v ’ ,6) ef =17.4; // i n mumens/ w a t t dp =1.2; // d e p r e c i a t i o n f a c t o r wlf =1.3; // w a s t e l i g h t f a c t o r uf =0.4; // u t i l i a z a t i o n f a c t o r l =50; // i n m e t e r s b =16; // i n m e t e r s n =16; // no . o f lamps lw =1000; // mscp i n w a t t s a = l * b ; // a r e a n i n mˆ2 tl = n * lw * ef ; // / t o t a l l u m e n s lwp =(( tl * uf ) /( wlf * dp ) ) ; // l u m e n s r e a c h i n g on t h e working plane 17 e = lwp / a ; // i l l u m i n a t i o n on t h e s u r f a c e i n l u m e n s /mˆ2 18 disp (e , ” i l l u m i n a t i o n on t h e s u r f a c e i n l u m e n s /mˆ2 ” )
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
43
Scilab code Exa 4.31 number and size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
// Example 4 . 3 1 / / s i z e and number o f p r o j e c t o r clc ; clear ; close ; format ( ’ v ’ ,6) watt =[300 ,500 ,1000 ,1500]; lum =[5000 ,9000 ,18000 ,27000]; // el =50; // i n l u x dp =0.8; // d e p r e c i a t i o n f a c t o r wlf =0.5; // w a s t e l i g h t f a c t o r uf =1.2; // u t i l i a z a t i o n f a c t o r l =60; // i n m e t e r s b =15; // i n m e t e r s lw =1000; // mscp i n w a t t s a = l * b ; // a r e a n i n mˆ2 tl = a * el // t o t a l l u m e n s lwp =(( tl * uf ) /( wlf * dp ) ) ; // l u m e n s r e a c h i n g on t h e working plane n = lwp / lum (2) ; // number o f p r o j e c t o r r e q u i r e d ang =2* atand (4.5/8) ; // s i z e disp ( ceil ( n +1) ,” number o f p r o j e c t o r s a r e ,= ” ) disp ( watt (2) ,” w a t t a g e i s , (W)=” ) disp ( ceil ( ang +1) ,” beam a n g l e i s , ( d e g r e e )=” ) disp ( ” ” + string ( round ( n ) +1) + ” p r o j e c t o r s o f ” + string ( watt (2) ) + ” w a t t s e a c h w i t h beam a n g l e o f ” + string ( round ( ang +1) ) + ” d e g r e e w i l l be r e q u i r e d ” )
44
Chapter 5 Refrigeration and Air conditioning
Scilab code Exa 5.1 power 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
// Example 5 . 1 : Power clc ; clear ; close ; // g i v e n d a t a : t1 =20; // i n d e g r e e C t2 =5; // i n d e g r e e C T = t1 - t2 ; A =3000; // volume o f a i r t o be c o n d i t i o n e d i n mˆ3 Ht =1220; // i n J H1 = A * Ht * T ; m =1000; // p e r mˆ3 Hl =2450*10^3; // l a t e n t h e a t i n J / kg w =5;; // i n kg M =( w * A ) / m ; H2 = T * Hl ; // i n J H =( H1 + H2 ) ; P = round ( H /(3600*1000) ) ; disp (P , ” Power r e q u i r e d , (kW) = ” ) 45
Scilab code Exa 5.2 rating of heater 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
// Example 5 . 2 : R a t i n g o f H e a t e r clc ; clear ; close ; // g i v e n d a t a : t1 =25; // i n d e g r e e C t2 =5; // i n d e g r e e C T = t1 - t2 ; A =6*5*4*(60/15) ; // volume o f a i r t o be c o n d i t i o n e d i n mˆ3/ h o u r Ht =1220; // i n J H1 = A * Ht * T ; m =1000; // p e r mˆ3 Hl =836*10^3; // h e a t l o s s i n J /C/h H2 = T * Hl ; // i n J / h o u r H =( H1 + H2 ) ; Rh = round ( H /(3600*1000) ) ; disp ( Rh , ” R a t i n g o f h e a t e r , (kW) =” )
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Chapter 7 Train Movement and Energy Consumption
Scilab code Exa 7.1 distance average speed and scheduled speed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
// Example 7 . 1 . / / d i s t a n c e , a v e r a g e s p e e d and s c h e d u l e d speed clc ; clear ; close ; format ( ’ v ’ ,6) a =5; // a c e l e r a t i o n i n kmphps t1 =30; // i n s e c o n d s vm = a * t1 ; //maximum s p e e d i n kmph tfr =10; // t i m e f o r f r e e r u n n i n g i n mins b =5; // r e t a r d a t i o n i n kmphps ts = vm / b ; // t i m e f o r r e t a r d a t i o n i n s e c o n d s dta =(( vm * t1 ) /(2*3600) ) ; // d i s t a n c e t r a v e l l e d d u r i n g acceleration period dtfr =(( vm * tfr *60) /(3600) ) ; // d i s t a n c e t r a v e l l e d during retardation period dtbp = dta ; // d i s t a n c e t r a v e l l e d d u r i n g b r e a k i n g p e r i o d td = dta + dtfr + dtbp ; // t o t a l d i s t a n c e b e t w e e n s t a t i o n s disp ( ” p a r t ( a ) ” ) 47
17 disp ( td , ” t o t a l d i s t a n c e b e t w e e n s t a t i o n i n km” ) 18 T =[0; t1 ;( t1 +( tfr *60) ) ;( t1 +( t1 +( tfr *60) ) ) ]; // 19 V =[0; vm ; vm ;0]; // 20 plot2d (T , V ) 21 xlabel ( ” Time i n s e c o n d s ” ) 22 ylabel ( ” Spped i n Km p e r Hour ” ) 23 va =( td *3600) /( t1 +( tfr *60) + ts ) ; // a v e r a g e s p e e d i n 24 25 26 27 28 29
kmph disp ( ” p a r t ( b ) ” ) disp ( va , ” a v e r a g e s p e e d i n kmph” ) tst =5; // s t o p t i m e i n mins vs =( td *3600) /( t1 +( tfr *60) + ts +( tst *60) ) ; // s h e d u l e d s p e e d i n kmph disp ( ” p a r t ( c ) ” ) disp ( vs , ” s h e d u l e d s p e e d i n kmph” )
Scilab code Exa 7.2 plot the curve 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
// Example 7 . 2 // draw t h e c u r v e clc ; clear ; close ; a =1.7; // a c e l e r a t i o n i n kmphps b =3.3; // kmphps s =1400; //m va =42; //kmph tr =(( s *10^ -3) / va ) *3600; // s e c o m d s k =((1/(2* a ) ) ) +((1/(2* b ) ) ) ; // vm =(( tr /(2* k ) ) - sqrt ((( tr ^2) /(4* k ^2) ) -((3600* s *10^ -3) / k ) ) ) ; // i n kmph t1 = vm / a ; // s e c o n d s t3 = vm / b ; // s e c o n d s t2 = tr -( t1 + t3 ) ; // s e c o n d s T =[0;( t1 ) ;( t1 + t2 ) ;( t1 + t2 + t3 ) ]; V =[0; vm ; vm ;0]; 48
17 18 19
plot2d (T , V ) ; xlabel ( ” Time i n s e c o n d s ” ) ylabel ( ” Spped i n Km p e r Hour ” )
Scilab code Exa 7.3 speed // Example 7 . 3 //maximum s p e e d clc ; clear ; close ; format ( ’ v ’ ,4) a =2.4; // a c e l e r a t i o n i n kmphps b =3.2; // r e t a r d a t i o n i n kmphps s =1.5; // i n km vs =45; // s h e d u l e s p e e d i n kmph ts =( s *3600) / vs ; // s h e d u l e t i m e i n s e c o n d s tst =20; // s t o p t i m e tr = ts - tst ; // a c t u a l t i m e f o r run i n s e c o n d s k =((1/(2* a ) ) +(1/(2* b ) ) ) ; // c o n s t a n t vm =(( tr /(2* k ) ) - sqrt ((( tr ^2) /(4* k ^2) ) -((3600* s ) / k ) ) ) ; // i n kmph 15 disp ( vm , ”maximum s p e e d i n kmph” )
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Scilab code Exa 7.4 sceduled speed 1 2 3 4 5 6 7 8
// Example 7 . 4 // s h e d u l e d s p e e d clc ; clear ; close ; format ( ’ v ’ ,4) s =1.5; // i n Km a =0.8; // a c e l e r a t i o n i n kmphps tsr =26; // t i m e f o r s t o p i n s e c o n d s 49
9 10 11 12 13 14 15 16 17 18 19 20
rm =1.3; // r a t i o b =3.2; // r e t a r d a t i o n i n kmphps k =((1/(2* a ) ) +(1/(2* b ) ) ) ; // c o n s t a n t T =1; // assume va1 =(3600* s ) / T ; // a v e r a g e s p p e d vm1 =( va1 * rm ) ; //maximum s p e e d vm = sqrt (( vm1 - va1 ) / k ) ; //maximum s p e e d i n kmph va = vm /1.3; // a c t u a s p e e d i n kmpj ta =(3600* s ) / va ; // a c t u a l t i m e i n s e c o n d s ts = ta + tsr ; // s h e d u l e t i m e vs =( s *3600) / ts ; // s h e d u l e s p e e d i n kmph disp ( vs , ” s c h e d u l e s p e e d i n kmph” )
Scilab code Exa 7.5 acceleration 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
// Example 7 . 5 : A c c e l e r a t i o n clc ; clear ; close ; // g i v e n d a t a : S =1; // i n km Vs =30; // i n km/h Ts =( S *3600) / Vs ; // i n s e c D =20; // d u r a t i o n o f s t o p i n s e c T = Ts - D ; // i n s e c Va =( S *3600) / T ; // A v e r a g e s p e e d i n km/ h Vm =1.25* Va ; // Maximum s p e e d i n km/h beta1 =3; // b r a k i n g r e t a r d a t i o n i n km/h / s e c A =(( Vm * T ) -( S *3600) ) / Vm ^2; B =1/(2* beta1 ) ; alfa =1/(2*( A - B ) ) ; disp ( alfa , ” The A c c e l e r a t i o n , a l f a (km/ h/ s e c ) = ” )
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Scilab code Exa 7.6 retardation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
// Example 7 . 6 : R e t a r d a t i o n clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,6) S =4; // i n km Vs =45; // i n km/h Ts =( S *3600) / Vs ; // i n s e c D =30; // d u r a t i o n o f s t o p i n s e c T = Ts - D ; // i n s e c Vm =70; // Maximum s p e e d i n km/h alfa =1.5; // i n km/h / s e c A =(( Vm * T ) -( S *3600) ) / Vm ^2; B =1/(2* alfa ) ; Beta =1/(2*( A - B ) ) ; disp ( Beta , ” R e t a r d a t i o n (km/ h / s e c ) = ” )
Scilab code Exa 7.7 duration of acceleration coasting and braking periods 1 2 3 4 5 6 7 8 9 10 11 12
// Example 7 . 7 : A c c e l e r a t i o n , C o a s t i n g and B r a k i n g periods clc ; clear ; close ; // g i v e n d a t a : S =1.6; // i n km Va =40; // i n km/h V1 =64; // i n km/h alfa =2.0; // i n km/ p / s e c Beta_c =0.16; // i n km/h / s e c Beta =3.2; // i n km/h / s e c t1 = V1 / alfa ; // i n s e c 51
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disp ( t1 , ” D u r a t i o n o f A c c e l e r a t i o n , t 1 ( s e c ) = ” ) T =( S *3600) / Va ; // i n s e c // Formula : T=(V1/ a l f a ) +((V1−V2 ) / B e t a c ) +(V2/ Beta ) V2 =( t1 +( V1 / Beta_c ) -T ) /((1/ Beta_c ) -(1/ Beta ) ) ; t2 =( V1 - V2 ) / Beta_c ; disp ( t2 , ” D u r a t i o n o f c o a s t i n g , t 2 ( s e c ) = ” ) t3 = V2 / Beta ; disp ( t3 , ” D u r a t i o n o f b r a k i n g , t 3 ( s e c ) = ” )
Scilab code Exa 7.8 torque // Example 7 . 8 : Torque clc ; clear ; close ; // g i v e n d a t a : W =200; // w e i g h t o f t r a i n i n t o n n e s D =0.9; // d i a m e t e r i n m G =(1/200) *100; // p e r c e n t a g e g r a d i e n t r =50; // i n N/ t o n n e gama =4; // g e a r r a t i o eta =0.80; // g e a r i n g e f f i c i e n c y We =1.10* W ; // i n t o n n e Vm =48; // maximum s p e e d i n km/h t1 =30; // i n s e c alfa = Vm / t1 ; // i n km/h / s e c Ft =(277.8* We * alfa ) +(98.1* W * G ) +( W * r ) ; // t r a c t i v e e f f e c t required in N 17 T1 =( Ft * D ) /( eta *2* gama ) ; // i n N−m 18 T = round ( T1 /8) ; 19 disp (T , ” Torque d e v e l o p e d by e a c h motor , T(N−m) = ” ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Scilab code Exa 7.9 time taken and current 52
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
// Example 7 . 9 : Time t a k e n and c u r r e n t clc ; clear ; close ; // g i v e n d a t a : V =3000; // l i n e v o l t a g e i n v o l t s W =200; // w e i g h t o f t r a i n i n t o n n e s D =0.9; // d i a m e t e r i n m G =(30/1000) *100; // p e r c e n t a g e g r a d i e n t r =50; // i n N/ t o n n e gama =4; // g e a r r a t i o Vm =50; // i n km/ h eta =0.9; // g e a r i n g e f f i c i e n c y We =1.10* W ; // i n t o n n e T =4*6000; // i n N−m eta_m =85/100; // e f f i c i e n c y o f motor Ft =( eta * T *2* gama ) / D ; A =(98.1* W * G ) +( W * r ) ; B = Ft - A ; alfa = B /(277.8* We ) ; // t r a c t i v e e f f e c t r e q u i r e d i n N t = Vm / alfa ; disp (t , ” Time t a k e n , t ( s e c ) = ” ) Po =( Ft * Vm ) /3600; // i n kw Pi = Po / eta_m ; It =( Pi *1000) / V ; // i n A I = It /4 disp (I , ” C u r r e n t drawn p e r motor , I (A) = ” )
Scilab code Exa 7.10 time taken and current 1 // Example 7 . 1 0 : 2 clc ; 3 clear ; 4 close ; 5 // g i v e n d a t a :
C u r r e n t and t i m e t a k e n
53
6 7 8 9 10 11 12 13 14 15 16 17 18 19
V =36; // s p e e d i n km/ h W =120; // i n t o n n e G =2; // i n p e r c e n t r =2*9.81; // i n N/ t o n n e Ft =(98.1* W * G ) +( W * r ) ; e =88/100; // e f f i c i e n c y o f m o t o r s and g e a r VL =1500; // l i n e v o l t a g e i n v o l t s Po =( Ft * V ) /3600; Pi = Po / e ; I =( Pi *1000) / VL ; bc =((98.1*(2+(0.1*2) ) ) /(277.8*1.1) ) ; // i n kmphps tt = V / bc ; // i n s e c o n d s disp (I , ” c u r r e n t r e q u i r e d i n a m p e r e s i s ” ) disp ( round ( tt ) ,” t i m e t a k e n t o come t o r e s t i n seconds i s ”)
Scilab code Exa 7.11 acceleration coasting retardation and scheduled speed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
// Example 7 . 1 1 . / / a c c e l e r a t i o n , c o a s t i n g r e t a r d a t i o n and s c h e d u l e d s p e e d clc ; clear ; close ; format ( ’ v ’ ,6) // g i v e n d a t a : t1 =24; // i n s e c t2 =69; // i n s e c t3 =11; // i n s e c V1 =48; // i n km/h alfa = V1 / t1 ; disp ( ” p a r t ( a ) ” ) disp ( alfa , ” A c c e l e r a t i o n (km/ h / s e c ) = ” ) r =58; // i n N/ t o n n e G =0; Beta = r /(277.8*1.1) ; 54
17 disp ( ” p a r t ( b ) ” ) 18 disp ( Beta , ” R e t a r d a t i o n ( kmphps ) = ” ) 19 V2 = V1 -( Beta * t2 ) ; 20 S = round ((( V1 * t1 ) /7200) +((( V1 + V2 ) * t2 ) /7200) +(( V2 * t3 ) 21 22 23 24 25 26 27 28 29
/7200) ) ; D =20; // d u r a t i o n o f s t o p i n s e c Ts = t1 + t2 + t3 + D ; Vs = round (( S *3600) / Ts ) ; disp ( ” p a r t ( c ) ” ) disp ( Vs , ” S c h e d u l e time , Vs ( kmph ) = ” ) D1 =15; // when t h e d u r a t i o n o f s t o p i n s e c Ts_dash = t1 + t2 + t3 + D1 ; Vs_dash =( S *3600) / Ts_dash ; disp ( Vs_dash , ” S c h e d u l e s p e e d , VS dash ( kmph ) = ” )
Scilab code Exa 7.12 sceduled speed // Example 7 . 1 2 : S c h e d u l e s p e e d clc ; clear ; close ; // g i v e n d a t a : t1 =30; // i n s e c t2 =50; // i n s e c t3 =20; // i n s e c alpha =2; // kmphps V1 = alpha *( t1 ) ; // i n km/h r =40; // i n N/ t o n n e G =1; bc =((98.1+ r ) ) /(277.8*1.1) ; // i n kmphps V2 = V1 -( bc * t2 ) ; //km/ h r S =((( V1 * t1 ) /7200) +((( V1 + V2 ) * t2 ) /7200) +(( V2 * t3 ) /7200) ); 16 D =30; // d u r a t i o n o f s t o p i n s e c 17 Ts = t1 + t2 + t3 + D ; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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18 Vs =(( S *3600) / Ts ) ; 19 disp ( Vs , ” S c h e d u l e time , Vs ( kmph ) = ” )
Scilab code Exa 7.13 maximum power and distance travelled // Example 7 . 1 3 : maximum power and t o t a l d i s t a n c e clc ; clear ; close ; format ( ’ v ’ ,5) // g i v e n d a t a : w =250; // i n t o n n e s we =(1+(10/100) ) * w ; // e f e c t i v e w e i g h t i n t o n n e s r =5*9.81; // i n N/ t o n n e G =1; // t1 =30; // i n s e c t2 =70; // i n s e c alpha =2; // kmphps V1 = alpha *( t1 ) ; // i n km/h ft =(277.8* we * alpha ) +(98.1* G * w ) +( w * r ) ; // i n n e w t o n s po =(( ft * V1 ) /3600) ; //maximum power o u t p u t i n kW n =0.97; // e f f i c i e n c y pi = po / n ; // i n kW G =1; bc =((98.1+ r ) ) /(277.8*1.1) ; // i n kmphps V2 = V1 -( bc * t2 ) ; //km/ h r beta1 =3; // r e t a r d a t i o n t3 = V2 / beta1 ; // i n s e c o n d s S =((( V1 * t1 ) /7200) +((( V1 + V2 ) * t2 ) /7200) +(( V2 * t3 ) /7200) ); 25 disp ( round ( pi ) ,”maximum power d e v e l o p e d by t r a c t i o n motor i s (kW) ” ) 26 disp (S , ” t o t a l d i s t a n c e t r a v e l l e d by t r a i n i n km i s ” ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
56
Scilab code Exa 7.14 energy consumption // Example 7 . 1 4 : Energy c o n s u m p t i o n clc ; clear ; close ; format ( ’ v ’ ,8) // g i v e n d a t a : Vm =52; //max s p e e d i n kmph t3 =15.8; // d u r a t i o n o f b r a k i n g i n s e c D =(1/2) * Vm *( t3 /3600) ; S =1400; // i n m S1 =( S *10^ -3) -D ; r =50; // i n N/ t o n n e WeBY_W =1.1; Ec =((0.01072* Vm ^2* WeBY_W ) /( S *10^ -3) ) +(0.2778* r *( S1 /( S *10^ -3) ) ) ; 15 disp ( Ec , ” e n e r g y c o n s u m p t i o n i n Wh i s ” )
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Scilab code Exa 7.15 specific energy consumption 1 2 3 4 5 6 7 8 9 10 11
// Example 7 . 1 5 : s p e c i f i c e n e r g y c o n s u m p t i o n clc ; clear ; close ; format ( ’ v ’ ,9) // g i v e n d a t a : w =1; // i n t o n n e s we =(1+(10/100) ) * w ; // e f e c t i v e w e i g h t i n t o n n e s S =1525; // i n m e t e r s r =52.6/1000; // i n N/ kg alpha =0.366; //m/ s ˆ2 57
12 13 14 15 16 17 18 19
V1 =12.2; // i n m/ s t1 = V1 / alpha ; // i n s e c o n d s ft = we * alpha + r ; // i n n e w t o n s ter =((1/2) * ft * V1 * t1 ) /3600; // i n watt−h o u r s seo = ter /( w * S ) ; // i n Wh/ kg−m n =0.65; // e f f i c i e n c y sec1 = seo / n // i n Wh/ kg−m disp ( sec1 , ” s p e c i f i c e n e r g y o n s u m p t i o n i n Wh/ kg−m” )
Scilab code Exa 7.16 sceduled speed and specific energy consumption 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
// Example 7 . 1 6 : S c h e d u l e s p e e d and S p e c i f i c e n e r g y consumption clc ; clear ; close ; // g i v e n d a t a : t1 =30; // i n s e c t2 =50; // i n s e c t3 =20; // i n s e c alpha =2; // kmphps V1 = alpha *( t1 ) ; // i n km/h r =40; // i n N/ t o n n e G =1; bc =((98.1+ r ) ) /(277.8*1.1) ; // i n kmphps V2 = V1 -( bc * t2 ) ; //km/ h r S =((( V1 * t1 ) /7200) +((( V1 + V2 ) * t2 ) /7200) +(( V2 * t3 ) /7200) ); D =15; // d u r a t i o n o f s t o p i n s e c Ts = t1 + t2 + t3 + D ; Vs =(( S *3600) / Ts ) ; disp ( Vs , ” S c h e d u l e s p e e d , Vs ( kmph ) = ” ) S1 =( V1 * t1 ) /7200; // i n m e t e r s r =50; // i n N/ t o n n e WeBY_W =1.1; 58
23 G =1; // 24 Ec =((0.01072* V1 ^2* WeBY_W ) /( S ) ) +(0.2778*(98.1* G + r ) *((
S1 ) /( S ) ) ) ; 25 N =0.75; // 26 Sec = Ec /0.75; // 27 disp ( Sec , ” S p e c i f i c e n e r g y c o n s u m p t i o n i n Wh/ tonne −km i s ”)
Scilab code Exa 7.17 sceduled speed and specific energy consumption 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
// Example 7 . 1 7 : S c h e d u l e s p e e d and s p e c i f i c e n e r g y consumption clc ; clear ; close ; // g i v e n d a t a : t1 =30; // i n s e c t2 =50; // i n s e c t3 =20; // i n s e c alpha =2; // kmphps V1 = alpha *( t1 ) ; // i n km/h r =40; // i n N/ t o n n e G = -1; bc =(( -98.1+ r ) ) /(277.8*1.1) ; // i n kmphps V2 = V1 -( bc * t2 ) ; //km/ h r S =((( V1 * t1 ) /7200) +((( V1 + V2 ) * t2 ) /7200) +(( V2 * t3 ) /7200) ); D =15; // d u r a t i o n o f s t o p i n s e c Ts = t1 + t2 + t3 + D ; Vs =(( S *3600) / Ts ) ; disp ( Vs , ” S c h e d u l e s p e e d , Vs ( kmph ) = ” ) S1 =( V1 * t1 ) /7200; // i n m e t e r s r =50; // i n N/ t o n n e WeBY_W =1.1; Ec =((0.01072* V1 ^2* WeBY_W ) /( S ) ) +(0.2778*(98.1* G + r ) *(( 59
S1 ) /( S ) ) ) ; 24 N =0.75; // 25 Sec = Ec /0.75; // 26 disp ( Sec , ” S p e c i f i c e n e r g y c o n s u m p t i o n i n Wh/ tonne −km i s ”)
Scilab code Exa 7.18 maximum power total energy consumption and specific energy consumption 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
// Example 7 . 1 8 . / / maximum power , t o t a l e n e r g y c o n s u m p t i o n and s p e c i f i c e n e r g y c o n s u m p t i o n clc ; clear ; close ; format ( ’ v ’ ,6) // g i v e n d a t a : W =100; // i n t o n n e We =1.1* W ; // i n t o n n e S =2.5; // d i s t a n c e i n km Va =50; // A v e r a g e s p e e d i n kmph Dr =(3600* S ) / Va ; alfa =1; // i n km/h / s e c Beta =2; // i n km/h / s e c T =180; r =40; // i n N/ t o n n e G =1; K =(1/(2* alfa ) ) +(1/(2* Beta ) ) ; Vm = round (( T /(2* K ) ) - sqrt (( T /(2* K ) ) ^2 -((3600* S ) / K ) ) ) ; // maximum s p e e d t1 = Vm / alfa ; // a c c e l e r a t i o n p e r i o d t3 = Vm / Beta ; // b r a k i n g p e r i o d t2 =T -( t1 + t3 ) ; // i n s e c Ft =(277.8* We * alfa ) +(98.1* W * G ) +( W * r ) ; P_max = round (( Ft * Vm ) /3600) ; disp ( ” p a r t ( a ) ” ) 60
25 disp ( P_max , ”Maximum power , ( kWh) = ” ) 26 e =60/100; // e f f i c i e n c y 27 Ft =(277.8* We * alfa ) +(98.1* W * G ) +( W * r ) ; 28 Ft_dash =(98.1* W * G ) +( W * r ) ; 29 P_max = round (( Ft * Vm ) /3600) ; 30 Et =((1/2) * Ft ) *( Vm /3600) *( t1 /3600) +(( Ft_dash * Vm )
/3600) *( t2 /3600) ; 31 Ec = Et / e ; 32 disp ( ” p a r t ( b ) ” ) 33 disp ( Ec , ” T o t a l Energy Consumption , Ec (kWh) = ” ) 34 Sec =( Ec *1000) /( W * S ) ; 35 disp ( ” p a r t ( c ) ” ) 36 disp ( Sec , ” S p e c i f i c Energy Consumption , (Wh/ tonne −km)
= ”)
Scilab code Exa 7.19 maximum power and energy taken 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
// Example 7 . 1 9 . //maximum power and e n e r g y t a k e n clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,7) W =203; // i n t o n n e We =1.1* W ; // i n t o n n e r =44; // N/ t o n n e G =(1/500) *100; // g r a d i e n t Vm =45; // maximum s p e e d i n kmph t1 =30; // i n s e c alfa = Vm / t1 ; // i n kmph Ft =(277.8* We * alfa ) +(98.1* W * G ) +( W * r ) ; // i n N Po =( Ft * Vm ) /3600; disp ( ” p a r t ( a ) ” ) disp ( Po , ” The maximum power o u t p u t , (kW) = ” ) e =60/100; // e f f i c i e n c y 61
19 Et =(1/2) *(( Ft * Vm ) /3600) *( t1 /3600) ; 20 E =( Et / e ) ; 21 disp ( ” p a r t ( b ) ” ) 22 disp (E , ” The e n e r g y t a k e n (kWh) = ” )
Scilab code Exa 7.20 maximum power and specific energy consumption 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
// Example 7 . 2 0 . maximum power and s p e c i f i c e n e r g y consumption clc ; clear ; close ; format ( ’ v ’ ,7) // g i v e n d a t a : W =16; // i n t o n n e We =1.1* W ; // i n t o n n e Vs =45; // i n kmph r =40; // i n N/ t o n n e S =2.8; // i n km Ts =( S *3600) / Vs ; Td =30; // i n s e c T = Ts - Td ; alfa =2; // i n kmphps Beta =3.2; // i n kmphps K =(1/(2* alfa ) ) +(1/(2* Beta ) ) ; Vm = round (( T /(2* K ) ) - sqrt (( T /(2* K ) ) ^2 -((3600* S ) / K ) ) ) ; // maximum s p e e d t1 = Vm / alfa ; // a c c e l e r a t i o n t i m e t3 = Vm / Beta ; // d u r a t i o n o f b r a k i n g t2 =T -( t1 + t3 ) ; // t i m e f f r e e run i n s e c Ft =(277.8* We * alfa ) +( W * r ) ; P_max =( Ft * Vm ) /3600; disp ( ” p a r t ( a ) ” ) disp ( P_max , ”Maximum power o u t p u t , (kW) = ” ) // a n s w e r i s wrong i n book 62
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Va =50; // A v e r a g e s p e e d i n kmph Dr =(3600* S ) / Va ; T =180; G =1; e =80/100; // e f f i c i e n c y Dt =(1/2) *(( Vm * t3 ) /3600) ; // d i s t a n c e t r a v e l l e d d u r i n g b r a k i n g p e r i o d i n km S1 =S - Dt ; // d i s t a n c e t r a v e l l e d w i t h power i n km So =(((0.01072* Vm ^2) / S ) *( We / W ) ) +((0.2778* r * S1 ) / S ) ; Sec = So / e ; disp ( ” p a r t ( b ) ” ) disp ( Sec , ” S p e c i f i c e n e r g y c o n s u m p t i o n , (Wh/ tonne −km) = ”) // a n s w e r i s wrong i n book
Scilab code Exa 7.21 Schedule speed specific energy consumption total energy consumption and distance 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
// Example 7 . 2 1 : S c h e d u l e s p e e d , s p e c i f i c e n e r g y c o n s u m p t i o n , t o t a l e n e r g y c o n s u m p t i o n and d i s t a n c e clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,6) t1 =30; // i n s e c t2 =40; // i n s e c t3 =30; // i n s e c alpha =2; // kmphps V1 = alpha *( t1 ) ; // i n km/h r =40; // i n N/ t o n n e G =1; bc =((98.1+ r ) ) /(277.8*1.1) ; // i n kmphps V2 = V1 -( bc * t3 ) ; //km/ h r Beta =2.5; // r e t a r d a t i o n 63
17 t4 = V2 / Beta ; // i n s e c o n d s 18 S =((( V1 * t1 ) /7200) +(( V1 * t2 ) /3600) +((( V1 + V2 ) * t3 ) /7200) 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
+(( V2 * t4 ) /7200) ) ; D =15; // d u r a t i o n o f s t o p i n s e c Ts = t1 + t2 + t3 + t4 + D ; Vs =(( S *3600) / Ts ) ; disp ( ” p a r t ( a ) ” ) disp ( Vs , ” S c h e d u l e time , Vs ( kmph ) = ” ) disp ( ” p a r t ( b ) ” ) S1 =(( V1 * t1 ) /7200) +(( V1 * t2 ) /3600) ; // i n 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; // disp ( Sec , ” S p e c i f i c e n e r g y c o n s u m p t i o n i n Wh/ tonne −km i s ”) disp ( ” p a r t ( c ) ” ) W =200; // tec =( Sec * W * S ) ; // disp ( tec *10^ -3 , ” t o t a l e n e r g y c o n s u m p t i o n i n kWh” ) disp ( ” p a r t ( d ) ” ) disp (S , ” t o t a l d i s t a n c e t r a v e l l e d i n Km i s ” )
Scilab code Exa 7.22 specific energy consumption 1 2 3 4 5 6 7 8
// Example 7 . 2 2 : s p e c i f i c e n e r g y c o n s u m p t i o n clc ; clear ; close ; // g i v e n d a t a : W =500; // t1 =60; // i n s e c t2 =5*60; // i n s e c 64
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t3 =3*60; // i n s e c alpha =2.5; // kmphps V1 = alpha *( t1 ) ; // i n km/h r =25; // i n N/ t o n n e G =1; bc =(((98.1*(8/1000) *100) + r ) ) /(277.8*1.1) ; // i n kmphps V2 = V1 -( bc * t3 ) ; //km/ h r Beta =3; // r e t a r d a t i o n t4 = V2 / Beta ; // i n s e c o n d s S =((( V1 * t1 ) /7200) +(( V1 * t2 ) /3600) +((( V1 + V2 ) * t3 ) /7200) +(( V2 * t4 ) /7200) ) ; D =15; // d u r a t i o n o f s t o p i n s e c Ts = t1 + t2 + t3 + t4 + D ; Vs =(( S *3600) / Ts ) ; S1 =(( V1 * t1 ) /7200) +(( V1 * t2 ) /3600) ; // i n km WeBY_W =1.1; G =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 ; // disp ( Sec , ” S p e c i f i c e n e r g y c o n s u m p t i o n i n Wh/ tonne −km i s ”)
Scilab code Exa 7.23 weight and number of axles 1 2 3 4 5 6 7 8
// Example 7 . 2 3 : w e i g h t o f t h e l o c o m o t i v e abd number of axles clc ; clear ; close ; // g i v e n d a t a : Wl =1; // W1 =400; // G =2; // i n p e r c e n t a g e 65
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mu =0.2; // alpha =1; // r =40; // x =(277.8*1.1* alpha +98.1* G + r ) /(9.81*1000) ; // wlo =( x * W1 ) /( mu - x ) ; // i n t o n n e s al =22; // a l l o w a b l e l o a d i n t o n n e s na = wlo / al ; // disp ( wlo , ” w e i g h t o f t h e l o c o m o t i v e i n t o n n e s ” ) disp ( round ( na ) ,” number o f a x l e s r e q u i r e d ” )
Scilab code Exa 7.24 weight and number of axles 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
// Example 7 . 2 4 : w e i g h t o f t h e l o c o m o t i v e abd number of axles clc ; clear ; close ; // g i v e n d a t a : W =12*30; // t o n n e s we =1.04*360; // t o n n e s r =5*9.81; // G =1; // i n p e r c e n t a g e mu =0.2; // alpha =0.8; // x =13.882; // y =0.041; // wlo =( x ) /( mu - y ) ; // i n t o n n e s al =20; // a l l o w a b l e l o a d i n t o n n e s na = wlo / al ; // disp ( wlo , ” w e i g h t o f t h e l o c o m o t i v e i n t o n n e s ” ) disp ( ceil ( na ) ,” number o f a x l e s r e q u i r e d ” )
Scilab code Exa 7.25 trailing weight and maximum gradiant 66
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// Example 7 . 2 5 . / / t r a i l i n g w e i g h t and maximum gradiant clc ; clear ; close ; format ( ’ v ’ ,6) // g i v e n d a t a : w1 =100; // t o n n e s w = w1 +500; // t o n n e s we =1.1* w ; // e f f e c t i v e w e i g h t alpha =1; // G =1; // r =45; // ft =((277.8* we * alpha ) +(98.1* w * G ) +( w * r ) ) ; // i n n e w t o n s ad =0.7; // a d e h s i v e p e r c e n t mu =( ft ) /(100*10^3*9.81* ad ) ; // w2 =130; // t o n n e s ad2 = w2 * G ; // tadw = w1 * ad + ad2 ; // t o n n e s tted = mu * tadw *9.81*1000; // n e w t o n e s W = tted /(277.8*1.1* alpha +98.1* alpha + r ) ; // i n t o n n e s trlw =W -( ad2 + w1 ) ; // disp ( ” p a r t ( a ) ” ) disp ( round ( trlw ) ,” t r a i l i g w e i g h t i n t o n n e s i s ” ) w2 = w1 +500+ ad2 ; // G1 =(( tted / w2 ) -(277.8*1.1+ r ) ) *(1/98.1) ; // disp ( ” p a r t ( b ) ” ) disp ( G1 , ”maximum g r a d i a n t i n p e r c e n t a g e i s ” )
Scilab code Exa 7.26 acceleration 1 // Example 7 . 2 6 ; a c c e l e r a t i o n 2 clc ; 3 clear ; 4 close ;
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// g i v e n d a t a : w1 =100; // t o n n e s w = w1 +500; // t o n n e s we =1.1* w ; // e f f e c t i v e w e i g h t alpha =1; // G =1; // r =45; // ft =((277.8* we * alpha ) +(98.1* w * G ) +( w * r ) ) ; // i n n e w t o n s ad =0.7; // a d e h s i v e p e r c e n t mu =( ft ) /(100*10^3*9.81* ad ) ; // w2 =130; // t o n n e s ad2 = w2 * G ; // tadw = w1 * ad + ad2 ; // t o n n e s tted = mu * tadw *9.81*1000; // n e w t o n e s W = tted /(277.8*1.1* alpha +98.1* alpha + r ) ; // i n t o n n e s trlw =W -( ad2 + w1 ) ; // w2 = w1 +500+ ad2 ; // acc =(( tted / w2 ) -(98.1+ r ) ) *(1/(277.8*1.1) ) ; // i n kmphps disp ( acc , ” a c c e l e r a t i o n i n kmphps i s ” )
Scilab code Exa 7.27 torque and weight 1 2 3 4 5 6 7 8 9 10 11 12 13
// Example 7 . 2 7 : Torque and minimum w e i g h t clc ; clear ; close ; // g i v e n d a t a : N =4; // number o f motor W =250; // i n t o n n e D =.95; // d i a m e t e r i n m G =1; // p e r c e n t a g e g r a d i e n t r =40; // i n N/ t o n n e eta =95/100; // g e a r e f f i c i e n c y gama =3; // g e a r r a t i o We =1.1* W ; 68
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Vm =40; // kmph t1 =20; // i n s e c o n d s alfa = Vm / t1 ; Ft =((277.8* We * alfa ) +(98.1* W * G ) +( W * r ) ) ; T =( Ft * D ) /( eta *2* gama ) ; Td = round ( T / N ) ; disp ( Td , ” Torque d e v e l o p e d by e a c h motor , Td (Nm) = ” ) mu =0.25; // a d h e s i v e c o e f f i c i e n t WL =( Ft /(9.81*1000) ) / mu ; Dw = round ( WL /.75) ; disp ( Dw , ” Dead w e i g h t o f l o c o m o t i v e , ( t o n n e s ) = ” )
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Chapter 8 Electric Traction Motors
Scilab code Exa 8.1 speed armature current characterstic 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
// Example 8 . 1 : Motor s p e e d clc ; clear ; close ; v =230; // i n v o l t s rm =0.3; // i n ohms Ia =[5;10;15;20;25;30;35;40]; // i n a m p e r e s T = [20;50;100;155;215;290;360;430]; // for i =1:8 eb ( i ) = v -( Ia ( i ) ) * rm ; // N ( i ) =(9.55* eb ( i ) * Ia ( i ) ) /( T ( i ) ) ; // disp ( ” s p e e d i n rpm i s f o r c u r r e n t ” + string ( Ia ( i ) ) + ” a m p e r e s ” + string ( round ( N ( i ) ) ) + ” RPM” ) end plot2d ( Ia , N ) xlabel ( ”ARMATURE CURRENT , I a IN AMPS” ) ylabel ( ”SPEED ,N IN RPM” ) xtitle ( ” Spped−Armature c u r r e n t c h a r a c t e r i s t i c ” )
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Scilab code Exa 8.2 speed torque curve 1 2 3 4 5 6 7 8 9 10 11 12 13 14
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// Example 8 . 2 : SPEED−TORQUE GRAPH clc ; clear ; close ; v =600; // i n v o l t s rm =0.8; // i n ohms N1 =600; // Ia =[20;40;60;80]; // i n a m p e r e s EMF =[215;381;485;550] for i =1:4 eb ( i ) = v -( Ia ( i ) ) * rm ; // N ( i ) =( N1 / EMF ( i ) ) * eb ( i ) ; // T ( i ) =(9.55* eb ( i ) * Ia ( i ) ) /( N ( i ) ) ; // disp ( ” s p e e d i n rpm i s f o r c u r r e n t ” + string ( Ia ( i ) ) + ” a m p e r e s ” + string ( round ( N ( i ) ) ) + ” RPM and Torque i n N−m i s ” + string ( T ( i ) ) + ” ” ) end plot2d (T , N ) xlabel ( ”TORQUE ,T IN Nm” ) ylabel ( ”SPEED ,N IN RPM” ) xtitle ( ” Speed−t o r q u e c u r v e ” )
Scilab code Exa 8.3 motor speed and current 1 2 3 4 5 6 7 8 9
// Example 8 . 3 : Motor s p e e d and c u r r e n t drawn clc ; clear ; close ; // g i v e n d a t a : N1 =640; // i n rpm I1 =15; // i n A I2 = sqrt ((2) * sqrt (2) * I1 ^2) ; N2 = round ((2* I1 * N1 ) / I2 ) ; 71
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disp ( I2 , ” C u r r e n t drawn , I 2 (A) = ” ) disp ( N2 , ” Motor s p e e d , N2 ( rpm ) = ” )
Scilab code Exa 8.4 speed and voltage 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
// Example 8 . 4 : s p e e d and v o l t a g e clc ; clear ; close ; n1 =700; // rpm n2 =750; // rpm rm =0.3; // i n ohms v =500; // i n v o l t s ib =50; // a m p e r e s eb1 =v -( ib * rm ) ; // i n v o l t s eb2 = eb1 ; // N =(( v -(2*( ib * rm ) ) ) /(( eb1 / n1 ) +( eb2 / n2 ) ) ) ; // pdv1 =(( eb1 / n1 ) * N ) + ib * rm ; // i n v o l t s pdv2 =(( eb1 / n2 ) * N ) + ib * rm ; // i n v o l t s disp ( round ( N ) ,” s p e e d i n rpm i s ” ) disp ( round ( pdv1 ) ,”PD a c r o s s machine 1 i n v o l t s i s ” ) disp ( round ( pdv2 ) ,”PD a c r o s s machine 2 i n v o l t s i s ” )
Scilab code Exa 8.5 current 1 // Example 8 . 5 : C u r r e n t drawn 2 clc ; 3 clear ; 4 close ; 5 format ( ’ v ’ ,5) 6 // g i v e n d a t a : 7 V =500; // i n v o l t s 8 Vm =40; // i n kmph
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Ft =1800; // i n N Rm =0.4; // i n ohm Lm =3200; // l o s s e s p e r motor i n w a t t Mo =( Ft * Vm *1000) /3600; Cl =3200; // c o n s a t a n t l o s s e s i n w a t t // f o r m u l s : Mi=Po+Cl+C l o s s e s // C l o s s e s=I ˆ2∗Rm // Mi=V∗ I // I 1 =(V+s q r t (Vˆ2 −(4∗Rm∗ (Mo+Cl ) ) ) ) / ( 2 ∗Rm) ; l e a v i n g a s g i v e s a very high value I1 =( V - sqrt ( V ^2 -4* Rm *( Mo + Cl ) ) ) /(2* Rm ) ; disp ( I1 , ” C u r r e n t drawn by e a c h motor , ( A) =” ) ; It = I1 *2; disp ( It , ” T o t a l c u r r e n t drawn , ( A) = ” )
Scilab code Exa 8.6 power delivered 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
// Example 8 . 6 . / / power d e l i v e r e d clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,6) Ft =35300; // i n N V =48; // i n kmph Po =(( Ft * V *1000) /3600) *10^ -3; Ft1 =55180; // i n N Pd = Po * sqrt ( Ft1 / Ft ) ; disp ( ” p a r t ( a ) ” ) disp ( Pd , ” power d e l i v e r e d (kW) = ” ) Pd1 = Po *( Ft1 / Ft ) ; disp ( ” p a r t ( b ) ” ) disp ( Pd1 , ” power d e l i v e r e d (kW) = ” )
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Scilab code Exa 8.7 new characterstics // Example 8 . 7 : s p e e d and t r a c t i v e e f f o r t clc ; clear ; close ; Ia =[60;120;180;240;300;360]; // i n a m p e r e s sp1 =[80;50;45;42;38;35]; // i n kmph tf1 =[1.7;5;10;14;16;20]; // i n n e w t o n s d1 =0.85; // i n m e t e r s d2 =0.9; // i n m e t e r s y1 =71/21; // y2 =74/19; // for i =1:6 V ( i ) =(( d2 / d1 ) *( y1 / y2 ) ) * sp1 ( i ) ; // i n kmph tf2 ( i ) =(( d1 / d2 ) *( y2 / y1 ) ) *( tf1 ( i ) ) ; // i n n e w t o n s disp ( ” f o r a r m a t u r e c u r r e n t ” + string ( Ia ( i ) ) + ” amperes , s p e e d i s ” + string ( V ( i ) ) + ” kmph and t r a c t i v e e f f o r i n thousand newtons i s ”+ string ( tf2 ( i ) ) + ” ” ) 16 end
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Scilab code Exa 8.8 motor speed 1 2 3 4 5 6 7 8
// Example 8 . 8 : s p e e d clc ; clear ; close ; n1 =500; // i n rpm d1 =90; // i n cm d2 =86; // i n cm v =600; // i n v o l t s 74
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vd =0.1; // d r o p eb1 =v -( vd * v ) ; // i n v o l t s A =[90 -86;90 90]; // B =[240;54000]; // X = A \ B ; // V1 = X (1 ,1) ; // i n v o l t s V2 = X (2.1) ; // i n v o l t s N1 = n1 *( V1 -( vd * v ) ) /( eb1 ) ; // N2 = N1 *( d1 / d2 ) ; // disp ( round ( N1 ) ,” s p e e d i n rpm i s ” ) disp ( round ( N2 ) ,” s p e e d i n rpm i s ” ) //N2 i s c a l c u l a t e d wrong i n t h e book
Scilab code Exa 8.9 power input and tractive efforts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
// Example 8 . 9 ; power i n p u t and t r a c t i v e e f f o r t s clc ; clear ; close ; ia =350; //A ib =305; //A v =600; //V pa =( v * ia ) /1000; //kW pb =( v * ib ) /1000; //kW disp ( ” ( i ) When m o t o r s a r e c o n n e c t e d i n p a r a l l e l and t r a i n s p e e d i s 40kmph” ) disp ( pa , ” power i n p u t t o motor A i s , (kW)=” ) disp ( pb , ” power i n p u t t o motor B i s , (kW)=” ) fta =1625; // kg ftb =1480; // kg disp ( fta , ” t r a c t i v e e f f o r o f motor A i s , ( kg )=” ) disp ( ftb , ” t r a c t i v e e f f o r o f motor B i s , ( kg )=” ) disp ( ” ( i i ) When m o t o r s a r e c o n n e c t e d i n s e r i e s and c u r r e n t i s 400A” ) rm =0.08; //ohm 75
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i =400; //A eba =v -( i * rm ) ; //V abb = eba ; //V va =38.5; //V vb =36.7; //V vx =(( v -2*( i * rm ) ) *(( va * vb ) /( va + vb ) ) ) / eba ; // Va =(( eba / va ) * vx ) +( i * rm ) ; //V Vb =(( eba / vb ) * vx ) +( i * rm ) ; //V pa1 =( Va * i ) /1000; //kW pb1 =( Vb * i ) /1000; //kW disp ( pa1 , ” power i n p u t t o motor A i s , (kW)=” ) disp ( pb1 , ” power i n p u t t o motor B i s , (kW)=” ) fta1 =1960; // kg ftb1 =2060; // kg disp ( fta1 , ” t r a c t i v e e f f o r o f motor A i s , ( kg )=” ) disp ( ftb1 , ” t r a c t i v e e f f o r o f motor B i s , ( kg )=” )
Scilab code Exa 8.10 linear synchronous and vehicle speed 1 2 3 4 5 6 7 8 9 10 11
// Example 8 . 1 0 ; l i n e a r s y n c h r o n o u s v e l o c i t y clc ; clear ; close ; f =50; // hz t =0.5; // i n m e t e r s =0.25; // vs =2* f * t *(3600/1000) ; //kmph vc = vs *(1 - s ) ; //kmph disp ( vs , ” l i n e a r s y n c h r o n o u s v e l o c i t y i n kmph i s ” ) disp ( vc , ” v e h i c l e s p e e d i n kmph i s ” )
76
Chapter 9 Control of Traction Motors
Scilab code Exa 9.1 energy lost and total energy 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
// Example 9 . 1 . / / e n e r g y l o s t and t o t a l e n e r g y clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,7) V =600; // i n v o l t s I =350; // i n A Ts =20; // i n s e c R =0.15; // i n ohm E_bse =( V /2) -( I * R ) ; E_bp =V -( I * R ) ; Tse =( E_bse / E_bp ) * Ts ; Tp = Ts - Tse ; Vd =V -(2* I * R ) ; Ed1 =( Vd /2) * I *( Tse /3600) ; Ed2 =(( V /2) /2) *2* I *( Tp /3600) ; El =( Ed1 + Ed2 ) *10^ -3; disp ( ” p a r t ( a ) ” ) disp ( El , ” Energy l o s t i n s t a r t i n g r h e s t a t , El (kWh) = ” ) 77
21 El_1 =(2*( I ^2) * R * Ts ) /(3600*1000) ; 22 disp ( ” p a r t ( b ) ” ) 23 disp ( El_1 , ” Energy l o s t i n motors , El (kWh) = ” ) 24 // a n s w e r i s wrong i n part b in the textbook 25 Et =(( V * I * Tse ) +(2* V * I * Tp ) ) /(3600*1000) ; 26 disp ( ” p a r t ( c ) ” ) 27 disp ( Et , ” T o t a l Energy , Et (kWh) = ” )
Scilab code Exa 9.2 rheostatic losses and train speed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
// Example 9 . 2 . r h e o s t a t i c l o s s e s and t r a i n s p e e d clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,7) V =600; // i n v o l t s I =300; // i n A Ts =15; // i n s e c R =0.1; // i n ohm E_bse =( V /2) -( I * R ) ; E_bp =V -( I * R ) ; Tse =( E_bse / E_bp ) * Ts ; Tp = Ts - Tse ; Vd =V -(2* I * R ) ; Ed1 =( round (( Vd /2) * I *( Tse /3600) ) *10^ -3) ; // disp ( ” p a r t ( i ) ” ) disp ( Ed1 , ” r h e o s t a t i c i n s e r i e s , Ed1 (kWh) = ” ) Ed2 =(( V /2) /2) *2* I *( Tp /3600) *10^ -3; disp ( Ed2 , ” r h e o s t a t i c i n p a r a l l e l , Ed2 (kWh) = ” ) Vm =29; // i n kmph alfa = Vm / Ts ; S = alfa * Tse ; disp ( ” p a r t ( i i ) ” ) disp (S , ” Speed a t t h e end o f s e r i e s p e r i o d , S (km/ h ) = 78
”)
Scilab code Exa 9.3 efficiency and speed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
// Example 9 . 3 . e f f i c i e n c y and s p e e d clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,5) V =600; // i n v o l t s I =200; // i n A Ts =20; // i n s e c R =0.1; // i n ohm E_bse =( V /2) -( I * R ) ; E_bp =V -( I * R ) ; Tse =( E_bse / E_bp ) * Ts ; Tp = Ts - Tse ; Vd =V -(2* I * R ) ; Mi =(( V * I * Tse ) /(2*3600) ) +(( V * I * Tp ) /3600) ; Er =(( Vd /4) * I *( Tse /3600) ) +((( V /2) /2) * I *( Tp /3600) ) ; El =( I ^2* R * Ts ) /(3600) ; Mo = Mi - Er - El ; eta =( Mo / Mi ) *100; disp ( ” p a r t ( a ) ” ) disp ( eta , ” S t a r t i n g e f f i c i e n c y , (%) = ” ) Vm =80; // i n kmph alfa = Vm / Ts ; S = alfa * Tse ; disp ( ” p a r t ( b ) ” ) disp (S , ” s p e e d , S ( kmph ) = ” )
Scilab code Exa 9.4 time duration speed and rheostatic losses 79
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
// Example 9 . 4 t i m e d u r a t i o n , s p e e d and r h e o s t a t i c losses clc clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,6) W =150; // i n t o n n e We =1.1* W ; // i n t o n n e s Vm =30; //kmph V =600; // i n v o l t s r =10; // N/ t o n n e I =300; // i n A R =0.1; // i n ohm Ft =4*15000; // i n N G =1; // g r a d i e n t i n % alfa =( Ft -( W * r ) -(98.1* W * G ) ) /(277.8* We ) ; Ts = Vm / alfa ; E_bse =( V /2) -( I * R ) ; E_bp =V -( I * R ) ; Tse =( E_bse / E_bp ) * Ts ; disp ( ” p a r t ( a ) ” ) disp ( Ts , ” D u r a t i o n o f s t a r t i n g p e r i o d , Ts ( s e c o n d s ) = ” ) disp ( Tse , ” D u r a t i o n f o r S e r i e s r u n n i n g , Tse ( s e c o n d s ) = ”) sptr = alfa * Tse ; // i n kmph disp ( ” p a r t ( b ) ” ) disp ( sptr , ” s p e e d o f t r a i n a t t r a n s i t i o n i n kmph i s ” ) sptr = alfa * Tse ; // i n kmph rls =(( V -(2* I * R ) ) /2) *(2* I ) *( Tse /3600) ; // w a t t s h o u r s rlp =(( V /2) /2) *(4* I ) *(( Ts - Tse ) /3600) ; // w a t t s h o u r s tl = rls + rlp ; // disp ( ” p a r t ( c ) ” ) disp ( rls , ” r h e o s t a t l o s s e s d u r i n g s e r i e s o p e r a t i o n i n W−h o u r s ” ) disp ( rlp , ” r h e o s t a t l o s s e s d u r i n g p a r a l l e l o p e r a t i o n i n W−h o u r s ” ) 80
34
disp ( tl , ” t o t a l l o s s e s i n W−h o u r s i s ” )
Scilab code Exa 9.5 diverter resistance // Example 9 . 5 : d i v e r t e r r e s i s t a n c e clc ; clear ; close ; format ( ’ v ’ ,6) nf =1; // n2 =1.25* nf ; // of =1; // of2 = nf / n2 ; // isef =1; // ise2 =0.66667; // ia2 =(1/ ise2 ) ; // idiv = ia2 - ise2 ; // rdiv = ise2 / idiv ; // disp ( rdiv *100 , ” d i v e r t e r r e s i s t a n c e r e q u i r e d a s percentage of the f i e l d r e s i s t a n c e i s ”) 16 // a n s w e r i s wrong i n t h e t e x t b o o k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Scilab code Exa 9.6 speed and drawbar pull 1 2 3 4 5 6 7 8 9
// Example 9 . 6 : draw c h r a c t e r s t i c s clc ; clear ; close ; format ( ’ v ’ ,6) Ia =[60;80;100;120;160;180]; // i n a m p e r e s sp1 =[47.4;40.3;35.8;33.9;29.8;28.5]; // i n kmph dpk =[440;700;970;1245;1800;2360]; // i n kg sp2 =[58.1;50;45;40.3;35;32]; // 81
10 for i =1:6 11 dpk1 ( i ) = (( dpk ( i ) ) *( sp1 ( i ) ) ) /( sp2 ( i ) ) ; // 12 disp ( ” f o r c u r r e n t ” + string ( Ia ( i ) ) + ” a m p e r e s
,
s p e e d i n kmph i s ” + string ( sp2 ( i ) ) + ” and drawbar p u l l i n kg i s ” + string ( dpk1 ( i ) ) + ” ” ) 13 end
82
Chapter 10 Braking Mechanical Consideration and Control Equipment
Scilab code Exa 10.1 braking torque 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
// Example 1 0 . 1 : b r a k i n g t o r q u e clc ; clear ; close ; I =[50;100;150;200;250]; // sp =[73.6;48;41.1;37.3;35.2]; T =[150;525;930;1335;1750]; v =600; // i n v o l t s rm =0.6; // eb =v -( I (2) * rm ) ; // i n v o l t s rh =3; // i n ohms tr = rh + rm ; // i n ohms i = eb / tr ; // i n a m p e r e s tr = T (3) ; // disp ( tr , ” b r a k i n g t o r q u e i s (N−m) ” )
83
Scilab code Exa 10.2 resistance 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
// Example 1 0 . 2 : r e i s t a n c e clc ; clear ; close ; I =[20;40;60;80]; // emf =[215;381;485;550]; // i n v o l t s emf2 =[202;357;455;516]; // lt =40*9.81; // i n N−m N =600; // rpm il = lt *(2* %pi *( N /60) ) ; // i n W ia =56; // i n a m p e r e s from c u r v e va =440; // i n v o l t s from g r a p h tr = va / ia ; // i n ohms tm =0.8; // i n ohms er = tr - tm ; // i n ohms disp ( er , ” e x t e r n a l r e s i s t a n c e t o be c o n n e c t e d a c r o s s t h e motor d u r i n g b r e a k i s i n ohm” )
Scilab code Exa 10.3 electrical energy and average power 1 2 3 4 5 6 7 8 9 10
// Example 1 0 . 3 : E l e c t r i c a l e n e r g y and a v e r a g e power clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,6) W =400; // i n t o n n e We =1.1* W ; // i n t o n n e S =2; // d i s t a n c e i n km G =2; // g r a d i e n t i n % 84
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
eta =75/100; // e f f i c i e n c y D =2; // d i s t a n c e i n km V1 =40; // i n km V2 =20; // i n km r =40; //N/ t o n n e Ea =(0.01072* We *( V1 ^2 - V2 ^2) ) *10^ -3; // i n kWh Ft =( W * r ) -(98.1* W * G ) ; M =( - Ft * S *1000) /(1000*3600) ; Et = Ea + M ; // t o t a l e n e r g y a v a i l a b l e Ee = eta * Et ; disp ( Ee , ” E l e c t r i c a l e n e r g y , Ee (kWh) = ” ) As =( V1 + V2 ) /2; // a v e r a g e s p e e d At = D / As ; // A v e r a g e t i m e t a k e n P = round ( Ee / At ) ; disp (P , ” A v e r a g e power , P(kW) = ” )
Scilab code Exa 10.4 energy returned 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
// Example 1 0 . 4 : Energy r e t u r n e d t o t h e l i n e clc ; clear ; close ; // g i v e n d a t a : W =2340; // i n t o n n e We =1.1* W ; // i n t o n n e G =100/80; // g r a d i e n t i n % eta =70/100; // e f f i c i e n c y V1 =60; // i n km V2 =36; // i n km r =5*9.81; //N/ t o n n e t =5*60; // i n s e c Ea =(0.01072* We *( V1 ^2 - V2 ^2) ) *10^ -3; // i n kWh Ft =( W * r ) -(98.1* W * G ) ; // t r a c t i v e e f f o r t i n N D =(( V1 + V2 ) /2) *(1000/3600) * t ; // d i s t a n c e moved i n m M =( - Ft * D ) /(1000*3600) ; 85
18 Et = Ea + M ; 19 El = eta * Et ; 20 disp ( El , ” Energy r e t u r n e d t o t h e l i n e , El (kWh) = ” )
Scilab code Exa 10.5 power 1 2 3 4 5 6 7 8 9 10 11 12 13 14
// Example 1 0 . 5 : Energy r e t u r n e d t o t h e l i n e clc ; clear ; close ; // g i v e n d a t a : W =500; // i n t o n n e G =(20*100) /1000; // g r a d i e n t i n % eta =75/100; // e f f i c i e n c y V =40; // i n kmph r =40; //N/ t o n n e Ft =( W * r ) -(98.1* W * G ) ; // t r a c t i v e e f f o r t i n N P =( - Ft * V ) /3600; // Power a v a i l a b l e i n kW Pf = round ( P * eta ) ; disp ( Pf , ” power f e d i n t o t h e l i n e , Pf (kW) = ” )
Scilab code Exa 10.6 power 1 2 3 4 5 6 7 8 9 10
// Example 1 0 . 6 : Power g e n e r a t e d clc ; clear ; close ; // g i v e n d a t a : OD =640; // v o l t a g e r e p r e s e n t by p h a s o r OD R =0.5; // r e a c t o r i n ohm Ia = OD / R ; V =400; // i n v o l t s alfa =38.66; // Phase a n g l e i n d e g r e e 86
11 P =( V * Ia * cosd ( alfa ) ) *10^ -3; 12 disp (P , ” Power g e n e r a t e d , P(kW) = ” )
87
Chapter 11 Power supply for electric traction
Scilab code Exa 11.1 total length 1 2 3 4 5 6 7 8 9 10 11
// Example 1 1 . 1 : T o t a l Length clc ; clear ; close ; // g i v e n d a t a : l =20; // i n m w =0.5; // w e i g h t p e r m e t e r i n kg T =500; // T e n s i o n a p p l i e d i n kg del =( w * l ^2) /(2* T ) ; two_S =2*( l +(2/3) *( del ^2/ l ) ) ; disp ( two_S , ” T o t a l Length (m) = ” )
Scilab code Exa 11.2 sag 1 // Example 1 1 . 2 : Sag 2 clc ;
88
3 4 5 6 7 8 9 10 11 12 13
clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,5) l =30; // i n m e t e r w =0.72; // w e i g h t p e r m e t e r i n kg E =640; // i n kg /cmˆ2 d =1; // d i a m e t e r i n cm T = E *( %pi /4) * d ^2; del =(( w * l ^2) /(2* T ) ) *100; disp ( del , ” s a g ( cm ) = ” )
Scilab code Exa 11.3 sag 1 2 3 4 5 6 7 8 9 10 11 12 13
// Example 1 1 . 3 : Sag clc ; clear ; close ; // g i v e n d a t a : l =30; // i n m e t e r w1 =0.9; // a v e r a g e w e i g h t o f c a t e n a r y w i r e i n kg /m w2 =1.2 // a v e r a g e w e i g h t o f t r o l l e y w i r e i n kg /m w3 =(20/100) * w2 // a v e r a g e w e i g h t o f d r o p p e r and f i t t i n g s i n kg /m w = w1 + w2 + w3 ; T =1000; // i n kg del =(( w * l ^2) /(2* T ) ) ; disp ( del , ” s a g (m) = ” )
Scilab code Exa 11.4 current 1 // Example 1 1 . 4 : 2 clc ;
Current
89
3 clear ; 4 close ; 5 // g i v e n d a t a : 6 I =300; // i n A 7 R =0.08; // i n ohm 8 Vd =6; // v o l t a g e d r o p i n v o l t s 9 I_dash =(( R *( I /2) ) - Vd ) / R ; 10 disp ( I_dash , ” C u r r e n t (A) = ” )
Scilab code Exa 11.5 potential // Example 1 1 . 5 : C u r r e n t clc ; clear ; close ; // g i v e n d a t a : a =7; // f a r end v o l t a g e i n v o l t s i =125; // i n A r =0.02; // i n ohm l =3; // i n km p =( i * r * l ^2) /2; I =(( p - a ) /( r * l ) ) ; // disp (p , ” p o t e n t i a l o f t h e t r a c k a t t h a f a r end o f t h e s e c t i o n in v o l t s i s ”) 13 disp (I , ” C u r r e n t c a r r i e d by −ve f e e d e r , I (A) = ” )
1 2 3 4 5 6 7 8 9 10 11 12
Scilab code Exa 11.6 current 1 // Example 1 1 . 6 : 2 clc ; 3 clear ; 4 close ; 5 // g i v e n d a t a :
Current
90
6 7 8 9 10 11 12 13 14 15
format ( ’ v ’ ,8) ix =200; // a m p e r e s r =0.02; // i n ohms x = poly (0 , ” x ” ) ; p = -19+12* x +0* x ^2; // y = roots ( p ) ; //km ipx = ix *(3 - y ) ; // i n a m p e r e s inx =2* ix ; // i n a m p e r e s it = ipx + inx ; // i n a m p e r e s disp ( it , ” c u r r e n t t h r o u g h n e g e t i v e b o o s t e r i n a m p e r e s i s ”)
Scilab code Exa 11.7 voltage and kW 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
// Example 1 1 . 7 : p o t e n t i a l d r o p and c a p a c i t y i f booster clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,8) ix =250; // a m p e r e s vb =2; // i n v o l t s r =0.02; // i n ohms x = poly (0 , ” x ” ) ; p = -27.6+16* x +0* x ^2; // y = roots ( p ) ; //km pc = vb +( ix * r *(1.6) ^2) /2; // i n v o l t s pd =(( ix * r *( y ^2) ) /2) ; // i n v o l t s tcurr = (1.6* ix ) +(( ix *(3.2 - y ) ) ) ; // i n a m p e r e s vnf = r * tcurr ; // i n v o l t s bnb = vnf - vb ; // i n v o l t s cb =(( bnb * tcurr ) /1000) ; // i n kw disp ( pc , ”maximum p o t e n t i a l d r o p on any two p o i n t s on the r a i l s in v o l t s i s ”) 91
20
disp ( cb , ” c a p a c i t y o f b o o s t e r i n kW i s ” )
Scilab code Exa 11.8 rating of the booster 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
// Example 1 1 . 8 : r a t i n g o f b o o s t e r clc ; clear ; close ; // g i v e n d a t a : format ( ’ v ’ ,8) i =200; // A/km r =0.01; // i n ohms /km x = poly (0 , ” x ” ) p = -20+8* x +0* x ^2; // y = roots ( p ) ; //km i1 =400; // i n a m p e r e s i2 =(4 - y ) * i // i n a m p e r e s tc = i1 + i2 ; // i n a m p e r e s vcn = r * tc ; // i n v o l t s nb = vcn -4; // i n v o l t s rb =( tc *10) /1000; // disp ( rb , ” r a t i n g o f t h e b o o s t e r i n kW i s ” )
Scilab code Exa 11.9 voltage 1 2 3 4 5 6 7 8
// Example 1 1 . 9 // v o l t a g e clc ; clear ; close ; format ( ’ v ’ ,5) vw =60; // i n v o l t s vt =12; // i n v o l t s tv = vw + vt ; // i n v o l t s 92
vs =600; // i n v o l t s va = vs - tv ; // i n v o l t s vr =578; // v o l t s vn =10; // i n v o l t s vtn = tv - vn ; // i n v o l t s vad = vs - vr ; // vp = vtn - vad ; // i n v o l t s disp ( ” p a r t ( a ) ” ) disp ( va , ” v o l t a g e a v a i l a b l e t o t r o l l e y when i t i s a t t h e f a r end w i t h o u t u s i n g b o o s t e r s i n v o l t s i s ” ) 18 disp ( ” p a r t ( b ) ” ) 19 disp ( ” p o s i t i v e b o o s t e r s h o u l d p r o v i d e b o o s t o f ” + string ( vp ) + ” v o l t s ” ) 9 10 11 12 13 14 15 16 17
93
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