Masters G.M. Renewable and Efficient Electric Power Systems
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608 USEFUL CONVERSION FACTORS
1 ton (metric) = 1000 kg
= 2204.622 lb (avoirdupois)
= 1.1023 ton (short)
FLOWRATE
1 cubic foot per second = 0.028316 m
3
/s
= 448.8 gal (U.S.)/min (gpm)
1 cubic foot per minute = 4.72 × 10
−4
m
3
/s
= 7.4805 gpm
1 gallon (U.S.) per minute = 6.31 × 10
−5
m
3
/s
1 million gallons per day = 0.0438 m
3
/s
1 million acre feet per year = 39.107 m
3
/s
1 cubic meter per second = 35.315 ft
3
/s (cfs)
= 2118.9 ft
3
/min (cfm)
= 22.83 × 10
6
gal/d
= 70.07 Ac-ft/d
DENSITY
1 pound per cubic foot = 16.018 kg/m
3
1 pound per gallon = 1.2 × 10
5
mg/L
1 kilogram per cubic meter = 0.062428 lb/ft
3
1 gram per cubic centimeter = 62.427961 lb/ft
3
CONCENTRATION
1 milligram per liter in water = 1.0 ppm
(specific gravity = 1.0)
= 1000 ppb
= 1.0 g/m
3
= 8.34 lb per million gal
PRESSURE
1 atmosphere = 76.0 cm Hg
= 14.696 lb/in.
2
(psia)
= 29.921 in. of Hg (32
◦
F)
= 33.8995 ft of H
2
O(32
◦
F)
= 101.325 kPa
USEFUL CONVERSION FACTORS 609
1 pound per square inch = 2.307 ft of H
2
O
= 2.036 in. Hg
= 0.06805 atm
1 Pascal (Pa) = 1N/m
2
= 1.45 × 10
−4
psia
1inchofmercury(32
◦
F) = 3386.4 Pa
(60
◦
F) = 3376.9 Pa
ENERGY
1 British Thermal Unit = 778 ft-lb
= 252 cal
= 1055 J
= 0.2930 Wh
1 quadrillion Btu = 10
15
Btu
= 1055 × 10
15
J
= 2.93 × 10
11
kWh
= 172 × 10
6
barrels (42-gal) of oil equivalent
= 36.0 × 10
6
metric tons of coal equivalent
= 0.93 × 10
12
cubic feet of natural gas equivalent
1 joule = 1N-m
= 9.48 × 10
−4
Btu
= 0.73756 ft-lb
1 kilowatt-hour = 3600 kJ
= 3412 Btu
= 860 kcal
1 kilocalorie = 4.185 kJ
POWER
1 kilowatt = 1000 J/s
= 3412 Btu/h
= 1.340 hp
1 horsepower = 746 W
= 550 ft-lb/s
1 quadrillion Btu per year = 0.471 million barrels of oil per day
= 0.03345 TW
APPENDIX B
SUN-PATH DIAGRAMS
Renewable and Efficient Electric Power Systems. By Gilbert M. Masters
ISBN 0-471-28060-7
2004 John W iley & Sons, Inc.
611
612 SUN-PATH DIAGRAMS
120°
90°
80°
70°
60°
50°
40°
30°
20°
10°
0°
105°
90°
75°
60°
45°
30°
15°
0°
−15°
−30°
−45°
−60°
−75°
−90°
−105°
−120°
6AM
6AM
7AM
8AM
9AM
10AM
11AM
7AM
8AM
9AM
10AM
11AM
NOON
NOON
SOUTHEAST WEST
SOUTH
EAST
WEST
M
AY
21
APR 21
MAR 21
MAR 21
JUN 21
FEB 21
DEC 21
DEC 21
DEC 21
NOV 21
OCT 21
SEP 21
AUG 21
JUL 21
JUN 21
DEC 21
NOV 21
OCT 21
SEP 21
AUG 21
JUL 21
JUN 21
1PM
2PM
3PM
4PM
5PM
6PM
1PM
2PM
3PM
4PM
5PM
6PM
SOLAR ALTITTUDE
90°
80°
70°
60°
50°
40°
30°
20°
10°
0°
SOLAR ALTITTUDE
SOLAR AZIMUTH
28N
120°
105°
90°
75°
60°
45°
30°
15°
0°
−15°
−30°
−45°
−60°
−75°
−90°
−105°
−120°
SOLAR AZIMUTH
JUN 21
MAY 21
APR 21
JA
N
2
1
FE
B
21
JAN 21
32 N
SUN-PATH DIAGRAMS 613
120°
90°
80°
70°
60°
50°
40°
30°
20°
10°
0°
105°
90°
75°
60°
45°
30°
15°
−15°
−30°
−45°
−60°
−75°
−90°
−105°
−120°
0°
SOLAR ALTITTUDE
SOLAR AZIMUTH
6AM
7AM
8AM
9AM
10AM
11AM
NOON
SOUTHEAST WEST
1PM
2PM
3PM
4PM
5PM
6PM
JUN 21
MAY 21
APR 21
MAR 21
FEB 21
JAN 21
DEC 21
DEC 21
NOV 21
OCT 21
SEP 21
AUG 21
JUL 21
JUN 21
90°
40 N
36 N
80°
70°
60°
50°
40°
30°
20°
10°
0°
SOLAR ALTITTUDE
120°
105°
90°
75°
60°
45°
30°
15°
0°
−15°
−30°
−45°
−60°
−75°
−90°
−105°
−120°
SOLAR AZIMUTH
NOON
SOUTHEAST WEST
6AM
7AM
8AM
9AM
10AM
11AM
1PM
2PM
3PM
4PM
5PM
6PM
JUNE 21
MAY 21
APR 21
MAR 21
FEB 21
JAN 21
DEC 21
DEC 21
NOV 21
OCT 21
SEP 21
AUG 21
JU
L 21
JU
N
21
614 SUN-PATH DIAGRAMS
120°
105°
90°
75°
60°
45°
30°
15°
0°
−15°
−30°
−45°
−60°
−75°
−90°
−105°
−120°
JUN 21
JUN 21
MAY 21
APR 21
MAR 21
FEB 21
JAN 21
JUN 21
MAY 21
AP
R
21
MAR 21
FEB 21
JAN 21
DEC 21
JULY 21
JUL 21
AU
G
2
1
SEPT 21
O
C
T
21
NOV 21
JUN 21
DEC 21
DEC 21
DEC 21
AU
G
21
SEPT 21
O
C
T
2
1
NOV 21
NOON
44 N
EAST SOUTH WEST
SOLAR AZIMUTH
120°
105°
90°
75°
60°
45°
30°
15°
0°
−15°
−30°
−45°
−60°
−75°
−90°
−105°
−120°
EAST
SOUTH
WEST
SOLAR AZIMUTH
SOLAR ALTITUDE
90°
80°
70°
60°
50°
40°
30°
20°
10°
0°
SOLAR ALTITUDE
48 N
NOON
90°
80°
70°
60°
50°
40°
30°
20°
10°
0°
6AM
6AM
7AM
8AM
9AM
10AM
11AM
1PM
2PM
3PM
4PM
5PM
6PM
7AM
8AM
9AM
10AM
11AM
1PM
2PM
3PM
4PM
5PM
6PM
APPENDIX C
HOURLY CLEAR-SKY
INSOLATION TABLES
Renewable and Efficient Electric Power Systems. By Gilbert M. Masters
ISBN 0-471-28060-7
2004 John W iley & Sons, Inc.
615
616 HOURLY CLEAR-SKY INSOLATION TABLES
Clear-Sky Insolation: Beam + Diffuse Latitude 20
◦
N
Solar Tracking Tilt Angles Latitude 20
◦
Solar Tracking Tilt Angles Latitude 20
◦
Time 1-Axis 2-Axis 0 203040506090 Time 1-Axis 2-Axis 0 203040506090
JANUARY 21 (W/m
2
) DECEMBER 21 (W/m
2
)
7, 5 341 359 58 103 122 138 149 156 151 7, 5 235 252 35 72 87 100 110 118 118
8, 4 786 828 303 418 459 486 499 498 409 8, 4 738 794 269 393 439 473 492 497 428
9, 3 923 973 525 670 715 739 740 721 540 9, 3 887 955 486 645 697 729 740 729 572
10, 2 983 1037 696 860 905 923 914 878 624 10, 2 951 1025 654 832 886 914 915 889 660
11, 1 1010 1067 804 978 1023 1037 1021 975 673 11, 1 980 1057 760 949 1003 1027 1021 985 711
12 1018 1076 841 1018 1063 1076 1057 1007 689 12 988 1066 796 988 1042 1065 1057 1017 728
kWh/day 9.10 9.60 5.61 7.08 7.51 7.72 7.70 7.46 5.48 kWh/day 8.57 9.23 5.20 6.77 7.27 7.55 7.61 7.45 5.71
FEBRUARY 21 (W/m
2
) NOVEMBER 21 (W/m
2
)
7, 5 523 530 121 162 176 185 189 188 154 7, 5 299 315 54 94 110 124 134 140 135
8, 4 856 867 381 460 479 486 478 456 318 8, 4 755 795 296 407 446 472 484 483 398
9, 3 973 986 610 710 730 728 705 662 425 9, 3 900 948 515 657 701 724 726 707 531
10, 2 1028 1043 786 901 919 910 875 814 499 10, 2 964 1017 685 845 889 907 899 864 616
11, 1 1053 1069 897 1020 1037 1024 981 908 545 11, 1 993 1049 792 962 1006 1020 1005 960 665
12 1061 1078 935 1061 1078 1063 1017 940 560 12 1002 1058 828 1002 1045 1059 1041 992 682
kWh/day 9.93 10.07 6.53 7.57 7.76 7.73 7.47 7.00 4.44 kWh/day 8.82 9.31 5.51 6.93 7.35 7.55 7.53 7.30 5.37
MARCH 21 (W/m
2
) OCTOBER 21 (W/m
2
)
7, 5 630 630 193 203 199 190 177 158 81 7, 5 456 461 112 148 161 169 172 171 141
8, 4 881 881 456 481 474 452 418 373 182 8, 4 808 818 368 443 462 468 461 441 311
9, 3 983 983 684 724 712 680 629 559 266 9, 3 937 949 593 690 709 708 686 645 419
10, 2 1034 1034 860 910 896 855 790 702 331 10, 2 997 1012 766 877 895 888 854 796 494
11, 1 1060 1059 970 1027 1011 965 892 792 371 11, 1 1026 1042 875 995 1012 1000 958 889 539
12 1067 1067 1008 1067 1051 1003 926 823 385 12 1035 1051 912 1035 1051 1038 994 921 554
kWh/day 10.24 10.24 7.34 7.76 7.63 7.29 6.74 5.99 2.85 kWh/day 9.48 9.62 6.34 7.34 7.53 7.50 7.26 6.81 4.36
APRIL 21 (W/m
2
) SEPTEMBER 21 (W/m
2
)
6, 6 84 86 14887764 6, 6 000000000
7, 5 654 673 258 223 196 164 128 90 32 7, 5 569 569 187 194 190 181 168 150 78
8, 4 847 871 510 476 439 389 330 261 41 8, 4 833 833 445 467 458 437 404 360 176
9, 3 937 962 727 700 657 595 516 423 88 9, 3 945 945 668 703 691 659 609 542 259
10, 2 986 1011 893 874 827 756 663 552 141 10, 2 1002 1002 840 886 870 830 767 681 322
11, 1 1013 1036 998 984 934 858 756 633 175 11, 1 1030 1030 947 1000 983 938 866 769 362
12 1022 1043 1034 1022 971 892 788 661 187 12 1039 1039 984 1039 1022 975 900 799 376
kWh/day 10.06 10.32 7.84 7.55 7.09 6.43 5.59 4.59 1.15 kWh/day 9.80 9.80 7.16 7.54 7.41 7.07 6.53 5.80 2.77
MAY 21 (W/m
2
) AUGUST 21 (W/m
2
)
6, 6 205 222 50 24 23 22 21 19 13 6, 6 65 67 12877664
7, 5 625 677 292 225 183 136 86 57 38 7, 5 607 627 251 217 192 162 128 91 36
8, 4 787 850 528 456 400 334 259 178 47 8, 4 809 833 498 465 429 381 323 257 48
9, 3 870 936 731 662 599 519 425 320 51 9, 3 905 931 711 684 642 581 505 415 91
10, 2 919 984 886 822 754 665 558 435 53 10, 2 959 984 874 854 807 738 648 540 142
11, 1 946 1009 984 923 853 759 643 509 55 11, 1 988 1011 976 961 912 837 739 619 175
12 958 1017 1017 958 887 790 672 534 55 12 998 1020 1011 998 948 871 770 646 187
kWh/day 9.66 10.37 7.96 7.18 6.51 5.66 4.66 3.57 0.57 kWh/day 9.66 9.93 7.65 7.38 6.93 6.28 5.47 4.50 1.18
JUNE 21 (W/m
2
) JULY 21 (W/m
2
)
6, 6 229 255 64 31 29 28 26 24 16 6, 6 188 204 48 25 24 23 21 19 13
7, 5 599 666 300 224 176 125 71 61 41 7, 5 600 652 288 223 181 136 87 60 40
8, 4 752 833 528 443 382 311 232 147 50 8, 4 765 829 521 449 395 330 256 176 50
9, 3 833 918 723 640 571 486 388 280 55 9, 3 851 918 720 652 590 511 419 316 55
10, 2 881 967 873 793 719 625 514 389 57 10, 2 901 968 874 810 743 655 549 428 58
11, 1 909 992 967 891 814 714 594 459 58 11, 1 930 994 970 909 840 746 632 500 59
12 921 1000 999 924 846 745 622 483 59 12 943 1003 1003 943 873 778 660 525 59
kWh/day 9.33 10.26 7.91 6.97 6.23 5.32 4.27 3.20 0.61 kWh/day 9.41 10.13 7.84 7.08 6.42 5.58 4.59 3.52 0.61
HOURLY CLEAR-SKY INSOLATION TABLES 617
Clear-Sky Insolation: Beam + Diffuse Latitude 25
◦
N
Solar Tracking Tilt Angles Latitude 25
◦
Solar Tracking Tilt Angles Latitude 25
◦
Time 1-Axis 2-Axis 0 203040506090 Time 1-Axis 2-Axis 0 203040506090
JANUARY 21 (W/m
2
) DECEMBER 21 (W/m
2
)
7, 5 185 195 25 50 61 71 78 83 84 7, 5 59 64 6 162024272930
8, 4 735 774 251 367 411 442 461 466 402 8, 4 673 723 213 334 381 417 441 452 407
9, 3 894 943 464 621 674 706 718 710 562 9, 3 853 918 421 588 648 688 708 708 585
10, 2 962 1015 629 811 867 898 902 880 664 10, 2 927 998 582 776 841 880 894 881 693
11, 1 993 1048 733 928 987 1015 1014 983 724 11, 1 960 1034 684 893 959 997 1006 985 755
12 1002 1058 769 969 1027 1055 1052 1018 744 12 970 1045 719 932 999 1037 1044 1020 775
kWh/day 8.54 9.01 4.97 6.52 7.03 7.32 7.40 7.26 5.62 kWh/day 7.91 8.52 4.53 6.15 6.70 7.05 7.19 7.13 5.72
FEBRUARY 21 (W/m
2
) NOVEMBER 21 (W/m
2
)
7, 5 454 460 95 133 147 157 162 163 140 7, 5 149 157 21 42 51 58 64 68 68
8, 4 827 838 343 429 455 467 466 451 334 8, 4 700 737 244 355 396 426 444 449 388
9, 3 955 968 564 679 708 717 704 671 463 9, 3 869 916 455 607 658 690 702 693 550
10, 2 1013 1028 733 869 900 904 882 834 553 10, 2 941 993 618 795 850 880 885 863 653
11, 1 1041 1056 840 989 1020 1022 993 935 609 11, 1 974 1028 721 912 969 997 996 966 713
12 1049 1065 877 1029 1061 1061 1031 969 627 12 984 1039 756 952 1009 1037 1034 1001 733
kWh/day 9.63 9.76 6.03 7.23 7.52 7.59 7.45 7.08 4.82 kWh/day 8.25 8.70 4.87 6.37 6.86 7.14 7.21 7.08 5.48
MARCH 21 (W/m
2
) OCTOBER 21 (W/m
2
)
7, 5 613 613 183 196 195 189 178 162 91 7, 5 384 388 85 118 130 138 143 144 124
8, 4 869 869 436 473 471 457 429 389 212 8, 4 776 786 330 411 435 447 446 433 323
9, 3 973 973 656 714 712 690 648 588 316 9, 3 916 928 546 658 686 694 683 652 453
10, 2 1025 1025 825 899 898 870 817 740 395 10, 2 981 995 713 845 875 879 858 813 544
11, 1 1051 1051 932 1016 1014 983 923 836 445 11, 1 1012 1027 818 962 993 994 967 912 599
12 1059 1059 968 1056 1054 1022 959 869 462 12 1021 1037 854 1002 1033 1034 1004 946 617
kWh/day 10.12 10.12 7.03 7.65 7.64 7.40 6.95 6.30 3.38 kWh/day 9.16 9.28 5.84 6.99 7.27 7.34 7.20 6.85 4.70
APRIL 21 (W/m
2
) SEPTEMBER 21 (W/m
2
)
6, 6 139 143 25 16 13 12 11 10 7 6, 6 0000 0 0 0 00
7, 5 664 683 267 237 212 181 147 108 33 7, 5 553 553 177 187 186 179 168 153 86
8, 4 847 871 510 489 457 413 358 293 62 8, 4 820 820 425 458 456 440 413 375 204
9, 3 935 960 719 712 678 624 553 467 143 9, 3 934 934 641 694 691 668 627 568 305
10, 2 983 1007 880 885 849 789 707 604 210 10, 2 992 992 806 875 872 844 792 717 383
11, 1 1009 1032 981 994 958 894 804 691 253 11, 1 1021 1021 910 989 986 954 895 810 431
12 1017 1039 1015 1032 995 930 838 721 267 12 1030 1030 946 1028 1024 992 930 842 448
kWh/day 10.17 10.43 7.78 7.70 7.33 6.76 6.00 5.07 1.68 kWh/day 9.67 9.67 6.86 7.43 7.40 7.16 6.72 6.09 3.27
MAY 21 (W/m
2
) AUGUST 21 (W/m
2
)
6, 6 282 306 76 42 32 31 28 26 17 6, 6 112 116 23 15 13 12 11 10 7
7, 5 645 698 314 251 210 163 112 60 39 7, 5 617 637 260 230 207 178 145 109 37
8, 4 794 857 541 481 431 369 297 217 47 8, 4 809 834 498 477 446 404 350 288 65
9, 3 872 938 737 686 632 559 472 371 51 9, 3 903 928 703 695 661 609 540 456 143
10, 2 919 984 887 846 789 710 610 494 81 10, 2 955 980 860 864 829 770 690 590 208
11, 1 945 1008 981 947 889 805 699 573 119 11, 1 983 1007 959 971 935 872 785 675 249
12 956 1016 1013 981 923 838 730 600 132 12 993 1015 993 1007 971 907 817 704 264
kWh/day 9.87 10.60 8.08 7.49 6.89 6.11 5.17 4.08 0.84 kWh/day 9.75 10.02 7.60 7.51 7.15 6.60 5.86 4.96 1.68
JUNE 21 (W/m
2
) JULY 21 (W/m
2
)
6, 6 307 342 95 52 39 37 35 32 21 6, 6 263 286 75 43 33 31 29 27 18
7, 5 622 691 327 253 206 154 99 63 42 7, 5 621 674 310 248 208 162 113 62 41
8, 4 761 842 546 473 416 349 272 188 51 8, 4 772 836 534 475 425 364 293 215 51
9, 3 837 923 734 669 608 530 437 333 55 9, 3 853 921 727 676 622 551 464 365 55
10, 2 883 968 879 822 758 673 569 449 57 10, 2 902 969 875 833 777 698 600 486 80
11, 1 910 993 969 919 853 764 653 524 70 11, 1 930 994 968 933 875 792 687 563 117
12 922 1001 1000 952 886 795 682 550 83 12 941 1002 999 966 908 824 717 590 130
kWh/day 9.56 10.52 8.10 7.33 6.65 5.81 4.81 3.73 0.67 kWh/day 9.62 10.36 7.98 7.38 6.79 6.02 5.09 4.03 0.86