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TABLES
TABLES
A
309
TABLE
A.I
Solar Irradiance
for Various Air
Masses
a
Air mass = 0.66, p = 0.170
= 0.66, /3i = 0.085 Wave length
0
1
4
7
10
1
4
7
10
0.940 0.950 0.955 0.965 0.975 0.985 1.018 1.082 1.094 1.098
847.0 837.0 828.5 811.5 794.0 776.0 719.2 620.0 602.0 596.0
313.4 296.5 321.1 344.4 576.9 544.6 617.5 512.9 464.1 503.7
95.0 86.3 102.3 120.4 346.0 316.1 391.0 290.4 303.1 304.1
39.6 35.0 44.1 55.1 224.6 201.2 247.5 164.4 210.8 183.6
18.5 16.0 21.2 27.8 150.1 132.4 156.7 93.1 149.9 110.9
286.9 271.6 294.2 315.7 529.1 499.8 567.8 473.1 428.4 465.0
66.7 60.7 72.1 85.0 244.9 224.2 279.4 210.3 220.0 220.9
21.3 18.9 23.9 30.0 122.7 110.3 137.5 93.5 120.3 105.0
7.6 6.7 8.8 11.6 63.2 56.1 67.6 41.5 67.3 49.9
1.101 1.128 1.131 1.137 1.144 1.147 1.178 1.189 1.193 1.222
591.8 560.5 557.0 550.1 542.0 538.5 507.0 496.0 492.0 464.3
504.8 135.1 152.2 143.1 191.2 174.5 399.3 402.2 424.0 391.8
362.7 27.7 35.3 31.7 57.4 48.2 195.1 214.5 310.8 235.3
267.3 9.1 12.6 11.0 24.2 19.3 95.4 114.4 233.3 141.3
198.8 3.6 5.3 4.5 11.6 8.8 46.6 61.0 176.6 84.9
466.1 124.9 140.7 132.4 176.9 161.5 370.0 372.8 393.1 363.6
263.6 20.2 25.8 23.2 42 A 35.3 143.8 158.4 229.7 174.7
153.0 5.3 7.3 6.4 14.1 11.2 55.9 67.3 137.4 83.9
89.5 1.6 2.4 2.1 5.3 4.1 21.7 28.6 82.9 40.3
1.236 1.264 1.276 1.288 1.314 1.335 1.384 1.432 1.457 1.472
451.2 426.5 416.7 406.8 386.1 369.7 343.7 321.0 308.6 301.4
390.8 329.2 342.6 347.3 298.3 190.6 5.7 44.6 85.4 77.4
254.1 209.7 238.6 216.1 137.6 85.0 0.1 5.4 20.6 17.4
165.2 140.0 172.6 134.4 63.5 46.7 0.0 1.3 7.7 6.2
107.4 94.3 126.3 83.7 29.3 27.7 0.0 0.4 3.3 2.6
363.0 306.1 318.7 323.2 277.9 177.6 5.3 41.7 80.0 72.4
189.1 156.7 178.6 162.1 103.6 64.2 0.1 4.1 15.8 13.3
98.5 84.1 104.0 81.3 38.6 28.6 0.0 0.8 4.8 3.9
51.3 45.5 61.2 40.7 14.4 13.7 0.0 0.2 1.7 1.3
1.542 1.572 1.599 1.608 1.626 1.644 1.650 1.676 1.732 1.782
270.4 257.3 245.4 241.5 233.6 225.6 223.0 212.1 187.9 166.6
239.3 222.6 216.0 208.5 206.7 197.9 195.7 181.9 161.5 136.7
165.9 168.1 166.7 157.4 160.7 152.4 150.9 114.8 102.5 75.6
115.0 130.4 131.5 122.1 127.5 120.1 119.1 72.4 65.1 41.8
79.7 102.1 104.5 95.7 101.9 95.5 94.7 45.7 41.3 23.1
224.5 209.0 203.0 195.9 194.3 186.1 184.1 171.2 152.2 129.0
128.5 130.7 129.9 122.7 125.6 119.3 118.2 90.1 80.9 59.9
73.6 83.9 85.0 79.1 82.8 78.3 77.6 47.5 43.0 27.9
42.1 54.4 56.0 51.4 55.0 51.8 51.4 25.0 22.9 12.9
310
1.862 1.955 2.008 2.014 2.057 2.124 2.156 2.201 2.266 2.320
138.2 112.9 102.0 101.2 95.6 87.4 83.8 78.9 72.4 67.6
4.0 42.7 69.4 74.7 69.5 70.0 66.0 66.1 61.6 57.2
0.1 14.5 35.8 45.5 41.3 35.9 32.3 49.1 46.8 43.8
0.0 6.8 17.7 28.8 25.3 18.4 15.8 38.0 36.8 33.8
0.0 3.6 6.4 17.8 14.8 9.5 7.7 29.7 29.3 26.8
3.8 40.5 65.7 70.8 66.0 66.4 62.7 62.8 58.6 54.4
0.1 11.6 28.9 36.7 33.4 29.2 26.3 40.1 38.4 35.5
0.0 4.6 12.2 19.8 17.5 12.8 11.0 26.7 26.0 24.0
0.0 2.1 3.8 10.4 8.7 5.6 4.6 17.9 17.9 16.5
2.338 2.356 2.388 2.415 2.453 2.494 2.537 2.900 2.941 2.954
66.3 65.1 62.8 61.0 58.3 55.4 52.4 35.0 33.4 32.8
54.7 52.0 36.0 32.5 29.6 20.3 4.6 2.9 6.0 5.7
39.9 36.3 18.7 15.8 13.7 6.8 0.4 0.2 1.0 0.9
30.4 26.5 11.7 9.4 7.9 3.2 0.1 0.0 0.3 0.3
23.4 19.6 7.8 6.0 5.0 1.7 0.0 0.0 0.1 0.1
52.1 49.5 34.3 31.0 28.2 19.4 4.4 2.8 5.7 5.5
32.8 29.9 15.5 13.0 11.3 5.6 0.3 0.2 0.8 0.8
21.6 18.9 8.3 6.7 5.7 2.3 0.1 0.0 0.2 0.2
14.4 12.1 4.8 3.7 3.1 1.1 0.0 0.0 0.1 0.1
2.973 3.005 3.045 3.056 3.097 3.132 3.156 3.204 3.214 3.245
32.1 30.8 28.8 28.2 26.2 24.9 24.1 22.5 22.1 21.1
8.7 7.8 4.7 4.9 3.2 6.8 18.7 2.1 3.4 3.9
2.2 1.8 0.7 0.8 0.4 1.7 12.6 0.2 0.5 0.7
0.9 0.7 0.2 0.2 0.1 0.7 8.9 0.0 0.1 0.2
0.4 0.3 0.1 0.1 0.0 0.3 6.3 0.0 0.0 0.1
8.4 7.5 4.5 4.7 3.1 6.5 17.9 2.0 3.3 3.8
1.8 1.6 0.6 0.7 0.3 1.5 10.7 0.2 0.4 0.6
0.6 0.5 0.1 0.2 0.1 0.5 6.7 0.0 0.1 0.2
0.3 0.2 0.0 0.1 0.0 0.2 4.2 0.0 0.0 0.1
3.260 3.285 3.317 3.344 3.403 3.450 3.507 3.538 3.573 3.633
20.6 19.7 18.8 18.1 16.5 15.6 14.5 14.2 13.8 13.1
3.7 14.2 12.9 4.2 12.3 12.5 12.5 11.8 10.9 10.8
0.6 8.5 6.9 0.9 7.8 8.9 9.9 8.8 5.4 8.3
0.2 5.1 3.5 0.3 5.1 6.7 8.1 6.9 2.6 6.7
0.1 2.8 1.3 0.1 3.2 5.0 6.7 5.5 1.3 5.5
3.5 13.7 12.4 4.1 11.9 12.0 12.1 11.3 10.5 10.4
0.5 7.3 5.9 0.8 6.7 7.7 8.5 7.6 4.6 7.1
0.1 3.9 2.7 0.2 3.9 5.1 6.2 5.3 2.0 5.2
0.0 1.9 0.9 0.1 2.2 3.5 4.6 3.8 0.9 3.8
3.673 3.696 3.712 3.765 3.812 3.888 3.923 3.948 4.045
12.6 12.3 12.2 11.5 11.0 10.4 10.1 9.9 9.1
9.1 10.4 10.9 9.5 8.9 8.1 8.0 7.8 6.7
6.1 8.2 9.0 7.2 6.7 5.6 5.6 5.5 4.1
4.6 6.7 7.6 5.9 5.4 4.0 4.2 4.0 2.6
3.5 5.6 6.5 4.8 4.4 2.9 3.1 3.0 1.5
8.8 10.1 10.5 9.1 8.6 7.8 7.7 7.6 6.5
5.3 7.1 7.8 6.3 5.8 4.8 4.9 4.8 3.6
3.5 5.2 5.9 4.6 4.2 3.1 3.3 3.2 2.0
2.5 3.9 4.6 3.4 3.1 2.0 2.2 2.1 1.1
889.2
448.7
255.2
153.8
800.2
303.1
133.3
63.4
Total W m- ) 2
1353 a
Expressed in W m
2
/im
H 0 , 20 mm; 0 , 3.4 mm. [From S15.] 2
3
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Tf cm vo O CM Tf CM VO VO VO VO
P» Tf — Tf VO VO — < „ .ior-voOTfvocM. Tf T f T f r o r o C M C M r o r o C M C M r o < O 0O 00
. o
CU 00 vO 00 VO
ONOOrO — V O O r O — — ON — O — — OOONCMOOCMCMOOVOCMONONONf
TfTfvOVOCMP-OvOCMCMCMOVOTfOOOVOCMON' O N v o r - O o o — ooo — 00rovovovo00voTfCMr~i TfTfrOTfTfrOrOTfVOTfTfTfTfVOTfCOTfVOTf"
3
ro
vo vo VO VO
ON vo VO 00
i ro oo t t Tf cm — — v o O o o O N T f v O o o v o r o r o v O I O — VO — VO — Tf VO P~ O O — — V O T f O V O V O > v o v o v o r ~ - v o v O v o v o v o v o v o v o v o » O T f v o v o T f 00 vo
OxONOOrO — v O O r o
OS
ON VO
v o O O x O C m — oor--Tfvo — — OOx — p~cmo — v o r ^ o o o r o — — vOTf< — O V O P - V O O N * — CMVOOOVOVO-— CMVO — — VOCMCMOOr-OOVOVO'— ON"— i vOvOTfvnvOTfvovovovovovnvOr--vOvOvOvovovnTfvovovOTf«nvovo'
O
OO VO
o — JO 00 vS £ CO vo
to
vo OvOOxvOoor-— rooOONOP~vOrooOOxONOOvOvor-oxvOvOvo — — vo O — OxrOP~OXON — — C M O x r O C M C M V O - © C O O N C M - OOOOOOXONVOVOrO vo VO VOVOVOVOVOTfVOVOVOVOVOVOVOVOVOVOVOvOVOVOTfVOP^VOTflo^OVO p- O 00 ro — vo O -
ON VO
- Tf Tf
VO Tf Tf vo O 00 CO
-
-
o
-
ro VO 00 CM VO
CM oo Tf vo CO VO vn VO ro cm ro vo vo vo — oo O ON Tf O Tf £ t? Tf Tf •«f £ ro ro Tf Tf cm ro Tf
o
o
T? Tf ro ro ^
VO o Tf CM CM
oo o 00
_
CM CM
Tf Tf ro ro Tf ^ 00 o
o oo VO 00 oo
M ^ O O mO <~ CO T-* EG T3 EG C
*C
'2 i S
111
Tables TABLE
315 A3
Seasonally
Averaged
Daily Direct-Normal Spring (M,A,M)
Solar Flux in Summer (J,J,A)
kWh/i 2a m
Fall (S,0,N)
Winter (D,J,F)
Albuquerque
7.6
8.2
6.9
5.8
Apalachicola Bismarck Blue Hill Boston
5.0 4.7 3.6 3.6
4.5
4.4
6.5 4.2 4.2
Brounsville Cape Hatteras Caribou Charleston
4.2 4.8
3.9 3.1 3.1 4.4
3.3 2.7 2.2 2.2
Columbia D o d g e City El Paso
4.3 5.9 8.0 6.9
5.9 4.3
5.8 4.9 6.0 3.9 5.8 7.1
3.2
4.0 3.4 3.7
3.1 3.9 3.1
4.1
2.9 4.6
5.5 6.9 6.7 4.6 3.9
6.0 4.8 3.7 2.3 2.7 2.5
Great Falls Lake Charles Madison
4.5 4.5 3.8 4.1
8.1 8.1 5.9 6.7 4.3 5.1
Medford Miami
4.5 4.3
7.5 3.5
3.7
1.5
3.5
Nashville N e w York Omaha Phoenix
3.9 3.4
3.6 2.8 4.1 6.6
3.9 2.4 2.0 3.2 5.3 4.1
3.3
Ely Fort Worth
Santa Maria
5.7
Seattle Washington, D C
4.8
4.6 3.8 6.0 8.0 6.9 7.4
3.8
4.3
4.6 7.8
a
From (K7).
3.8 3.3
5.2 3.2
1.5 2.4
Appendix
316 TABLE
A
A A
Elliptic Integrals
of the Second
Kind
E(
a
- s i n « sin e)Klo 2
2
« V
0°
0° 2 4 6 8
0 0 0 0 0
0. 08726 0. 08726 0.08726 0. 08726 0. 08726
646 633 592 525 432
0.17453 0. 17453 0. 17452 0. 17452 0. 17451
293 185 864 330 587
0.26179 0.26179 0. 26178 0.26176 0.26174
939 579 503 715 224
0.34906 0. 34905 0.34903 0.34899 0.34893
585 742 218 025 181
0.43633 0.43631 0.43626 0.43618 0.43607
231 608 745 665 403
0. 52359 0. 52357 0. 52348 0. 52335 0. 52315
878 119 856 123 981
10 12 14 16 18
0 0 0 0 0
0. 08726 0.08726 0. 08725 0. 08725 0. 08725
313 168 999 806 590
0.17450 0. 17449 0.17448 0. 17446 0.17444
636 485 137 599 879
0.26171 0.26167 0.26162 0. 26157 0. 26151
041 182 664 510 743
0. 34885 0. 34876 0. 34866 0. 34853 0.34840
714 657 055 954 412
0.43593 0.43575 0.43555 0.43531 0.43505
Oil 552 106 765 633
0. 52291 0. 52261 0. 52227 0. 52187 0. 52142
511 821 039 317 828
20 22 24 26 28
0 0 0 0 0
0. 08725 0. 08725 0. 08724 0. 08724 0.08724
352 094 816 521 208
0.17442 0.17440 0.17438 0.17436 0. 17433
985 926 712 353 862
0.26145 0.26138 0.26131 0. 26123 0. 26114
391 485 056 141 778
0. 34825 0. 34809 0.34791 0.34773 0. 34753
492 262 800 187 510
0.43476 0.43445 0.43411 0.43375 0.43337
831 488 749 767 709
0. 52093 0. 52040 0. 51982 0. 51921 0. 51856
770 357 827 436 461
30 32 34 36 38
0 0 0 0 0
0. 08723 0. 08723 0. 08723 0. 08722 0. 08722
881 540 187 824 453
0. 17431 0.17428 0. 17425 0. 17422 0.17419
250 529 714 817 852
0.26106 0.26096 0.26087 0. 26077 0.26067
005 867 405 666 697
0.34732 0.34711 0. 34689 0.34666 0. 34642
863 342 050 093 580
0.43297 0.43256 0.43212 0.43168 0.43122
749 075 880 368 748
0.51788 0.51716 0. 51643 0. 51566 0. 51488
193 944 040 820 638
40 42 44 46 48
0 0 0 0 0
0. 08722 0. 08721 0. 08721 0. 08720 0.08720
075 692 307 920 535
0.17416 0.17413 0.17410 0. 17407 0.17404
835 779 700 613 531
0.26057 0.26047 0.26036 0.26026 0.26016
545 261 893 492 110
0.34618 0.34594 0. 34569 0.34545 0. 34520
625 343 850 266 710
0.43076 0.43029 0.42981 0. 42933 0.42885
236 055 431 594 776
0. 51408 0.51327 0. 51246 0. 51163 0.51081
862 866 037 767 454
50 52 54 56 58
0 0 0 0 0
0. 08720 0. 08719 0. 08719 0. 08719 0.08718
152 774 402 039 686
0.17401 0.17398 0.17395 0.17392 0.17389
472 449 477 571 745
0.26005 0.25995 0.25985 0.25975 0.25966
795 600 574 765 224
0.34496 0. 34472 0.34448 0. 34425 0.34402
302 162 409 159 529
0.42838 0.42791 0.42744 0.42699 0.42655
212 134 775 368 138
0.50999 0. 50918 0. 50838 0.50759 0.50683
501 310 287 831 341
60 62 64 66 68
0 0 0 0 0
0. 08718 0. 08718 0. 08717 0.08717 0.08717
345 017 704 408 130
0. 17387 0.17384 0. 17381 0.17379 0.17377
013 388 883 511 283
0.25956 0.25948 0.25939 0. 25931 0.25924
996 126 660 640 104
0.34380 0. 34359 0.34339 0.34320 0. 34302
631 575 465 404 487
0.42612 0.42571 0.42531 0.42494 0.42459
308 097 712 358 224
0. 50609 0. 50537 0. 50469 0. 50404 0. 50343
207 811 523 700 686
70 72 74 76 78
0 0 0 0 0
0. 08716 0.08716 0. 08716 0. 08716 0. 08716
871 633 416 223 053
0.17375 0. 17373 0. 17371 0. 17370 0.17368
210 302 568 018 659
0.25917 0.25910 0.25904 0.25899 0.25894
090 634 767 519 917
0.34285 0.34270 0. 34256 0. 34243 0. 34233
805 443 478 984 022
0.42426 0.42396 0.42368 0.42344 0.42322
495 339 913 363 817
0. 50286 0. 50234 0.50186 0. 50143 0. 50106
804 359 633 886 351
80 82 84 86 88
0 0 0 0 0
0. 08715 0. 08715 0.08715 0. 08715 0.08715
909 789 695 628 588
0.17367 0.17366 0.17365 0.17365 0. 17364
498 539 789 250 926
0.25890 0.25887 0.25885 0.25883 0.25882
983 737 195 370 271
0.34223 0.34215 0.34209 0.34205 0.34202
650 915 857 507 889
0.42304 0.42289 0.42277 0.42268 0.42263
389 175 258 700 547
0. 50074 0.50047 0. 50026 0.50011 0. 50003
232 707 923 993 003
90
0
0. 08715 574
10°
5°
['"»"] 5 15 25 35 45 55 65 75 85
0 0 0 0 0 0 0 0 0
0.08726 0. 08725 0.08724 0. 08723 0.08721 0. 08719 0.08717 0. 08716 0.08715
562 905 671 006 113 220 554 317 659
15°
0.17364 818
m
0.17452 0.17447 0.17437 0.17424 0.17409 0.17394 0.17380 0.17370 0.17365
624 391 550 275 157 015 680 770 493
20°
0.25881 905 [ "4 (
0.26177 0.26160 0.26127 0.26082 0.26031 0.25980 0.25935 0.25902 0.25884
7 ) 9
]
698 165 157 567 693 639 592 064 192
25°
0.34202 014
[" (
6)2 5
0.34901 0.34860 0.34782 0.34677 0. 34557 0.34436 0. 34329 0.34250 0.34207
]
329 188 632 648 562 714 797 043 467
30°
0.42261 826
0.50000 000
[- ] (
6)4
5
0.43623 0.43543 0.43394 0.43190 0.42957 0.42721 0.42512 0.42356 0.42272
105 791 028 776 525 938 769 271 556
0.52342 0.52207 0. 51952 0.51605 0. 51204 0. 50798 0.50436 0.50164 0. 50018
670 785 597 197 932 838 656 622 720
Compiled from K. Pearson, Tables of the complete and incomplete elliptic integrals,Cambridge Univ. Press, Cambridge, England, 1934 (with permission). Known errors have been corrected.
317
Tables
TABLE
AA
{Continued) E{*\«)=- {* ( l - s i n 2 a s i n 35°
(T 2 4 6 8
40°
45°
2
50°
55°
60°
0.61086 0.61082 0.61069 0.61047 0.61018
524 230 365 983 171
0.69813 0.69806 0.69788 0. 69756 0.69713
170 905 136 935 427
0.78539 0.78531 0.78505 0.78461 0.78401
816 125 085 792 409
0. 87266 0.87254 0.87220 0. 87162 0.87081
463 883 183 487 998
0.95993 0.95978 0.95933 0.95859 0.95755
109 184 459 083 301
04719 04701 04644 04551 04421
755 051 996 764 646
10 12 14 16 18
0.60980 0.60933 0.60879 0.60817 0.60748
055 793 577 636 229
0.69657 0. 69590 0.69511 0. 69420 0.69318
784 226 023 492 999
0.78324 0.78230 0.78120 0. 77994 0. 77853
162 343 308 473 323
0.86979 0.86853 0. 86707 0.86539 0. 86350
001 863 031 034 481
0.95622 0.95461 0.95271 0.95054 0.94810
460 005 478 522 878
1.04255 1. 04052 1. 03814 1. 03542 1.03236
047 491 615 177 049
20 22 24 26 28
0.60671 0. 60588 0.60498 0.60402 0.60300
652 229 319 308 616
0. 69206 0. 69084 0.68953 0. 68812 0.68663
954 814 083 308 077
0.77697 0. 77527 0.77343 0.77147 0.76939
402 316 735 387 059
0.86142 0.85914 0.85668 0.85405 0.85126
062 545 781 695 295
0.94541 0.94246 0.93928 0.93587 0.93225
386 984 709 699 186
1.02897 1. 02526 1.02126 1. 01696 1. 01238
221 804 023 224 873
30 32 34 36 38
0. 60193 0.60081 0.59966 0. 59846 0. 59723
687 994 035 332 431
0.68506 0.68341 0.68171 0.67994 0.67813
023 817 170 830 578
0.76719 0.76489 0.76250 0. 76003 0. 75749
599 908 947 726 309
0.84831 0. 84522 0.84201 0.83868 0.83525
663 958 414 340 115
0.92842 0.92441 0.92022 0.91588 0.91140
504 083 452 234 150
1. 00755 1. 00247 0.99717 0.99167 0.98598
556 977 966 469 560
40 42 44 46 48
0.59597 0.59470 0. 59341 0.59211 0. 59081
897 312 278 406 324
0.67628 0.67439 0.67248 0.67056 0.66863
229 630 651 191 167
0.75488 0.75223 0.74954 0. 74682 0.74409
809 383 234 605 773
0.83173 0.82814 0.82449 0.82080 0.81709
189 080 369 700 775
0.90680 0.90209 0.89731 0.89246 0.88758
017 742 325 858 513
0.98013 0.97414 0.96803 0.96184 0.95558
430 397 899 497 873
50 52 54 56 58
0.58951 0.58823 0, 58696 0,58571 0, 58450
664 065 171 622 056
0.66670 0.66479 0.66290 0.66104 0.65922
515 183 130 317 707
0. 74137 0. 73865 0.73597 0.73332 0.73074
047 766 286 979 229
0.81338 0.80968 0.80601 0.80239 0.79884
346 217 230 262 217
0.88268 0.87779 0.87293 0.86812 0.86340
551 305 184 660 261
0.94929 0.94300 0.93673 0.93051 0.92439
830 285 272 931 505
60 62 64 66 68
58332 58218 58109 58006 57908
103 382 497 032 549
0.65746 0.65575 0.65412 0.65257 0.65110
255 905 585 197 612
0.72822 0.72578 0. 72345 0.72122 0.71911
416 915 085 260 737
0.79538 0. 79202 0. 78879 0. 78571 0. 78279
015 582 839 685 987
0.85878 0. 85430 0.84997 0.84583 0.84191
561 169 709 811 082
0.91839 0.91254 0.90689 0.90146 0.89630
329 821 460 778 323
70 72 74 76 78
0, 57817 0,57733 0, 57657 0.57588 0.57528
584 641 189 663 450
0.64973 0.64847 0.64731 0. 64628 0.64537
667 154 812 328 322
0.71714 0.71532 0. 71366 0.71216 0.71085
767 545 196 766 210
0.78006 0. 77753 0. 77521 0.77312 0.77129
562 157 434 952 143
0.83822 0.83479 0.83165 0.82882 0.82631
090 335 223 031 879
0.89143 0.88690 0.88273 0.87896 0.87563
642 237 530 810 185
80 82 84 86 88
0.57476 0. 57434 0. 57400 0.57376 0. 57362
897 302 912 921 470
0.64459 0.64394 0. 64344 0.64307 0.64286
347 879 316 973 075
0. 70972 0. 70879 0.70805 0.70753 0. 70721
381 019 745 050 289
0.76971 0.76840 0.76737 0.76663 0.76619
298 544 830 912 339
0.82416 0.82238 0.82097 0.81996 0.81935
694 177 770 631 604
0.87275 0. 87036 0. 86847 0.86712 0.86629
520 381 970 068 990
90
0.57357 644
0.64278 761
[f ] m
.70710 678
0.76604 444
( 3
5 15 25 35 45 55 65 75 85
0.61059 0.60849 0.60451 0. 59906 0.59276 0.58633 0.58057 0.57621 0.57387
734 557 051 618 408 563 051 910 732
0.69774 0.69467 0.68883 0.68083 0.67152 0.66196 0.65333 0.64678 0.64324
083 152 790 664 549 758 844 548 351
0.78485 0.78059 0. 77247 0.76128 0. 74818 0.73464 0.72232 0.71289 0.70776
586 337 109 304 650 525 215 304 799
0. 87194 0.86625 0.85539 0.84036 0.82265 0.80419 0.78723 0.77414 0. 76697
199 642 342 234 424 500 820 195 232
0.81915 204
0.86602 540
[ -| ] (
0.95899 0.95166 0.93760 0.91807 0.89489 0.87052 0.84788 0. 83019 0.82042
)5
964 385 971 186 714 066 276 625 232
1. 04603 1. 03682 1.01914 0.99445 0.96495 0.93361 0.90415 0. 88079 0.86773
012 664 662 152 146 692 063 972 361
(continued)
Appendix
318 TABLE
AA
A
{Continued) (1 sin-'« sin-' 75°
70°
65°
80°
85°
90°
0 2 4 6 8
1.13446 1.13423 1.13354 1.13240 1.13081
401 517 929 837 573
1.22173 1.22145 1.22063 1.21926 1.21735
048 628 443 717 820
1.30899 1.30867 1.30770 1. 30609 1.30385
694 442 767 916 297
1. 39626 1. 39589 1. 39477 1.39291 1. 39031
340 024 165 030 062
1.48352 1. 48310 1.48182 1. 47970 1.47674
986 448 929 717 288
1. 57079 1.57031 1. 56888 1. 56649 1.56316
633 792 372 679 223
10 12 14 16 18
1.12877 1.12629 1.12338 1.12004 1.11628
602 522 066 099 624
1.21491 1.21193 1.20844 1.20443 1.19992
274 748 065 195 262
1. 30097 1.29747 1.29335 1.28863 1.28331
484 215 393 089 541
1. 1. 1. 1. 1.
38697 38292 37815 37268 36651
886 302 292 017 823
1.47294 1.46831 1.46287 1.45662 1.44959
312 652 363 693 085
1.55888 1.55368 1.54755 1. 54052 1. 53259
720 089 458 157 729
20 22 24 26 28
1.11212 1.10757 1.10265 1. 09736 1. 09173
778 834 204 439 228
1. 19492 1.18945 1.18352 1.17715 1.17036
542 465 618 743 745
1.27742 1.27096 1.26396 1.25643 1.24840
153 502 337 578 326
1. 1. 1. 1. 1.
35968 35218 34405 33531 32596
233 961 903 146 967
1.44178 1.43321 1.42392 1.41391 1.40321
179 813 023 049 335
1. 52379 1. 51414 1.50366 1.49236 1.48029
921 692 214 871 266
30 32 34 36 38
1. 08577 1. 07950 1. 07295 1. 06614 1. 05909
404 942 961 728 660
1.16317 1.15560 1.14768 1.13943 1.13087
686 796 469 273 946
1.23988 1. 23091 1.22151 1.21170 1.20152
858 635 305 705 870
1.31605 1. 30560 1.29463 1. 28318 1.27128
841 436 629 499 343
1. 39185 1.37986 1. 36727 1. 35411 1. 34041
532 503 328 306 965
1.46746 1. 45390 1.43966 1.42476 1.40923
221 780 215 031 972
40 42 44 46 48
1. 05183 1. 04438 1. 03677 1. 02904 1.02122
322 435 875 677 034
1.12205 1. 11298 1.10371 1. 09426 1. 08468
408 760 291 484 023
1.19101 1.18018 1. 16909 1.15777 1.14625
036 648 366 077 899
1.25896 1.24627 1.23324 1.21991 1.20633
675 240 019 241 398
1.32623 1. 31158 1.29652 1.28110 1.26535
066 614 865 340 837
39314 37650 35937 34180 32384
025 433 700 606 218
50 52 54 56 58
1. 01333 1. 00542 0.99751 0.98966 0.98190
305 010 835 632 414
1. 07499 1.06525 1.05550 1. 04578 1.03614
796 908 682 671 663
1.13460 1.12284 1.11104 1.09923 1.08748
200 604 010 604 883
1.19255 1. 17861 1.16458 1.15051 1.13645
255 873 621 210 710
1.24934 1.23311 1.21672 1.20024 1.18373
449 580 971 724 339
1. 30553 1.28695 1.26814 1.24918 1.23012
909 374 653 162 722
60 62 64 66 68
0.97427 0.96681 0.95958 0.95261 0.94595
354 780 158 084 256
1.02663 1.01731 1. 00822 0.99942 0.99099
689 023 192 966 354
1. 1. 1. 1. 1.
07585 06440 05318 04228 03176
669 132 814 653 998
1. 12248 1.10866 1. 09507 1.06178 1. 06889
590 752 580 986 476
1.16725 1.15089 1.13472 1.11882 1.10330
747 364 145 658 172
1.21105 1. 19204 1. 17317 1.15454 1.13624
603 568 938 668 437
70 72 74 76 78
0.93965 0.93376 0.92833 0.92340 0.91901
447 462 088 024 802
0.98297 0.97544 0.96845 0. 96208 0.95638
583 068 360 074 776
1.02171 1. 01220 1.00333 0.99517 0.98783
634 781 091 606 670
1.05648 1. 04465 1.03350 1. 02317 1.01376
221 133 951 331 904
1.08824 1.07377 1. 06000 1. 04707 1.03513
773 505 556 504 640
1.11837 1.10106 1. 08442 1. 06860 1.05377
774 217 522 953 692
80 82 84 86 88
0.91522 0.91206 0.90956 0. 90776 0. 90667
691 588 905 445 305
0.95143 0.94729 0.94400 0. 94162 0.94017
847 297 544 171 677
0.98140 0.97598 0.97165 0. 96849 0.96657
781 331 228 392 142
1.00543 0.99831 0.99255 0.98830 0.98568
295 000 019 025 915
1.02436 1.01495 1.00715 1.00123 0.99748
393 896 650 026 392
1. 04011 1.02784 1. 01723 1. 00864 1. 00258
440 362 692 796 409
90
0.90630 779
m r]
0.939694)i262 4)11 7
0.96592 583
1.22001 1.20649 1.18039 1.14359 1.09900 1.05063 1. 00378 0.96518 0.94269
1. 30698 1.29106 1.26026 1.21665 1.16345 1.10513 1. 04769 0.99915 0.96992
7
5 15 25 35 45 55 65 75 85
1.13303 1.12176 1.10005 1.06958 1. 03292 0.99358 0.95606 0.92579 0.90857
553 337 236 479 660 365 Oil 978 873 a
From (A6).
878 962 569 813 829 981 508 626 813
342 728 405 853 846 448 389 744 212
m
0.98480 775
1. 39393 1. 37550 1.33976 1.28896 1.22661 1.15755 1.08838 1. 02823 0.99022
358 358 099 903 050 065 943 305 779
0.99619 470
1. 00000 000
[ -I O ] (
1.48087 1.45984 1.41900 1.36076 1.28885 1.20849 1.12673 1. 05342 1.00394
384 990 286 208 906 656 373 632 027
4
1. 56780 1. 54415 1.49811 1.43229 1. 35064 1. 25867 1.16382 1.07640 1.01266
)4
907 050 493 097 388 963 796 511 353
Tables TABLE Normal
319 A.5 Probability
Integral
F(z)
dt
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0 0.1 0.2 0.3 0.4
0.5000 0.5398 0.5793 0.6179 0.6554
0.5040 0.5438 0.5832 0.6217 0.6591
0.5080 0.5478 0.5871 0.6255 0.6628
0.5120 0.5517 0.5910 0.6293 0.6664
0.5160 0.5557 0.5948 0.6331 0.6700
0.5199 0.5596 0.5987 0.6368 0.6736
0..5239 0..5636 0..6026 0,.6406 0,.6772
0..5279 0.,5675 0..6064 0..6443 0..6808
0.5319 0.5714 0.6103 0.6480 0.6844
0.5359 0.5753 0.6141 0.6517 0.6879
0.5 0.6 0.7 0.8 0.9
0.6915 0.7257 0.7580 0.7881 0.8159
0.6950 0.7291 0.7611 0.7910 0.8186
0.6985 0.7324 0.7642 0.7939 0.8212
0.7019 0.7357 0.7673 0.7967 0.8238
0.7054 0.7389 0.7704 0.7995 0.8264
0.7088 0.7422 0.7734 0.8023 0.8289
0..7123 0,.7454 0..7764 0 .8051 0 .8315
0..7157 0..7486 0..7794 0,.8078 0..8340
0.7190 0.7517 0.7823 0.8106 0.8365
0.7224 0.7549 0.7852 0.8133 0.8389
1.0 1.1 1.2 1.3 1.4
0.8413 0.8643 0.8849 0.9032 0.9192
0.8438 0.8665 0.8869 0.9049 0.9207
0.8461 0.8686 0.8888 0.9066 0.9222
0.8485 0.8708 0.8907 0.9082 0.9236
0.8508 0.8729 0.8925 0.9099 0.9251
0.8531 0.8749 0.8944 0.9115 0.9265
0 .8554 0 .8770 0 .8962 0 .9131 0 .9279
0 .8577 0..8790 0 .8980 0,.9147 0,.9292
0.8599 0.8810 0.8997 0.9162 0.9306
0.8621 0.8830 0.9015 0.9177 0.9319
1.5 1.6 1.7 1.8 1.9
0.9332 0.9452 0.9554 0.9641 0.9713
0.9345 0.9463 0.9564 0.9649 0.9719
0.9357 0.9474 0.9573 0.9656 0.9726
0.9370 0.9484 0.9582 0.9664 0.9732
0.9382 0.9495 0.9591 0.9671 0.9738
0.9394 0.9505 0.9599 0.9678 0.9744
0,.9406 0 .9515 0 .9608 0 .9686 0 .9750
0..9418 0 .9525 0,.9616 0 .9693 0,.9756
0.9429 0.9535 0.9625 0.9699 0.9761
0.9441 0.9545 0.9633 0.9706 0.9767
2.0 2.1 2.2 2.3 2.4
0.9772 0.9821 0.9861 0.9893 0.9918
0.9778 0.9826 0.9864 0.9896 0.9920
0.9783 0.9830 0.9868 0.9898 0.9922
0.9788 0.9834 0.9871 0.9901 0.9925
0.9793 0.9838 0.9875 0.9904 0.9927
0.9798 0.9842 0.9878 0.9906 0.9929
0 .9803 0 .9846 0 .9881 0 .9909 0 .9931
0 .9808 0,.9850 0 .9884 0 .9911 0 .9932
0.9812 0.9854 0.9887 0.9913 0.9934
0.9817 0.9857 0.9890 0.9916 0.9936
2.5 2.6 2.7 2.8 2.9
0.9938 0.9953 0.9965 0.9974 0.9981
0.9940 0.9955 0.9966 0.9975 0.9982
0.9941 0.9956 0.9967 0.9976 0.9982
0.9943 0.9957 0.9968 0.9977 0.9983
0.9945 0.9959 0.9969 0.9977 0.9984
0.9946 0.9960 0.9970 0.9978 0.9984
0 .9948 0 .9961 0 .9971 0 .9979 0 .9985
0,.9949 0 .9962 0,.9972 0,.9979 0..9985
0.9951 0.9963 0.9973 0.9980 0.9986
0.9952 0.9964 0.9974 0.9981 0.9986
3.0 3.1 3.2 3.3 3.4
0.9987 0.9990 0.9993 0.9995 0.9997
0.9987 0.9991 0.9993 0.9995 0.9997
0.9987 0.9991 0.9994 0.9995 0.9997
0.9988 0.9991 0.9994 0.9996 0.9997
0.9988 0.9992 0.9994 0.9996 0.9997
0.9989 0.9992 0.9994 0.9996 0.9997
0 .9989 0 .9992 0 .9994 0 .9996 0 .9997
0..9989 0,.9992 0..9995 0,.9996 0..9997
0.9990 0.9993 0.9995 0.9996 0.9997
0.9990 0.9993 0.9995 0.9997 0.9998
320 TABLE
Appendix
A
A.6
Absorptance
and Emittance
Values for Various
Materials"
Short-wave absorptance
Substance
Long-wave emittance
a e
Class I substances: Absorptance to emittance ratios less than 0.5
Magnesium carbonate, M g C 0 White plaster S n o w , fine particles, fresh White paint, 0.017 in., on aluminum Whitewash on galvanized iron White paper White enamel on iron Ice, with sparse snow cover S n o w , ice granules Aluminum oil base paint White powdered sand 3
0.025-0.04 0.07 0.13 0.20 0.22 0.25-0.28 0.25-0.45 0.31 0.33 0.45 0.45
0.79 0.91 0.82 0.91 0.90 0.95 0.90 0.96-0.97 0.89 0.90 0.84
0.03-0.05 0.08 0.16 0.22 0.24 0.26-0.29 0.28-0.5 0.32 0.37 0.50 0.54
Class II substances: Absorptance to emittance ratios between 0.5 and 0.9 A s b e s t o s felt Green oil base paint Bricks, red A s b e s t o s cement board, white Marble, polished W o o d , planed oak Rough concrete Concrete Grass, green, after rain Grass, high and dry Vegetable fields and shrubs, wilted Oak leaves Frozen soil Desert surface Common vegetable fields and shrubs Ground, dry plowed Oak woodland Pine forest Earth surface as a whole (land and sea, no clouds)
0.25 0.50 0.55 0.59 0.5-0.6
—
0.60 0.60 0.67 0.67-0.69 0.70 0.71-0.78
—
0.75 0.72-0.76 0.75-0.80 0.82 0.86 0.83
0.50 0.56 0.60 0.61 0.61
0.50 0.90 0.92 0.96 0.90 0.90 0.97 0.88 0.98 0.90 0.90 0.91-0.95 0.93-0.94 0.90 0.90 0.90 0.90 0.90
0.83 0.82 0.83-0.89 0.91 0.96
—
—
—
0.62 0.68 0.68 0.76 0.78 0.78-0.82
—
Tables TABLE
321 A.6
(Continued)
Class III substances: Absorptance to emittance ratios b e t w e e n 0.8 and 1.0 Grey paint Red oil base paint A s b e s t o s , slate A s b e s t o s , paper Linoleum, red-brown Dry sand Green roll roofing Slate, dark grey Old grey rubber Hard black rubber Asphalt pavement Black cupric oxide on copper Bare moist ground Wet sand Water Black tar paper Black gloss paint Small hole in large b o x , furnace, or enclosure " H o h l r a u m , " theoretically perfect black body
0.75 0.74 0.81 0.84 0.82 0.88 0.89
0.95 0.90 0.% 0.93-0.96 0.92 0.90 0.91-0.97
—
0.79 0.82 0.84
— 0.91 0.91 0.93
— —
0.86 0.90-0.95
0.93 0.91 0.90 0.91 0.94 0.93 0.90 0.99 1.00
—
— — — —
0.96 0.95 0.95 0.95-0.96 0.93 0.90 0.99 1.00
0.95 0.95 0.96 0.98 1.00 1.00 1.00 1.00
Class IV substances: Absorptance to emittance ratios greater than 1.0 Black silk velvet Alfalfa, dark green Lampblack Black paint, 0.017 in., on aluminum Granite Graphite High ratios, but absorptances less than 0.80 Dull brass, copper, lead Galvanized sheet iron, oxidized Galvanized iron, clean, new Aluminum foil Magnesium Chromium Polished zinc Deposited silver (optical reflector) untarnished
0.99 0.97 0.98 0.94-0.98 0.55 0.78
0.97 0.95 0.95 0.88 0.44 0.41
1.02 1.02 1.03 1.07-1.11 1.25 1.90
0.2-0.4 0.80 0.65 0.15 0.30 0.49 0.46 0.07
0.4-0.65 0.28 0.13 0.05 0.07 0.08 0.02 0.01
1.63-2.0 2.86 5.00 3.00 4.30 6.13 23.00
322 TABLE
Appendix A.6
A
{Continued) Class V substances: Selective surfaces
Plated metals: Black sulfide on metal Black cupric oxide on sheet aluminum Copper (5 x 10~ c m thick) on nickel or silver-plated metal Cobalt oxide on platinum Cobalt oxide on polished nickel Black nickel oxide on aluminum Black chrome Particulate coatings: Lampblack on metal Black iron oxide, 47 grain size, on aluminum Geometrically enhanced surfaces: Optimally corrugated greys Optimally corrugated selectives Stainless-steel wire mesh Copper, treated with N a C 1 0 and N a O H
0.92 0.08-0.93
0.10 0.09-0.21
9.20
0.93-0.94 0.85-0.93 0.87
0.24-0.40 0.06-0.1 0.09
3.90 14.5-15.: 9.80
0.89 0.95 0.63-0.86 0.87
0.77 0.16 0.23-0.28 0.13
1.20 5.90 2.7-3.0 6.69
5
2
a
From (K2).
Tables TABLE Interest
323 A.7 Factors
for Various
Discount 3%
Rates
INTEREST FACTORS FOR DISCRETE C O M P O U N D I N G PERIODS
UNIFORM SERIES
SINGLE PAYMENT Compound Amount Factor N
N)
Present Worth Factor
Capital Recovery Factor
(P/F, 3, N)
(A/P.3.N)
1
1.0300
.97087
1.0300
2 3 4
1.0609 1.0927
.94260 .91514
.52262 .35354
11255 1.1592
.88849
.26903 .21836
1.1940 1.2298 1.2667 1.3047
.83749
(F/P, 3.
5 6 7 8 9
.86261
.81310 .78941
10
1
3439
.76642 .74410
11
1.3842 1 4257
72243 .70139
1.4685
68096 .66113 .64187
12 13 14
1 5125 1.5579
15 16 17 18 19
1 6046 1.6528 1.7024 1 7534
20
1
21
1.8602
22 23 24
1
9160
1 2
9735 0327
25 26 27
8060
62318 60502 58740 .57030 .55369
.18836
5.4170 6.2301 7.0195
15460 .13051
7.7859 8.5300
07961 .07595 .07271
12
560
13
165
11 2 9 5 11.937
13.753 14 323 14 877
.11246 09844 .08723 .07808 .07046 06403 .05853 05377 04961 .04595 04271
1.0000 2.0299 3.0908 4.1835 5.3090 6.4682 7.6622 8.8920 10.158 11.463 12.807 14.191 15.617 17.085 18.598 20.156 21.760 23.413
03982
25
03722
26.869
115
28.675 30.535
15
414
.03487 .03275 03082
2.0937
47762
.05743
16.935 17.412
.02905 .02743
34 425 36.457
2.1565
.46370 45020
.05594 05457
02594 .02457 02212 02102
2
3565
43709
05329
17.876 18 3 2 6 18 7 6 3
42436 41200
.05212 .05102
19 1 8 8 19.600
40000
35
2 5000 2 5750 2 6522 2 7318 2.8137
40 45 50
3 3 4
2619 7814 3837
55 60
5 5
0819 8913
26445 22812 19678 16974
65
6 7 9 10 12
8296 9173 1783 640 334
14642 12630 10895 09398 08107
14 16
299 576
06993 06033 05204
j
.23903
(F/A.3.N)
15 9 3 6 16.443
2.4272
90 95 100
.49262 .32354
4.5796
9.2524 9.9537 10.634
.06982
3,N)
1.0000
2.8285 3.7170
10808 .10046 09403 .08853 .08377
.06722
(A/F,
06275 .06082 05905
2 2212 2.2878
70 75 80 85
.11723
3,N)
.9709 1.9134
Compound Amount Factor
.06487
29 30 31
.14246 12844
(PIA,
Sinking Fund Factor
.53756 52190 50670 49194
28
32 33 34
.18460 .16051
Present Worth Factor
19.217
38835 37 704 .36606 .35539 30657
05000 04905 .04816 04732 .04654 04326 04079 03887 03735 03613
20
000
20.388 20.765 2 1 . 1 31 21
486
23 1 14 24 518 25.729 26 774
.02329
02000 01905 .01816 01732 .01654 01326 01079 .00887 00735
27.675
00613 00515 00434 00367
.03311 03265
28 452 29 123 29.701 30 200 30 630
03226 03193 03165
31 0 0 2 31 3 2 2 31.598
03515 03434 03367
32.451
Gradient Factor (A/G,
3,N)
.0000 .4920 .9795 1.4622 1.9401 2.4129 2.8809 3.3440 3.8022 4.2555
N 1 2 3 4 5 6 7 8 9 10
4.7040 5.1475 5.5863 6.0201 6.4491
11 12 13 14
6.8732
16 17
7.2926 7.7072 8.1169 8.5219 8.9221 9.3176 9.7084 10.094
15
18 19 20 2'l 22 23 24
10.475
25
38.551 40.707
10.852 11.224
26 27
42.929 45.217
11.592 11.954
28
47.573
12.313
30
50 000 52 500 55.075 57.727
12.666 13.016 13 360 13.700
31 32 33 34
60.459
14
036
35
75
15.649 17.154
40
397
92.715 112 79 136 06 163 04 194 230
32 57
0031 1 .00265
272 321 377
61 33 82
00226 00193 00165
443 519 607
31 22 23
29
45 50 55
ie 556 19.859 21 0 6 6
60
22 183 23 213 24.162 25.034 25.834
65 70 75 80 85
26 27
566 234
27.843
90 95 100
(continued)
324 TABLE
A.7
Appendix (Continued) 8% Interest Factors for Discrete Compounding Periods SINGLE Compound Amount Factor
(F/P, 8,
N)
PAYMENT Present Worth Factor (P/F, 8.
UNIFORM Capital Recovery Factor
N)
(A/P,
8.
N)
SERIES
Present Worth
Sinking
Factor
Factor
(PIA, 8 . N)
F und
(A/F,
8, N )
Compound Gradient
Amount Factor
(F/A,
8,
Factor
N)
2
1.0800 1.1664
.92593 .85734
1.0800 56077
.9259 1.7832
1.0000 .48077
1.0000 2.0799
3 4
1.2597 1.3604
.79383
38803
.30804
.73503
.30192
2.5770 3.3121
5
1.4693
.68059
.25046
3.9926
.22192 .17046
3.2463 4.5060 5.8665
6 7
1 5868 1.7138
.21632 .19207
4.6228 5.2063
.13632 .1 1 2 0 7
7.3358 8.9227
8
.50025 .46320
.17402 16008 .14903
5.7466 6.2468 6.7100
.09402
9 10
1.8509 1.9989 2.1589
.63017 .58349 .54027
11 12
2.5181 2.7196 2.9371 3.1721
.12642 .12130 .11683
7 1389 7.5360 7.9037
15
42889 .39712 36770 .34046 .31524
.14008 .13270
13 14
.06008 .05270 .04652 .04130 .03683
16 17
3.4259
2.3316
.29189 .27027
.11298 .10963 .10670 .10413 .10185
8.2442 8.5594 8.8513
18
3.6999 3.9959
19 20
4.3156 4.6609
21
5.0337 5.4364
.19866 .18394
5.8713
.17032 .15770
.09983 .09803 .09642 .09498
.14602
.09368
.13520 .12519 .11592 .10733 .09938
.09251 .09145 .09049 .08962 .08883
10.809 10.935 11.051 11.158 11.257
22 23 24 25
6.3410 6.8483
26 27
7.3962
28 29
8.6269 9.3171
7.9879
.25025 .23171 .21455
9.1216 9.3718 9.6035 9.8181 10.016 10.200 10.371 10.528 10.674
.08008 .06903
.03298 .02963 .02670 .02413 .02185 .01983 .01803 .01642 .01498 .01368 .01251 .01145 .01049
10.636 12.487 14.486
(A/G,
8,N) .0000 .4807 .9487
1.4038 1.8463
N 1 2 3 4 5 6 7
2.2762 2.6935 3.0984
8
3.4909 3.8712
9 10
16.645
4.2394
11
18.976 21.495 24.214
4.5956 4.9401 5.2729 5.5943
12 13 14 15
5.9045 6.2036
16 17 18 19
27.151 30.323 33.749 37.449 41.445 45.761 50.422 55.455 60.892 66.763 73.104 79.953 87.349 95.337
6.4919 6.7696 7.0368 7.2939 7.5411 7.7785 8.0065
20 21 22 23 24
8.2253
25
8.4351
26 27
8.6362 8.8288
28 29
.00962
103.96
9.0132
.00883
113.28
9.1896
30
30
10.062
31
10.867
.09202
.08811
11.349
.00811
123.34
9.3583
31
32 33 34
11 . 7 3 6
.08520
.08745
11.434
.08685
11.513
13.689
.07889 .07305
134.21 145.94
9.5196
12.675
.00745 .00685
.08630
.00630
158.62
35
14.785
.06764
.08580
11.586 11.654
32 33 34
.00580
172.31
40 45
21.724
.04603
.08386
11.924
31.919
.03133
40 45
.02132
12.108 12.233
10.569 11.044
46.900
.08259 .08174
259.05 386.49
50 55
.00386 .00259 .00174
573.75
68.911
.01451 .00988
.08118 .08080
12.318 12.376
.00118 .00080
1253.1
11.410 11.690 11.901
50 55 60
.08054
12.416 12.442
.00054 .00037
1847.1 2719.9
12.060
.08037 .08025 .08017
12.461 12.473
.00025 .00017
4002.3
12.481
.00012
5886.6 8655.2
65 70 75 80
.08012
12.265 12.330 12.377
.08008 .08005 .08004
12.487 12.491 12.494
.00008 .00005 .00004
12723.9 18701.5 27484.5
60
101.25
65
148.77
70 75 80 85
218.59
.00672 .00457
321.19 471.93 693.42
.00311 .00212 .00144
90 95 100
1018.8 1497.0 2199.6
.00098 .00067 .00045
848.89
9.6736 9.8207 9.9610
12.178
12.411 12.436 12.454
35
85 90 95 100
A
Tables TABLE
325 4.7
(Continued) 10% Interest Factors for Discrete Compounding Periods SINGLE
PAYMENT
Compound Amount Factor (F/P. 10,
N)
UNIFORM
SERIES
Present Worth
Capital Recovery
Present Worth
Sinking
Factor
Factor
Factor
Factor
(P/F, 10. N )
(AIP,
10,
N) (PIA,
10,
1
1.1000
2
1.2100
.82645
.57619
1.7355
3 4
1.3310 1.4641
.75132
2.4868
.68302
.40212 .31547
5
1.6105
.62092
.26380
.90909
6 7
1 7 7 1 5
.56448
1.9487
8
1.1000
.9091
3.1698 3.7907
F und
N) (AIF,
10,
1.0000
Compound Amount Factor
N) (FIA,
10.N) 1.000 2.0999 3.3099
Gradient Factor
(AIG,
10.N)
N
.0000
1
.4761 .9365
2
.47619 .30212 .21547
4.6409
1.3810
3 4
.16380
6.1050
1.8100
5
7.7155
2.2234
9.4870
2.6215
6 7
4.3552
.51316
.22961 .20541
4.8683
.12961 .10541
2.1435 2.3579
.46651 42410
.18745 .17364
5.3349 5.7589
.08745 .07364
11.435 13.579
3.0043
8
9
3.3722
10
2.5937
.38555
.16275
6.1445
.06275
15.937
3.7253
9 10
11
2.8530 3.1384
.35050
.15396
6.4950
.05396
18.530
4.0639
11
12
6.8136
.04676
3.4522 3.7974
.31863 .28967
.14676
13 14
.14078
7.1033
4.3883 4.6987
.26333
4.9954
.23940
7.3666 7.6060
13 14
4.1771
13575 .13147
21.383 24.522 27.974
15
.04078 .03575 .03147
31.771
5.2788
15
16 17
4.5949
.21763
.12782
7.8236
.02782
35.949
5.5492
5.0544
.19785
.12466
8.0215 8.2013
.02466
40.543
8.3649
45.598 51.158
5.8070 6.0524
16 17
.02193 .01955
57.273
6.2860 6.5080
18
5.5598
.17986
.12193
19
6.1158
.16351
.11955
6.7273
.14865
.11746
8.5135
.01746
21
7.4001
.13513
.11562
22
8.1401 8.9541
.12285
.11401 .11257
8.6486 8.7715
.01562 .01401 .01257
64.001 71.401 79.541
6.9188 7.1084
88.495 98.344
7.2879 7.4579
20
23 24 25
9.849? 10.834
.11168 .10153 .09230
8.8832 8.9847
6.7188
.11130 .11017
9.0770
.01130 .01017
.10916
9.1609
.00916
109.17
7.6185
.00826
121.09 134.20 148.62
7.7703 7.9136 8.0488
12
18 19 20 21 22 23 24 25 26 27
26 27
11.917 13.109
08391 07628
28
.06935 .06304
.10826 .10745 10673
9.2372 9.3065
29
14.420 15.862
9.3696
.00745 .00673
30
17.448
.05731
10608
9.4269
.00608
164.48
8.1761
30
9.4790 9.5263 9.5694
.00550 .00497
181.93
8.2961 8.4090
31
31
19.193
.05210
32
21 .113 23.224
.04736
10550 .10497
.04306 .03914
.10450 .10407
.03559
.10369
9.6085 9.6441
.02210
9.7790 9.8628
33 34 35
25.546 28 101
40
45.257
201.13 222.24
.00369
271.01
8.7085
35
.00226
442.57
9.0962
40
718.87
9.3740 9.5704
45
.01372
117.38 189.04
.00852
.10086
9.9148
.00086
.00529
10053
9.9471
.00053
1163.8 1880.4
60
304.46
.00328
.10033
9.9671
.00033
65
490.34
.00204
.10020
9.9796
.00020
70
789.69
.00127
.10013
9.9873
.00013
.00079
10008
9.9921
.00049
.10005
9.9951
.00008 .00005
12709.0 20474.0
75 80
1271.8 2048.2
32 33 34
8.5151 8.6149
50 55
72.887
29
245.46
.00450 .00407
.10226 10139
45
28
.00139
50 55
3034.6
9.7075 9.8022
60
4893.4
9.8671
65
7886.9
9.9112 9.9409
70 75
9.9609
80
85
3298.7
.00030
.10003
9.9969
.00003
32979.7
9.9742
85
90 95
5312.5 8555.9
.10002
53120.2 85556.8
13780.6
9.9981 9.9988 9.9992
.00002 .00001
100
.00019 .00012 .00007
.00001
137796.1
9.9830 9.9889 9.9927
90 95 100
.10001 .10001
(continued)
326 TABLE
Appendix
A.7
(Continued) 12% Interest Factors for Discrete Compounding Periods SINGLE Compound Amount Factor
.V 1
2 3 4 5 6 7
(F/P,
12.
N)
PAYMENT Present Worth Factor (P/F.
12.N)
1 1200 1.2544
.89286 .79719
1.4049 1.5735 1.7623
.71178 .63552 .56743
UNIFORM Capital Recovery F actor
(A/P.
12.N)
Present Worth
12.
F und Factor N)
(A/F,
12.
3.0373 3.6047 4.1114
.12323
8.115
4.5637
.09912 .08130
10.088 12.299 14.775 17.548
8
.45235 .40388
.24323 .21912 .20130
9 10
2.7730 3.1058
36061 .32197
.18768 .17698
11
3.4785 3.8959 4.3634
.28748 .25668 .22918 .20462 .18270
.16842 .16144
5.9376 6.1943 6.4235 6.6281 6.8108
.04842 .04144
.15568 .15087 . 14682
.16312 .14565 .13004
.14339
6.9739
.02339
.14046 .13794 .13576 .13388
7.1196 7.2496 7.3657 7.4694
.02046 .01794
.11611 .10367
16 17
6.1303
18
7.6899 8.6126 9.6462
19 20
6.8659
4.9676 5.3282 5.6502
.06768 .05698
.03568 .03087 .02682
.01576 .01388
10.803 12.100 13.552
.09256 .08264
.13224
7.5620
.01224
.13081 .12956
7.6446 7.7184
.01081
.07379
15.178
.06588 .05882
.12846 .12750
-'.7843 7.8431
.00956 .00846 .00750
.05252 .04689 .04187
.12665 .12590 .12524
7.8956 7.9425 7.9844
.00665 .00590 .00524
29.959
.03738 .03338
.12466 .12414
8.0218 8.0551
.00466 .00414
31
33.554
.02980
.12369
8.0849
.00369
32 33 34
37.581 42.090 47.141
.12328 .12292
8.1116 8.1353
.00328 .00292
.12260
35
52.798
.02661 .02376 .02121 .01894
8.1565 8.1755
.00260 .00232
8.2437
.00130 .00074
21 22 23 24 25
16.999
26 27 28
19.039 21.324
29 30
40 45 50
23.883 26.749
93.049 163.98 288.99
.12232
.01075 .00610
.12130 .12074
.00346
.12042
8.2825 8.3045
.00042
Gradient F actor
1 2 , N ) (A/G,
.47170 .29635 .20924 .15741
1.0000
.50663
15
(F/A,
.8929 1.6900 2.4018
1.9738
4.8870 5.4735
Amount Factor N)
1.1200 .59170 .41635 .32924 .27741
2.2106 2.4759
12 13 14
Compound
Sinking
Factor
(PIA,
SERIES
1.0000 2.1200 3.3743 4.7793 6.3528
12.N)
0000 .4717 .9246 1.3588 1.7745 2.1720 2.5514 2.9131
N 1 2 3 4 5 6 7
3.2573 3.5846
8 9 10
20.654
3.8952
11
24.132 28.028 32.392 37.279
4.1896 4.4682 4.7316 4.9802
12 13 14
42.752 48.883
5.2146 5.4352 5.6427
16 17
55.749 63.439 72.051
5.8375 6.0201
81.698 92.501 104.60
6.1913 6.3513 6.5009
118.15 133.33
6.6406 6.7708
150.33 169.37
6.8920 7.0049 7.1097 7.2071 7.2974
190.69 214.58 241.32 271.28 304.84 342.42 384.51
15
18 19 20 21 22 23 24 25 26 27 28 29 30
7.3810
31
7.4585 7.5302 7.5964
32 33 34
431.65
7.6576
35
767.07
7.8987
40 45
1358.2 2399.9
8.0572 8.1597
50
A
Tables TABLE
327 A.7
{Continued) 15% Interest Factors for Discrete Compounding Periods
SINGLE Compound Amount Factor .V 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
(F/P. 15,
N)
Present Worth Factor (P/F. 15,
1.1500 1.3225
.86957 .75614
1.5208 1.7490 2.0113
.65752 .57175 .49718
2.3130 2.6600 3.0590 3.5178 4.0455
.43233 .37594 .32690
4.6523 5.3502 6.1527 7.0756 8.1369 9.3575
UNIFORM
PAYMENT Capital Recovery Factor
N) (A/P,
15.
N)
Present Worth Factor (PM.
15,
.8696
3.3521
.14832
.26424
3.7844 4.1604
.11424
8.7536
.24036 .22285 .20957
15,N)
N
.0000
1
.4651 .9071
2 3 4
1.3262 1.7227
5 6 7
.09036 .07285 .05957
11.066 13.726 16.785
2.0971 2.4498 2.7813 3.0922
.04925
20.303
3.3831
10
8 9
.21494
.19107
5.2337
.04107
24.349
3.6549
11
.18691 .16253 .14133
.18448 .17911
5.4206 5.5831 5.7244
.03448 .02911 .02469 .02102
29.001 34.351 40.504
3.9081 4.1437
12 13 14
.01795 .01537
55.716 65.074
.12290 .10687
.17469 .17102 .16795 .16537
5.8473 5.9542 6.0471 6.1279
25
32.918
.03038
.15470
26 27
.02642 .02297 .01997 .01737
.15407
28 29
37.856 43.534 50.064 57.574
30
66.210
.01510
.15230
6.5659
31 32
76.141
.01313
.15200
6.5791
87.563
.01142 .00993 .00864
.15173 .15150
6.5905 6.6004
.00751
.15131 .15113
6.6091 6.6166
.00373 00186 .00092
15056 .15028 .15014
6.6417
267.85 538.75 1083.6
Factor
(A/G,
.19925
24.891 28.624
40 45 50
Gradient
4.4873 4.7715 5.0187
.28426 .24719
.15842 .15727
115.80 133.17
15. N)
.29832
.05313 .04620 .04018 .03493
35
(F/A,
3.4724 4.9933 6.7423
18.821 21.644
33 34
15, N )
.28798 .20027
.15976
100.69
(A/F,
1.6257
.16319 .16134
22 23 24
Amount Factor
2.2832 2.8549
.06110
21
Compound
F und Factor
1.000 2.1499
.09293 .08081 .07027
18
Sinking
1.0000 .46512
1.1500 .61512 .43798 .35027
10.761 12.375 14.231 16.366
19 20
N)
SERIES
.15628 .15543
.15353 .15306 .15265
6.1982 6.2593 6.3124 6.3586 6.3988 6.4337 6.4641 6.4905 6.5135 6.5335 6.5508
6.6543 6.6605
.01319 .01134 .00976 .00842 .00727 .00628 .00543 .00470 .00407 .00353 .00306 .00265 .00230 .00200 .00173 .00150 .00131 .00113 .00056 .00028 .00014
47.579
4.3623 4.5649 4.7522
15 16 17
75.835 88.210 102.44
4.9250 5.0842 5.2307
18 19
5.3651
20
118.80
5.4883
21
137.62 159.27
5.6010 5.7039 5.7978 5.8834
22 23 24
184.16 212.78
5
9612
25 26 27
245.70 283.56 327.09 377.16 434.73
6.0318 6.0959 6.1540
500.94
6.2541
31
577.08 664.65 765.34
6.2970
32 33 34
881.14
6.4018
35
6.5167
40 45
1779.0 3585.0 7217.4
6
2066
6.3356 6.3705
6.5829 6.8204
28 29 30
50
(continued)
Appendix
328 TABLE
A.7
(Continued) 20% Interest Factors for Discrete Compounding Periods SINGLE PAYMENT Compound Amount Factor
N 1
(F/P, 20, JV)
Present Worth Factor
UNIFORM SERIES Capital Recovery Factor
(P/F, 20, JV) (A/P,
Present Worth Factor
20, JV) (P/A,
Sinking Fund Factor
20, JV) (A/F,
Compound Amount Factor
20, JV) (F/A,
Gradient Factor
20, JV) (A/G.
20, JV)
JV
2 3 4 5
1.2000 1.4400 1.7280 2.0736 2.4883
.83333 .69445 .57870 .48225 .40188
1.2000 .65455 .47473 .38629 .33438
.8333 1.5277 2.1064 2.5887 2.9906
1.0000 .45455 .27473 .18629 .13438
1.0000 2.1999 3.6399 5.3679 7.4415
.0000 .4545 .8791 1.2742 1.6405
1 2 3 4 5
6 7 8 9 10
2.9859 3.5831 4.2998 5.1597 6.1917
.33490 .27908 .23257 .19381 .16151
30071 .27742 .26061 .24808 .23852
3.3255 3.6045 3.8371 4.0309 4.1924
.10071 .07742 .06061 .04808 .03852
9.9298 12.915 16.498 20.798 25.958
1.9788 2.2901 2.575<5 2.8364 3.0738
6 7 8 9 10
11 12 13 14 15
7.4300 8.9160 10.699 12.839 15.406
.13459 .11216 .09346 .07789 06491
.23110 .22527 .22062 .21689 .21388
4.3270 4.4392 4.5326 4.6105 4.6754
.03110 .02527 .02062 .01689 .01388
32.150 39.580 48.496 59.195 72.034
3.2892 3.4840 3.6596 3.8174 3.9588
11 12 13 14 15
16 17 18 19 20
18.488 22.185 26623 31.947 38 337
.05409 .04507 .03756 .03130 .02608
.21144 .20944 .20781 .20646 .20536
4.7295 4.7746 4.8121 4.8435 4.8695
.01144 .00944 .00781 .00646 .00536
87.441 105.92 128.11 154.73 186.68
4.0851 4.1975 4.2975 4.3860 4.4643
16 17 18 19 20
21 22 23 24 25
46.004 55.205 66.246 79.495 95.394
02174 .01811 .01510 .01258 .01048
.20444 .20369 .20307 .20255 .20212
4.8913 4.9094 4.9245 4.9371 4.9475
.00444 .00369 .00307 .00255 .00212
225.02 271.02 326.23 392.47 471.97
4.5333 4.5941 4.6474 4.6942 4.7351
21 22 23 24 25
;
26 27 28 29 30
114.47 137.36 164.84 197.81 237.37
.00874 .00728 .00607 .00506 .00421
.20176 .20147 .20122 .20102 .20085
4.9563 4.9636 4.9696 4.9747 4.9789
.00176 .00147 .00122 .00102 .00085
567.36 681.84 819.21 984.05 1181.8
4.7708 4.8020 4.8291 4.8526 4.8730
26 27 28 29 30
31 32 33 34 35
284.84 341.81 410.17 492.21 590.65
.00351 .00293 .00244 .00203 .00169
.20070 .20059 .20049 .20041 .20034
4.9824 4.9853 4.9878 4.9898 4.9915
.00070 .00059 .00049 .00041 .00034
1419.2 1704.0 2045.8 2456.0 2948.2
4.8907 4.9061 4.9193 4.9307 4.9406
31 32 33 34 35
.00068 .00027 .00011
.20014 .20005 .20002
4.9966 4.9986 4.9994
.00014 .00005 .00002
7343.6 18281.3 45497.2
4.9727 4.9876 4.9945
40 45 50
40 45 50
1469.7 3657.1 9100.1
A
Tables TABLE
329 A.7
{Continued) 25% Interest Factors for Discrete Compounding Periods UNIFORM SERIES
SINGLE PAYMENT Compound Amount Factor N
Present Worth Factor
Capital Recovery Factor
Present Worth Factor
Sinking Fund Factor
Compound Amount Factor
Gradient Factor
(F/P, 25, N) ( P / F , 25, N) (A/P. 25, N ) ( P M , 25,N) (A/F, 25. N ) ( F M , 25.N)
N 1 2 3 4 5
1 2 3 4 5
1.2500 1.5625 1.9531 2.4414 3.0518
.80000 .64000 .51200 .40960 .32768
1.2500 .69444 .51230 .42344 .37185
.8000 1.4400 1.9520 2.3616 2.6893
1.0000 .44444 .26230 .17344 .12185
6 7 8 9 10
3.8147 4.7684 5.9605 7.4506 9.3132
.26214 .20972 .16777 .13422 .10737
.33882 .31634 .30040 .28876 .28007
2.9514 3.1661 3.3289 3.4631 3.5705
.08882 .06634 .05040 .03876 .03007
11.259 15.073 19.842 25.802 33.253
1.8683 2.1424 2.3872 2.6048 2.7971
6 7 8 9 10
1.0000 2.2500 3.8125 5.7656 8.2070
.00000 44444 .85246 1.2249 1.5631
11 12 13 14 15
11.642 14.552 18.190 22.737 28.422
.08590 .06872 .05498 .04398 .03518
.27349 .26845 .26454 .26150 .25912
3.6564 3.7251 3.7801 3.8241 3.8593
.02349 .01845 .01454 .01150 .00912
42.566 54.208 68.760 86.949 109.687
2.9663 3.1145 3.2437 3.3559 3.4530
11 12 13 14 15
16 17 18 19 20
35.527 44 409 55.511 69.389 86.736
.02815 .02252 .01801 .01441 .01153
.25724 .25576 .25459 .25366 .25292
3.8874 3.9099 3.9279 3.9424 3.9539
.00724 .00576 .00459 .00366 .00292
138.109 173.636 218.045 273.556 342.945
3.5366 3.6084 3.6698 3.7222 3.7667
16 17 18 19 20
21 22 23 24 25
108.420 135.525 169.407 211.758 264.698
.00922 .00738 .00590 .00472 .00378
.25233 .25186 .25148 .25119 .25095
3.9631 3.9705 3.9764 3.9811 3.9849
.00233 .00186 .00148 .00119 .00095
429.681 538.101 673.626 843.033 1054.791
3.8045 3.8365 3.8634 3.8861 3.9052
21 22 23 24 25
26 27 28 29 30
330.872 413.590 516.988 646.235 807.794
.00302 .00242 .00193 .00155 .00124
.25076 .25061 .25048 .25039 .25031
3.9879 3.9903 3.9923 3.9938 3.9950
.00076 .00061 .00048 .00039 .00031
1319.489 1650.361 2063.952 2580.939 3227.174
3.9212 3.9346 3.9457 3.9551 3.9628
26 27 28 29 30
31 32 33 34 35
1009.742 1262.177 1577.722 1972.152 2465.190
.00099 .00079 .00063 .00051 .00041
.25025 .25020 .25016 .25013 .25010
3.9960 3.9968 3.9975 3.9980 3.9984
.00025 .00020 .00016 .00012 .00010
4034.968 5044.710 6306.887 7884.609 9856.761
3.9693 3.9746 3.9791 3.9828 3.9858
31 32 33 34 35
330
Appendix
TABLE
A
A.8
Conversion
Factors
Physical quantity Area
Conversion factor
Symbol A
1 ft = 0.0929 m 1 i n = 6.452 x 10" m 1 l b / f t = 16.018 k g / m 1 slug/ft = 515.379 k g / m 1 Btu = 1055.1 J 1 cal = 4.186 J 1 ft l b = 1.3558 J 1 h p / h r = 2.685 x 10 J 1 i b = 4.448 N 1 Btu/hr - 0.2931 W 1 B t u / s e c = 1055.1 W 1 B t u / h / f t = 3.1525 W / m 1 B t u / h / f t / F = 5.678 W / m / K 1 ft = 0.3048 m 1 in. = 2.54 c m 1 mile = 1.6093 km 1 l b = 0.4536 kg 1 slug = 14.594 kg 1 l b / h = 0.000126 k g / s e c 1 l b / s e c = 0.4536 k g / s e c 1 hp = 745.7 W 1 f t / l b / s e c = 1.3558 W 1 B t u / s e c = 1055.1 W 1 B t u / h = 0.293 W 1 l b / i n . = 6894.8 Pa ( N / m ) 1 l b / f t = 47.88 Pa ( N / m ) 1 atm = 101,325 Pa ( N / m ) 1 langley = 41,860 J / m 1 B t u / l b / ° F = 4187 J / k g / K 1 B t u / l b = 2326.0 J / k g 1 c a l / g = 4184 J / k g T(°R) = (9/5)T(K) T(°F) = [T(°C)](9/5) + 32 T(°F) = [T(K) - 273.15](9/5) + 32 1 B t u / h / f t / ° F = 1.731 W / m / K 1 b / ° F / B t u = 1.8958 K / W 1 f t / s e c = 0.3048 m / s e c 1 m i l e / h = 0.44703 m / s e c 1 l b / f t / s e c = 1.488 N / s e c / m 1 c P = 0.00100 N / s e c / m 1 f t / s e c = 0.09029 m / s e c 1 f t / h = 2.581 x 10" m / s e c 1 ft = 0.02832 m 1 i n . = 1.6387 x 1 0 m 1 gal ( U . S . liq.) = 0.003785 m 1 f t / m i n = 0.000472 m / s e c 2
2
2
Density
P
4
2
3
3
m
3
Heat, energy, or work
QorW
3
f
6
Force Heat flow rate
F
Heat flux Heat-transfer coefficient Length
q/A h L
Mass
m
Mass flow rate
m
Q
f
2
2
2
2
m
m
m
Power
W
f
Pressure
P
2
2
f
2
2
f
2
Radiation Specific heat capacity Internal energy or enthalpy
1 c e or h
Temperature
T
Thermal conductivity Thermal resistance Velocity
k
Viscosity, dynamic
p
V
2
m
m
2
m
2
Viscosity, kinematic
V
2
2
2
Volume
V
5
3
2
3
3
5
3
3
Volumetric flow rate
Q
3
3
A
309
TABLE
A.I
Solar Irradiance
for Various Air
Masses
a
Air mass = 0.66, p = 0.170
= 0.66, /3i = 0.085 Wave length
0
1
4
7
10
1
4
7
10
0.940 0.950 0.955 0.965 0.975 0.985 1.018 1.082 1.094 1.098
847.0 837.0 828.5 811.5 794.0 776.0 719.2 620.0 602.0 596.0
313.4 296.5 321.1 344.4 576.9 544.6 617.5 512.9 464.1 503.7
95.0 86.3 102.3 120.4 346.0 316.1 391.0 290.4 303.1 304.1
39.6 35.0 44.1 55.1 224.6 201.2 247.5 164.4 210.8 183.6
18.5 16.0 21.2 27.8 150.1 132.4 156.7 93.1 149.9 110.9
286.9 271.6 294.2 315.7 529.1 499.8 567.8 473.1 428.4 465.0
66.7 60.7 72.1 85.0 244.9 224.2 279.4 210.3 220.0 220.9
21.3 18.9 23.9 30.0 122.7 110.3 137.5 93.5 120.3 105.0
7.6 6.7 8.8 11.6 63.2 56.1 67.6 41.5 67.3 49.9
1.101 1.128 1.131 1.137 1.144 1.147 1.178 1.189 1.193 1.222
591.8 560.5 557.0 550.1 542.0 538.5 507.0 496.0 492.0 464.3
504.8 135.1 152.2 143.1 191.2 174.5 399.3 402.2 424.0 391.8
362.7 27.7 35.3 31.7 57.4 48.2 195.1 214.5 310.8 235.3
267.3 9.1 12.6 11.0 24.2 19.3 95.4 114.4 233.3 141.3
198.8 3.6 5.3 4.5 11.6 8.8 46.6 61.0 176.6 84.9
466.1 124.9 140.7 132.4 176.9 161.5 370.0 372.8 393.1 363.6
263.6 20.2 25.8 23.2 42 A 35.3 143.8 158.4 229.7 174.7
153.0 5.3 7.3 6.4 14.1 11.2 55.9 67.3 137.4 83.9
89.5 1.6 2.4 2.1 5.3 4.1 21.7 28.6 82.9 40.3
1.236 1.264 1.276 1.288 1.314 1.335 1.384 1.432 1.457 1.472
451.2 426.5 416.7 406.8 386.1 369.7 343.7 321.0 308.6 301.4
390.8 329.2 342.6 347.3 298.3 190.6 5.7 44.6 85.4 77.4
254.1 209.7 238.6 216.1 137.6 85.0 0.1 5.4 20.6 17.4
165.2 140.0 172.6 134.4 63.5 46.7 0.0 1.3 7.7 6.2
107.4 94.3 126.3 83.7 29.3 27.7 0.0 0.4 3.3 2.6
363.0 306.1 318.7 323.2 277.9 177.6 5.3 41.7 80.0 72.4
189.1 156.7 178.6 162.1 103.6 64.2 0.1 4.1 15.8 13.3
98.5 84.1 104.0 81.3 38.6 28.6 0.0 0.8 4.8 3.9
51.3 45.5 61.2 40.7 14.4 13.7 0.0 0.2 1.7 1.3
1.542 1.572 1.599 1.608 1.626 1.644 1.650 1.676 1.732 1.782
270.4 257.3 245.4 241.5 233.6 225.6 223.0 212.1 187.9 166.6
239.3 222.6 216.0 208.5 206.7 197.9 195.7 181.9 161.5 136.7
165.9 168.1 166.7 157.4 160.7 152.4 150.9 114.8 102.5 75.6
115.0 130.4 131.5 122.1 127.5 120.1 119.1 72.4 65.1 41.8
79.7 102.1 104.5 95.7 101.9 95.5 94.7 45.7 41.3 23.1
224.5 209.0 203.0 195.9 194.3 186.1 184.1 171.2 152.2 129.0
128.5 130.7 129.9 122.7 125.6 119.3 118.2 90.1 80.9 59.9
73.6 83.9 85.0 79.1 82.8 78.3 77.6 47.5 43.0 27.9
42.1 54.4 56.0 51.4 55.0 51.8 51.4 25.0 22.9 12.9
310
1.862 1.955 2.008 2.014 2.057 2.124 2.156 2.201 2.266 2.320
138.2 112.9 102.0 101.2 95.6 87.4 83.8 78.9 72.4 67.6
4.0 42.7 69.4 74.7 69.5 70.0 66.0 66.1 61.6 57.2
0.1 14.5 35.8 45.5 41.3 35.9 32.3 49.1 46.8 43.8
0.0 6.8 17.7 28.8 25.3 18.4 15.8 38.0 36.8 33.8
0.0 3.6 6.4 17.8 14.8 9.5 7.7 29.7 29.3 26.8
3.8 40.5 65.7 70.8 66.0 66.4 62.7 62.8 58.6 54.4
0.1 11.6 28.9 36.7 33.4 29.2 26.3 40.1 38.4 35.5
0.0 4.6 12.2 19.8 17.5 12.8 11.0 26.7 26.0 24.0
0.0 2.1 3.8 10.4 8.7 5.6 4.6 17.9 17.9 16.5
2.338 2.356 2.388 2.415 2.453 2.494 2.537 2.900 2.941 2.954
66.3 65.1 62.8 61.0 58.3 55.4 52.4 35.0 33.4 32.8
54.7 52.0 36.0 32.5 29.6 20.3 4.6 2.9 6.0 5.7
39.9 36.3 18.7 15.8 13.7 6.8 0.4 0.2 1.0 0.9
30.4 26.5 11.7 9.4 7.9 3.2 0.1 0.0 0.3 0.3
23.4 19.6 7.8 6.0 5.0 1.7 0.0 0.0 0.1 0.1
52.1 49.5 34.3 31.0 28.2 19.4 4.4 2.8 5.7 5.5
32.8 29.9 15.5 13.0 11.3 5.6 0.3 0.2 0.8 0.8
21.6 18.9 8.3 6.7 5.7 2.3 0.1 0.0 0.2 0.2
14.4 12.1 4.8 3.7 3.1 1.1 0.0 0.0 0.1 0.1
2.973 3.005 3.045 3.056 3.097 3.132 3.156 3.204 3.214 3.245
32.1 30.8 28.8 28.2 26.2 24.9 24.1 22.5 22.1 21.1
8.7 7.8 4.7 4.9 3.2 6.8 18.7 2.1 3.4 3.9
2.2 1.8 0.7 0.8 0.4 1.7 12.6 0.2 0.5 0.7
0.9 0.7 0.2 0.2 0.1 0.7 8.9 0.0 0.1 0.2
0.4 0.3 0.1 0.1 0.0 0.3 6.3 0.0 0.0 0.1
8.4 7.5 4.5 4.7 3.1 6.5 17.9 2.0 3.3 3.8
1.8 1.6 0.6 0.7 0.3 1.5 10.7 0.2 0.4 0.6
0.6 0.5 0.1 0.2 0.1 0.5 6.7 0.0 0.1 0.2
0.3 0.2 0.0 0.1 0.0 0.2 4.2 0.0 0.0 0.1
3.260 3.285 3.317 3.344 3.403 3.450 3.507 3.538 3.573 3.633
20.6 19.7 18.8 18.1 16.5 15.6 14.5 14.2 13.8 13.1
3.7 14.2 12.9 4.2 12.3 12.5 12.5 11.8 10.9 10.8
0.6 8.5 6.9 0.9 7.8 8.9 9.9 8.8 5.4 8.3
0.2 5.1 3.5 0.3 5.1 6.7 8.1 6.9 2.6 6.7
0.1 2.8 1.3 0.1 3.2 5.0 6.7 5.5 1.3 5.5
3.5 13.7 12.4 4.1 11.9 12.0 12.1 11.3 10.5 10.4
0.5 7.3 5.9 0.8 6.7 7.7 8.5 7.6 4.6 7.1
0.1 3.9 2.7 0.2 3.9 5.1 6.2 5.3 2.0 5.2
0.0 1.9 0.9 0.1 2.2 3.5 4.6 3.8 0.9 3.8
3.673 3.696 3.712 3.765 3.812 3.888 3.923 3.948 4.045
12.6 12.3 12.2 11.5 11.0 10.4 10.1 9.9 9.1
9.1 10.4 10.9 9.5 8.9 8.1 8.0 7.8 6.7
6.1 8.2 9.0 7.2 6.7 5.6 5.6 5.5 4.1
4.6 6.7 7.6 5.9 5.4 4.0 4.2 4.0 2.6
3.5 5.6 6.5 4.8 4.4 2.9 3.1 3.0 1.5
8.8 10.1 10.5 9.1 8.6 7.8 7.7 7.6 6.5
5.3 7.1 7.8 6.3 5.8 4.8 4.9 4.8 3.6
3.5 5.2 5.9 4.6 4.2 3.1 3.3 3.2 2.0
2.5 3.9 4.6 3.4 3.1 2.0 2.2 2.1 1.1
889.2
448.7
255.2
153.8
800.2
303.1
133.3
63.4
Total W m- ) 2
1353 a
Expressed in W m
2
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H 0 , 20 mm; 0 , 3.4 mm. [From S15.] 2
3
Appendix
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Tables TABLE
315 A3
Seasonally
Averaged
Daily Direct-Normal Spring (M,A,M)
Solar Flux in Summer (J,J,A)
kWh/i 2a m
Fall (S,0,N)
Winter (D,J,F)
Albuquerque
7.6
8.2
6.9
5.8
Apalachicola Bismarck Blue Hill Boston
5.0 4.7 3.6 3.6
4.5
4.4
6.5 4.2 4.2
Brounsville Cape Hatteras Caribou Charleston
4.2 4.8
3.9 3.1 3.1 4.4
3.3 2.7 2.2 2.2
Columbia D o d g e City El Paso
4.3 5.9 8.0 6.9
5.9 4.3
5.8 4.9 6.0 3.9 5.8 7.1
3.2
4.0 3.4 3.7
3.1 3.9 3.1
4.1
2.9 4.6
5.5 6.9 6.7 4.6 3.9
6.0 4.8 3.7 2.3 2.7 2.5
Great Falls Lake Charles Madison
4.5 4.5 3.8 4.1
8.1 8.1 5.9 6.7 4.3 5.1
Medford Miami
4.5 4.3
7.5 3.5
3.7
1.5
3.5
Nashville N e w York Omaha Phoenix
3.9 3.4
3.6 2.8 4.1 6.6
3.9 2.4 2.0 3.2 5.3 4.1
3.3
Ely Fort Worth
Santa Maria
5.7
Seattle Washington, D C
4.8
4.6 3.8 6.0 8.0 6.9 7.4
3.8
4.3
4.6 7.8
a
From (K7).
3.8 3.3
5.2 3.2
1.5 2.4
Appendix
316 TABLE
A
A A
Elliptic Integrals
of the Second
Kind
E(
a
- s i n « sin e)Klo 2
2
« V
0°
0° 2 4 6 8
0 0 0 0 0
0. 08726 0. 08726 0.08726 0. 08726 0. 08726
646 633 592 525 432
0.17453 0. 17453 0. 17452 0. 17452 0. 17451
293 185 864 330 587
0.26179 0.26179 0. 26178 0.26176 0.26174
939 579 503 715 224
0.34906 0. 34905 0.34903 0.34899 0.34893
585 742 218 025 181
0.43633 0.43631 0.43626 0.43618 0.43607
231 608 745 665 403
0. 52359 0. 52357 0. 52348 0. 52335 0. 52315
878 119 856 123 981
10 12 14 16 18
0 0 0 0 0
0. 08726 0.08726 0. 08725 0. 08725 0. 08725
313 168 999 806 590
0.17450 0. 17449 0.17448 0. 17446 0.17444
636 485 137 599 879
0.26171 0.26167 0.26162 0. 26157 0. 26151
041 182 664 510 743
0. 34885 0. 34876 0. 34866 0. 34853 0.34840
714 657 055 954 412
0.43593 0.43575 0.43555 0.43531 0.43505
Oil 552 106 765 633
0. 52291 0. 52261 0. 52227 0. 52187 0. 52142
511 821 039 317 828
20 22 24 26 28
0 0 0 0 0
0. 08725 0. 08725 0. 08724 0. 08724 0.08724
352 094 816 521 208
0.17442 0.17440 0.17438 0.17436 0. 17433
985 926 712 353 862
0.26145 0.26138 0.26131 0. 26123 0. 26114
391 485 056 141 778
0. 34825 0. 34809 0.34791 0.34773 0. 34753
492 262 800 187 510
0.43476 0.43445 0.43411 0.43375 0.43337
831 488 749 767 709
0. 52093 0. 52040 0. 51982 0. 51921 0. 51856
770 357 827 436 461
30 32 34 36 38
0 0 0 0 0
0. 08723 0. 08723 0. 08723 0. 08722 0. 08722
881 540 187 824 453
0. 17431 0.17428 0. 17425 0. 17422 0.17419
250 529 714 817 852
0.26106 0.26096 0.26087 0. 26077 0.26067
005 867 405 666 697
0.34732 0.34711 0. 34689 0.34666 0. 34642
863 342 050 093 580
0.43297 0.43256 0.43212 0.43168 0.43122
749 075 880 368 748
0.51788 0.51716 0. 51643 0. 51566 0. 51488
193 944 040 820 638
40 42 44 46 48
0 0 0 0 0
0. 08722 0. 08721 0. 08721 0. 08720 0.08720
075 692 307 920 535
0.17416 0.17413 0.17410 0. 17407 0.17404
835 779 700 613 531
0.26057 0.26047 0.26036 0.26026 0.26016
545 261 893 492 110
0.34618 0.34594 0. 34569 0.34545 0. 34520
625 343 850 266 710
0.43076 0.43029 0.42981 0. 42933 0.42885
236 055 431 594 776
0. 51408 0.51327 0. 51246 0. 51163 0.51081
862 866 037 767 454
50 52 54 56 58
0 0 0 0 0
0. 08720 0. 08719 0. 08719 0. 08719 0.08718
152 774 402 039 686
0.17401 0.17398 0.17395 0.17392 0.17389
472 449 477 571 745
0.26005 0.25995 0.25985 0.25975 0.25966
795 600 574 765 224
0.34496 0. 34472 0.34448 0. 34425 0.34402
302 162 409 159 529
0.42838 0.42791 0.42744 0.42699 0.42655
212 134 775 368 138
0.50999 0. 50918 0. 50838 0.50759 0.50683
501 310 287 831 341
60 62 64 66 68
0 0 0 0 0
0. 08718 0. 08718 0. 08717 0.08717 0.08717
345 017 704 408 130
0. 17387 0.17384 0. 17381 0.17379 0.17377
013 388 883 511 283
0.25956 0.25948 0.25939 0. 25931 0.25924
996 126 660 640 104
0.34380 0. 34359 0.34339 0.34320 0. 34302
631 575 465 404 487
0.42612 0.42571 0.42531 0.42494 0.42459
308 097 712 358 224
0. 50609 0. 50537 0. 50469 0. 50404 0. 50343
207 811 523 700 686
70 72 74 76 78
0 0 0 0 0
0. 08716 0.08716 0. 08716 0. 08716 0. 08716
871 633 416 223 053
0.17375 0. 17373 0. 17371 0. 17370 0.17368
210 302 568 018 659
0.25917 0.25910 0.25904 0.25899 0.25894
090 634 767 519 917
0.34285 0.34270 0. 34256 0. 34243 0. 34233
805 443 478 984 022
0.42426 0.42396 0.42368 0.42344 0.42322
495 339 913 363 817
0. 50286 0. 50234 0.50186 0. 50143 0. 50106
804 359 633 886 351
80 82 84 86 88
0 0 0 0 0
0. 08715 0. 08715 0.08715 0. 08715 0.08715
909 789 695 628 588
0.17367 0.17366 0.17365 0.17365 0. 17364
498 539 789 250 926
0.25890 0.25887 0.25885 0.25883 0.25882
983 737 195 370 271
0.34223 0.34215 0.34209 0.34205 0.34202
650 915 857 507 889
0.42304 0.42289 0.42277 0.42268 0.42263
389 175 258 700 547
0. 50074 0.50047 0. 50026 0.50011 0. 50003
232 707 923 993 003
90
0
0. 08715 574
10°
5°
['"»"] 5 15 25 35 45 55 65 75 85
0 0 0 0 0 0 0 0 0
0.08726 0. 08725 0.08724 0. 08723 0.08721 0. 08719 0.08717 0. 08716 0.08715
562 905 671 006 113 220 554 317 659
15°
0.17364 818
m
0.17452 0.17447 0.17437 0.17424 0.17409 0.17394 0.17380 0.17370 0.17365
624 391 550 275 157 015 680 770 493
20°
0.25881 905 [ "4 (
0.26177 0.26160 0.26127 0.26082 0.26031 0.25980 0.25935 0.25902 0.25884
7 ) 9
]
698 165 157 567 693 639 592 064 192
25°
0.34202 014
[" (
6)2 5
0.34901 0.34860 0.34782 0.34677 0. 34557 0.34436 0. 34329 0.34250 0.34207
]
329 188 632 648 562 714 797 043 467
30°
0.42261 826
0.50000 000
[- ] (
6)4
5
0.43623 0.43543 0.43394 0.43190 0.42957 0.42721 0.42512 0.42356 0.42272
105 791 028 776 525 938 769 271 556
0.52342 0.52207 0. 51952 0.51605 0. 51204 0. 50798 0.50436 0.50164 0. 50018
670 785 597 197 932 838 656 622 720
Compiled from K. Pearson, Tables of the complete and incomplete elliptic integrals,Cambridge Univ. Press, Cambridge, England, 1934 (with permission). Known errors have been corrected.
317
Tables
TABLE
AA
{Continued) E{*\«)=- {* ( l - s i n 2 a s i n 35°
(T 2 4 6 8
40°
45°
2
50°
55°
60°
0.61086 0.61082 0.61069 0.61047 0.61018
524 230 365 983 171
0.69813 0.69806 0.69788 0. 69756 0.69713
170 905 136 935 427
0.78539 0.78531 0.78505 0.78461 0.78401
816 125 085 792 409
0. 87266 0.87254 0.87220 0. 87162 0.87081
463 883 183 487 998
0.95993 0.95978 0.95933 0.95859 0.95755
109 184 459 083 301
04719 04701 04644 04551 04421
755 051 996 764 646
10 12 14 16 18
0.60980 0.60933 0.60879 0.60817 0.60748
055 793 577 636 229
0.69657 0. 69590 0.69511 0. 69420 0.69318
784 226 023 492 999
0.78324 0.78230 0.78120 0. 77994 0. 77853
162 343 308 473 323
0.86979 0.86853 0. 86707 0.86539 0. 86350
001 863 031 034 481
0.95622 0.95461 0.95271 0.95054 0.94810
460 005 478 522 878
1.04255 1. 04052 1. 03814 1. 03542 1.03236
047 491 615 177 049
20 22 24 26 28
0.60671 0. 60588 0.60498 0.60402 0.60300
652 229 319 308 616
0. 69206 0. 69084 0.68953 0. 68812 0.68663
954 814 083 308 077
0.77697 0. 77527 0.77343 0.77147 0.76939
402 316 735 387 059
0.86142 0.85914 0.85668 0.85405 0.85126
062 545 781 695 295
0.94541 0.94246 0.93928 0.93587 0.93225
386 984 709 699 186
1.02897 1. 02526 1.02126 1. 01696 1. 01238
221 804 023 224 873
30 32 34 36 38
0. 60193 0.60081 0.59966 0. 59846 0. 59723
687 994 035 332 431
0.68506 0.68341 0.68171 0.67994 0.67813
023 817 170 830 578
0.76719 0.76489 0.76250 0. 76003 0. 75749
599 908 947 726 309
0.84831 0. 84522 0.84201 0.83868 0.83525
663 958 414 340 115
0.92842 0.92441 0.92022 0.91588 0.91140
504 083 452 234 150
1. 00755 1. 00247 0.99717 0.99167 0.98598
556 977 966 469 560
40 42 44 46 48
0.59597 0.59470 0. 59341 0.59211 0. 59081
897 312 278 406 324
0.67628 0.67439 0.67248 0.67056 0.66863
229 630 651 191 167
0.75488 0.75223 0.74954 0. 74682 0.74409
809 383 234 605 773
0.83173 0.82814 0.82449 0.82080 0.81709
189 080 369 700 775
0.90680 0.90209 0.89731 0.89246 0.88758
017 742 325 858 513
0.98013 0.97414 0.96803 0.96184 0.95558
430 397 899 497 873
50 52 54 56 58
0.58951 0.58823 0, 58696 0,58571 0, 58450
664 065 171 622 056
0.66670 0.66479 0.66290 0.66104 0.65922
515 183 130 317 707
0. 74137 0. 73865 0.73597 0.73332 0.73074
047 766 286 979 229
0.81338 0.80968 0.80601 0.80239 0.79884
346 217 230 262 217
0.88268 0.87779 0.87293 0.86812 0.86340
551 305 184 660 261
0.94929 0.94300 0.93673 0.93051 0.92439
830 285 272 931 505
60 62 64 66 68
58332 58218 58109 58006 57908
103 382 497 032 549
0.65746 0.65575 0.65412 0.65257 0.65110
255 905 585 197 612
0.72822 0.72578 0. 72345 0.72122 0.71911
416 915 085 260 737
0.79538 0. 79202 0. 78879 0. 78571 0. 78279
015 582 839 685 987
0.85878 0. 85430 0.84997 0.84583 0.84191
561 169 709 811 082
0.91839 0.91254 0.90689 0.90146 0.89630
329 821 460 778 323
70 72 74 76 78
0, 57817 0,57733 0, 57657 0.57588 0.57528
584 641 189 663 450
0.64973 0.64847 0.64731 0. 64628 0.64537
667 154 812 328 322
0.71714 0.71532 0. 71366 0.71216 0.71085
767 545 196 766 210
0.78006 0. 77753 0. 77521 0.77312 0.77129
562 157 434 952 143
0.83822 0.83479 0.83165 0.82882 0.82631
090 335 223 031 879
0.89143 0.88690 0.88273 0.87896 0.87563
642 237 530 810 185
80 82 84 86 88
0.57476 0. 57434 0. 57400 0.57376 0. 57362
897 302 912 921 470
0.64459 0.64394 0. 64344 0.64307 0.64286
347 879 316 973 075
0. 70972 0. 70879 0.70805 0.70753 0. 70721
381 019 745 050 289
0.76971 0.76840 0.76737 0.76663 0.76619
298 544 830 912 339
0.82416 0.82238 0.82097 0.81996 0.81935
694 177 770 631 604
0.87275 0. 87036 0. 86847 0.86712 0.86629
520 381 970 068 990
90
0.57357 644
0.64278 761
[f ] m
.70710 678
0.76604 444
( 3
5 15 25 35 45 55 65 75 85
0.61059 0.60849 0.60451 0. 59906 0.59276 0.58633 0.58057 0.57621 0.57387
734 557 051 618 408 563 051 910 732
0.69774 0.69467 0.68883 0.68083 0.67152 0.66196 0.65333 0.64678 0.64324
083 152 790 664 549 758 844 548 351
0.78485 0.78059 0. 77247 0.76128 0. 74818 0.73464 0.72232 0.71289 0.70776
586 337 109 304 650 525 215 304 799
0. 87194 0.86625 0.85539 0.84036 0.82265 0.80419 0.78723 0.77414 0. 76697
199 642 342 234 424 500 820 195 232
0.81915 204
0.86602 540
[ -| ] (
0.95899 0.95166 0.93760 0.91807 0.89489 0.87052 0.84788 0. 83019 0.82042
)5
964 385 971 186 714 066 276 625 232
1. 04603 1. 03682 1.01914 0.99445 0.96495 0.93361 0.90415 0. 88079 0.86773
012 664 662 152 146 692 063 972 361
(continued)
Appendix
318 TABLE
AA
A
{Continued) (1 sin-'« sin-' 75°
70°
65°
80°
85°
90°
0 2 4 6 8
1.13446 1.13423 1.13354 1.13240 1.13081
401 517 929 837 573
1.22173 1.22145 1.22063 1.21926 1.21735
048 628 443 717 820
1.30899 1.30867 1.30770 1. 30609 1.30385
694 442 767 916 297
1. 39626 1. 39589 1. 39477 1.39291 1. 39031
340 024 165 030 062
1.48352 1. 48310 1.48182 1. 47970 1.47674
986 448 929 717 288
1. 57079 1.57031 1. 56888 1. 56649 1.56316
633 792 372 679 223
10 12 14 16 18
1.12877 1.12629 1.12338 1.12004 1.11628
602 522 066 099 624
1.21491 1.21193 1.20844 1.20443 1.19992
274 748 065 195 262
1. 30097 1.29747 1.29335 1.28863 1.28331
484 215 393 089 541
1. 1. 1. 1. 1.
38697 38292 37815 37268 36651
886 302 292 017 823
1.47294 1.46831 1.46287 1.45662 1.44959
312 652 363 693 085
1.55888 1.55368 1.54755 1. 54052 1. 53259
720 089 458 157 729
20 22 24 26 28
1.11212 1.10757 1.10265 1. 09736 1. 09173
778 834 204 439 228
1. 19492 1.18945 1.18352 1.17715 1.17036
542 465 618 743 745
1.27742 1.27096 1.26396 1.25643 1.24840
153 502 337 578 326
1. 1. 1. 1. 1.
35968 35218 34405 33531 32596
233 961 903 146 967
1.44178 1.43321 1.42392 1.41391 1.40321
179 813 023 049 335
1. 52379 1. 51414 1.50366 1.49236 1.48029
921 692 214 871 266
30 32 34 36 38
1. 08577 1. 07950 1. 07295 1. 06614 1. 05909
404 942 961 728 660
1.16317 1.15560 1.14768 1.13943 1.13087
686 796 469 273 946
1.23988 1. 23091 1.22151 1.21170 1.20152
858 635 305 705 870
1.31605 1. 30560 1.29463 1. 28318 1.27128
841 436 629 499 343
1. 39185 1.37986 1. 36727 1. 35411 1. 34041
532 503 328 306 965
1.46746 1. 45390 1.43966 1.42476 1.40923
221 780 215 031 972
40 42 44 46 48
1. 05183 1. 04438 1. 03677 1. 02904 1.02122
322 435 875 677 034
1.12205 1. 11298 1.10371 1. 09426 1. 08468
408 760 291 484 023
1.19101 1.18018 1. 16909 1.15777 1.14625
036 648 366 077 899
1.25896 1.24627 1.23324 1.21991 1.20633
675 240 019 241 398
1.32623 1. 31158 1.29652 1.28110 1.26535
066 614 865 340 837
39314 37650 35937 34180 32384
025 433 700 606 218
50 52 54 56 58
1. 01333 1. 00542 0.99751 0.98966 0.98190
305 010 835 632 414
1. 07499 1.06525 1.05550 1. 04578 1.03614
796 908 682 671 663
1.13460 1.12284 1.11104 1.09923 1.08748
200 604 010 604 883
1.19255 1. 17861 1.16458 1.15051 1.13645
255 873 621 210 710
1.24934 1.23311 1.21672 1.20024 1.18373
449 580 971 724 339
1. 30553 1.28695 1.26814 1.24918 1.23012
909 374 653 162 722
60 62 64 66 68
0.97427 0.96681 0.95958 0.95261 0.94595
354 780 158 084 256
1.02663 1.01731 1. 00822 0.99942 0.99099
689 023 192 966 354
1. 1. 1. 1. 1.
07585 06440 05318 04228 03176
669 132 814 653 998
1. 12248 1.10866 1. 09507 1.06178 1. 06889
590 752 580 986 476
1.16725 1.15089 1.13472 1.11882 1.10330
747 364 145 658 172
1.21105 1. 19204 1. 17317 1.15454 1.13624
603 568 938 668 437
70 72 74 76 78
0.93965 0.93376 0.92833 0.92340 0.91901
447 462 088 024 802
0.98297 0.97544 0.96845 0. 96208 0.95638
583 068 360 074 776
1.02171 1. 01220 1.00333 0.99517 0.98783
634 781 091 606 670
1.05648 1. 04465 1.03350 1. 02317 1.01376
221 133 951 331 904
1.08824 1.07377 1. 06000 1. 04707 1.03513
773 505 556 504 640
1.11837 1.10106 1. 08442 1. 06860 1.05377
774 217 522 953 692
80 82 84 86 88
0.91522 0.91206 0.90956 0. 90776 0. 90667
691 588 905 445 305
0.95143 0.94729 0.94400 0. 94162 0.94017
847 297 544 171 677
0.98140 0.97598 0.97165 0. 96849 0.96657
781 331 228 392 142
1.00543 0.99831 0.99255 0.98830 0.98568
295 000 019 025 915
1.02436 1.01495 1.00715 1.00123 0.99748
393 896 650 026 392
1. 04011 1.02784 1. 01723 1. 00864 1. 00258
440 362 692 796 409
90
0.90630 779
m r]
0.939694)i262 4)11 7
0.96592 583
1.22001 1.20649 1.18039 1.14359 1.09900 1.05063 1. 00378 0.96518 0.94269
1. 30698 1.29106 1.26026 1.21665 1.16345 1.10513 1. 04769 0.99915 0.96992
7
5 15 25 35 45 55 65 75 85
1.13303 1.12176 1.10005 1.06958 1. 03292 0.99358 0.95606 0.92579 0.90857
553 337 236 479 660 365 Oil 978 873 a
From (A6).
878 962 569 813 829 981 508 626 813
342 728 405 853 846 448 389 744 212
m
0.98480 775
1. 39393 1. 37550 1.33976 1.28896 1.22661 1.15755 1.08838 1. 02823 0.99022
358 358 099 903 050 065 943 305 779
0.99619 470
1. 00000 000
[ -I O ] (
1.48087 1.45984 1.41900 1.36076 1.28885 1.20849 1.12673 1. 05342 1.00394
384 990 286 208 906 656 373 632 027
4
1. 56780 1. 54415 1.49811 1.43229 1. 35064 1. 25867 1.16382 1.07640 1.01266
)4
907 050 493 097 388 963 796 511 353
Tables TABLE Normal
319 A.5 Probability
Integral
F(z)
dt
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0 0.1 0.2 0.3 0.4
0.5000 0.5398 0.5793 0.6179 0.6554
0.5040 0.5438 0.5832 0.6217 0.6591
0.5080 0.5478 0.5871 0.6255 0.6628
0.5120 0.5517 0.5910 0.6293 0.6664
0.5160 0.5557 0.5948 0.6331 0.6700
0.5199 0.5596 0.5987 0.6368 0.6736
0..5239 0..5636 0..6026 0,.6406 0,.6772
0..5279 0.,5675 0..6064 0..6443 0..6808
0.5319 0.5714 0.6103 0.6480 0.6844
0.5359 0.5753 0.6141 0.6517 0.6879
0.5 0.6 0.7 0.8 0.9
0.6915 0.7257 0.7580 0.7881 0.8159
0.6950 0.7291 0.7611 0.7910 0.8186
0.6985 0.7324 0.7642 0.7939 0.8212
0.7019 0.7357 0.7673 0.7967 0.8238
0.7054 0.7389 0.7704 0.7995 0.8264
0.7088 0.7422 0.7734 0.8023 0.8289
0..7123 0,.7454 0..7764 0 .8051 0 .8315
0..7157 0..7486 0..7794 0,.8078 0..8340
0.7190 0.7517 0.7823 0.8106 0.8365
0.7224 0.7549 0.7852 0.8133 0.8389
1.0 1.1 1.2 1.3 1.4
0.8413 0.8643 0.8849 0.9032 0.9192
0.8438 0.8665 0.8869 0.9049 0.9207
0.8461 0.8686 0.8888 0.9066 0.9222
0.8485 0.8708 0.8907 0.9082 0.9236
0.8508 0.8729 0.8925 0.9099 0.9251
0.8531 0.8749 0.8944 0.9115 0.9265
0 .8554 0 .8770 0 .8962 0 .9131 0 .9279
0 .8577 0..8790 0 .8980 0,.9147 0,.9292
0.8599 0.8810 0.8997 0.9162 0.9306
0.8621 0.8830 0.9015 0.9177 0.9319
1.5 1.6 1.7 1.8 1.9
0.9332 0.9452 0.9554 0.9641 0.9713
0.9345 0.9463 0.9564 0.9649 0.9719
0.9357 0.9474 0.9573 0.9656 0.9726
0.9370 0.9484 0.9582 0.9664 0.9732
0.9382 0.9495 0.9591 0.9671 0.9738
0.9394 0.9505 0.9599 0.9678 0.9744
0,.9406 0 .9515 0 .9608 0 .9686 0 .9750
0..9418 0 .9525 0,.9616 0 .9693 0,.9756
0.9429 0.9535 0.9625 0.9699 0.9761
0.9441 0.9545 0.9633 0.9706 0.9767
2.0 2.1 2.2 2.3 2.4
0.9772 0.9821 0.9861 0.9893 0.9918
0.9778 0.9826 0.9864 0.9896 0.9920
0.9783 0.9830 0.9868 0.9898 0.9922
0.9788 0.9834 0.9871 0.9901 0.9925
0.9793 0.9838 0.9875 0.9904 0.9927
0.9798 0.9842 0.9878 0.9906 0.9929
0 .9803 0 .9846 0 .9881 0 .9909 0 .9931
0 .9808 0,.9850 0 .9884 0 .9911 0 .9932
0.9812 0.9854 0.9887 0.9913 0.9934
0.9817 0.9857 0.9890 0.9916 0.9936
2.5 2.6 2.7 2.8 2.9
0.9938 0.9953 0.9965 0.9974 0.9981
0.9940 0.9955 0.9966 0.9975 0.9982
0.9941 0.9956 0.9967 0.9976 0.9982
0.9943 0.9957 0.9968 0.9977 0.9983
0.9945 0.9959 0.9969 0.9977 0.9984
0.9946 0.9960 0.9970 0.9978 0.9984
0 .9948 0 .9961 0 .9971 0 .9979 0 .9985
0,.9949 0 .9962 0,.9972 0,.9979 0..9985
0.9951 0.9963 0.9973 0.9980 0.9986
0.9952 0.9964 0.9974 0.9981 0.9986
3.0 3.1 3.2 3.3 3.4
0.9987 0.9990 0.9993 0.9995 0.9997
0.9987 0.9991 0.9993 0.9995 0.9997
0.9987 0.9991 0.9994 0.9995 0.9997
0.9988 0.9991 0.9994 0.9996 0.9997
0.9988 0.9992 0.9994 0.9996 0.9997
0.9989 0.9992 0.9994 0.9996 0.9997
0 .9989 0 .9992 0 .9994 0 .9996 0 .9997
0..9989 0,.9992 0..9995 0,.9996 0..9997
0.9990 0.9993 0.9995 0.9996 0.9997
0.9990 0.9993 0.9995 0.9997 0.9998
320 TABLE
Appendix
A
A.6
Absorptance
and Emittance
Values for Various
Materials"
Short-wave absorptance
Substance
Long-wave emittance
a e
Class I substances: Absorptance to emittance ratios less than 0.5
Magnesium carbonate, M g C 0 White plaster S n o w , fine particles, fresh White paint, 0.017 in., on aluminum Whitewash on galvanized iron White paper White enamel on iron Ice, with sparse snow cover S n o w , ice granules Aluminum oil base paint White powdered sand 3
0.025-0.04 0.07 0.13 0.20 0.22 0.25-0.28 0.25-0.45 0.31 0.33 0.45 0.45
0.79 0.91 0.82 0.91 0.90 0.95 0.90 0.96-0.97 0.89 0.90 0.84
0.03-0.05 0.08 0.16 0.22 0.24 0.26-0.29 0.28-0.5 0.32 0.37 0.50 0.54
Class II substances: Absorptance to emittance ratios between 0.5 and 0.9 A s b e s t o s felt Green oil base paint Bricks, red A s b e s t o s cement board, white Marble, polished W o o d , planed oak Rough concrete Concrete Grass, green, after rain Grass, high and dry Vegetable fields and shrubs, wilted Oak leaves Frozen soil Desert surface Common vegetable fields and shrubs Ground, dry plowed Oak woodland Pine forest Earth surface as a whole (land and sea, no clouds)
0.25 0.50 0.55 0.59 0.5-0.6
—
0.60 0.60 0.67 0.67-0.69 0.70 0.71-0.78
—
0.75 0.72-0.76 0.75-0.80 0.82 0.86 0.83
0.50 0.56 0.60 0.61 0.61
0.50 0.90 0.92 0.96 0.90 0.90 0.97 0.88 0.98 0.90 0.90 0.91-0.95 0.93-0.94 0.90 0.90 0.90 0.90 0.90
0.83 0.82 0.83-0.89 0.91 0.96
—
—
—
0.62 0.68 0.68 0.76 0.78 0.78-0.82
—
Tables TABLE
321 A.6
(Continued)
Class III substances: Absorptance to emittance ratios b e t w e e n 0.8 and 1.0 Grey paint Red oil base paint A s b e s t o s , slate A s b e s t o s , paper Linoleum, red-brown Dry sand Green roll roofing Slate, dark grey Old grey rubber Hard black rubber Asphalt pavement Black cupric oxide on copper Bare moist ground Wet sand Water Black tar paper Black gloss paint Small hole in large b o x , furnace, or enclosure " H o h l r a u m , " theoretically perfect black body
0.75 0.74 0.81 0.84 0.82 0.88 0.89
0.95 0.90 0.% 0.93-0.96 0.92 0.90 0.91-0.97
—
0.79 0.82 0.84
— 0.91 0.91 0.93
— —
0.86 0.90-0.95
0.93 0.91 0.90 0.91 0.94 0.93 0.90 0.99 1.00
—
— — — —
0.96 0.95 0.95 0.95-0.96 0.93 0.90 0.99 1.00
0.95 0.95 0.96 0.98 1.00 1.00 1.00 1.00
Class IV substances: Absorptance to emittance ratios greater than 1.0 Black silk velvet Alfalfa, dark green Lampblack Black paint, 0.017 in., on aluminum Granite Graphite High ratios, but absorptances less than 0.80 Dull brass, copper, lead Galvanized sheet iron, oxidized Galvanized iron, clean, new Aluminum foil Magnesium Chromium Polished zinc Deposited silver (optical reflector) untarnished
0.99 0.97 0.98 0.94-0.98 0.55 0.78
0.97 0.95 0.95 0.88 0.44 0.41
1.02 1.02 1.03 1.07-1.11 1.25 1.90
0.2-0.4 0.80 0.65 0.15 0.30 0.49 0.46 0.07
0.4-0.65 0.28 0.13 0.05 0.07 0.08 0.02 0.01
1.63-2.0 2.86 5.00 3.00 4.30 6.13 23.00
322 TABLE
Appendix A.6
A
{Continued) Class V substances: Selective surfaces
Plated metals: Black sulfide on metal Black cupric oxide on sheet aluminum Copper (5 x 10~ c m thick) on nickel or silver-plated metal Cobalt oxide on platinum Cobalt oxide on polished nickel Black nickel oxide on aluminum Black chrome Particulate coatings: Lampblack on metal Black iron oxide, 47 grain size, on aluminum Geometrically enhanced surfaces: Optimally corrugated greys Optimally corrugated selectives Stainless-steel wire mesh Copper, treated with N a C 1 0 and N a O H
0.92 0.08-0.93
0.10 0.09-0.21
9.20
0.93-0.94 0.85-0.93 0.87
0.24-0.40 0.06-0.1 0.09
3.90 14.5-15.: 9.80
0.89 0.95 0.63-0.86 0.87
0.77 0.16 0.23-0.28 0.13
1.20 5.90 2.7-3.0 6.69
5
2
a
From (K2).
Tables TABLE Interest
323 A.7 Factors
for Various
Discount 3%
Rates
INTEREST FACTORS FOR DISCRETE C O M P O U N D I N G PERIODS
UNIFORM SERIES
SINGLE PAYMENT Compound Amount Factor N
N)
Present Worth Factor
Capital Recovery Factor
(P/F, 3, N)
(A/P.3.N)
1
1.0300
.97087
1.0300
2 3 4
1.0609 1.0927
.94260 .91514
.52262 .35354
11255 1.1592
.88849
.26903 .21836
1.1940 1.2298 1.2667 1.3047
.83749
(F/P, 3.
5 6 7 8 9
.86261
.81310 .78941
10
1
3439
.76642 .74410
11
1.3842 1 4257
72243 .70139
1.4685
68096 .66113 .64187
12 13 14
1 5125 1.5579
15 16 17 18 19
1 6046 1.6528 1.7024 1 7534
20
1
21
1.8602
22 23 24
1
9160
1 2
9735 0327
25 26 27
8060
62318 60502 58740 .57030 .55369
.18836
5.4170 6.2301 7.0195
15460 .13051
7.7859 8.5300
07961 .07595 .07271
12
560
13
165
11 2 9 5 11.937
13.753 14 323 14 877
.11246 09844 .08723 .07808 .07046 06403 .05853 05377 04961 .04595 04271
1.0000 2.0299 3.0908 4.1835 5.3090 6.4682 7.6622 8.8920 10.158 11.463 12.807 14.191 15.617 17.085 18.598 20.156 21.760 23.413
03982
25
03722
26.869
115
28.675 30.535
15
414
.03487 .03275 03082
2.0937
47762
.05743
16.935 17.412
.02905 .02743
34 425 36.457
2.1565
.46370 45020
.05594 05457
02594 .02457 02212 02102
2
3565
43709
05329
17.876 18 3 2 6 18 7 6 3
42436 41200
.05212 .05102
19 1 8 8 19.600
40000
35
2 5000 2 5750 2 6522 2 7318 2.8137
40 45 50
3 3 4
2619 7814 3837
55 60
5 5
0819 8913
26445 22812 19678 16974
65
6 7 9 10 12
8296 9173 1783 640 334
14642 12630 10895 09398 08107
14 16
299 576
06993 06033 05204
j
.23903
(F/A.3.N)
15 9 3 6 16.443
2.4272
90 95 100
.49262 .32354
4.5796
9.2524 9.9537 10.634
.06982
3,N)
1.0000
2.8285 3.7170
10808 .10046 09403 .08853 .08377
.06722
(A/F,
06275 .06082 05905
2 2212 2.2878
70 75 80 85
.11723
3,N)
.9709 1.9134
Compound Amount Factor
.06487
29 30 31
.14246 12844
(PIA,
Sinking Fund Factor
.53756 52190 50670 49194
28
32 33 34
.18460 .16051
Present Worth Factor
19.217
38835 37 704 .36606 .35539 30657
05000 04905 .04816 04732 .04654 04326 04079 03887 03735 03613
20
000
20.388 20.765 2 1 . 1 31 21
486
23 1 14 24 518 25.729 26 774
.02329
02000 01905 .01816 01732 .01654 01326 01079 .00887 00735
27.675
00613 00515 00434 00367
.03311 03265
28 452 29 123 29.701 30 200 30 630
03226 03193 03165
31 0 0 2 31 3 2 2 31.598
03515 03434 03367
32.451
Gradient Factor (A/G,
3,N)
.0000 .4920 .9795 1.4622 1.9401 2.4129 2.8809 3.3440 3.8022 4.2555
N 1 2 3 4 5 6 7 8 9 10
4.7040 5.1475 5.5863 6.0201 6.4491
11 12 13 14
6.8732
16 17
7.2926 7.7072 8.1169 8.5219 8.9221 9.3176 9.7084 10.094
15
18 19 20 2'l 22 23 24
10.475
25
38.551 40.707
10.852 11.224
26 27
42.929 45.217
11.592 11.954
28
47.573
12.313
30
50 000 52 500 55.075 57.727
12.666 13.016 13 360 13.700
31 32 33 34
60.459
14
036
35
75
15.649 17.154
40
397
92.715 112 79 136 06 163 04 194 230
32 57
0031 1 .00265
272 321 377
61 33 82
00226 00193 00165
443 519 607
31 22 23
29
45 50 55
ie 556 19.859 21 0 6 6
60
22 183 23 213 24.162 25.034 25.834
65 70 75 80 85
26 27
566 234
27.843
90 95 100
(continued)
324 TABLE
A.7
Appendix (Continued) 8% Interest Factors for Discrete Compounding Periods SINGLE Compound Amount Factor
(F/P, 8,
N)
PAYMENT Present Worth Factor (P/F, 8.
UNIFORM Capital Recovery Factor
N)
(A/P,
8.
N)
SERIES
Present Worth
Sinking
Factor
Factor
(PIA, 8 . N)
F und
(A/F,
8, N )
Compound Gradient
Amount Factor
(F/A,
8,
Factor
N)
2
1.0800 1.1664
.92593 .85734
1.0800 56077
.9259 1.7832
1.0000 .48077
1.0000 2.0799
3 4
1.2597 1.3604
.79383
38803
.30804
.73503
.30192
2.5770 3.3121
5
1.4693
.68059
.25046
3.9926
.22192 .17046
3.2463 4.5060 5.8665
6 7
1 5868 1.7138
.21632 .19207
4.6228 5.2063
.13632 .1 1 2 0 7
7.3358 8.9227
8
.50025 .46320
.17402 16008 .14903
5.7466 6.2468 6.7100
.09402
9 10
1.8509 1.9989 2.1589
.63017 .58349 .54027
11 12
2.5181 2.7196 2.9371 3.1721
.12642 .12130 .11683
7 1389 7.5360 7.9037
15
42889 .39712 36770 .34046 .31524
.14008 .13270
13 14
.06008 .05270 .04652 .04130 .03683
16 17
3.4259
2.3316
.29189 .27027
.11298 .10963 .10670 .10413 .10185
8.2442 8.5594 8.8513
18
3.6999 3.9959
19 20
4.3156 4.6609
21
5.0337 5.4364
.19866 .18394
5.8713
.17032 .15770
.09983 .09803 .09642 .09498
.14602
.09368
.13520 .12519 .11592 .10733 .09938
.09251 .09145 .09049 .08962 .08883
10.809 10.935 11.051 11.158 11.257
22 23 24 25
6.3410 6.8483
26 27
7.3962
28 29
8.6269 9.3171
7.9879
.25025 .23171 .21455
9.1216 9.3718 9.6035 9.8181 10.016 10.200 10.371 10.528 10.674
.08008 .06903
.03298 .02963 .02670 .02413 .02185 .01983 .01803 .01642 .01498 .01368 .01251 .01145 .01049
10.636 12.487 14.486
(A/G,
8,N) .0000 .4807 .9487
1.4038 1.8463
N 1 2 3 4 5 6 7
2.2762 2.6935 3.0984
8
3.4909 3.8712
9 10
16.645
4.2394
11
18.976 21.495 24.214
4.5956 4.9401 5.2729 5.5943
12 13 14 15
5.9045 6.2036
16 17 18 19
27.151 30.323 33.749 37.449 41.445 45.761 50.422 55.455 60.892 66.763 73.104 79.953 87.349 95.337
6.4919 6.7696 7.0368 7.2939 7.5411 7.7785 8.0065
20 21 22 23 24
8.2253
25
8.4351
26 27
8.6362 8.8288
28 29
.00962
103.96
9.0132
.00883
113.28
9.1896
30
30
10.062
31
10.867
.09202
.08811
11.349
.00811
123.34
9.3583
31
32 33 34
11 . 7 3 6
.08520
.08745
11.434
.08685
11.513
13.689
.07889 .07305
134.21 145.94
9.5196
12.675
.00745 .00685
.08630
.00630
158.62
35
14.785
.06764
.08580
11.586 11.654
32 33 34
.00580
172.31
40 45
21.724
.04603
.08386
11.924
31.919
.03133
40 45
.02132
12.108 12.233
10.569 11.044
46.900
.08259 .08174
259.05 386.49
50 55
.00386 .00259 .00174
573.75
68.911
.01451 .00988
.08118 .08080
12.318 12.376
.00118 .00080
1253.1
11.410 11.690 11.901
50 55 60
.08054
12.416 12.442
.00054 .00037
1847.1 2719.9
12.060
.08037 .08025 .08017
12.461 12.473
.00025 .00017
4002.3
12.481
.00012
5886.6 8655.2
65 70 75 80
.08012
12.265 12.330 12.377
.08008 .08005 .08004
12.487 12.491 12.494
.00008 .00005 .00004
12723.9 18701.5 27484.5
60
101.25
65
148.77
70 75 80 85
218.59
.00672 .00457
321.19 471.93 693.42
.00311 .00212 .00144
90 95 100
1018.8 1497.0 2199.6
.00098 .00067 .00045
848.89
9.6736 9.8207 9.9610
12.178
12.411 12.436 12.454
35
85 90 95 100
A
Tables TABLE
325 4.7
(Continued) 10% Interest Factors for Discrete Compounding Periods SINGLE
PAYMENT
Compound Amount Factor (F/P. 10,
N)
UNIFORM
SERIES
Present Worth
Capital Recovery
Present Worth
Sinking
Factor
Factor
Factor
Factor
(P/F, 10. N )
(AIP,
10,
N) (PIA,
10,
1
1.1000
2
1.2100
.82645
.57619
1.7355
3 4
1.3310 1.4641
.75132
2.4868
.68302
.40212 .31547
5
1.6105
.62092
.26380
.90909
6 7
1 7 7 1 5
.56448
1.9487
8
1.1000
.9091
3.1698 3.7907
F und
N) (AIF,
10,
1.0000
Compound Amount Factor
N) (FIA,
10.N) 1.000 2.0999 3.3099
Gradient Factor
(AIG,
10.N)
N
.0000
1
.4761 .9365
2
.47619 .30212 .21547
4.6409
1.3810
3 4
.16380
6.1050
1.8100
5
7.7155
2.2234
9.4870
2.6215
6 7
4.3552
.51316
.22961 .20541
4.8683
.12961 .10541
2.1435 2.3579
.46651 42410
.18745 .17364
5.3349 5.7589
.08745 .07364
11.435 13.579
3.0043
8
9
3.3722
10
2.5937
.38555
.16275
6.1445
.06275
15.937
3.7253
9 10
11
2.8530 3.1384
.35050
.15396
6.4950
.05396
18.530
4.0639
11
12
6.8136
.04676
3.4522 3.7974
.31863 .28967
.14676
13 14
.14078
7.1033
4.3883 4.6987
.26333
4.9954
.23940
7.3666 7.6060
13 14
4.1771
13575 .13147
21.383 24.522 27.974
15
.04078 .03575 .03147
31.771
5.2788
15
16 17
4.5949
.21763
.12782
7.8236
.02782
35.949
5.5492
5.0544
.19785
.12466
8.0215 8.2013
.02466
40.543
8.3649
45.598 51.158
5.8070 6.0524
16 17
.02193 .01955
57.273
6.2860 6.5080
18
5.5598
.17986
.12193
19
6.1158
.16351
.11955
6.7273
.14865
.11746
8.5135
.01746
21
7.4001
.13513
.11562
22
8.1401 8.9541
.12285
.11401 .11257
8.6486 8.7715
.01562 .01401 .01257
64.001 71.401 79.541
6.9188 7.1084
88.495 98.344
7.2879 7.4579
20
23 24 25
9.849? 10.834
.11168 .10153 .09230
8.8832 8.9847
6.7188
.11130 .11017
9.0770
.01130 .01017
.10916
9.1609
.00916
109.17
7.6185
.00826
121.09 134.20 148.62
7.7703 7.9136 8.0488
12
18 19 20 21 22 23 24 25 26 27
26 27
11.917 13.109
08391 07628
28
.06935 .06304
.10826 .10745 10673
9.2372 9.3065
29
14.420 15.862
9.3696
.00745 .00673
30
17.448
.05731
10608
9.4269
.00608
164.48
8.1761
30
9.4790 9.5263 9.5694
.00550 .00497
181.93
8.2961 8.4090
31
31
19.193
.05210
32
21 .113 23.224
.04736
10550 .10497
.04306 .03914
.10450 .10407
.03559
.10369
9.6085 9.6441
.02210
9.7790 9.8628
33 34 35
25.546 28 101
40
45.257
201.13 222.24
.00369
271.01
8.7085
35
.00226
442.57
9.0962
40
718.87
9.3740 9.5704
45
.01372
117.38 189.04
.00852
.10086
9.9148
.00086
.00529
10053
9.9471
.00053
1163.8 1880.4
60
304.46
.00328
.10033
9.9671
.00033
65
490.34
.00204
.10020
9.9796
.00020
70
789.69
.00127
.10013
9.9873
.00013
.00079
10008
9.9921
.00049
.10005
9.9951
.00008 .00005
12709.0 20474.0
75 80
1271.8 2048.2
32 33 34
8.5151 8.6149
50 55
72.887
29
245.46
.00450 .00407
.10226 10139
45
28
.00139
50 55
3034.6
9.7075 9.8022
60
4893.4
9.8671
65
7886.9
9.9112 9.9409
70 75
9.9609
80
85
3298.7
.00030
.10003
9.9969
.00003
32979.7
9.9742
85
90 95
5312.5 8555.9
.10002
53120.2 85556.8
13780.6
9.9981 9.9988 9.9992
.00002 .00001
100
.00019 .00012 .00007
.00001
137796.1
9.9830 9.9889 9.9927
90 95 100
.10001 .10001
(continued)
326 TABLE
Appendix
A.7
(Continued) 12% Interest Factors for Discrete Compounding Periods SINGLE Compound Amount Factor
.V 1
2 3 4 5 6 7
(F/P,
12.
N)
PAYMENT Present Worth Factor (P/F.
12.N)
1 1200 1.2544
.89286 .79719
1.4049 1.5735 1.7623
.71178 .63552 .56743
UNIFORM Capital Recovery F actor
(A/P.
12.N)
Present Worth
12.
F und Factor N)
(A/F,
12.
3.0373 3.6047 4.1114
.12323
8.115
4.5637
.09912 .08130
10.088 12.299 14.775 17.548
8
.45235 .40388
.24323 .21912 .20130
9 10
2.7730 3.1058
36061 .32197
.18768 .17698
11
3.4785 3.8959 4.3634
.28748 .25668 .22918 .20462 .18270
.16842 .16144
5.9376 6.1943 6.4235 6.6281 6.8108
.04842 .04144
.15568 .15087 . 14682
.16312 .14565 .13004
.14339
6.9739
.02339
.14046 .13794 .13576 .13388
7.1196 7.2496 7.3657 7.4694
.02046 .01794
.11611 .10367
16 17
6.1303
18
7.6899 8.6126 9.6462
19 20
6.8659
4.9676 5.3282 5.6502
.06768 .05698
.03568 .03087 .02682
.01576 .01388
10.803 12.100 13.552
.09256 .08264
.13224
7.5620
.01224
.13081 .12956
7.6446 7.7184
.01081
.07379
15.178
.06588 .05882
.12846 .12750
-'.7843 7.8431
.00956 .00846 .00750
.05252 .04689 .04187
.12665 .12590 .12524
7.8956 7.9425 7.9844
.00665 .00590 .00524
29.959
.03738 .03338
.12466 .12414
8.0218 8.0551
.00466 .00414
31
33.554
.02980
.12369
8.0849
.00369
32 33 34
37.581 42.090 47.141
.12328 .12292
8.1116 8.1353
.00328 .00292
.12260
35
52.798
.02661 .02376 .02121 .01894
8.1565 8.1755
.00260 .00232
8.2437
.00130 .00074
21 22 23 24 25
16.999
26 27 28
19.039 21.324
29 30
40 45 50
23.883 26.749
93.049 163.98 288.99
.12232
.01075 .00610
.12130 .12074
.00346
.12042
8.2825 8.3045
.00042
Gradient F actor
1 2 , N ) (A/G,
.47170 .29635 .20924 .15741
1.0000
.50663
15
(F/A,
.8929 1.6900 2.4018
1.9738
4.8870 5.4735
Amount Factor N)
1.1200 .59170 .41635 .32924 .27741
2.2106 2.4759
12 13 14
Compound
Sinking
Factor
(PIA,
SERIES
1.0000 2.1200 3.3743 4.7793 6.3528
12.N)
0000 .4717 .9246 1.3588 1.7745 2.1720 2.5514 2.9131
N 1 2 3 4 5 6 7
3.2573 3.5846
8 9 10
20.654
3.8952
11
24.132 28.028 32.392 37.279
4.1896 4.4682 4.7316 4.9802
12 13 14
42.752 48.883
5.2146 5.4352 5.6427
16 17
55.749 63.439 72.051
5.8375 6.0201
81.698 92.501 104.60
6.1913 6.3513 6.5009
118.15 133.33
6.6406 6.7708
150.33 169.37
6.8920 7.0049 7.1097 7.2071 7.2974
190.69 214.58 241.32 271.28 304.84 342.42 384.51
15
18 19 20 21 22 23 24 25 26 27 28 29 30
7.3810
31
7.4585 7.5302 7.5964
32 33 34
431.65
7.6576
35
767.07
7.8987
40 45
1358.2 2399.9
8.0572 8.1597
50
A
Tables TABLE
327 A.7
{Continued) 15% Interest Factors for Discrete Compounding Periods
SINGLE Compound Amount Factor .V 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
(F/P. 15,
N)
Present Worth Factor (P/F. 15,
1.1500 1.3225
.86957 .75614
1.5208 1.7490 2.0113
.65752 .57175 .49718
2.3130 2.6600 3.0590 3.5178 4.0455
.43233 .37594 .32690
4.6523 5.3502 6.1527 7.0756 8.1369 9.3575
UNIFORM
PAYMENT Capital Recovery Factor
N) (A/P,
15.
N)
Present Worth Factor (PM.
15,
.8696
3.3521
.14832
.26424
3.7844 4.1604
.11424
8.7536
.24036 .22285 .20957
15,N)
N
.0000
1
.4651 .9071
2 3 4
1.3262 1.7227
5 6 7
.09036 .07285 .05957
11.066 13.726 16.785
2.0971 2.4498 2.7813 3.0922
.04925
20.303
3.3831
10
8 9
.21494
.19107
5.2337
.04107
24.349
3.6549
11
.18691 .16253 .14133
.18448 .17911
5.4206 5.5831 5.7244
.03448 .02911 .02469 .02102
29.001 34.351 40.504
3.9081 4.1437
12 13 14
.01795 .01537
55.716 65.074
.12290 .10687
.17469 .17102 .16795 .16537
5.8473 5.9542 6.0471 6.1279
25
32.918
.03038
.15470
26 27
.02642 .02297 .01997 .01737
.15407
28 29
37.856 43.534 50.064 57.574
30
66.210
.01510
.15230
6.5659
31 32
76.141
.01313
.15200
6.5791
87.563
.01142 .00993 .00864
.15173 .15150
6.5905 6.6004
.00751
.15131 .15113
6.6091 6.6166
.00373 00186 .00092
15056 .15028 .15014
6.6417
267.85 538.75 1083.6
Factor
(A/G,
.19925
24.891 28.624
40 45 50
Gradient
4.4873 4.7715 5.0187
.28426 .24719
.15842 .15727
115.80 133.17
15. N)
.29832
.05313 .04620 .04018 .03493
35
(F/A,
3.4724 4.9933 6.7423
18.821 21.644
33 34
15, N )
.28798 .20027
.15976
100.69
(A/F,
1.6257
.16319 .16134
22 23 24
Amount Factor
2.2832 2.8549
.06110
21
Compound
F und Factor
1.000 2.1499
.09293 .08081 .07027
18
Sinking
1.0000 .46512
1.1500 .61512 .43798 .35027
10.761 12.375 14.231 16.366
19 20
N)
SERIES
.15628 .15543
.15353 .15306 .15265
6.1982 6.2593 6.3124 6.3586 6.3988 6.4337 6.4641 6.4905 6.5135 6.5335 6.5508
6.6543 6.6605
.01319 .01134 .00976 .00842 .00727 .00628 .00543 .00470 .00407 .00353 .00306 .00265 .00230 .00200 .00173 .00150 .00131 .00113 .00056 .00028 .00014
47.579
4.3623 4.5649 4.7522
15 16 17
75.835 88.210 102.44
4.9250 5.0842 5.2307
18 19
5.3651
20
118.80
5.4883
21
137.62 159.27
5.6010 5.7039 5.7978 5.8834
22 23 24
184.16 212.78
5
9612
25 26 27
245.70 283.56 327.09 377.16 434.73
6.0318 6.0959 6.1540
500.94
6.2541
31
577.08 664.65 765.34
6.2970
32 33 34
881.14
6.4018
35
6.5167
40 45
1779.0 3585.0 7217.4
6
2066
6.3356 6.3705
6.5829 6.8204
28 29 30
50
(continued)
Appendix
328 TABLE
A.7
(Continued) 20% Interest Factors for Discrete Compounding Periods SINGLE PAYMENT Compound Amount Factor
N 1
(F/P, 20, JV)
Present Worth Factor
UNIFORM SERIES Capital Recovery Factor
(P/F, 20, JV) (A/P,
Present Worth Factor
20, JV) (P/A,
Sinking Fund Factor
20, JV) (A/F,
Compound Amount Factor
20, JV) (F/A,
Gradient Factor
20, JV) (A/G.
20, JV)
JV
2 3 4 5
1.2000 1.4400 1.7280 2.0736 2.4883
.83333 .69445 .57870 .48225 .40188
1.2000 .65455 .47473 .38629 .33438
.8333 1.5277 2.1064 2.5887 2.9906
1.0000 .45455 .27473 .18629 .13438
1.0000 2.1999 3.6399 5.3679 7.4415
.0000 .4545 .8791 1.2742 1.6405
1 2 3 4 5
6 7 8 9 10
2.9859 3.5831 4.2998 5.1597 6.1917
.33490 .27908 .23257 .19381 .16151
30071 .27742 .26061 .24808 .23852
3.3255 3.6045 3.8371 4.0309 4.1924
.10071 .07742 .06061 .04808 .03852
9.9298 12.915 16.498 20.798 25.958
1.9788 2.2901 2.575<5 2.8364 3.0738
6 7 8 9 10
11 12 13 14 15
7.4300 8.9160 10.699 12.839 15.406
.13459 .11216 .09346 .07789 06491
.23110 .22527 .22062 .21689 .21388
4.3270 4.4392 4.5326 4.6105 4.6754
.03110 .02527 .02062 .01689 .01388
32.150 39.580 48.496 59.195 72.034
3.2892 3.4840 3.6596 3.8174 3.9588
11 12 13 14 15
16 17 18 19 20
18.488 22.185 26623 31.947 38 337
.05409 .04507 .03756 .03130 .02608
.21144 .20944 .20781 .20646 .20536
4.7295 4.7746 4.8121 4.8435 4.8695
.01144 .00944 .00781 .00646 .00536
87.441 105.92 128.11 154.73 186.68
4.0851 4.1975 4.2975 4.3860 4.4643
16 17 18 19 20
21 22 23 24 25
46.004 55.205 66.246 79.495 95.394
02174 .01811 .01510 .01258 .01048
.20444 .20369 .20307 .20255 .20212
4.8913 4.9094 4.9245 4.9371 4.9475
.00444 .00369 .00307 .00255 .00212
225.02 271.02 326.23 392.47 471.97
4.5333 4.5941 4.6474 4.6942 4.7351
21 22 23 24 25
;
26 27 28 29 30
114.47 137.36 164.84 197.81 237.37
.00874 .00728 .00607 .00506 .00421
.20176 .20147 .20122 .20102 .20085
4.9563 4.9636 4.9696 4.9747 4.9789
.00176 .00147 .00122 .00102 .00085
567.36 681.84 819.21 984.05 1181.8
4.7708 4.8020 4.8291 4.8526 4.8730
26 27 28 29 30
31 32 33 34 35
284.84 341.81 410.17 492.21 590.65
.00351 .00293 .00244 .00203 .00169
.20070 .20059 .20049 .20041 .20034
4.9824 4.9853 4.9878 4.9898 4.9915
.00070 .00059 .00049 .00041 .00034
1419.2 1704.0 2045.8 2456.0 2948.2
4.8907 4.9061 4.9193 4.9307 4.9406
31 32 33 34 35
.00068 .00027 .00011
.20014 .20005 .20002
4.9966 4.9986 4.9994
.00014 .00005 .00002
7343.6 18281.3 45497.2
4.9727 4.9876 4.9945
40 45 50
40 45 50
1469.7 3657.1 9100.1
A
Tables TABLE
329 A.7
{Continued) 25% Interest Factors for Discrete Compounding Periods UNIFORM SERIES
SINGLE PAYMENT Compound Amount Factor N
Present Worth Factor
Capital Recovery Factor
Present Worth Factor
Sinking Fund Factor
Compound Amount Factor
Gradient Factor
(F/P, 25, N) ( P / F , 25, N) (A/P. 25, N ) ( P M , 25,N) (A/F, 25. N ) ( F M , 25.N)
N 1 2 3 4 5
1 2 3 4 5
1.2500 1.5625 1.9531 2.4414 3.0518
.80000 .64000 .51200 .40960 .32768
1.2500 .69444 .51230 .42344 .37185
.8000 1.4400 1.9520 2.3616 2.6893
1.0000 .44444 .26230 .17344 .12185
6 7 8 9 10
3.8147 4.7684 5.9605 7.4506 9.3132
.26214 .20972 .16777 .13422 .10737
.33882 .31634 .30040 .28876 .28007
2.9514 3.1661 3.3289 3.4631 3.5705
.08882 .06634 .05040 .03876 .03007
11.259 15.073 19.842 25.802 33.253
1.8683 2.1424 2.3872 2.6048 2.7971
6 7 8 9 10
1.0000 2.2500 3.8125 5.7656 8.2070
.00000 44444 .85246 1.2249 1.5631
11 12 13 14 15
11.642 14.552 18.190 22.737 28.422
.08590 .06872 .05498 .04398 .03518
.27349 .26845 .26454 .26150 .25912
3.6564 3.7251 3.7801 3.8241 3.8593
.02349 .01845 .01454 .01150 .00912
42.566 54.208 68.760 86.949 109.687
2.9663 3.1145 3.2437 3.3559 3.4530
11 12 13 14 15
16 17 18 19 20
35.527 44 409 55.511 69.389 86.736
.02815 .02252 .01801 .01441 .01153
.25724 .25576 .25459 .25366 .25292
3.8874 3.9099 3.9279 3.9424 3.9539
.00724 .00576 .00459 .00366 .00292
138.109 173.636 218.045 273.556 342.945
3.5366 3.6084 3.6698 3.7222 3.7667
16 17 18 19 20
21 22 23 24 25
108.420 135.525 169.407 211.758 264.698
.00922 .00738 .00590 .00472 .00378
.25233 .25186 .25148 .25119 .25095
3.9631 3.9705 3.9764 3.9811 3.9849
.00233 .00186 .00148 .00119 .00095
429.681 538.101 673.626 843.033 1054.791
3.8045 3.8365 3.8634 3.8861 3.9052
21 22 23 24 25
26 27 28 29 30
330.872 413.590 516.988 646.235 807.794
.00302 .00242 .00193 .00155 .00124
.25076 .25061 .25048 .25039 .25031
3.9879 3.9903 3.9923 3.9938 3.9950
.00076 .00061 .00048 .00039 .00031
1319.489 1650.361 2063.952 2580.939 3227.174
3.9212 3.9346 3.9457 3.9551 3.9628
26 27 28 29 30
31 32 33 34 35
1009.742 1262.177 1577.722 1972.152 2465.190
.00099 .00079 .00063 .00051 .00041
.25025 .25020 .25016 .25013 .25010
3.9960 3.9968 3.9975 3.9980 3.9984
.00025 .00020 .00016 .00012 .00010
4034.968 5044.710 6306.887 7884.609 9856.761
3.9693 3.9746 3.9791 3.9828 3.9858
31 32 33 34 35
330
Appendix
TABLE
A
A.8
Conversion
Factors
Physical quantity Area
Conversion factor
Symbol A
1 ft = 0.0929 m 1 i n = 6.452 x 10" m 1 l b / f t = 16.018 k g / m 1 slug/ft = 515.379 k g / m 1 Btu = 1055.1 J 1 cal = 4.186 J 1 ft l b = 1.3558 J 1 h p / h r = 2.685 x 10 J 1 i b = 4.448 N 1 Btu/hr - 0.2931 W 1 B t u / s e c = 1055.1 W 1 B t u / h / f t = 3.1525 W / m 1 B t u / h / f t / F = 5.678 W / m / K 1 ft = 0.3048 m 1 in. = 2.54 c m 1 mile = 1.6093 km 1 l b = 0.4536 kg 1 slug = 14.594 kg 1 l b / h = 0.000126 k g / s e c 1 l b / s e c = 0.4536 k g / s e c 1 hp = 745.7 W 1 f t / l b / s e c = 1.3558 W 1 B t u / s e c = 1055.1 W 1 B t u / h = 0.293 W 1 l b / i n . = 6894.8 Pa ( N / m ) 1 l b / f t = 47.88 Pa ( N / m ) 1 atm = 101,325 Pa ( N / m ) 1 langley = 41,860 J / m 1 B t u / l b / ° F = 4187 J / k g / K 1 B t u / l b = 2326.0 J / k g 1 c a l / g = 4184 J / k g T(°R) = (9/5)T(K) T(°F) = [T(°C)](9/5) + 32 T(°F) = [T(K) - 273.15](9/5) + 32 1 B t u / h / f t / ° F = 1.731 W / m / K 1 b / ° F / B t u = 1.8958 K / W 1 f t / s e c = 0.3048 m / s e c 1 m i l e / h = 0.44703 m / s e c 1 l b / f t / s e c = 1.488 N / s e c / m 1 c P = 0.00100 N / s e c / m 1 f t / s e c = 0.09029 m / s e c 1 f t / h = 2.581 x 10" m / s e c 1 ft = 0.02832 m 1 i n . = 1.6387 x 1 0 m 1 gal ( U . S . liq.) = 0.003785 m 1 f t / m i n = 0.000472 m / s e c 2
2
2
Density
P
4
2
3
3
m
3
Heat, energy, or work
QorW
3
f
6
Force Heat flow rate
F
Heat flux Heat-transfer coefficient Length
q/A h L
Mass
m
Mass flow rate
m
Q
f
2
2
2
2
m
m
m
Power
W
f
Pressure
P
2
2
f
2
2
f
2
Radiation Specific heat capacity Internal energy or enthalpy
1 c e or h
Temperature
T
Thermal conductivity Thermal resistance Velocity
k
Viscosity, dynamic
p
V
2
m
m
2
m
2
Viscosity, kinematic
V
2
2
2
Volume
V
5
3
2
3
3
5
3
3
Volumetric flow rate
Q
3
3