東京における傾斜面への日射量

551．521
The
Amount of Solar R＆diat董on Fa且且ing on a T量lted
Surfaしce in Tokyo（Lat35041／N），Es】pec董＆lly
inC・mexi・nwiththeOptimumMounting
Angle in the Outdoor We紬ering Test
by
Kl．Sekihara
ハ46」60プologJ6αl R6s（3α70h1％sあ」％」6， 7「o海ツo
（Received May14，1965）
Abstract
Solar and sky radiation falling on a tilted surface in Tokyo was
calculated on the basis of sunshine recording data by use of the formulae
proposed by PAGE．The results were compared with the observed global
radiation and tumed out to be in good agreement．
The efnciency of the radiation collector was discussed as a function
of the sloping angle of the plate．It was concluded that the maximum
emciency is to be obtained by a plate of a slope lower by several degrees
than that of the latitudinal angle itself．The order of magnitude of
that difference proved to be 1％or so．
1．Introduction
The importance of the assessment of solar radiation is pointed out by many
authors from the standpoint of solar energy utilization3s in flat plate collectors and
heating of buildings by solar radiation。The optimum mounting angle of the outdoor
weathering test is another problem in this apPlication especially conceming the effect
of ultraviolet ra（iiation．
So far，the measurement of solar radiation falling on a horizontal surface has
been carried out by means of the EpPly pyranometer，the Mo11−type solarimeter and
the Robitsch actinographs。In our country most observations were done by use of
the Robitsch actinographs until the begiming of the IGY．The calibrations were
chiefly done on the basis of the measurement of direct sun radiation through rather
inadequate assumptions based on BERLAGE’s formulae．On account of this unfortunate
situation the reliability of data before the IGY is open to some criticism，which we
would like to discuss in another paper．
Thanks to the effort of many people in charge of the solar radiation measure−
ment at the Japan Meteorological Agency a new network based on the EpPley pyrano−
meter has been started in the IGY・So the author was able to obtain su伍ciently
accurate data that have been calibrated following the intemational scale．
Conceming the assessment of solar and sky radiation falling on a tilted surface，
1965
Amount of Solar Radiation Falling on a Tilted Surface in Tokyo
39
UcHIDA of Tokyo University has done a pioneering theoretical work an（1SAITo and
others have recently presented comprehensive experimental and theoretical results．
Especially the work of SAITo and others（1964）contains a continuous measurement
of five years and also the assessment of solar radiation from the data of the sunshine
record。Their work is still going on and is expected to yield fruitful results．
But considering from the present status of these problems the author thinks that
the work of PAGE（1961）that was presented at the United Nations Conference at Rome
on Applied Solar，Geothermal and Wind Energy contains the most comprehensive
study on the assessment of solar radiation based on su伍ciently numerous experi−
mental data and also is very convenient because it gives the method of calculation
of solar radiation falling on any desired tilted plane including the reasonable assess−
ment of sky radiation．
So the author decided to make calculations based on PAGE’s work．
2． The metho（［of Page，s calculation （1961）
The essentials of PAGE’s method are composed of five steps，namely，1．assess−
ment of the daily total amomt of solar and sky radiation falling on a horizontal
surface，2．that of（玉iffuse sky ra（1iation 3． separation of （1irect solar radiation， 4．
that of direct solar ra（iiation on a tilte（1surface，5．that of（iiffuse sky1’adiation on
a tilte（1surface．
The process of the lst step is similar to that of Angstr6m’s type based on
the
data of sunshine recor（1er．
Thus the（iaily total amount of solar and sky radiation Q is expressed as follows：
（1）
Q−Q・（α＋6芳）・
Here（20is the daily total amount of solor radiation falling on a horizontal surface
outside the earth’s atmosphere，刎ノ〉is the mean dαily amount of bright sunshine
hours divided by maximum possible ones．
This formula was already used by other authors but Page’s distinction lies in
the determination of the constantsαand6．On the basis of tremendous data of
solar radiation measurement and the simultaneous sunshine records at many stations
from400S to400N he proposes thatα＝0．23andわ＝；0。52are appropriate。
In the second step he proposes as the formula of diffuse sky ra（玉iation the fo1一
lowing：
（2〉
PH−Q（6＋4暑）・・
This parabolical relationship between diffuse sky radiation jDE and global radia−
tion Q is a characteristic of Page’s theory and it seems adequate from many
simultaneous observational results． He determined the constants as C＝1．00and4
＝＝一1．13．
40
K．Sekihara
Vo1．XVI No．1
Now．the component of direct solar radiation is easily・obtainable by simple subtrac−
tion of（2）from（1）．
Then the process of converting the direct horizontal component to any tilted
compo耳ent is a logically simple one of straightforward trigonometric calculation，
although，actually，it consists of very elaborate processes．
In the meantime Page did this calculation and made a table of conversion factors，
so that the author could compute this amomt from graphical interpolations。
Assessment of the contribution of diffuse sky radiation as well as that of ground
reflexion is very di伍cult and remains imperfect because of such unknown factors
as dust scattering an（1cloud reflexion．
At the present stage，however，it seems there is no other way than to assume
a homogeneous isotropic sky radiation applying a simple geometrical consideration
to both of them．The best possible way is to admit some factors for the sky bright−
ness of the solar si（1e to allow for the unbalance of intensity distribution（1ue to㌻he
forward scattering of aeroso1εparticles an（1also the forward reflexion by the cloud．・
Thus the final formula can be written as follows：
（3）
Σ（1＋Z）＋・7）s＝∫sΣ1psinθ＋κCOS2一のH＋sin2一・7E，
2 2
where
Σ（1＋P＋7）s daily total of radiation falling on a tilte（i plane
Σ1psinθ
∫s
daily total of direct sun ra（iiation falling on a horizontal Plane
a factor to be multiplied to a tilted plane
z）E
diffuse sky ra（iiation falling on a horizontal Plane
h
a factor to be multiplie（1 a￠cor（iing as the sky radiation in this
7H
α
context is solar side or antisolar side，taking values between1。2
an（10。8rather arbitrarily
a contribution（lue to groun（1reHexion an（1is expresse（1as7H＝；yQ
where y means albedo of the ground
． an angle of slope of the plane．
3・ Assessment of globa星raαiation at Tokyo（Lat35041！）and the checking of Page，s
formula
Although the formula（1）is checked by PAGE on the basis of data for many
places and periods，they were chie且y for stations in the Westem world．So further、
study is necessary in order to establish its validity in the Asiatic area．And rather
laborious statistical study will be required before we can arrive at a definite con、
clusion．
But・for the present・the principal objective of this paper is to investigate the
inHuence of the angle of slope，so the author is content with a limited examination
based on t瓦e IGY data at Tokyo only（J・MA・，1957，1958，1962）．Consequently the
conclusion here arrived at shol（i be considere（i as a qualitative one．
1965
Amount of Solar Radiation Fa11ing on a Tilted Surf3ce in Tokyo
Table1．
41
Calculated and Observed Values of
Global Radiation at Tokyo during
IGY period。（cal／cm2／day），after eq．
400
（1），and Re｛．」．M．A．（1957，1958）．
監レ
！へ、
ノ、
July Aug．Sept． Oct．
Nov．・ Dec．
ク
6
500
／
1￠／N
＼、
㎞
e
，T
57
．41 ．46 ．21 ．40 ．53 54
Q（cal）
337 429 266 274 247 208
Q（obs）
307 425 289 208 238 199
Q
＼ z
、、ノ
200
e
，T
58
㎞
％／N
ob50rved
Jan．
Feb， Mar． Apr． May June
．62 ．60 ．43 ．41 。47 ．40
Q（ca1）
245 308 327 383 457 444
Q（obs）
236 302 330 381 458 450
e
，T
58
㎞
％／1〉
＿＿＿＿oolc“10書ed
10
oL」一山＿一一＿一
July Aug． Sept． Oct．
Nov． Dec．
．29 ．39 36 ．34 ．38 ．62
Q（ca1）
376 392 329 255 208 224
Q（obs）
362 385 285 246 201 206
789101Il2125456789iO”12
’57 ■58
Mo n量h
Fig．1． Calculated and observed
global radiation at Tokyo
during the period of IGY
（cal／cm2／daジ）．
Table l and Fig。1show the data of sunshine record and the calculated global
radiation as well as the observed one．As can be seen in Fig．1，the general agree−
ment could be said to be satisfactory both in general trend and in absolute values．
4． Radiation falling on a tilte（［plane an（［its emciency
The slope of angle considere（i was15。，250，35。and45。respectively． The
percentage sunshine data were adopted from the Climatic Table published by the
Japan Meteorological Agency．They are the mean monthly values covering1931
through1960．
As to the calculation of PE，isotropic diffuse sky・1ight was assumed without
reference to the various tilting angles of the plate．This is not exactly tme because
it is obvious that the intensity of sky radiation becomes more and more intense as
it becomes nearer to the sun both in clear and cloudy conditions．This problem is
not finally settled，but Page discusses it considerably in（1etai1， conclu（ling that the
difference is very small within the limited angles of slope now in discussion。
Conceming the effect of ground reflection the albedo was taken as O．25，which
is r今asonable in the usual meteorological conditions of this district．
The original data and the details of the process of calculation not contained in
the original paper of PAGE are tabulated in Table2an（1Table3．The final results
are given、in Table4．Here we are interested in the values of relative e伍ciency to
those of the horizontal Plane． They are given in the last column of Table4and
shown in Fig．2．
42
K．Sekihara
Table2。
VoL XVI No．1
Mean monthly amount of daily tota田ux of radiation outside the earth’s
atmosphere（Qo），percentage of smshine record（％／ノv），calculated global
radiation（Q），calculated diffuse radiation（PH），at Tokyo（Lat35041ノ）
（cal／cm2／day）（Calculated by eq．（1）and eq．（2））。
Month
。倒 H
Q％QP
1
2
570
34
234
126
108
445
60
240
94
146
Table3．
Month
45。
350
250
150
3
726
47
341
160
181
4
870
46
409
192
217
5
972
45
447
215
232
6
1010
34
414
224
190
8
7
9 10 11
912
49
438
201
237
990
41
436
218
218
783
37
329
174
155
47
227
107
120
12
408
56
212
87
125
Ratio（∫5）of the mean monthly direct solar radiation falling on an
inclined plane facing to equator as compared to that of horizontal
plane，at Lat35。（Calculated graphically from PAGE’s Table）．
1
2
3
4
5
6
7
8
9
1．96
1．84
1．67
1．44
1．58
1．53
1．45
1．32
1．25
1．25
1．21
1．15
0．97
1．02
1．06
1．05
0．80
0．89
0．94
0．98
0。73
0．83
0．91
0．96
0．75
0．84
0．92
0．97
0．88
0．91
1．00
1．02
1．11
1．13
1．13
1．10
Table4．
622
39
267
136
131
484
10 11
1．44
1．42
1．34
1．26
1．81
1．72
1．58
1．39
12
2．05
1．91
1．71
1．48
Calculated shortwave radiation falling on an inclined plane at Lat35。，
by eq．（3）using mean sunshine record at Tokyo，（cal／cm2／day）．
Month
Angle of
inClinatiOn
450
350
250
150
1 2 3 4 5
376
359
337
303
240
00
287
284
280
267
234
376
379
375
366
341
388
404
417
418
409
385
411
428
441
447
6
346
370
391
404
414
7 8 9 10 11
367
391
414
428
436
397
408
433
441
438
331
341
345
343
329
315
315
308
299
267
316
308
295
273
227
12 Sum Ratio
338
322
299
271
212
4221
4292
4322
4254
3993
1．057
1．074
1．082
1．065
1．000
［
Here it is noticeable that the maximum
e伍ciency is attained at aboutα＝250，namely
ΦLO
》
the slope lower by ten degrees than the latitude
xコ
ロ
葬
of Tokyo（L．35。41！）．
室
o
‘
の
Also in this figure we can notice that the
◎
order of magnitude of the gain of e伍ciency
あ
ゆ
・器
is about several per cent and the d迂ferellce be−
至0・
‡
囮
tweenα＝250and35Q is about1％or so．
o
）
o
o
In the mean time it is clear thatα＝450
that was conventionally adopted in case of the
肛
weathering test of natural exposure is not
loo 200 30ρ 400 500
TII甑gA剛3ρく
Fig．
2．
E伍ciency of nat plate solar
collector with varying
energy
angle of slope（facing to equater）。
adequate in our low Iatitudes．
1965
Amount of Solar Radiation Falling on a Tilted Surface in Tokyo
is easy to see．The gain of solar
radiation in the summer season
will be large as compared with
the loss in the winter season．
G．C．NEwLAND and others（1963）．
Now the details will be more
clearly understood in Fig．3where
the three（iifferent components of
calculated values are drawn re．
spectively whenα＝25。andα＝350．
We can see the above−men．
tioned gain in the summer season
that the contribution of diffuse
also is accelerating that tendency．
The contribution of reflected radi．
ation from the ground is small
and can be neglected．
Nowwemaysafelyconclude
that both in the flat plate collector
of solar energy and in case of the
〆！＼／！、
！￥／、
！、、／、
！
、
、
N
x
＼、
、 ’
、》の一
、 DlrecセSun
へ
、ハ￥！、
＼ r＼＿／、、
、 7 ！、× 、
！
／
覧 7 ！￥、
、ノ／、／＼、
！
、 γ ！！￥！￥
、ノ〆 V ￥￥一ノ
1
ノ
、ノノ￥
ノヤ
∠ ￥￥
！ Diffuse S財y ￥
！
ノ
∠
！
！
＼
！
￥
／
￥、
sky light is rather large and it
！へ／、
、
ation． But it will be noticeable
T。奮d （一一一一雄25・
￥＼
in the curve of （iirect sun radi．
αz350
ト＼
This was already mentioned by
C O ︵︵
of α＝；350 in the curve of Fig．2
O O ， O O
emciency apPears atα＝二25。instead
器oεおので窪＝〇三5宅〇三〇三5＝oモσ艦⑪︶o雪t2のもx三し琶oΣあ三芒oΣ
The reason whythemaximum
むミ監o＼一g︾4 3 2 ー
5． Concluaing remarks
43
桑
Ground RefreC†ed
一一一一一一一一一一一眉一一一一一一一一
123 56789101112
断o轟愉
Fig．3． Components of short wave radiation
weathering test of natural ex−
falling on vary量ng 量nclined surfaces at
Tokyo（Lat。35041ノ）．
posure，the maximum e伍ciency
α： angle of slope of the surface．
will be obtained by the surface
of a slope slightly lower，probably between5。and10。，thanthe angle of the latitude
concerned．
R⑳矧z66s
Japan Meteorological Agency，1957，1958：Report of radiation observation。
Japan Meteorological Agency，1962＝Monthly mean values at varying stations，Climatic table
of Japan，No．2．
NEw黙D G．C，，SGRLEN R。M。and TA凹B聰R J．W．，1963：0ptimum mounting angle for outdoor
weathe血g of plastics，Materials Research＆Standards（June）。
PAGE，」．K．，1961：The estimation of monthly mean v＆1ues of daily total shortwave radiation
on vertical and inclined surfaces from sunshine records for latitu（ies40。north400
south，Paper、presented to the United Nations Conference on new sources of energy
at Rome，10May1961．Agenda Item III，A．
44
VoL XVI No．1
K．Sekihara
SAITo，H．，MATsuo，Y．and OcEIFuJI，：K．，1964：』On the solar−radiation and its issue of the
application to engineering use，Joum。S．H。A。S。E．，38、4，260−279．
東京における傾斜面への日射量
関原
彊
東京における月別平均日射量1日積算値をPA伽の提出した経験式により日照率のデータを用いて計算
した。水平面日射量の計算値はIGYの期間についての実測値と，非常によい一致を示し，この方法が有効
であることを示している。
傾斜面については赤道方向にむかい450，35。，25。，15。の各傾斜角の面への日射量を計算した。その
結果日射量受熱の効率としては，緯度350の東京における最有効傾斜角は250附近にあり，その効率の
得は1％程度であることが判つた。
この原因は夏季における受熱量の得が冬季における損失を上廻つているためであるとして説明される。

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