C.S.T.B. solar diagrams

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C.S.T.B. solar diagrams

December

1964

A R C H C O U N C I L O T T A W A C A N A D A

C

.

S

.

T

.

B

.

SOLAR DIAGRAMS by

C. S. T . B . SOLAR DIAGRAMS

by

D. G . Stephenson

Knowledge of the a p p a r e n t position of the sun a t different t i m e s and d a t e s i s e s s e n t i a l f o r the design of shading s y s t e m s and the d e t e r m i n a t i o n of heat gain through windows. T a b l e s of s o l a r altitude and a z i m u t h a n g l e s a r e available ( 1 , 2), but they a r e l e s s convenient f o r m a n y p u r p o s e s than a g r a p h i c a l p r e s e n t a t i o n of the s a m e d a t a .

N e a r l y a l l the s o l a r c h a r t s o r g r a p h s t h a t have been published a r e in p o l a r f o r m , i. e . a v e c t o r gives s o l a r a z i m u t h by i t s d i r e c t i o n and altitude by i t s length. Some c h a r t s make the length d i r e c t l y proportional t o the altitude angle and o t h e r s make the length proportional t o t h e cotangent of the altitude angle. The D i a g r a m m e s S o l a i r e s p r e p a r e d

by

the C e n t r e Scientifique e t Technique du Bgtiment in F r a n c e a r e of t h i s l a t t e r type. E a c h c h a r t p r e s e n t s the s o l a r position d a t a f o r a l l t i m e s and d a t e s f o r one specific latitude.

The C . S. T . B. c h a r t s can be thought of a s the d i a l f o r a horizontal sun clock t h a t h a s a gnomon of length d standing v e r t i c a l l y a t the p r i n c i p a l point 0 . F i g u r e 1 i s a h a l f - s c a l e reproduction of the c h a r t f o r a latitude of 48 d e g r e e s . As a s u n - c l o c k d i a l the c h a r t h a s to be o r i e n t e d s o t h a t the

X Y

line i s exactly n o r t h and south, with the X a r r o w pointing toward the e q u a t o r . T h e shadow of the point of the gnomon m o v e s along a path like t h o s e labelled Courbe A t o G. T h e s e a r e the shadow paths f o r different d a t e s ; a t n o r t h l a t i t u d e s A is f o r 21 J u n e , B f o r 21 May and 21 J u l y and s o on t o G , which i s f o r 21 D e c e m b e r . T h e s e c u r v e s a r e r e f e r r e d to a s the d a t e l i n e s . The s t r a i g h t l i n e s that i n t e r s e c t the d a t e l i n e s go through points on t h e m w h e r e the shadow of the t i p of the gnomon would be a t a p a r t i c u l a r t i m e of day. F o r e x a m p l e , the i n t e r s e c t i o n of the line m a r k e d 10 with the c u r v e A i n d i c a t e s the position of the shadow t i p a t 1 0 a . m . on 21 June. T h e slightly d a r k e r l i n e s a r e f o r the h o u r s indicated by t h e n u m b e r s adjacent t o t h e m and the l i g h t e r l i v e s a r e f o r e v e r y 1 0 m i n u t e s between the h o u r s .

Whenever t i m e is mentioned in t h i s note, l o c a l a p p a r e n t t i m e ( L . A. T . )

i s m e a n t . T h i s i s the t i m e indicated by the shadow on a sun dial. It can d i f f e r f r o m s t a n d a r d t i m e by a l m o s t a n hour f o r p l a c e s n e a r the boundaries between t i m e zones. The c o r r e c t i o n of s t a n d a r d t i m e t o L . A . T . i s d e s c r i b e d in BRN 47.

The C . S . T . B . h a s published, in English a s well a s in F r e n c h , a c o n c i ~ l _ note on the m a i n u s e s of t h e i r c h a r t s , but t h e r e a r e two applications

n u t :zlc~ tioned. Both d e r i v e f r o m the cotangent type of plot used in the c h a r t s and r e p r e s e n t p a r t of the advantage of t h i s type of c h a r t o v e r the d i r e c t altitude -

.

-

- 2 - b r o c h u r e by giving additional u s e s . Positioning a Model

The shadows c a s t by shading devices o r by one p a r t of a building -

onto another can be d e t e r m i n e d quite e a s i l y by using a model. It i s only n e c e s s a r y to position it in relation t o a b e a m of light In the s a m e way a s the r e a l building will s i t with r e s p e c t to the sun. One method of positioning a model is by using a heliodon QBRN 47), but the C . S. T

.

B . c h a r t s can a l s o be used f o r t h i s purpose.

The model i s attached t o a drawing board and the C , S. T . B . c h a r t f o r the a p p r o p r i a t e latitude placed beside it on the board. The c h a r t and model a r e s o a r r a n g e d that the building h a s the c o r r e c t orientation r e l a t i v e t o the North-South a x i s of the c h a r t . A s m a l l cone of height equal t o the distance d shown on the c h a r t is located with its apex d i r e c t l y above t h e principal point 0 of the c h a r t . If the model and the c h a r t a r e s e t in d i r e c t sunshine ( o r illuminated by any other p a r a l l e l b e a m of light), t h e point of the shadow c a s t by the cone indicates the t i m e and date when that p a r t i c u l a r shadow p a t t e r n will o c c u r . Alternatively, i f the shadows a r e t o be found f o r any specified t i m e and d a t e , it is only n e c e s s a r y t o move the drawing board s o a s t o make the point of the -shadow coincide with the i n t e r s e c t i o n of the p a r t i c u l a r t i m e and date l i n e s .

The shadows on and around the model a r e then a s they would be f o r the r e a l building a t that p a r t i c u l a r t i m e and d a t e .

Constructinp: Horizontal and Vertical Shadow Angles

It is often n e c e s s a r y t o d e t e r m i n e the position of shadows when t h e r e

is no model available. T h i s can be done quite r e a d i l y using plan and elevation drawings i f t h e horizontal and v e r t i c a l shadow angles a r e available. The H. S. A. is the angle on a plan drawing between a line perpendicular t o the wall and

t h e projection of the s u n ' s r a y s on the horizontal plane. S i m i l a r l y , the V. S. A . i s the angle, on a v e r t i c a l section drawing of the wall, between a line perpendicular t o t h e wall and the projection of the s u n v s r a y s on the plane of the drawing.

The H. S. A. and V. S. A. can be obtained by a simple construction

on a sheet of t r a c i n g p a p e r laid over the C . S. T . B. c h a r t f o r the p a r t i c u l a r latitude. F i g u r e 2 shows a n example. The f i r s t s t e p is t o d r a w , through point 0 a s t r a i g h t line with the s a m e a z i m u t h as the wall in question. This i s the "wall liner1. F o r t h i s application the a r r o w ,

X ,

points to the t r u e North and the wall line will cut the angle s c a l e around the p e r i m e t e r of the c h a r t a t the wall azimuth angle. Then the point P i s located a t the intersection of the t i m e and date l i n e s on the underlying c h a r t corresponding t o the t i m e and d a t e f o r which the shadow angles a r e r e q u i r e d . A line i s drawn f r o m P perpendicular to the wall l i n e , cutting it a t Q. A line i s a l s o drawn f r o m P through 0 and the angle OPQ i s the horizontal shadow angle.

R

i s located on the wall line s o that the distance f r o m Q t o R i s equal t o the length of t h e line labelled "Distance d" on the upper p a r t of the c h a r t . The angle Q P R i s the v e r t i c a l shadow angle.

-

3 -

Finding the P o s i t i o n of Shadows on V e r t i c a l Walls

The boundaries of the shadows on a wall, whether f r o m a shading

device O F a n adjacent object, can be found by projecting the outline of the shading

object on the wall, t h e l i n e s of projection being p a r a l l e l t o the s u n ' s r a y s . The shadow angle d i a g r a m obtained by the method d e s c r i b e d above can b e used t o find the s o l a r projection of a point on the wall. T h e p r o c e d u r e i s shown i n F i g u r e 3 .

Z i s the s h o r t e s t distance f r o m the point A t o the wall, i . e .

,

A B i s perpendicular to the plane of the wall. T h e s o l a r projection of point A i s a t D, which i s a

d i s t a n c e X m e a s u r e d horizontally and Y m e a s u r e d v e r t i c a l l y f r o m B. The d i s t a n c e s X and Y a r e r e l a t e d to the d i s t a n c e Z and the shadow angles by the e x p r e s s i o n s

X = Z x tangent H. S.A.

Y

= Z x tangent V.S.A.

The angle d i a g r a m i n the lower p a r t of F i g u r e 3 shows how X and Y can be d e t e r m i n e d d i r e c t l y . The d i s t a n c e Z i s laid off f r o m P along PQ and

X

and Y m e a s u r e d a s shown.

Insolation on a V e r t i c a l Surface

The insolation (i. e . incident s o l a r e n e r g y ) , both d i r e c t and diffuse, on a n y wall can be found by using one of the o v e r l a y c h a r t s in conjunction with the a p p r o p r i a t e s o l a r d i a g r a m . The values indicated on the o v e r l a y s h e e t s a r e in w a t t s / s q m e t r e ; t h e s e c a n be converted t o ~ t u / f t ~ h r by multiplying t h e m by 0.317.

The o v e r l a y s h e e t s No. 4 , 5 and

.b

a r e based on the F r e n c h s t a n d a r d f o r insolation, which i s slightly l e s s f o r any given condition than the s t a n d a r d u s e d in the United S t a t e s . The insolation on walls facing North, E a s t , South and West h a s been m e a s u r e d a t Ottawa f o r about t h r e e y e a r s , and t h e s e r e c o r d s show that the insolation frequently e x c e e d s the values indicated by both the

A m e r i c a n and F r e n c h s t a n d a r d s . On a v e r y c l e a r d a y i t can exceed the values in the c h a r t s by about 25 p e r cent when t h e r e i s n o snow on the ground. (In w i n t e r , the radiation r e f l e c t e d f r o m a snow s u r f a c e can i n c r e a s e the radiation falling on a wall by a f u r t h e r 25 p e r cent. ) When m o r e d a t a a r e available, it will be possible t o p r e p a r e a l t e r n a t i v e o v e r l a y c h a r t s a p p r o p r i a t e f o r Canada. In the m e a n t i m e , the F r e n c h D i a g r a m m e s

-

d e P u i s s a n c e can be u s e d t o e s t i m a t e the insolation that c a n be expected on a typical cloudless day..

Angle of Incidence

The angle of incidence of the s o l a r b e a m on any f l a t s u r f a c e i s defined a s the angle between the s o l a r b e a m and a line perpendicular t o the

s u r f a c e . The angle of incidence a t a v e r t i c a l s u r f a c e facing in any d i r e c t i o n c a n be found by using o v e r l a y No. 3 i n conjunction with the s o l a r d i a g r a m f o r the a p p r o p r i a t e latitude. (It cannot be u s e d with the c h a r t s f o r latitudes

g r e a t e r than 52 d e g r e e s because the d i s t a n c e d i s different f o r the high latitude c h a r t s . )

- - - - .- 7 .

- 4 -

Overlay No. 3 is laid on the s o l a r d i a g r a m with i t s principal point d i r e c t l y over the principal point of the c h a r t , and with the b a s e line acting a s the wall line. The incident angle, f o r any t i m e and date r e p r e s e n t e d by a point

P on the s o l a r d i a g r a m can be obtained by estimating the co-ordinate of P

F

relative t o the curved co-ordinate l i n e s on the overlay. The angles m a r k e d on the c h a r t a r e the complements of the incident angles; f o r example, if P i s under the curved line m a r k e d 70 deg, the angle of incidence i s 90-70, o r 20 d e g r e e s .

References:

1. Brown, G.

,

and T . Tuominen. S o l a r Position a t Various Hours, Dates and Latitudes

-

T a b l e s . Rapport 7 5 Byggforskningen, Stockholm, 1962.

2 .

U.

S. Navy Hydrographic Office. T a b l e s of Computed Altitude and Azimuth. Publication 2 14.

F I G U R E 2