FINAL DRAFT UGANDA 
STANDARD  
  FDUS 858
First Edition
2009-mm-dd
 
Reference numbe r
FDUS 858: 2009
 ©UNBS 2009 
  
Method of test for exposure of solar collector cover 
materials to natural weathering under conditions simulating stagnation mode  
 FDUS 858: 2009 
ii © UNBS 2009 – All rights reserved
 Compliance with this standard does not, of itself confer immunity from legal obligations 
A Uganda Standard does not purport to include all necessary provisions of a contract. Users are 
responsible for its correct application  
© UNBS  2009  
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilised in any 
form or by any means, electronic or mechanical, in cluding photocopying and microfilm, without prior written 
permission from UNBS. 
Requests for permission to reproduce this document should be addressed to 
The Executive Director 
Uganda National Bureau of Standards 
P.O. Box 6329 
Kampala  
Uganda 
Tel: 256 41 4505 995 
Fax: 256 41 4286 123 
E-mail: unbs@infocom.co.ug 
Web: www.unbs.go.ug FDUS 858: 2009 
©  UNBS 2009 – All rights reserved iii
 Contents  
Foreword………………………………………………………………………………………………..…………iv 
1   Scope ....................................................................................................................................................1  
2   Normative references ..........................................................................................................................1  
3    Definitions ............................................................................................................................................1  
4    Significance and use ...........................................................................................................................2  
5    Weathering box test fixture ...............................................................................................................2  
5.1    Test fixture requirements ...................................................................................................................2  
5.2   Contents of the weathering box test fixture ......................................................................................4  
5.3    Test specimen ......................................................................................................................................5  
5.4    Sample mounting ............................................................................................................................... .6 
5.5    Assembly of weathering box ..............................................................................................................6  
6    Natural weathering exposure .............................................................................................................6  
7    Report ...................................................................................................................................................7  
8    Precision and bias ............................................................................................................................... 8
Annex A (informative) Calculation of exposure test fixture heat losses ......................................................9  
Annex B (informative) Determination of variable-angle exposure schedule ...............................................9  
 
 FDUS 858: 2009 
iv © UNBS 2009 – All rights reserved
 Foreword 
Uganda National Bureau of Standards (UNBS) is a parastatal under the Ministry  of Tourism, Trade and 
Industry established under Cap 323, of the Laws of Uganda.  UNBS is mandated to co-ordinate the 
elaboration of standards and is  
(a) a member of International Organisation for Standardisation (ISO) and  
(b) a contact point for the WHO/FAO Codex A limentarius Commission on Food Standards, and  
(c) the National Enquiry Point on TBT/SPS Agr eements of the World Trade Organisation (WTO). 
The work of preparing Uganda Standards is carried out through Technical Committees. A Technical 
Committee is established to deliberate on standards in a gi ven field or area and consists of representatives of 
consumers, traders, academician s, manufacturers, governme nt and other stakeholders. 
Draft Uganda Standards adopted by the Technical Committ ee are widely circulated to stakeholders and the 
general public for comments. The committee reviews the comments before recommending the draft standards 
for approval and declaration as Uganda Standards by the National Standards Council.  
Committee membership 
The following organisations were represented on su bcommittee on Solar Energy, SC 3 under the Energy 
management standards Technical Committee, UNBS/ TC 13 in the development of this standard: 
• Battery Masters (U) Limited 
• Equator-sun (U) Limited 
• Incafex Solar Systems 
• Makerere University 
• Renewable Energy Department, Minist ry of Energy and Mineral Development 
• Solar Masters 
• Sonnerkraft Solar Systems 
• Uganda Institute of Professional Engineers 
• Uganda National Bureau of Standards 
• Uganda National Plumbers Association 
• Ultratec (U) Limited 
 
 FINAL DRAFT UGANDA STANDARD FDUS 858: 2009
 
© UNBS 2009 – All rights reserved  1
 Method of test for e xposure of solar collector cover materials 
to natural weathering under conditions simulating stagnation 
mode  
1 Scope 
1.1 This practice covers a procedure for the exposure of solar collector cover materials to the natural 
weather environment at elevated temper atures that approximate stagnation conditions in solar collectors 
having a combined back and edge loss coefficient of less than 1.5 W/(m2 • °C). 
1.2 This practice is suitable for exposure of both glass and  plastic solar collector cover materials. Provisions 
are made for exposure of single and double cover asse mblies to accommodate the need for exposure of both 
inner and outer solar collector cover materials. 
1.3 This practice does not apply to cover materials for evacuated collectors, photovoltaic cells, flat-plate 
collectors having a combined back and edge loss coefficient greater than 1.5 W/(m2 • °C), or flat-plate 
collectors whose design incorporates means fo r limiting temperatures during stagnation. 
2 Normative references 
The following referenced documents are indispensable for the application of this standard. For dated 
references, only the edition cited applies. For undated references, the latest edition of the referenced 
document (including any amendments) applies. 
FDUS 859, Standard practice for exposure of cover materials for solar collectors to natural weathering under 
conditions simulating operational mode 
FDUS 861, Method of test for evaluating absorptive solar receiver materials when exposed to conditions 
simulating stagnation in solar collectors with cover plates 
ISO 291, Plastics — Standard atmospheres for conditioning and testing 
ISO 4665, Rubber, vulcanized or thermoplastic — Resistance to weathering 
ISO 16871, Plastics piping and ducting systems — Plastics pipes and fittings — Method for exposure to direct 
(natural) weathering  
FDUS ISO 9488, Solar energy — Vocabulary 
3 Definitions 
For the purposes of this Uganda Standard, the definitions given in FDUS ISO 9488 shall apply. FDUS 858: 2009 
2 © UNBS 2009 – All rights reserved
 4 Significance and use 
4.1 This practice describes a weathering box test fixture and establishes limits for t he heat loss coefficients. 
Uniform exposure guidelines are provided to minimize  the variables encountered during outdoor exposure 
testing. 
4.2 Since the combination of elevated temperature and solar radiation may cause some solar collector 
cover materials to degrade more rapidly than either exposure alone, a weathering box that elevates the 
temperature of the cover materials is used. 
4.3 This practice may be used to assist in the evaluation of solar collector cover materials in the stagnation 
mode. No single temperature or procedure can duplicate the range of temperatures and environmental 
conditions to which cover materials may be exposed durin g stagnation conditions. To assist in evaluation of 
solar collector cover materials in the operational mode,  FDUS 859 should be used. Insufficient data exist to 
obtain exact correlation between the behavior of materials exposed in accordance with this practice and actual 
in-service performance. 
4.4 This practice may also be useful in comparing the performance of different materials at one site or the 
performance of the same material at different sites, or both. 
4.5 Means of evaluating the effects of weathering are provided in FDUS 859,  and in other test methods that 
evaluate material properties. 
4.6 Exposures of the type described in this practice may be used to evaluat e the stability of solar collector 
cover materials when exposed outdoors to the varied infl uences that comprise weather. Exposure conditions 
are complex and changeable. Important factors are material  temperature, climate, time of year, presence of 
industrial pollution, etc. Generally, because it is difficu lt to define or measure precisely the factors influencing 
degradation due to weathering, results of  outdoor exposure tests must be taken as indicative only. Repeated 
exposure testing at different seasons over a period of more than one year is required to confirm exposure 
tests at any one location. Control samples must always  be used in weathering tests for comparative analysis. 
5 Weathering box test fixture 
5.1 Test fixture requirements 
5.1.1 The weathering box test fixture shall be cons tructed such that the combined back and edge loss 
coefficient is less than 1.5 W/(m2.°C) (see Note below). The method for determining this coefficient is outlined 
in Annex A of this practice. The distance between the absorber and the closest cover plate shall be between 
13 mm and 38 mm. For a double-cover exposure the separa tion between the inner and outer cover shall be 
between 13 mm and 38 mm. Not more than 10 % of the abs orber plate area shall be shaded when the sun is 
at a 30° angle with the plane of the front surface of the exposure box. 
NOTE A good flat-plate solar collector has a combined back and edge loss coefficient of less than about 1.5 
W/(m2.°C). 
5.1.2 Boxes that meet the requirements of 5.1.1 are described in Table 1. Figure 1 and Figure 2 illustrate 
the weathering box test fixtures. Although Figure 1 shows a square box, any shape is permitted if the 
requirements in 5.1.1 are met. Annex A of this standar d describes the method for determining the combined 
back and edge loss coefficient. FDUS 858: 2009 
© UNBS 2009 – All rights reserved  3
 Table 1 — Examples of weathering box test fixtures with combined heat loss coefficient for back and 
edge losses less than 1.5 W/(m2.°C) 
 Example 1 Example 2 
Box material steel aluminum 
Insulation material glass fiber glass fiber 
l, length of aperture inside edge insulation 0.25 m 0.61 m 
W, width of aperture inside edge insulation 0.13 m 0.61 m 
h, distance from top of absorber to bottom of cover plate 0.013 m 0.038 m 
Aa, area of aperture of test fixture A a = (l x W) 0.033 m20.372 m2
Ab, area of back insulation Ab = (l x W) 0.033 m20.372 m2
Ae, area of edge insulation Ae = 2(l x W)h 0.01 m20.093 m2
db, thickness of back insulation 0.077 m 0.05 m 
dc, thickness of box 0.001 m 0.002 m 
de, thickness of edge insulation 0.013 m 0.025 m 
Kb, conductivity of back insulation 0.038 W/(m.oC) 0.038 W/(m.oC) 
Kc, conductivity of box 43 W/(m.oC) 204 W/(m.oC) 
Ke, conductivity of edge insulation 0.038 W/(m.oC) 0.038 W/(m.oC) 
Ab/Aa 1 1 
Ae/Aa 0.305 0.25 
db/Kb 2.03 m2.oC/W 1.32 m2.oC/W 
dc/Kc 2.33  10-5 m2.oC/W 9.83   10-6 m2.oC/W 
de/Ke 0.342 m2.oC/W 0.658 m2.oC/W 
UL, back = UL, edge 1.38 W/(m2.oC) 1.14 W/(m2.oC) 
 
 
Figure 1 – Top view of weathering box test fixture 
 
 FDUS 858: 2009 
4 © UNBS 2009 – All rights reserved
 
 
Figure 2 – Assembled weathering box test fixture 
5.2 Contents of the weathering box test fixture 
5.2.1  These include: 
a) box,  
b) insulation,  
c) absorber,  
d) box top 
e) spacer  
f) glazing frame, and  
g) adhesive tapes. 
5.2.2 The box may have any dimensions and be made of any material as long as the requirements in 5.1.1 
are met. A weep hole shall be drilled at the lower end of the bottom of the box to provide drainage and to 
minimize moisture accumulation. FDUS 858: 2009 
© UNBS 2009 – All rights reserved  5
 NOTE It is desirable that the box and box top be made of a material that will be unaffected by the exposure 
environment. A metal resistant to corrosion encountered in the environment would be suitable. If wood is used, it should 
be painted or treated on the exterior to ma ke it resistant to moisture . In certain climates only rot-resistant wood should be 
used to minimize deterioration during exposure . 
5.2.3 The insulation shall be a material suitable for use at a high temperature (for example, 150 °C). 
NOTE Insulation materials having resins or binders shoul d not be used because elevat ed temperatures may cause 
the resin or binder to deteriorate and outgas. Outgassing pr oducts condense on the cover material causing changes in the 
solar transmittance of the solar collector cover material. 
5.2.4 The absorber shall be of an adequate size to cove r the interior surface of the weathering box 
aperture. The absorber shall have a flat black nonselect ive coating having an absorpt ance not less than 0.90 
after exposure. 
5.2.5 The box top shall be of an adequate size to fit over the box. 
NOTE 4 The box top is intended to protect the edges of the test specimen in contact with the box from reaching 
excessively high temperatures, to minimize exposure of the adhesive tape to sunlight, and to minimize moisture 
penetration into the exposure test fixture. 
5.2.6 The glazing frame is intended to hold the cover plate material. The glazing frame shall have 
dimensions similar to the perimeter of the box. For a double-cover exposure the frame shall provide a 
separation between the two cover plates of not less than 13 mm or greater than 38 mm. Exact dimensions of 
the frame are related to the require ments in 5.1.1. A vent hole may be drilled at one end of the glazing frame 
to provide drainage and to minimize moisture accumulation. 
5.2.7 The spacer shall provide a separation of 13 mm to 38 mm between the absorber and the closest 
cover plate. Exact dimensions of the spacer  are related to the requirements in 5.1.1. 
NOTE Certain designs of weathering boxes may eliminate the need for the spacer. 
5.2.8 The adhesive tapes shall be stable when exposed to moisture and elevated temperatures. They shall 
be compatible with the specific materials from which the box, glazing frame, box top, and cover plate are made. 
5.2.9 Organic materials are potential sources of outgassi ng and shall be eliminated from the interior of the 
weathering box where possible. For example, metallic pa rts shall be cleaned to remove traces of grease or 
other foreign matter. Other possible sources of out gassing include coatings an d sealants. Test fixture 
components containing organic materials (for example, absorber coatings or  insulation) shall be heated in an 
oven at 150 °C for 24 h before the test fixture is asse mbled. This should minimize outgassing that result from 
deterioration of the organic components exposed to elevated temperatures . 
5.3 Test specimen 
5.3.1 The test specimen shall be of an adequate size to co ver the aperture of the box or glazing frame and 
to permit suitable attachment. 
NOTE Adequate allowances should be made for mate rials that will undergo dimensional changes due to 
temperature. 
5.3.2 The test specimen identification marks shall not interf ere with either the exposure or the subsequent 
testing. FDUS 858: 2009 
6 © UNBS 2009 – All rights reserved
 5.4 Sample mounting 
5.4.1 Rigid and semi-rigid glazings 
5.4.1.1 Lay the test specimen for single cover exposure directly on either the spacer or the glazing 
frames. If used, the frame is then placed on the spacer in the weathering box (see Figure 2). 
5.4.1.2 Lay the test specimen for inner cover exposur e of a double cover assembly on the spacer or 
attach it to the glazing frame before the glaz ing frame is placed in the box (see Figure 2). 
5.4.1.3 Lay the test specimen for outer cover exposur e of a double cover assembly on the top of the 
glazing frame (see Figure 2). 
5.4.2 Films 
Place film test specimens on the glazing frame using adhesive transfer tape to hold the test specimen taut. It 
is essential that uniform tensioning be obtained prior to applying the tape. Then place the frame in the box 
similar to 5.4.1.1, 5.4.1.2, and 5.4.1.3. 
5.5 Assembly of weathering box 
5.5.1 Slide the various parts of the weat hering box test fixture into position. The outer glazing must be 
roughly flush with the top side of the box. The position of an inner glazing, if used, shall be nearest the bottom 
of the box. 
5.5.2 After assembly, seal the frame and outer glazing in  place with an adhesive tape to prevent moisture 
intrusion. Place the box top on the box (see Figure 2). 
6 Natural weathering exposure 
6.1 Mount the weathering boxes in a backed condition us ing 13-mm exterior grade plywood on weathering 
racks. The racks shall be capable of having the angles  adjusted and have their axis of rotation on an east-
west line. 
6.2 Use a variable angle exposure to maximize solar ra diation incident upon the weathering box. Adjust the 
racks according to the schedule given in Table 2. Positive rack angles face south. Choose the angles so that the weathering boxes are never clos er to the horizontal than by 5° . Other variable exposure schedules 
requiring more than four adjustments per year ma y be used. The method for determining the variable angle 
exposure schedule is described in Annex B of this practice. 
Table 2 — Variable-angle rack adjustment schedule using four changes per year A,B
Calendar  period  
Dates Days of year 
Latitude  ± 2.5 3/2 to 4/11 61 to 101 
(Latitude – 16) ± 2.5 4/12 to 8/31 102 to 243 
Latitude ± 2.5 9/1 to 10/10 244 to 283 
(Latitude + 16) ± 2.5 10/11 to 3/1 284 to 60 
A This exposure schedule may be used in both northern and southern hemispheres. The latitude in the southern hemisphere is negat ive. 
Positive rack angles face south. 
B The incident angle of beam radiation ( ө) at solar noon for a south-facing collector is ≤ 8o. 
 FDUS 858: 2009 
© UNBS 2009 – All rights reserved  7
 6.3 When a number of weathering boxes are exposed simultaneously, mount the boxes side by side with 
the sides not touching. 
6.4 Do not clean the solar collector cover materials during exposure. 
6.5 Visually inspect the test specimens at intervals of  not more than one month. Record all changes in 
appearance. 
7 Report 
7.1 The report shall include the following: 
a) description of the weathering box test fixtur e and its calculated combined back and edge loss 
coefficient;; 
b) whether the solar collector cover materials are exposed as a single- or double-cover configuration and 
whether the test specimen was the inner or outer cover; 
c) complete identification of the solar collector outer cover material(s); 
d) complete identification of the solar collector inner cover material(s) (if any); 
e) description of the test specimen attachment and mounting procedures; 
f) latitude, longitude, altitude, and address of the test ing site including a description of the type of 
climate;; 
g) exposure data: 
i) calendar dates of exposure; and 
ii) variable-angle rack adjustment schedule; 
h) climatological data: 
i) radiant energy (J/m2) measured in the plane of the weathering boxes; and 
ii) monthly maximum, minimum, and mean temperatures; 
i) summary of the changes observed in the periodic visual inspections; 
j) Description of control specimens, and 
k) Any deviation from this practice. 
7.2 Other data that are desirable to report, if available are: 
a) optional climatological data: 
i) daily maximum, minimum, and mean percent relative humidity; 
ii) daily hours of wetness; 
iii) daily total inches of rainfall; 
iv) daily maximum and minimum ambient temperature; FDUS 858: 2009 
8 © UNBS 2009 – All rights reserved
 v) daily radiant energy; and 
vi) wind direction and velocity. 
b) type of atmosphere, for example, indu strial, and level of air pollutants, 
c) ultraviolet radiation, and 
d) maximum absorber plate temperature. 
8 Precision and bias 
No information is presented about either  the precision or bias of this test method, since the test result is non-
quantitative. 
 
 
 
 
 
 
 
 
 
 
 
 FDUS 858: 2009 
© UNBS 2009 – All rights reserved  9
 Annex A 
(normative) 
 
Calculation of exposure test fixture heat losses 
A.1 Scope 
This annex outlines the method for determining the comb ined back and edge loss coefficient for an exposure 
test fixture as referenced in 4.1.1 of this practice. 
A.2 Procedure 
A.2.1 Assumptions 
A.2.1.1 One-dimensional heat transfer (neglect corner effects) 
A.2.1.2 The temperature of the outside surface of t he box is equal to the ambient temperature 
A.2.1.3 The temperature of the inside surface of the edge insulation is equal to the absorber plate 
temperature. (A conservative assumption; the insi de edge temperature would average less than the absorber 
plate temperature). 
A.2.2 Symbols 
Q loss, total   total heat loss of test fixture 
Q loss, back   heat loss of back of test fixture 
Q loss, top    heat loss of top of test fixture 
Q loss, edge   heat loss from the edges of test fixture 
UL    combined loss coefficient of back, edge, and top of test fixture 
UL, B   loss coefficient of back of test fixture 
UL, E   loss coefficient of edges of test fixture 
UL, T   loss coefficient of top of test fixture 
h    distance from top of absorber to bottom of cover plate 
l    length of aperture inside edge insulation 
w    width of aperture inside edge insulation 
Aa    area of aperture of test fixture 
Ab    area of back insulation ( Ab = l × w) 
Ae    area of edge insulation ( Ae = 2(l + w)h) FDUS 858: 2009 
10 © UNBS 2009 – All rights reserved
 db    thickness of back insulation 
de    thickness of edge insulation 
de   thickness of box 
Kb    thermal conductivity of back insulation 
Ke   thermal conductivity of edge insulation 
Kc    thermal conductivity of box 
Tp    temperature of absorber plate 
Ta    temperature of ambient air 
Tc    temperature of box 
A.2.3 Heat loss coefficient calculations 
A.2.3.1 General equations 
Qloss, total   =  Q loss, back  + Q loss, edge  + Q loss, top ,             ( A . 1 )  
or 
AaUL(Tp – Ta) = AaUL,B(Tp – Ta) + A aUL,E(Tp – Ta) + A aUL,T(Tp – Ta)       (A.2) 
where: 
all UL values are referenced to aperture area, Aa. Dividing by Aa(Tp - Ta), 
UL = U L,B + U L,E + U L,T                 ( A . 3 )  
To keep different sizes of the test fixtures thermally equivalent, the sum of the loss coefficients, UL,B, UL,E, and 
UL, T must remain constant. The top loss coefficient can be held fairly constant by keeping the cover distance 
above the absorber plate between 13 mm and 38 mm. With this constraint, the sum of the edge loss 
coefficient, UL, E, and the back loss coefficient, CL,B, must remain constant. Therefore, 
UL.B + U L,E =  c o n s t a n t                  ( A . 4 )  
A.2.3.2 Determination of heat loss coefficient ( UL,B) for back of test fixture 
The heat loss through the back of a test fixture is equal to: 
() a p B L a back loss T T U A Q− = , ,  
  =  () ( c p b b bT T d K A− /)
  = ()()a c c c bT T d K A− /                 ( A . 5 )  
Reduction of Eq A.5 yields 
UL,B = ) / ( ) / (/
c c b ba b
K d K dA A
+               ( A . 6 )  
This reduction I accomplished by: FDUS 858: 2009 
© UNBS 2009 – All rights reserved  11
   ()  = a pT T−() c pT T−  + (              ( A . 7 )  )a cT T−
Substituting quantities from Eq A.5 into Eq A.7,  
  
B L aback loss
U AQ
,, = () b b bback loss
d K AQ
/, + ()c c bback loss
d K AQ
/,            ( A . 8 )  
Dividing by Qloss,back 
  
B L aU A,1
 = 
b bb
KAd+ 
c bc
KAd               ( A . 9 )  
Then, 
  UL,B = () ( )c c b ba b
K d K dA A
/ //
+                    ( A . 1 0 )  
A.2.3.3 Determination of heat loss coefficient ( UL,E) for edge of test fixture 
The heat loss through the edge of the test fixture is equal to: 
   =  edge loss Q , () a p E L aT T U A− ,
    =   () ( c p e e eT T d K A− /)
)
)    =                    ( A . 1 1 )  () ( a c e e eT T d K A− /
Reducing Eq. A.11 yields: 
  () ( Kc dc Ke deAa AeE UL/ //,+=               ( A . 1 2 )  
This reduction is achieved by: 
   () () ( Ta Tc Tc Tp Ta Tp)−+ − =−             ( A . 1 3 )  
Substituting quantities from Eq. A.11 into Eq. A.13 
   () ()dc Kc Aeedge Qloss
de Ke Aeedge Qloss
E AaULedge Qloss
/,
/,
,,+ =           ( A . 1 4 )  
Dividing by Q loss,edge
   AeKcdc
AeKede
E AaUL+ =,1             ( A . 1 5 )  
Then,  
   () ( )Kc dc Ke deAa AeE UL/ //,+=              ( A . 1 6 )  FDUS 858: 2009 
12 © UNBS 2009 – All rights reserved
 A.2.3.4 Combined heat loss coefficient fo r back and edge losses from test fixture 
The combined heat loss coefficient for back and edge lo sses from the test fixture is found by adding Eq A.6 
and Eq A.12. Then: 
 
 
  () () () ( )c c e ea e
c c b ba b
E L B LK d K dA A
K d K dA AU U/ //
/ //
, ,+++= +       ( A . 1 7 )  
For most designs: 
   , and d1 /≈a bA A b/Kb and d e/Ke  >> d c/Kc            ( A . 1 8 )  
Therefore: 
   () () ()e e a e b b E L B Ld K A A d K U U/ / / , , + = +          ( A . 1 9 )  
A.2.4 Examples of calculations for heat loss coefficient and shading factor 
These are examples of how to determine the combined h eat loss coefficient and the shading factor for the 
exposure test fixtures described in T able 1 and in 4.1.2 of this practice. 
A.2.4.1 For rectangular test fixt ure, Example 1 from Table 1: 
 () () () ( )Kc dc Ke deAa Ae
Kc dc Kb dbAa AbE UL B UL/ //
/ //, ,+++= +       ( A . 2 0 )  
If:  
  and  , 305 . 0 / , 1 /= = Aa Ae Aa Aa
 db/Kb = 2.03 m2.oC/W, 
 d c/Kc = 2.33 x 10-5 m2.oC/W 
 d e/Ke = 0.342 m2.oC 
Then: 
  d b/ Kb >> d c/ Kc and d e/ Ke >> d c/ Ke            ( A . 2 1 )  
Therefore, Eq A.19 can be used. 
() () ( de Ke Aa Ae db Kb UL B UL/ / / , , + = + ) 
   = 0.49 W/(m2.oC) + (0.49 W/(m2.oC) 
UL,B + UL,E = 1.38 W/(m2.oC) 
To determine the shading of the absorber: FDUS 858: 2009 
© UNBS 2009 – All rights reserved  13
   y zh zshade.% 100 . tan . .%θ=              ( A . 2 2 )  
where: 
z  = north-south dimension of absorber, 
y  = east-west dimension of absorber, 
h  = height from absorber to top of outer cover plate, and 
θ  = solar beam angle of incidence (15° ≈ 1 h from solar noon). 
If: 
θ =  3 0 °                      ( A . 2 3 )  
z = 0.25 m (9.8 in.) 
y =0.13 m (5.2 in.) 
h = 0.01 3m (0.5 in.) 
 ) 13 . 0 )( 25 . 0 (% 100 30 tan ). 013 . 0 ).( 25 . 0 (%m mx m mshade=  
  8 . 5 %= shade
A.2.4.2 For square test fixtur e, Example 2 from Table 1: 
() () () ( )Kc dc Ke deAa Ae
Kc dc Kb dbAa AbE UL B UL/ //
/ //, ,+++= +           ( A . 2 4 )  
If: 
Ab/Aa = 1, A e/Aa = 0.25, and 
db/Kb = 1.32 m2.°C/W , 
dc/Kc = 9.8 × 10-5 m2.°C/W 
de/Ke = 0.658 m2.°C 
Then: 
db/Kb >> d c/Kc and de/Ke >> d c/Kc
Therefore, Eq A.19 can be used. 
UL,B + U L,E   = (Kb/db) + (Ae/Aa)(Ke/de) 
= 0.76 W/(m2.°C) + 0.38 W/(m2. ° C )              ( A . 2 5 )  
UL,B + U L,E = 1.14 W/(m2. ° C )                 ( A . 2 6 )  
To determine the shading of the absorber Eq A.22 is used. 
If: 
θ =  3 0 °                    ( A . 2 3 )  
z = 0.61 m (24 in.) 
y =0.61 m (24 in.) 
h = 0.038 m (1.5 in.) FDUS 858: 2009 
14 © UNBS 2009 – All rights reserved
 ) 61 . 0 )( 61 . 0 (% 100 30 tan ). 038 . 0 ).( 61 . 0 (%m mx m mshade=  
   6 . 3 %= shadeFDUS 858: 2009 
© UNBS 2009 – All rights reserved  15
 Annex B 
(normative) 
 
Determination of variable-angle exposure schedule  
The direction of beam solar radiation can be determi ned by equations provided in Duffie and Beckman. The 
geometric relationships between a plane of any particular orientation relative to the earth at any time (whether 
that plane is fixed or moving relative to the earth) and the incoming beam solar radiat ion, that is, the position 
of the sun relative to that plane, can be described in terms of several angles. These angles, and the 
relationship between them are: 
φ   latitude (north positive); 
δ  declination (that is, the angular position of the su n at solar noon with respect to the plane of the 
equator) (north positive); 
s   the angle between the horizontal and the plane (that is, the slope) (facing south is positive); 
γ  the surface azimuth angle, that is, the deviation of the normal to surface from the local meridian, the 
zero point being due south, east positive, and west negative; 
ω  hour angle, solar noon being zero, and each hour equaling 15° of longitude with mornings positive 
and afternoons negative (for example, ω = +15 for 11:00, and ω = −37.5 for 14:30); 
θ  the angle of incidence of beam radiation, the angle being measured between the beam and the 
normal to the plane. The declination, δ, can be found from the approximate equation  
⎥⎦⎤
⎢⎣⎡⎟
⎠⎞⎜
⎝⎛+=365284360 sin 45 . 23nδ               ( B . 1 )  
where: 
n is the day of the year. The relation between θ and the other angles is given by 
ω γ δωγφδωφδγφδ φδθ
sin sin sin coscos cos sin sin cos cos cos cos cos cos sin cos sin cos sin sin cos
ss s s s + + + − =
(B.2 
Eq B.2 reduces to the following for a south-facing collector: 
  () ()ωδφδφθ cos cos cos sin sin cos s s −+−=             ( B . 3 )  
At solar noon, ω=0 and cos ω=1; therefore 
   () ()δφδφθ cos cos sin sin cos s s −+−=             ( B . 4 )  
Using the identity: () B A B A B Acos cos sin sin cos + = − , Eq X2.2 becomes: 
  ()[]δφθ −−= s cos cos                 ( B . 5 )  
Therefore: FDUS 858: 2009 
16 © UNBS 2009 – All rights reserved
   δφθ− − =s                 ( B . 6 )  
In order to make θ = 0, the following must be true 
  δφ− = optS                  ( B . 7 )  
Where: 
optS  Optimal collector slope, 
Φ  latitude, and 
δ  declination of sun. 
To maximize the incident solar radiation upon the cover plate materials, the angle of incidence of the beam 
solar radiation, θ, should be as close to 0 as possible at solar noon. This can be achieved by periodically 
adjusting the slope of the exposure fixture. The optimal slope may be determined by Eq B.7. 
Example: 
Find optimum slope for Gaithersburg, Md., on May 3. 
Φ  = 39.1 ° (latitude) 
n = 123 (day of year for May 3)              (B.8) 
From Eq A.29, 
  (⎥⎦⎤
⎢⎣⎡+ = 123 284365360sin 45 . 23δ )            ( B . 9 )  
  5 . 15=δo                  ( B . 1 0 )  
Therefore: 
  6 . 23 5 . 15 1 . 39= − = − = δφ optSo            ( B . 7 )  
Using Eq B.7, Table B.1 and Table B.2 were developed for variable-angle exposure schedules necessary to 
keep the angle of incidence of the beam solar radiation, ( θ), less than 4° and 6°. Other exposure schedules 
may be calculated using this approach. 
 
 
 
 
 
 
 
 FDUS 858: 2009 
© UNBS 2009 – All rights reserved  17
 Table B.1 – Variable-angle rack adjustment schedule using ten changes per year A,B
Calendar  period Rack tilt angle, o
Dates Days of year 
Latitude  + 12 2-7 to 3-1 38 to 60 
Latitude + 4 3-2 to 3-21 61 to 80 
Latitude – 4 3-22 to 4-11 81 to 101 
Latitude – 12 4-12 to 5-4 102 to 124 
Latitude – 20 5-5 to 8-7 125 to 219 
Latitude  -12 8-8 to 8-31 220 to 243 
Latitude  - 4 9-1 to 9-20 244 to 263 
Latitude  + 4 9-21 to 10-10 264 to 283 
Latitude  + 12 10-11 to 11-2 284 to 306 
Latitude  + 20 11-3 to 2-6 307 to 37 
AThis exposure schedule may be used in both northern and so uthern hemispheres. The lati tude in the southern 
hemisphere is negative. Positive rack angles face south. 
B The incident angle of beam radiation ( ө) at solar noon for a south-facing collector is ≤ 4o. 
 
Table B.2 – Variable-angle rack adjustment schedule using six changes per year A,B
Calendar  period Rack tilt angle, o
Dates Days of year 
Latitude  +6 2-19 to 3-21 50 to 80 
Latitude – 6 3-22 to 4-22 81 to 112 
Latitude – 18 4-23 to 8-20 113 to 232 
Latitude – 6 8-21 to 9-20 233 to 263 
Latitude + 6 9-21 to 10-22 264 to 294 
Latitude +18 10-23 to 2-18 295 to 49 
A This exposure schedule may be used in both northern an d southern hemispheres. The latitude in the southern 
hemisphere is negative. Positive rack angles face south. 
B The incident angle of beam radiation ( ө) at solar noon for a south-facing collector is ≤ 6o. 
 
 
 
 
 FDUS 858: 2009 
© UNBS 2009 – All rights reserved  
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thereunder. This mark can be used only by those licens ed under the certification mark scheme operated by 
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 FDUS 858: 2009 
 
ICS 27.160 
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