Overview of Exposure Angle Considerations for Service Life Prediction

Henry K. Hardcastle III
Atlas Weathering Services Group

Abstract 

This paper reviews selected considerations of exposure angle effect on materials weathering degradation. Calculation of solar angle of incidence is reviewed for surfaces with different slope angles. Historical UV irradiance measurement data is reviewed as a function of exposure angle. Empirical degradation as a function of exposure angle is reviewed for three materials. 

Introduction 

It is important for treatments of Service Life Prediction (SLP) to account for the effect of exposure angle on materials degradation. This paper presents several considerations including solar angle of incidence, empirical solar radiation measurements at different angles, and degradation rates of several materials at different exposure angles. This presentation is grouped into three parts: 

  • Calculation of Solar Angle of Incidence 
  •  Radiation Measurements as a Function of Exposure Angle 
  •  Materials Degradation Measurements as a Function of Exposure Angle (Experimental) 

Calculation of Solar Angle of Incidence 

 Irradiance represents one of the most important variables effecting weathering of materials in outdoor service. When materials are exposed at professional weathering laboratories, measurements of incident radiation are usually available. When exposures are conducted at remote locations, however, solar radiation impinging on surfaces must be estimated. 

 Models and calculations of solar irradiance are straightforward for simple situations but become more complex as exposure situations approach in-service conditions. The solar source itself has been well characterized and is considered stable for most purposes regarding materials performance. Most researchers accept the 1353 - 1373 W/m^2 solar constant estimates for extraterrestrial environments. There is little evidence to suggest this estimate will change by an important amount in the near future. 

 The solar flux impinging on terrestrial surfaces, however, varies according to daily and yearly cyclic causes. These effect solar radiation in two ways. First, as the angle of incidence of flux on the surface changes, the light density changes. Second, the effect of air mass filters the solar radiation. Thus, a materials orientation or angle in service environments is a critical consideration in service life prediction. The angle of incidence of sunlight for a surface at any angle, at any location on the earth, can be determined by the following calculation from Duffie and Beckman (1980): 

  Cos ? = sin ? sin ? cos ? - sin ? cos ? sin ? cos ? + cos ? cos ? cos ? cos ? 

 + cos ? sin ? sin ? cos ? cos ? 

 + cos ? sin ? sin ? sin ?

 Where ? represents latitude 

 ? represents solar declination at solar noon 

 ? represents the slope of the surface 

 ? represents the surface azimuth angle 

 ? represents the angle of the sun east or west of local meridian 

 ? represents angle of incidence 

 The declination, ?, can be found from the equation of Cooper (1969): 

 ? = 23.45 sin (360 (284 + n)) 

 365 

 This calculation can be used to solve for the volume of angles of incidence a surface is exposed to throughout the year at a location. For instance, a surface oriented horizontally at Miami, Florida experiences solar angles of incidence depicted in Graph 1. This graph shows the angle of incidence as an output due to time of day and day of year. 

 As a surface changes angle from horizontal, the family of angle of incidences changes significantly. For instance, Graph 2 shows angles of incidence of a 26-degree south exposure angle in Miami, Florida, Graph 3 shows angles of incidence for a 45-degree south exposure and Graph 4 shows a vertical, south-facing surface's solar angle of incidence for a year. Graphs 1-4 dramatically illustrate the different solar environments surfaces experience simply by altering the single variable of exposure angle. 

 d = 23.45 sin ( 360 ( 284 + n ) ) 365 This calculation can be used to solve for the volume of angles of incidence a surface is exposed to throughout the year at a location. For instance, a surface oriented horizontally at Miami, Florida experiences solar angles of incidence depicted in Graph 1. This graph shows the angle of incidence as an output due to time of day and day of year. As a surface changes angle from horizontal, the family of angle of incidences changes significantly. For instance, Graph 2 shows angles of incidence of a 26-degree south exposure angle in Miami, Florida, Graph 3 shows angles of incidence for a 45-degree south exposure and Graph 4 shows a vertical, south-facing surface's solar angle of incidence for a year. Graphs 1-4 dramatically illustrate the different solar environments surfaces experience simply by altering the single variable of exposure angle.

Graph 1. Miami Exposure, Horizontal
Graph 2. Miami Exposure, 26-degrees south
Graph 3. Miami Exposure, 45-degrees south

Changing a surface's exposure azimuth also dramatically changes a surface's solar environment. Graphs 5 and 6 show a surface at 45 degrees slope angle facing southeast (135 degrees) and west (270 degrees), respectively. Not only are these two orientations subject to different solar irradiance variables, but an interaction between orientation angle and local climatic conditions may also exist. In south Florida over several months of the summer season, afternoons are significantly more cloudy than mornings. Thus, even if a good correlation exists with morning solar dosages, SLP models may require a weighting factor for afternoon irradiance estimates derived for western facing orientations.

Graph 5. Miami Exposure, 45-degrees southeast
Graph 6. Miami Exposure, 45 degrees west

Changing a surface's latitude also dramatically shifts the distribution of solar angles of irradiance. Graphs 7 and 8 show angles of incidence for a 90-degree south-facing surface in Phoenix, Arizona and Moscow, Russia. A vertical surface in Moscow's summer encounters a very different set of incident angles than a similarly oriented surface in Phoenix or Miami.

Graph 7. Phoenix Exposure, Vertical south
Graph 8. Moscow Exposure, Vertical south

The angle of incidence variable alone cannot be used as a robust co variable for irradiance dosage. Coupled with each angle of incidence is a particular air mass through which the sunlight must travel. Air mass significantly effects the spectral power distribution of the solar source. The accepted standard extraterrestrial solar spectral power distribution published in ASTM E 490 shows irradiance values of 1074W/m^2 m m at 340nm. As the extraterrestrial radiation undergoes absorption, scattering, and other optical effects, the spectral power distribution is modified as represented in ASTM E 892 which shows an irradiance value of 435.3 W/m^2 m m at 340nm. Air mass is defined as the ratio of optical thickness of the atmosphere through which beam radiation passes to the optical thickness if the sun were at zenith (Air Mass = 1 when sun is directly overhead, Air Mass = 2 when sun is at 60° from overhead). This is why solar spectral distribution can be expected to change for different elevations if other variables are held constant. 

 Another important consideration for angle's effect on SLP models is that for each angle of incidence, there is a particular air mass associated with that angle of incidence and possibly a unique solar spectral power distribution. Thus it will be important for SLP models to account for the wavelength dependency of each materials photodegradation rates in light of angle of incidence and air mass for a particular in-service orientation and location. It will also be necessary to account for the local environment's effect on air quality including the ratio of diffuse to direct beam component and, specifically, for clouds in the local environment. Partially hazy or cloudy days represent additional sources of variability that must be treated in theoretical models. 

Radiation Measurements as a Function of Exposure Angle

 Given the complex interactions of variables in converting angle of incidence to solar dose, it is often easier and more accurate to simply measure solar radiation in reference environments. Atlas Weathering Services Group measures solar radiation and maintains historical radiation data on a professional basis for a variety of surface orientations and locations. 

 Graph 9 shows historical daily radiation measurements for 26-degree oriented south surface from 1990 to 1998. These measurements were made with calibrated Epply Laboratories TUVR instruments and showed accumulated energy deposited from 295-385 nm. The graph plots median actual values, mean statistical values, and ± 1.96 standard deviations from the mean (95% confidence estimate) for the 1990 to 1998 time period. Interpreting this graph indicates that two different randomly selected days may differ anywhere from 0 to 1.6 MJ/m^2 UV dose. This level of variation may be important for in-service exposures and service life times of one or several days. Testing of skin response and specialty materials designed for rapid decomposition may be required to account for this type of daily variation. Many materials designed for the exterior service environment, however, undergo service lives involving much thicker time slices and require larger UV dosages to show significant photodegradation. 

 Graph 10 shows historical monthly total UV radiation measurements for a 26 degree south oriented surface from 1990 to 1998. Interpreting this graph indicates that exposures for two different Julys may differ only from approximately 22 to 32 MJ/m^2 UV dose within ± 1.96 standard deviations. Again, this variation may be important for those materials with service life times on the scale of one month. The focus of most materials SLP, however, is on materials with a multi-year in-service life expectancy. 

Graph 9. Daily Solar Radiation, Miami
Graph 10. Monthly Solar Radiation, Miami (Note: The ± 1.96 Standard Deviation lines widen in the ninth month due to an assignable cause in 1992 when hurricane Andrew passed over the measurement site. Radiation measurements were discontinued for many days reducing n and increasing the standard deviations.)

Graph 11 shows historical yearly total UV radiation measurements for a 26-degree oriented surface from 1990 to 1997. Interpreting this graph indicates that exposures for any two different years may differ only from approximately 250 to 350 MJ/m^2 UV with in ± 1.96 standard deviations. The actual yearly totals from 1990 to 1997 show a moderately good agreement with the statistical mean for the 1990 to 1997 period. Actual totals for this data shown no discernable trends or cyclic patterns. If the variation depicted in Graph 11 were considered analogous to a plot of output of a manufacturing process (i.e., control chart), most manufacturing process engineers would interpret this as evidence of a relatively stable process in a state of statistical control. 

 It is the multi-year time slice and predictability of solar irradiance dosage at the multi-year level of context that is important for the vast majority of materials designed for exterior in-service use conditions. Graphs 12, 13, 14 and 15 show distributions of historical yearly total UV radiation dosages for a selection of angles facing due south measured at Atlas Laboratories in Phoenix, Arizona and Miami, Florida from calibrated and maintained Epply TUVR radiometers. 

Graph 11. Yearly Solar Radiation, Miami, At Latitude
Graph 12. Yearly Solar Radiation, Miami, 45°
Graph 13. Yearly Solar Radiation, Miami, 45°
Graph 14. Yearly Solar Radiation, Phoenix, At Latitude
Graph 15. Yearly Solar Radiation, Phoenix, 45°

Materials Degradation Measurements as a Function of Exposure Angle (Experimental) 

 If materials degradation were solely a function of UV dose, one could expect degradation rates to co-vary with the functions depicted in graphs of the previous section. Experience and empirical data indicate, however, that a much more complex system of variables and interactions operates to degrade many materials. In order to gain some simple insights and appreciation for these complex systems, Atlas Weathering Services Group designed and conducted two very simple experiments involving the effect of exposure angle on materials degradation and one small empirical study involving measurements of finished construction components after exposure in the end-use environment. 

 Experiment A: Effect of Exposure Angle on Development of Yellowness in Clear Polystyrene Reference Materials. 

 Research Question: 

If a polystyrene reference material is exposed at different angles, will differences in rates of change of Yellowness Index correspond with different dosages of UV measured at these exposure angles? 

 Polystyrene plastic lightfastness standard material specimens were randomly selected from a single production lot obtained from Test Fabrics, Inc. This material is typically used as a standard reference material for monitoring controlled irradiance, water-cooled xenon arc apparatus. Two randomly selected specimen sets were placed on outdoor exposure at Atlas's SFTS Laboratory in Miami, Florida and Atlas's DSET Laboratory in Phoenix, Arizona during the summer of 1999. Replicate pairs were placed on different angles of exposure simultaneously. The degradation in yellowness index ( ASTM E 313) was measured at periodic intervals of exposure from May to August 1999. 

 During this exposure period, accumulated solar UV radiation dose was measured using Epply Laboratories TUVR radiometers at these sites oriented to the same exposure angles as the specimens. 

 Results: 

The data obtained for this experiment is shown in Graphs 16 and 17. 

Graph 17 Yellowing of Polystyrene Based on Exposure Time

Discussion:

The results indicate a strong positive correlation between accumulated UV dose due to angle of exposure and Yellowness Index. Besides UV dose there also appears to be at least one variable that effects development of Yellowness Index that is linked to the different locations. The character of Yellowness Index development in the Florida exposure differs from that of the Arizona exposure. This difference is significant and important. It is these significant and important differences between predicted values and empirical results that represent a critical limitation to theoretical SLP models now and possibly in the future.

Experiment B: Effect of Exposure Angle on Color and Gloss Change of Brown Coil Coated Cylinders.

Research Question:

If a short length of continuous coil coated metal is formed into a cylinder and placed on exposure, will color and gloss changes at different locations on the cylinder indicate the effect of exposure angle on materials' weathering characteristics?

Materials and Apparatus:

Lengths of commercially available brown coil coated construction material were obtained and fitted as cylinders around circular pipe substrates. Cylinders were placed on exposure with the long axis oriented east and west at Atlas' SFTS and DSET Laboratories in Miami, Florida and Phoenix, Arizona respectively.

Each cylinder was carefully indexed so that repeated color and gloss measurements could be taken at specific target areas. The index marks corresponded to different angles of exposure. After one year, the coil coated material was removed from cylinders and measured for color (ASTM D2244, D65, 10 degree, CIE L*,a*,b* RSIN) and gloss (ASTM D523 60degree gloss).

Results:

The results of the 1-year exposure and measurements are shown in graphs 18 - 21.

Graph 18. Phoenix Exposure Effect on Brown Coil Color
Graph 19. Phoenix Exposure Effect on Brown Coil Gloss
Graph 20. Miami Exposure Effect on Brown Coil Color
Graph 21. Miami Exposure Effect on Brown Coil Gloss

Discussion:

The results of the exposure and measurements show good characterization of the effect of weathering on a single specimen as a function of exposure angle. The Arizona exposed cylinder showed a peak in L* values approximately at the horizontal orientation. There did not appear to be important differences between areas within 30° south of the horizontal orientation. The slope of the curve on the south-facing surface appeared more gradual than the slope of the north facing orientations.

The Florida exposed cylinder showed a considerably different weathering behavior. At angles of incidence greater than 40° from vertical, the change in L* value as a function of exposure angle behaved in a manner co-varying with solar irradiance. As exposure angles decreased to less than 40° from vertical, the materials weathering behavior dramatically shifted. The angle considerations associated with service life prediction at angles less than 40° from vertical do not appear to pertain to angles greater than 40° from vertical for this material in specific environments. Failure of SLP models to account for this type of significant and important consideration of exposure angle (as well as other variables) may result in catastrophic unexpected failures for users of such insufficient models.

Figure 1. Cylinder in Florida Exposure With Condensation

Figure 1, along with a separately published Atlas paper, may indicate presence of liquid water at night (effective nighttime soaking) as the over riding variable and root cause for the shift in degradation behavior for this material at near horizontal orientations.

The Florida cylinder, however, did not show a shift in weathering behavior for gloss as it did for color. SLP modes must consider different weathering behaviors. Not only must material dependencies be taken into account, but SLP models must also consider different material characteristics and attributes being measured. Degradation phonemna for color L* values is very different than degradation phonema for 60° gloss values for this material in Florida exposure.

Empirical Study: Finished Construction Components After Exposure in Service Environments

Research Question:

What are the degradation characteristics of a commercial material in end-use environments as a function of azimuth exposure angle. 

Materials and Apparatus:

Due to the empirical nature of this study, material composition, length of exposure and initial values are unknown. Only the location and orientation of the construction unit is known. This may also be the case for many real world studies of materials in service use. A commercial parking lot in Fort Lauderdale, Florida which had sets of lampposts in relatively unobstructed areas was selected. These posts were octagonal vertical columns approximately 12 inches in cross section. The steel was coated with a dark green industrial coating of moderate gloss. These posts were oriented near vertically with one of the faces due south (see Fig. 2)

Fig 2. Octagonal Lampposts in Ft. Lauderdale.

Four of the posts were thoroughly measured using a hand-held Hunter Miniscan spherical colorimeter (LAV, RSIN, CIE L*,a*,b* 10 deg observer) for color and using a BYK Tri-Gloss hand-held glossmeter for 60 degree specular gloss. Each of the surfaces of the octagonal structure were measured at four haphazardly selected locations between five and eight feet above ground with the mean reported. Measurements were conducted in June 1999 on a cloudy day to preclude large temperature differences on the different faces of the structures.

Results:

Figures 22, 23 and 24 show the data obtained for L*, b* and 60 degree gloss respectively.

Graph 22. Distribution of L* Values on Ft. Lauderdale Lampposts
Graph 23. Distribution of b* Values on Ft. Lauderdale Lampposts
Graph 24. Distribution of Gloss Values on Ft. Lauderdale Lampposts

Discussion: 

The results of the measurements show a good characterization of the effect of weathering on specimens' color and gloss as a function of azimuth angle. It may be possible to use existing in-use examples such as this to check SLP model results in an empirical way. If a relationship between irradiance dosage as a function of angle is characterized, it may be possible to correlate the relationship to distributions such as those shown in Graphs 18 - 21 showing degradation as a function of angle. Understanding this correlation may allow a simple estimate of degradation due to solar irradiance dose vs. degradation due to other factors. In this way, researchers may gain insights as to the relative importance ranking of the solar irradiance variable with respect to other variables. 

Summary 

 This paper has presented several contextual levels of considerations regarding exposure angle effects on service life prediction. Some of the effects of exposure angle on service life prediction can be considered very simple, straightforward effects predicted by Newtonian physics and geometry, such as solar angle of incidence. Other effects of exposure angles on service life predictions can be quite complex and involve special cases of material dependencies and local climates as seen with empirical data presented here within. A truly robust and useful SLP model should predict service life of specific materials in actual "in-service" conditions and not only in simple theoretical artificial or hypothetical simulations. Understanding real world considerations including effects of exposure angles along with these considerations in SLP models will improve the usefulness of SLP models

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