Int J Biometeorol (2004) 49:113–129DOI 10.1007/s00484-004-0214-6

O R I G I N A L A R T I C L E

K. Kubaha · D. Fiala · J. Toftum · A. H. Taki

Human projected area factors for detailed directand diffuse solar radiation analysis

Received: 3 October 2003 / Revised: 28 April 2004 / Accepted: 19 May 2004 / Published online: 20 July 2004� ISB 2004

Abstract Projected area factors for individual segmentsof the standing and sedentary human body were modelledfor both direct and diffuse solar radiation using detailed3D geometry and radiation models. The local projectedarea factors with respect to direct short-wave radiation area function of the solar azimuth angle (a) between0�<a<360� and the solar altitude (b) angles between�90�<b<+90�. In case of diffuse solar radiation from theisotropic sky the local human projected area factors weremodelled as a function of the ground albedo (r) rangingbetween 0<r<1. The model was validated against avail-able experimental data and showed good general agree-ment with projected area factors measured for both thehuman body as a whole and for local quantities. Scientistscan use the equations to predict the inhomogeneous ir-radiation and absorption of direct and diffuse solar radi-ation and UV-radiation at surfaces of the human body. Inconjunction with detailed multi-node models of humanthermoregulation the equations can be used to predict thephysiological implications of solar radiation and outdoorweather conditions on humans.

Keywords Solar radiation · Human radiation geometry ·UV-dose · Outdoor climate · Modelling

Introduction

Radiative heat exchange with the environment plays animportant role in the human heat transfer and thermalcomfort. In buildings, occupants are frequently exposed toinhomogeneous radiation, e.g. in the proximity of coldwindows, hot radiators, or due to solar radiation trans-mitted through glazed fa�ades. Such asymmetric condi-tions can make indoor environments thermally uncom-fortable, cause restrictions in the usability and function-ality of spaces and reduce occupants’ productivity in thework place. In cars and aircraft cabins such uncomfort-able conditions can slow down the reactions of driversand pilots. Critical, life-threatening situations arise forpeople such as firefighters on duty or workers in metalwork factories who are exposed to thermal radiation fromfire and intense heat.

Outdoors, both direct and diffuse solar radiation canreach levels at which the impact on human thermalcomfort and the perceived outdoor temperature is over-whelming. Besides perceptual effects, there are varioushealth implications of human exposure to solar radiationthat require a careful consideration, Kimlin et al. (2002).Thereby, a detailed knowledge of the human radiant ge-ometry and its local characteristics is required in caseswhere the risk of skin injury arises. The risk of injury dueto overdose of UV-radiation, for example, depends on thelocal radiation geometry of exposed body parts rather thanon global quantities. Despite the need for local charac-teristics, however, only the overall radiation data for thehuman body as a whole is available.

The amount of solar radiation received by a persondepends on the projected area factor (fp) as a geom-etry-related, direction-dependent radiation parameter ofthe human body. Over decades the human projectedarea factors and solar heat load have been subjectto various experimental investigations. Underwood andWard (1966), e.g. measured projected area factors of 25standing male and female persons using photographicmethods. The authors developed empirical formulae forpredicting the fp-factors of the human body as a whole

K. Kubaha · D. Fiala ())Institute of Energy and Sustainable Development,De Montfort University,Leicester, UKe-mail: dfiala@dmu.ac.ukTel.: +44-116-2577971Fax: +44-116-2577981

J. ToftumInternational Centre for Indoor Environment and Energy,Technical University of Denmark,Lyngby, Denmark

A. H. TakiSchool of Architecture,De Montfort University,The Gateway, Leicester, UK

based on measurements obtained for seven different al-titudes and three azimuth angles.

Fanger (1970) carried out extensive experimental trialsto determine the projected area factors of 20 male andfemale subjects in the standing and sedentary position forazimuth and altitude angles between 0� to 180� and 0� to90�, respectively. In these experiments, the camera waspositioned at a relatively large distance (about 7 m) fromthe subjects to simulate the case of parallel rays fromdirect solar radiation. The original results were presentedin form of graphs. Other authors (e.g. Steinman et al.1988; Rizzo et al. 1991) have used Fanger’s data to de-veloped formulae for calculating the human projectedarea factors for use in computerised procedures. Morerecently, Jones et al. (1998) measured projected areafactors of a full-scale manikin for a range of azimuth andaltitude angles between 0�<a<180� and �90�<b<+90�(referring to the centre of the body) using a similarmethod employed by Fanger. The distance between thecamera and the manikin however was set at 4.3 m and3.7 m for positive and negative altitude angles, respec-tively. In contrast to other experiments, Jones et al. (1998)did not only measure the overall projected area factors ofthe body as a whole but also provided local quantities forindividual body segments. Also alternative approaches toprojected area factor concept to calculate solar heat loadon human body have been developed by various authors,e.g. Breckenridge and Goldman (1972), Blazejczyk et al.(1992). Blazejczyk (1996), for example, proposed equa-tions for assessing the amount of solar radiation absorbedby man using basic meteorological parameters.

To date, sophisticated computer simulation softwaretools are available which make detailed modelling of thehuman radiative heat exchange with the surrounding en-vironment possible. There is a growing interest to predicthuman physiological and perceptual responses in variousdisciplines of science and technology, and, over decades,several multi-segmental models of the human thermalsystem (e.g. Stolwijk 1971; Fiala et al. 1999, 2001, 2003;Huizenga et al. 2001) have emerged that enable the effectof wide-ranging environmental conditions on human be-ings to be quantified. In recent years also software havebecome available using which detailed 3D models of thehuman body geometry can be generated for almost anybody posture. Diverse CFD packages and thermal analysistools are capable of predicting radiation exchange dealingwith highly complex and boundary conditions geometries(such as the human body).

The level of detail and the accuracy in prediction maketoday’s numerical radiation models superior to experi-mental investigations in several respects. There are hardlyany restrictions regarding the considered geometricalconfigurations; the simulations can be run with the highintensity source at an infinite distance from the humanbody for any solar angle that can be exactly adjusted. Inaddition to direct radiation, it is also possible to studydiffuse solar radiation effects for which no experimentalresults seem to exist. Predictions include detailed infor-mation on the solar irradiation mapping over the three

dimensional human body surface. Besides overall bodydata, it is thus possible to obtain information also on theeffect of local body characteristics which is required fordetailed human radiation analysis.

Over the past years, several studies of the human ra-diative heat exchange have been carried out using nu-merical methods. Miyazaki et al. (1995), for example,considered the human body as consisting of several cy-lindrical parts and verified measured effective radiationarea factors of the human body using the Monte Carlomethod. Tanabe et al. (2000) used realistic 3D geometrymodels and solar heat gain calculations to predict pro-jected area factors with respect to direct solar radiation forsedentary and standing subjects. As most experimentalstudies, however, overall human radiation data rather thanlocal quantities were provided.

In this study numerical simulation techniques and de-tailed geometry models are used to predict projected areafactors for individual segments of the human body. Theaim of the work is to develop formulae for predictinglocal fp-factors of standing and sedentary humans withrespect to both direct and diffuse solar radiation thatscientists and engineers can use to perform detailed short-wave radiation analysis, e.g. in conjunction with modelsof human thermoregulation, facial cooling and allowableexposure times, or models for predicting the UV-dose atexposed body parts.

Methodology

Human body models

The human body for both the standing and sedentary posture, wasmodelled as having left-right symmetry and a stress-free positionusing commercial software (Curious Labs 2000). The softwareenabled generating detailed 3D models of the human body for al-most any body postures. Each model consisted of 10,995 smallsurface elements that provided sufficient detail for the radiationsimulations (Fig. 1). With a height of 1.75 m and a DuBois’ area of1.83 m2 this body size was felt as representing an average malesubject, DuBois and DuBois (1916). The elements were groupedtogether into 19 main body parts (Table 1) subdivided into 59spatial sectors (Fig. 2) for which the local projected area factorswere to be modelled.

Fig. 1 The human body geometry models used in the study

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Radiation simulations

The humanoid geometries were imported into a thermal analysissoftware package (ThermoAnalytics 2001) which uses a voxel-based ray tracing technique to predict the absorbed short-waveradiation energy at each of the 10,995 surface elements. Thescheme subdivides the scene to be ray-traced into small volumeelements, or voxels. Rays were cast from each element to all othersurrounding voxels and the high intensity source and the intersec-tions were determined. The software calculated the amount of solarflux, Qa,i, absorbed by each surface element from the incident solarradiation using the elements’ short-wave absorptivities and the

apparent areas predicted by the voxel based ray-tracing scheme. Atthis stage the surface elements were defined as black body radiatorswith an absorptivity of one to simplify the subsequent calculations.The results were then postprocessed integrating the elementalfluxes to obtain projected area factors for individual body sectors.Thereby, the total amount of short-wave radiation absorbed by abody sector consisting of n surface elements was obtained as thesum of predicted nodal quantities, Qa,i. For a group of surfacenodes, the projected area factor, fp, which is defined as the ratiobetween the projected area and the actual surface area of a sector, isthus presented as

fp ¼1qs

Pn

i¼1Qa;i

Pn

i¼1Ai

ð1Þ

where fp is the projected area factor of an individual body sector,Qa,i solar radiation absorbed by surface element i (W), qs incidentsolar radiation flux (W/m2), and Ai area of surface element i (m2).

The projected area factors were calculated for both direct anddiffuse short-wave radiation. For the direct short-wave radiation,the simulation procedure calculated the projected area factorsacross a range of azimuth angles, a, from 0� to 360� (due north,clockwise) and altitude angles, b, from �90� to 90� (Fig. 3). For thediffuse short-wave radiation case, the area factors were calculatedby varying the ground albedo, r, between 0 and 1 (assuming iso-tropic, i.e. homogeneously radiating sky).

Regression analysis

Simple and polynomial regression was used to develop the equa-tions. In case of direct solar radiation the fp-factors were consideredas functions of the solar azimuth and solar altitude angles a and b,and as functions of the ground albedo r in case of diffuse solarradiation. If any regression coefficient was not significantly dif-ferent from zero at the 0.95 confidence level, a new regression wasrun without the non-significant variable. The two-tailed populationt-test was applied to determine the significance level of the re-gression coefficients.

Table 1 Surface areas of individual body sectors

Body parts Body sectors Surface area (m2)

Head Head 0.0525Forehead 0.005

Face Anterior 0.0193Exterior (L/R) 0.011

Neck Anterior 0.005Exterior (L/R) 0.0094Posterior 0.0068

Shoulder Left 0.0205Right 0.0205

Thorax Anterior 0.1115Inferior (L/R) 0.0093Posterior 0.0916

Abdomen Anterior 0.1104Inferior (L/R) 0.0401Posterior 0.1091

Upper arm (L/R) Anterior 0.0144Exterior 0.0292Inferior 0.0098Posterior 0.0143

Lower arm (L/R) Anterior 0.0092Exterior 0.0269Inferior 0.0268Posterior 0.0124

Hand (L/R) Handback 0.0285Palm 0.0276

Upper leg (L/R) Anterior 0.0466Exterior 0.0503Inferior 0.0407Posterior 0.0386

Lower leg (L/R) Lower anterior 0.0254Lower exterior 0.039Lower inferior 0.0335Lower posterior 0.0372

Foot (L/R) Instep 0.04Sole 0.0203

Fig. 2 Subdivision of the humanoid into individual body sectors

Fig. 3 Variation of the solar altitude (b) and azimuth angle (a) inthe study

115

Modelling local projected area factors

Direct solar radiation

Analysis of the post-processed data indicated that formost parts of the human body the projected area factorcurves for direct solar radiation (i.e. with respect to par-allel rays) can be described as periodic, i.e. cosine or sinefunctions of the solar azimuth angle, a. As an example,the projected area factors predicted by the ray-tracingtechnique for the posterior thorax of a standing person areplotted in Fig. 4.

The trend of each curve can be commonly describedusing the following mathematical expression

fp ¼ A cos C1aþ C0ð Þ þ B ð2Þwhere fp=projected area factor of the body sector for agiven b, a=azimuth angle (rad), C1, C0=regression coef-ficients

A ¼ fp;max � fp;min

2ð3Þ

B ¼ fp;max þ fp;min

2ð4Þ

fp,max=the maximum projected area factor, fp,min=theminimum projected area factor.

The coefficients C1 and C0 were determined by re-gression analysis using a rearranged Eq. 2

cos�1 fp � B

A

� �

¼ C1aþ C0 ð5Þ

The coefficients A, B, C0 and C1 were not constant butvaried depending on the solar altitude angle, b. As anexample, these coefficients obtained for the posteriorthorax are plotted against b in Fig. 5

The functions of these coefficients were determinedusing polynomials up to an order of four (see appendix,Tables 3, 4, 5).

In contrast to body parts that were fully exposed to thebeam of direct radiation, Eq. 2 did not perform well forsectors that were hidden/partly hidden by other body partsat certain solar angles. As an example, in Fig. 6, suchdiscrepancies between simulated data and fp-factors pre-

Fig. 4 The course of projected area factors predicted for the pos-terior thorax of a standing person

Fig. 5 The regression coeffi-cients for the posterior thoraxbody sector

116

dicted using Eq. 2 are apparent for azimuth angles210�<a<350� where the shoulder was “shaded” by thehead.

It was, therefore, necessary to account for this “shad-ing” effect by modelling the so called “shading-function”as a part of the final solution for each body sector. For thispurpose, Eq. 2 was extended as follows

fp ¼ A cos C1aþ C0ð Þ þ B½ �S ð6Þwhere S is the shading function.

To model S, a number of different concepts were de-veloped and tested. Thereby, the use of tanh functionsturned out to be the most suitable approach

S ¼ 1þ tanh D1aþ D0ð Þ2

þ tanh E1aþ E0ð Þ2

ð7Þ

where D1, D0, E1, and E0 represent coefficients to bedetermined by regression analysis. Also these coefficientsdepended on the solar altitude, b, as shown for theshoulder body elements in Fig. 7. The results of thepolynomial regressions for each coefficient are listed inappendix, Tables 6, 7, 8, 9.

Because of the symmetry of the humanoid modelsused in the study the results obtained for the right-handbody parts were applicable also to the left-hand side bodyelement. For left-hand side body sectors, however, thereverse azimuth angle a*=2p�a has to be used withEqs. 6, 7.

Diffuse solar radiation

In case of diffuse solar radiation the projected area fac-tors, fp,dif could be described as linear functions of theground albedo for each body part

fp;dif ¼ g1rþ g0 ð8Þwhere fp,dif projected area factor of a body sector,r=ground albedo, g0 and g1 regression coefficients ofindividual body sector.

The results of the regression analysis are provided inTable 10.

Fig. 6 Inadequacy of Eq. 2 to predict fp-factors for sun positionswhere the body sector (right shoulder, standing posture) was hiddenby another body part

Fig. 7 The regression coeffi-cients of the shading functionfor the shoulder body sector

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Results

In the verification and validation process to which thenew model was subjected, the predictions of the fp-factorsfor each body sector of the standing and the sedentaryhuman were first verified against simulation results ob-tained by the voxel-based ray tracing technique.

The results obtained for the head and the posteriorthorax of the standing person exposed to the direct solarradiation are shown in Fig. 8. The irradiation of solar rayson both sectors was not obstructed by other body parts. Inboth cases the fp-curves therefore exactly replicated thecosine function as described by Eq. 2. As can be seen, thepredictions agreed well with the results of the ray-tracingsimulations across the whole range of the azimuth andaltitude angles, a and b.

Some, partly significant, deviations from the ideal co-sine-shape trend are apparent from Fig. 9 in which thefp-factors are plotted for the anterior face and the rightshoulder. For the case of anterior face the upper legs of thesedentary posture hindered a full irradiation of solar rayson this body part causing a remarkable fall in fp at a solaraltitude of b=�60�. In case of the right shoulder the ap-preciable discrepancies from an ideal cosine-shape ob-served for 0�<b<60� between 210�<a<330� were causedby the head. The shading function of the regression modelaccounted appropriately for these shadowing effects.

The analysis of the results indicated that for manybody sectors, there was no or little effect of the bodyposture (i.e. standing and sedentary) on the local projectedarea factors. For other body parts, however, significantdiscrepancies occurred. Fig. 10 displays the differences

for two body parts.

Fig. 8 Comparison of predicted and simulated projected area factor for two “unshaded” body parts, i.e. head (left) and posterior thorax(right) of the standing person

Fig. 9 Effect of shadowing by other body parts on projected area factor of the anterior face (left) and the right shoulder (right) sector of asedentary person

118

For symmetry reasons, the local projected area factorswere modelled explicitly only for the right-hand side bodyelements. The application of these regression results toboth, the right and the left lower arm (anterior) is dem-

onstrated in Fig. 11. As described previously the reverseazimuth angle a*=2p-a was used with Eqs. 6, 7 to predictthe fp-factors of the left hand-side body part in Fig. 11(right).

Fig. 10 The effect of body posture on the local projected area factors of the forehead and the anterior abdomen

Fig. 11 Projected area factors of the right and left lower anterior arm predicted for a standing posture

119

Finally, six examples for projected area factors withrespect to diffuse solar radiation are shown in Fig. 12,indicating a linear relationship between fp, dif and theground albedo, r, however with variable slopes. As incase of fp,dif, there was little effect of the body posture forsome body sectors (e.g. anterior face in Fig. 12). For otherbody parts, however, significant discrepancies occurredcaused by changes in the orientation of individual bodyparts (e.g. anterior upper legs in Fig. 12) and/or shad-owing effects through other body parts (anterior abdomenin Fig. 12).

Validation and discussion

To date, most experimental data is available just for thewhole human body. To enable a comparison with thesemeasurements, the predicted results obtained for indi-vidual body sectors were therefore integrated over the

whole body surface. Furthermore, in most cases, experi-mental fp-factors have been presented as a ratio of theprojected body area and the effective radiation area (ra-ther than the actual surface area). For validation purposeshence also the predicted values were weighted by theeffective radiation area factor of the humanoid modelused in this study (feff=0.84 and 0.78 for the standing andsedentary posture, respectively).

The results for the standing posture are compared withmeasured data obtained by Underwood and Ward (1966),Fanger (1970) and Jones et al. (1998) in Fig. 13. Themarks indicate the experimental results whereas linesrepresent the predicted overall projected area factors asintegrated over the humanoid’s surface. Generally, thebest agreement between predicted and measured valueswas achieved for the detailed experiments carried out byFanger (1970). For most altitude and azimuth angles thediscrepancy was typically about 5% relative error. Greaterdiscrepancies resulted for the overall fp-factors measured

Fig. 12 Projected area factorcurves for diffuse solar radia-tion of the anterior face (stand-ing and sedentary), anterior ab-domen (standing and sedentary)and upper anterior legs (stand-ing and sedentary)

120

by Jones et al. (1998) at b=�30� and b=�60�. For thesealtitude angles, however, the measured quantities werepartly greater than for frontal exposures which seems lessplausible and difficult to reproduce by rigorous numericaltechniques. The lowest level of agreement resulted for theless detailed experiments of Underwood and Ward (1966)who measured the human fp-factors for seven altitudesbut only for three azimuth angles (0�, 45� and 90�). Thelargest discrepancy with twice as high predicted fp-factorsof Underwood and Ward resulted for b=90�. It should benoted that the effective radiation area of the subjects inthe experiments was unknown and thus the feff of thehumanoid model was used instead to weight the measuredvalues in Fig. 13 representing a possible source of error.

The predicted overall projected area factors of thesedentary posture are compared against the experimentalresults of Fanger (1970) in Fig. 14. Similarly to thestanding posture a good general agreement between pre-diction (solid lines) and experiment (data points) wasobtained for most altitude and azimuth angles. An ex-ception formed fp-factors at an altitude angle of b=15�and a<60�/a>300� for which the discrepancy between

Fig. 13 Comparison of predicted projected area factors for the whole body in standing posture with experimental results obtained by: a)Underwood and Ward (1966), b) Fanger (1970), c) Jones et al. (1998)

Fig. 14 Comparison of predicted overall projected area factors forthe sedentary posture with experimental results obtained by Fanger(1970)

121

prediction and measurement was greater than 10% rela-tive error.

The results of this study were also compared with thesimulation results obtained by other authors. A compari-son with the overall projected area factors predicted byTanabe et al. (2000) for standing and sedentary postures isshown in Fig. 15. The models agreed with each otherwithin 7% relative error. The greatest relative discrep-ancies occurred at b=90� for both postures where thepresent regression model (which is based on more de-tailed geometry models) predicted the fp-factors to becloser to the experimental results of Fanger (1970) than tothe numerical results of Tanabe et al. (2000). It is inter-esting to note that this study confirmed the results ofTanabe et al. with respect to the maximum fp-factors fora<60� and a>300� (sedentary posture) not exceeding 0.31which contrasts the experimental results of Fanger withfp,max=0.34.

In contrast to direct solar radiation no experimentaldata were found for fp-factors with respect to diffuse solarradiation in the literature. Various authors (e.g. Fanger1970; Horikoshi et al. 1990; Miyazaki et al. 1995; Tanabeet al. 2000), however, reported on measured effectiveradiation area factors for the human body as a whole. Theeffective radiation area factor is defined as the ratio be-tween the effective radiation area and the actual surfacearea of the human body. Thereby, the effective radiationarea is that area of the human body that is presented to theenvironment contributing to the radiation exchange with adiffusely radiating homogeneous enclosure. The experi-mentally observed human effective radiation area factorscould therefore be directly compared with the predictedoverall projected area factors obtained for diffuse radia-tion from the isotropic sky provided the ground albedo, r,equals unity. The overall projected area factors for diffuseradiation were obtained by integration of local quantitiesand are compared with the experimental results fromvarious authors in Table 2.

The results of the present study agreed well (within 5%relative error) with data obtained by Bedford, Horikoshiand Miyazaki but they are greater (13% relative error)than those obtained, e.g. by Fanger and Tanabe. It ishypothesized that these discrepancies were due to dif-ferences in the body posture considered. In this study thegeometry models for both the standing and sedentaryposture represented relaxed, stress-free position. In con-trast, other studies considered compact geometry modelsand subjects with extremities closely attached to eachother or to the body.

While most investigations have dealt with the overallradiation characteristics of the human body, to date, alsosome information is available on measured local quanti-ties. In Fig. 16, the predicted local projected area factorsof individual body parts with respect to direct radiationare compared with the corresponding measured data ob-tain by Jones et al. (1998). To make a comparison pos-

Fig. 15 Comparison of predicted projected area factors of the whole body with simulation results obtained by Tanabe et al. (2000)

Table 2 Comparison of predicted overall projected area factors fordiffuse solar radiation with measured effective radiation area fac-tors

Description Effective radiation area factor

Standing posture Sedentary posture

Nude Clothed Nude Clothed

Present study 0.84 0.78Bedforda 0.82 0.72Guibertb 0.73 0.65Fangerc 0.73 0.87 0.7 0.77Horikoshid 0.8 0.91 0.74 0.8Miyazakie 0.83 0.78Tanabef 0.74 0.69a Bedford (1935).b Guiber and Taylor (1952).c Fanger (1970).d Horikoshi et al. (1990).e Miyazaki et al. (1995).f Tanabe et al. (2000).

122

sible the predictions referring to individual spatial bodysectors were integrated locally to obtain fp-factors of thebody parts according to the experimental set-up. Unfor-tunately, no experimental data were found with which tocompare predicted local fp-factors for diffuse radiation.

As in the case of overall factors, also the predictedlocal fp-factors agreed generally well with the measure-ments reproducing both the trend and absolute values for

most body sectors. The average deviation including allangles and body sectors was Dfp=€0.03. Partly largediscrepancies however resulted for non-central bodysectors such as feet. A thorough analysis of the resultsassumed that the discrepancies were most likely associ-ated with the following differences between model andexperiment.

Fig. 16 Comparison of local projected area factors predicted for individual body parts with measured data using a standing manikin, Joneset al. (1998)

123

Besides differences in posture that were suggested tocause discrepancies between predicted and measured lo-cal fp-values particularly in extremities, there were alsosome differences in the segmentation of the computermodel and the manikin used in the trials.

However, the main point was probably that the simu-lations were performed for parallel rays with the highintensity source at an infinite distance from the humanbody but the experiments were conducted for finite dis-

tances between the body and the camera. In case of theJones et al. experiment the distance was 4.3 m for positivealtitude angles and 3.7 m for negative altitude angles,respectively. To this point the azimuth and the altitudeangles of the camera were measured from the centre ofthe manikin. There was good agreement with the mea-sured fp-factors for body parts that were close to the bodycentre such as stomach and chest. For body parts such ashead, face, upper arms and feet, however, a lower level

Fig. 16 (continued)

124

of agreement between prediction and experiment wasachieved. This was because the position of the camera,i.e. the angles a and b, relative to the body centre, in-creasingly deviated from the position relative to the in-dividual body parts, and thus from the direction of theparallel rays in the simulations.

Conclusion

In this study, regression equations for predicting localprojected area factors of standing and sedentary personswere developed using detailed computer models of thehuman body geometry and numerical ray-tracing tech-niques. The new regression model was developed for bothdiffuse and direct solar radiation. Validation tests showedgood general agreement with measured data for bothoverall and local quantities. Discrepancies between pre-dicted and measured data appeared to be associatedmainly with differences in posture and with the fact thatthe simulations were performed for parallel rays with thehigh intensity source being at an infinite distance from thebody whereas the experiments were performed for finitedistances.

The projected area factor equations developed in thisstudy can be used to predict the irradiation and absorptionof direct and diffuse solar radiation over the 3D surface ofthe human body. Bio-meteorologists and other scientistscan use the equations to perform detailed analysis of theeffect of solar radiation on human beings exposed tooutdoor weather conditions. This information can serve,for example, to develop bio-climatic charts and rationallyderived operative temperatures which characterise theoutdoor climate conditions including the effect of solarradiation on humans.

The presented equations may prove useful especiallywhen used in conjunction with detailed, multi-segmentalmodels of the human thermoregulatory system and ther-mal comfort. With these models the thermal effect ofdirect and diffuse solar radiation on humans and the as-sociated physiological and perceptual implications can bequantified. Another possible application of the equations,besides any thermal effects, is the prediction of the UV-dose and the assessment of the associated health risks andpossible injuries to exposed body parts.

Appendix

Tables 3, 4, 5, 6, 7, 8, 9, 10

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125

Tab

le4

Pol

ynom

ial

ofth

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sic

cosi

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(Eq.

2),

B¼P4 j¼

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and

the

corr

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28

126

Tab

le6

Pol

ynom

ial

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cien

tD

1of

the

shad

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func

tion

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q.7)

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tion

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tion

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tion

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128

References

Bedford T (1935) The effective radiating surface of the humanbody. J Hyg Camb 35:303–306

Blazejczyk K (1996) Assessment of solar radiation absorbed byman based on simple meteorological parameters, 7th Interna-tional Conference on Environmental Ergonomics, Israel, Con-ference proceedings

Blazejczyk K, Nilsson H, Holmer I (1992) A modified equation forthe calculation of solar heat load in man, 5th InternationalConference on Environmental Ergonomics, Maastricht, Con-ference proceedings

Breckenridge JR, Goldman RF (1972) Human solar heat load.ASHRAE, Trans 78(1):110–119

Curious Labs (2000) POSER4: the premier 3D character animationand figure design tool. Curious Labs, Santa Cruz

DuBois D, DuBois EF (1916) A formula to estimate approximatesurface area, if height and weight are known. Arch Intern Med17:863–871

Fanger PO (1970) Thermal comfort. McGraw-Hill, New YorkFiala D, Lomas KJ, Stohrer M (1999) A computer model of human

thermoregulation for a wide range of environmental conditions:the passive system. J Appl Physiol 87:1957–1972

Fiala D, Lomas KJ, Stohrer M (2001) Computer prediction of hu-man thermoregulatory and temperature responses to a widerange of environmental conditions. Int J Biometeorol 45:143–159

Fiala D, Lomas KJ, Stohrer M (2003) First principles modelling ofthermal sensation responses in steady state and transient con-ditions. ASHRAE Trans 109:179–186

Guibert A, Taylor CL (1952) Radiation area of the human body. JAppl Physiol 5:24–37

Horikoshi T, Tsuchikawa T, Kobayashi Y, Miwa E, Kurazumi Y,Hirayama K (1990) The effective radiation area and angle factorbetween man and a rectangular plane near him. ASHRAE Trans96(1):60–66

Huizenga C, Hui Z, Arens E (2001) A model of human physiologyand comfort for assessing complex thermal environments.Building Environ 36:691–699

Jones BW, Hong S, McCullough EA (1998) Detailed projected areadata for the human body. ASHRAE Trans 104(2):1327–1339

Kimlin M, Prisi A, Carter B, Turnbull D (2002) Comparison of thesolar spectral ultraviolet irradiance in motor vehicles withwindows in an open and closed position. Int J Biometeorol46(3):150–156

Miyazaki Y, Saito M, Seshimo Y (1995) A study of evaluation non-uniform environments by human body model. J Hum LivingEnviron 2(1):92–100

Rizzo G, Franzitta G, Cannistraro G (1991) Algorithms for thecalculation of the mean projected area of seated and standingpersons. Energy and Buildings 17:221–230

Steinman M, Kalisperis LN, Summers LH (1988) Angle factordetermination from a person to inclined surfaces. ASHRAETrans 94(1):1809–1823

Stolwijk JAJ (1971) A mathematical model of physiological andbehavioural temperature regulation in man. NASA contractorreport CR-1855. NASA, Washington

Tanabe S, Narita C, Ozeki Y, Konishi M (2000) Effective radiationarea of human body calculated by a numerical simulation.Energy and Buildings 32:205–215

ThermoAnalytics (2001) RadTherm Technical Documentation.Thermo Analytics, Calumet

Underwood CR, Ward EJ (1966) The solar radiation area of man.Ergonomics 9:155–168

Table 10 Polynomial of thecoefficients g0, g1 of the fp,diffunction for the diffuse short-wave radiation (Eq. 8) and thecorresponding correlation coef-ficient, R

Body sectors Standing posture Sedentary posture

g0 g1 R g0 g1 R

Head 0.6460 0.3183 1.00 0.6423 0.3211 1.00Forehead 0.5194 0.4675 1.00 0.5295 0.4495 1.00Face (anterior) 0.3701 0.4716 1.00 0.3777 0.4465 1.00Face (exterior) 0.4318 0.4588 1.00 0.4354 0.4488 1.00Neck (anterior) 0.3425 0.4367 1.00 0.3532 0.4137 1.00Neck (posterior) 0.5783 0.3650 1.00 0.5671 0.3757 1.00Shoulder 0.8119 0.0927 1.00 0.7982 0.0866 1.00Thorax (anterior) 0.5603 0.3711 1.00 0.5723 0.3399 1.00Thorax (posterior) 0.4850 0.4739 1.00 0.4892 0.4995 1.00Abdomen (anterior) 0.3970 0.4954 1.00 0.3101 0.1801 1.00Abdomen (posterior) 0.4328 0.4558 1.00 0.4025 0.7381 1.00Upper arm (anterior) 0.3505 0.4036 1.00 0.2165 0.2585 1.00Upper arm (posterior) 0.4745 0.4576 1.00 0.5701 0.4464 1.00Lower arm (anterior) 0.5132 0.3639 1.00 0.3529 0.0726 1.00Lower arm (posterior) 0.3473 0.6165 1.00 0.3101 0.7620 1.00Hand (handback) 0.3966 0.4861 1.00 0.6053 0.1090 1.00Hand (palm) 0.1879 0.1894 1.00 0.0757 0.1787 1.00Upper leg (anterior) 0.4106 0.4619 1.00 0.6037 0.1081 1.00Upper leg (posterior) 0.4181 0.5203 1.00 0.3131 0.4627 1.00Lower leg (anterior) 0.4374 0.4898 1.00 0.2558 0.3077 1.00Lower leg (posterior) 0.4673 0.4728 1.00 0.4269 0.4972 1.00Foot (instep) 0.5608 0.3005 1.00 0.3663 0.3743 1.00

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