Common clothing area factor estimation equations are inaccurate for highly insulating (Icl>2 clo) and non-western loose-fitting clothing ensembles.

The aim of this study was to evaluate the equations for calculating the clothing area factor (fcl) used in the standards based on data sets of clothing ensembles, that are meant to provide thermal comfort over a wide range of climatic conditions from hot summer days to extremely cold winter. Over 10 equations for fcl calculations were selected from the international standards and the literature. At first a theoretical comparison based on a range of insulation values was performed. Then the data sets were used to compare the equations and measurements on real clothing systems. Most of the fcl calculation equations do give reasonably good results for western type and industrial clothing with basic insulation (Icl) up to 1.5 clo. Above the Icl of 2 clo, the error in the calculations based on traditional equations increases considerably and they overestimate fcl. Some new equations were suggested for modern clothing systems. Oppositely, for non-western clothing (for hot climate), the available equations did give good match only for very light clothing sets and commonly underestimated the real fcl. For such sets and and fashion clothes their own equations maybe needed, that count for various design aspects, e.g. fit, draping etc.

Introduction

Besides climate factors (air temperature, mean radiant temperature, air velocity, humidity) and activity level / metabolic heat production, many standards for evaluating human exposure to thermal environments, e.g. ISO 79331) (heat), ISO 77302) (indoor climate), ISO 110793) (cold) use basic clothing insulation (Icl) as one of the input variables. Clothing ensemble insulation can be measured on a thermal manikin4, 5) or estimated based on available literature or databases where other, similar clothing items and ensembles have been measured6,7,8,9,10,11). Manikin measurements do provide directly the total (IT) or resultant total (IT,r) insulation. In order to calculate Icl from IT an air layer insulation (Ia) and clothing area factor (fcl) are needed: (1)

fcl is the ratio of the outer surface area of the clothed body to the surface area of the nude body, and it counts for the increase in the surface, that is in contact with surrounding air where the heat exchange occurs. Ia can be measured on a nude manikin and is commonly an essential part of manikin testing as one of the solid reference values, while fcl can be estimated by photographic method, 3D scanning etc.7, 11,12,13,14,15,16) or calculating based on the variety of equations in the literature and standards3, 8, 17). However, as the equations commonly are based on databases, that to a large extent are based on indoor and moderate climate clothing, then it can be assumed, that for heavy protective clothing, the equations are not valid. ISO 99208) also defines the application range of the equations between 0.2 and 1.7 clo. In this large database, there are seldom occurring any combinations that have fcl over 1.5, while the calculations according to the most equations exceed 1.5 when Icl reaches above 1.5–2 clo. An exception from the other equations is one developed during Subzero project18) that focused especially on measurements of cold protective clothing on thermal manikins6, 17).

The aim of this study was to evaluate the equations for calculating the clothing area factor used in the standards based on professional modular clothing system offered for ambulance personnel, that is meant to provide thermal comfort over a wide range of climatic conditions from hot summer days to extremely cold Nordic winter19). In addition, some other databases, including the one of non-western clothing7), were utilized for comparison in order to widen the scope of this work.

Materials and Methods

Clothing

The clothing elements were acquired from a Swedish manufacturer Taiga AB and were selected based on assumptions, that the various layers were designed to work together in any of the possible combinations. 27 items were selected and tested on a thermal manikin Tore at Lund University thermal environment laboratory in stationary mode in wind still conditions. Based on the ISO 9920 summation method over 100 realistic clothing ensemble insulation values were calculated, and finally, 14 sets (Fig. 1) were selected to cover as evenly as possible the estimated basic insulation range from 0.63 (T1) to 3.33 (T14) clo. The insulation of the selected sets was measured on a thermal manikin and clothing area factor was estimated with the photographic method based on 2 pictures: a side and a front view, following the recommendations of Havenith et al7). The measured insulation of selected sets ranged from 0.53 (T1) to 3.19 (T13) clo. Table 1 shows the total and basic insulation19) and total and clothing evaporative resistance20) of selected clothing combinations, and the measured fcl. The full details of the measurements, and description of the clothing items and the ensembles is available in Kuklane and Toma19).

Fig. 1.

14 sets consisting of items from the Taiga AB ambulance system. Number under each figure defines number of items in the set. Details of the items are available in Kuklane and Toma19).

Table 1.

cl from photographic method, total and basic clothing insulation, and total evaporative resistance and clothing evaporative resistance of selected clothing combinations (for methodological background see Kuklane 29), Toma 20), Toma 30)).

	fcl	IT	Icl	Ret	Recl
		(m2K/W)	(m2K/W)	(m2Pa/W)	(m2Pa/W)
AL*	1.00	0.094
SK**	1.03	0.131	0.040	9.1
T1	1.15	0.164	0.082	17.1	8.9
T2	1.18	0.197	0.118	22.2	14.3
T3	1.27	0.277	0.204	30.9	23.5
T4	1.29	0.290	0.218	39.2	31.9
T5	1.39	0.336	0.269	66.9	60.1
T6	1.38	0.380	0.312	68.3	61.5
T7	1.28	0.298	0.226	47.4	40.1
T8	1.44	0.431	0.366	92.2	85.6
T9	1.40	0.386	0.319	88.4	81.6
T10	1.44	0.430	0.365	96.6	90.0
T11	1.41	0.440	0.373	95.7	89.0
T12	1.49	0.546	0.484	114.9	108.6
T13	1.49	0.557	0.495	121.9	115.6
T14	1.45	0.525	0.460	112.9	106.4

*AL is air layer insulation measured on nude manikin.

**SK is the textile skin that was used only during evaporative resisitance measurements.

Additionally, some datasets, e.g. Subzero18) and database for non-western clothing7) etc., were utilized in the analysis to avoid one-sided discussion on the topic.

Calculation of clothing area factor (fcl)

According to ISO 110793) and ISO 79331) (based on McCullough et al.9)) fcl shall be calculated by equation: where

However, in the algorithm available in the official IREQ webpage3) (http://www.eat.lth.se/fileadmin/eat/Termisk_miljoe/IREQ2009ver4_2.html) the equation is used in the form ofwhere is also available (row 195, in heat storage estimation where is used in IREQ related calculations (row 74, for IREQ iteration).

Also, a different version of this equation is published in Patty’s Industrial Hygiene chapter on cold stress21):

It is a question why the equations in the standards differ. It is even more unclear why the standard on cold protection3) and related publications21) present different equations with similar digits in the used numbers.

According to ISO 99208), the clothing area factor is calculated according to the following equations: if if

According to ISO 77302) if clothing insulation is above 0.078 m2K/W then

As mentioned in the Introduction there are two other ways available to calculate fcl, that have been developed especially for cold protective clothing in the course of the Subzero project17, 18). They are based on total clothing insulation (IT) measured by parallel method (IT)22) and on Icl:

The equation with IT is valid if it is measured at low air velocity where natural convection dominates. It may be very convenient to use, as IT is the value that we acquire directly from the manikin test.

In a recent publication on modern western clothing database Smallcombe et al.10) suggest new equations:orif with fixed constant. These last equations were tested by Smallcombe et al.10) for basic clothing insulation less than 1 clo, i.e. the range covered also by the standards.

Equations 2, 3, 6, 7, 9, 10, 11, 12 and 13 were used in comparison. In order to evaluate and compare the equations various steps were performed. In order to study the differences systematically, a theoretical list of the insulation was created (0–5 clo with steps of 0.25 until 2 clo and further by 0.5 clo) and the equations were compared. However, as some equations utilized different insulation than basic clothing insulation in calculations, then also several databases were used, e.g. non-western clothing7), Subzero project17, 18), separate unpublished data sets etc., were scanned for measured fcl and relevant insulation values. The data was used to compare the equations and measurements on real clothing. Thereafter, the combinations of the ambulance clothing were utilized to picture the differences within the same clothing system.

Results and Discussion

Comparison based on theoretical clothing basic insulation

Comparison of the theoretical list (Fig. 2) showed that equation 2 gave the highest values followed by ISO 99208) equations (Eq. 7; Eq. 8 is identical but adapted for different insulation unit (clo)), and Eq. 9 from ISO 77302). However, the results did not differ considerably and stayed in the same range being reasonable up to about 2 clo, but reaching to 2.32 to 2.53 for 5 clo. The equation used for fcl calculation in ISO 11079 algorithm (Eq. 3) provided considerably lower values even when similar Icl was used in the equation instead of Iclr (1.93 for 5 clo). If all theoretical insulation values were reduced by 20% to simulate corresponding Iclr, then the difference with the results by standard equations was even larger (1.74 for 5 clo). If to look in ISO 99208) tables with clothing ensembles’ Icl and fcl, then of those many combination only very few reach fcl of 1.5 or above, and none is above 2. The range and values for the higher insulation values from 1.5–2 clo are much more similar to the ones acquired by Eq. 3.

Fig. 2.

Theoretical cl calculation results with measured cl from Taiga ambulance (AMB) system for reference. Red lines with arrows mark cl of 1.5 and insulation of 2.0 clo.

Smallcombe et al.10) did check fcl and Icl relationship with modern western indoor clothing and suggested new equations (equations 12 and 13) that give somewhat lower fcl than the original equations, while the calculations for higher insulation values still stay in the same range as the standard equations (equations 2, 7–9) provide, i.e. far above 1.5. The difference may have been caused by modern clothing being in general more tight fitting than the ones from the previous decades.

Non-western clothing

When comparing measured and estimated fcl of non-western clothing7) (Fig. 3) then it can be seen that instead of over-estimating the fcl, the calculations underestimated them. Many of these clothes were traditional, 1–2 layer thin clothing sets for hot climates with loose fit and covering large body areas for being able to ventilate well during motion and to protect skin from solar (UV) radiation, i.e. in opposite to the modern western clothing trends. The measured fcl was commonly higher than the estimated one. Very light clothing (full body not covered, sets with several layers (for cold season in warm countries) or the ones influenced by western style were often the closest points to the line of identity and for the standard calculations. Although, for these type of clothes (wide, loose fitting) a separate equation with fixed constant can be suggested:

Fig. 3.

Comparison of estimated and measured cl of non-western clothing based on Havenith 7).

then due to relatively high variation (R2=0.601, Fig. 3), the adjustments may be required based on specific clothing (design) parameters, e.g. fit, draping, layering etc. On the other hand, this equation may make a reasonably correct estimation of fcl for some specific fashion styles. The equation is very close to the one developed by Havenith et al.7) (as based on practically the same dataset). The equation is also close to an equation suggested by Ke and Wang23) for Chinese traditional minority groups’ clothing that also represent relatively loose-fitting garments. In that study fcl was derived with a 3D scanning methodology instead of the photographic method.

Cold protective clothing

Completely opposite trend was observed for the cold protective clothing (Icl>1.5clo, Fig. 4). Only the lower end (for 1.5–2 clo) of the standard calculations stayed reasonably close to the line of identity. At the same time, modifications of Eq. 2, the Eqs. 3, 5 and 63, 21) and the equations from Subzero project, Eqs. 10 and 1117) provided reasonably close measured and estimated fcl values. It allows to assume that the possible suspected errors in IREQ algorithms3) and in Holmér21), all addressing cold protection, have been intentional adjustments. The closest to the line of identity for this small set of protective clothing were Eqs. 6 and 10. It would be positive to use Eq. 10 as the manikin measurements provide total clothing insulation and if measured according to ISO 99208) suggestions in static and low wind conditions (<0.2 m/s) then fcl of heavy protective clothing could be estimated directly.

Fig. 4.

Comparison of estimated and measured cl of cold protective clothing from various published studies where cl by photographic method was available6, 19) and from some unpublished data sets.

Ambulance clothing system

The same trend as for cold protective clothing was observed also for the ambulance clothing system that included a sequence from light clothing to heavy protective ensembles (Fig. 5).

Fig. 5.

Measured vs estimated cl of Taiga AB ambulance clothing system.

If now the specific clothing sets were compared, then the outcome differed depending on the set. Subzero equations (Eqs. 10 and 11)17) and ISO 110793) equation (Eq. 3) provided very similar results that did fit well not only with Subzero sets, but also with other modern professional clothing and sets with high insulation. In some cases, these clothing sets could be with quite low insulation while the calculated fcl was in a reasonable range compared to the measurements by photographic method. Subzero results were available for ISO 110793) developers and thus Eqs. 3 and 6 may have got inspiration from Eqs. 10 and 11.

Protective clothing against extreme heat, i.e. with insulation layers, would most probably act as cold protective clothing, and thus, Eqs. 3, 6, 10 and 11 are expected to be more relevant in those cases. Based on ambulance system the Subzero Eq. 10 could be modified by changing intercept and then the closest results to the line of identity can be acquired (Fig. 5):

Simultaneously, creating trendlines for the whole ambulance system separately, it can be seen that the best fit is given by a curvilinear line (Fig. 6). The suggested equation in this case is:

Fig. 6.

Clothing area factor (cl) relation with basic insulation (cl) for Taiga AB ambulance clothing system.

The general curvilinear (parabolic) relationship between fcl and Icl was recently also suggested by Ke and Wang23). Although they showed linear relationships between local intrinsic clothing insulation and local fcl, they demonstrated a curvilinear relationship between local intrinsic clothing insulation and local clothing air gap size23). Thus, considering special clothing systems and advanced thermo-physiological predictions, then it might be useful to create such clothing system specific relationships for these, too.

Expected impact of using fcl on Icl calculation and physiological responses

Although nowadays it is possible to measure clothing area by 3D scanning, then photographic method is still widely used7, 10). A reason for that may be that photographic method is a cost-effective and simple method that has been validated in numerous studies and backed up by international standards. There are some studies that allow comparison of photographic and 3D scanning methods for fcl calculation12, 14). The study by McCullough et al.14) showed that the 3D method gave in average somewhat higher fcl than the photographic method. Their study covered a range of protective clothing and they recommended the use of the photographic method. Another, a recent study12), provided basic parameters for advanced modelling and compared mainly local values and different postures, but also a variety of evaluation methods on 2 indoor garment ensembles. This thorough study provided the 3D scanning accuracy values, too. However, as the focus of that study was on individual body areas and body postures, then it was not possible to utilize it directly for comparing 3D scanning with the commonly used whole body fcl estimation in standing posture by the photographic method. The difference for various body areas differed and was not always in the same direction even for the used 2 types of the indoor clothing ensembles. In spite of the higher claimed accuracy of 3D scanning method, this method is not easily available for occupational health and safety specialists in the field because of the cost, and following the standards allows a more simple approach. For wider use of 3D scanning method it needs to be standardized and interlaboratory round robin testing is needed together with the comparison of the other available methods. Furthermore, the new fcl algorithms for wide range of clothing insulation have to be developed based on 3D scanning. Until then the suggested improvement of the fcl calculation provided in this paper is still useful.

A separate question is how much fcl affects insulation calculation and any predictions’ outcome. For example, EN 34224) omits fcl in Icl calculations (there is Icl = Itot−Ia). The motivation has been that in the case of cold protective clothing the subtracted part would be up to about 0.1/1.5=0.07 m2K/W and skipping fcl in the calculation would put the worker on more safe side in relation to cold. If the purpose of the testing is plain certification and comparison of clothing ensembles, then it does not really matter very much if fcl is used. However, if the aim is to use the measured values for modelling and prediction, then the use of fcl is justified. If to count maximal fcl of a clothing ensemble being 1.5 by measurements and 2.0 by calculations, then the difference in Icl estimation could be 0.02 m2K/W. This is around the insulation difference where human start feeling the difference between various ensembles. Brady et al.25) stated that the influence of fcl on Icl is generally small. However, the subjective feeling or an objective measure, e.g. skin temperature change will also depend on total insulation of clothing ensemble itself. In a way, depending on cooling/heating speed and local sensitivity of skin, this outcome of the discussion would match with the predictions by Fojtlín et al12). In their study based on physiological model predictions the mean skin temperature differed 0.4 °C and local skin temperatures up to 0.6 °C due to differences in local fcl values.

General discussion

Equations 2, 7–9 did fit best with insulations <1.5 clo, and for non-western clothing7) even above 2 clo. It seems that the number of the layers, fit (tight or loose), the presence of thermal liners/layers that fill the air gaps between textile layers and possibly the flexibility of the textiles plays role in the outcome7, 11, 13, 23, 26).

The modern professional clothing, especially for cold conditions contain tight fitting underwear and thermal liners that fill open space between different garments, while non-western and other traditional and warm weather clothes are loose fitting and adding an additional layer increases the outer surface relatively more compared to increase in insulation. For cold protective garments, it is probably not the case—relatively rigid outer layer’s outer surface is not able to expand too much and defines the surface area and it can’t be expanded much. Instead large air gaps between garments are filled with insulation materials of the thermally protective middle layers.

For improving ISO 110793) (see also the critical review by d’Ambrosio Alfano et al.27) and any predictions for highly protective clothing the relationships between the listed factors and fcl need to be studied, developed and validated. Until then equations from ISO 11079 algorithms (Eq. 3)3) and Holmér (Eq. 6)21) or from Subzero project (Eqs. 10 and 11)17) could be used for basic clothing insulation above 1.5 clo but should certainly be used if above 2 clo. With relatively light clothes in warm climates (>+10 °C) and for estimated basic insulation less than 1.5–2 clo ISO 99208) equations (Eqs. 7, 8) should be used. In the range of 1.5 to 2 clo the equation choice could be decided depending on the fact, if prediction models for warm or cold climate are used (above or below 10°C).

A separate question is, if and how much different approaches of fcl calculation affect IREQ prediction outcome. In order to be sure of proper predictions, the changes in the model must be investigated and tested against available databases of human exposures to cold and actual physiological responses while based on other studies12, 25) there can be expected a small but observable difference.

Any mobile decision-making tools using physiological and clothing models for thermo physiological evaluation of the environment and personal or professional advice, e.g. ClimApp28), should count with the deviations created in the calculations from fcl estimations. The range of using the equations should be limited by the range of clothing insulation, but even better if design factors could be considered. The latter may be difficult in practice while modern technology could provide a solution, e.g. by taking a picture of the clothing ensemble and feeding it to a specific algorithm.

Conclusion

Most of the clothing area factor (fcl) calculation equations do give reasonably good results for western type and industrial clothing with basic insulation (Icl) up to 1.5 clo. Above the basic clothing insulation of 2 clo, the error in the calculations based on traditional equations (2, 7–9) and the ones suggested by Smallcombe et al. (Eqs. 12 and 13)10) increases considerably and they overestimate fcl. The calculation accuracy by these equations in the range of 1.5–2 clo may still be acceptable, while it can be strongly recommended to use equations developed during Subzero project and related equations instead. These equations (10, 11 and 15) should be used for clothing with basic insulation above 2 clo.

For modern clothing systems based on western industrial clothing a curvilinear relationship between Icl and fcl gives the best fit over the wide range of insulation values. However, this relationship may be related only to this system and must be validated on other clothing ensembles. Considering that often very similar materials and close design is utilized for modern industrial clothing, then it can be expected, that the generalization is possible and the use of Eq. 16 can be widened.

For non-western clothing (for hot climate), that with their variety may also represent the wide variation in fashion the available equations do give good match only for very light clothing and commonly underestimate the real fcl. For such sets their own equation is needed, but as the variety is large then for reasonable accuracy various design aspects, e.g. fit, draping etc., should be included in the calculations.

Disclaimer

The opinions or assertions contained herein are the private views of the authors and are not to be construed as official or as reflecting the views of their respective organizations.