Estimating thermal resistance of dry infant bedding — Part 1: a theoretical
mathematical model
C. A. Wilson and R. M. Laing1)
1) C. A. Wilson is a Lecturer and R. M. Laing an Associate Professor in Clothing and Textile
Sciences, at the University of Otago, Dunedin, New Zealand
T: + 64 3 479 7546; Email:c.wilson@otago.ac.nz
Abstract
The purpose of this work was to develop a model for estimating 'dry' and 'wet' thermal
resistance of bedding during use. The model takes into account proportions of the body
covered by different bedding arrangements, and the effects of an infants sleep position and
method of tucking on thickness, thermal resistance and heat loss. Predictions of thermal
resistance using various published formulae are compared with those from this study.
Key words: insulation, multiple textile layers, air spaces, SIDS
1
Introduction
The possible link between thermal stress and SIDS (Sudden Infant Death Syndrome) has lead
to evaluations into how the thermal resistance and other characteristics of bedding assemblies
affects heat loss from the infant body (Bolton, et al., 1996; Fleming, et al., 1990; Nelson, et al.,
1989; Ponsonby, et al., 1992; Wailoo, et al., 1989; Wigfield, et al., 1993). Differences in sleep
position, method of tucking, and bedding products used have also been identified between
case and control infants (L'Hoir, et al., 1998; Williams, et al., 1996). For example, infants
sleeping in the prone position and those using a duvet have both been linked to increased risk
of SIDS, while firm tucking and use of a 'drycot' (a 'waterproof' under-bedding layer) have
been linked to reduced risk (L'Hoir, et al., 1998; Williams, et al., 1996; Wilson, et al., 1994).
Precisely how these variables affect the risk of SIDS is unclear. However, the method of
tucking, infant sleep position and the type of bedding affect the thermal resistance of bedding
during use (Wilson, et al., 2000; Wilson, et al., 1999b).
In an attempt to assess the risk of SIDS, different methods for estimating the thermal resistance
of clothing and bedding have been developed. Most are based on the assumption that the
covering(s) is of uniform thickness and thus resistance over the surface of both the bed and
body is uniform. Thermal resistance of bedding which consists of multiple-layers is also
commonly assumed to be estimated by adding either the thickness (Bolton, et al., 1996; Tuohy
and Tuohy, 1990) or 'dry' thermal resistance (Ponsonby, et al., 1992; Wigfield, et al., 1993;
Williams, et al., 1996) of individual layers measured flat. Estimates are commonly based on
measurements of 'dry' thermal resistance determined by Clulow (1978; 1986). The effect of
variables such as tucking and sleep position on the arrangement of bedding and air space(s)
formed during use has only recently been taken into account (Wilson, et al., 1999a; Wilson, et
al., 2000; Wilson, et al., 1999b).
During use, bedding adopts one of two possible configurations depending on it's position in
relation to the human body: i) that immediately over the body where minimal air spaces are
formed between bedding layers, and ii) adjacent to the body where larger air spaces are formed
between textile layers (Wilson, et al., 1998). This three-dimensional arrangement of bedding
affects the surface area in each configuration (i.e. minimal air spaces were estimated to be
approximately 18% of the bedding cross section in the lateral and 36% in the prone and supine
positions) (Wilson, et al., 1999b). Thus, the proportion of the bedding surface area with
minimal air spacing is relatively small. A further complicating factor is that the thickness of
bedding immediately over the body can be less than the thickness of bedding adjacent to the
body (by approximately 1000%) (Wilson, et al., 1998). Using the thickness or thermal resistance
of the multiple-layer bedding with minimal air spaces between layers to estimate the overall
insulation appears likely to result in incorrect estimates. Consequently, the relationship
between thermal resistance of bedding during use and SIDS may not have been adequately
assessed.
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
The aim of this work was to develop a theoretical mathematical model for estimating thermal
resistance of upper-bedding which accommodates the effects of sleep position and method of
tucking on the bedding configuration and thus thermal resistance.
2
Theoretical analysis
This model of the three-dimensional bedding system is based on the following assumptions:
i
the thickness of clothing does not contribute to overall thermal resistance of the
bedding;
ii
the infant chest is circular and the body (excluding the head) is thus
represented by the frustum of a cone;
iii
the mattress and bedding beyond the feet and edges of the bed form superinsulating barriers (i.e. no heat is lost from the body along the x-axis (Figure 1a
and b) and thus the effective surface area available for heat transfer does not
extend to the edges of the bed;
iv
heat loss through bedding immediately adjacent to the body ranges from
negligible along the x-axis to almost the equivalent to that which occurs
immediately over the body at the z-axis;
v
the proportion of the bedding with minimal air spacing between layers remains
constant along the length of the 'body' (y-axis) because as the diameter of the
'body' decreases along its length the width of the bedding across the x-axis
decreases; and
vi
as the diameter of the 'body' decreases along its length the combined thickness
of the bedding plus air layers adjacent to the 'body' decreases.
a
Axes describing the orientation of the bedding in use
z
y
Length
Height
Body
90°
x
0°
Width
b
Distance along the bedding surface (x axis)
z
zi+1
zi
bi
x
xi xi+1
á
á á
100mm 300mm 450mm
c
Surface area of the nude 'body'
df3
z
y
df2 or D3
df1 or D2
l3
l2
D1
Section 3
l1
Section 2
Section 1
x
Figure 1
Orientation of the bedding during use and variables used to estimate the width of the bedding
surface (x axis) and surface area of each section of the 'body' (y axis)
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
A number of surface areas and proportions of the body are required to estimate heat loss i.e.
the nude surface area of the body; the effective surface area of the bedding; the proportions of
the bedding surface area across the width of the bed (x-axis) with minimal air spaces and with
air layers between; and the proportions of the bedding surface area along the y-axis.
The nude surface area, represented by the frustum of a cone excluding the frustum ends
(Figure 2a), is:
(1)
" D+ df %
A = πl $
'
# 2 &
where:
A
D
df
l
=
=
=
surface area of the frustum (m2), i.e. the nude surface
maximum diameter of the frustum (m) i.e. the chest
minimum diameter of the frustum (m) i.e. foot length
=
length of the frustum (m) i.e. recumbent length (crown to foot)
(Booth, 1975)
Coverings change the surface from which heat is lost and also increase the surface area
available for transfer. The distance between two sites along the bedding cross-section (x-axis)
was used to determine the length of the surface. The two boundary sites were selected by
examining bedding cross-sections and considering the extent of contact between the upper
sheet and mattress layer (Wilson, et al., 1999b). Total distance along the surface of the bedding
(Figure 1b) and distances over and adjacent to the body were estimated for two sleep positions
(lateral and prone/supine) and three tucking arrangements (loosely, or firmly tucked or
swaddled) according to:
(2)
8
bT =
∑b
i
i=1
where:
bT
bi
=
=
total distance of the external bedding surface along the x axis (mm)
surface distance of segment i between sites (mm) e.g. 100 to 150 mm (Figure 1b)
"
bi = $
#
i
xi
zi
=
=
=
(z i +1 − z i ) 2 + ( xi +1 − xi )2 %'&
segment across the width of the mattress surface (50 mm), i = 1-10
measurement site i = 1-8 (mm), i.e. sites 100 to 500 mm
thickness of bedding at site xi (mm)
and
b over =
∑
i
where:
biover
biadj
=
=
bi over
and
badj =
∑
bi adj
i
surface distance of bedding over the body along the x axis (mm)
surface of bedding adjacent to the body along the x axis (mm)
Proportions of the bedding over and adjacent to the body were thus:
badj
b
x over = over and xadj =
bT
bT
where:
xover
=
xadj
=
(3)
(4)
proportion of the external enclosing surface (i.e. the bedding) over the body with
minimal air spaces between
proportion of the external enclosing surface adjacent to the body with air spaces
between
Distance along the surface of the bedding across the foot (Figure 2b) was estimated by
comparing the total distance across the surface of the bedding (determined using the bedding
cross-section across the shoulders of the 'body') with the perimeter of the nude 'body' for each
sleep and tucking position according to:
(5)
Dper. = πD
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
and distance aT estimated:
aT = bT
(6)
df per
Dper
The effective surface area of the bedding was therefore:
Aeff = 0.5l ( aT + bT ) (1− 0. 21c )
where:
Dper
aT
df per
Aeff
c
(7)
=
=
=
=
perimeter of the 'body' (m),
distance across the bedding surface (x axis) at the 'bottom' of the 'body'
perimeter of the 'body' (m),
total surface area of the bedding available to transfer heat to the ambient
=
environment (m2)
constant, where c=1 if the head is uncovered and c=0 if the head is covered.
a
Frustum of a cone
b
Surface area of a trapezoid
aT
l
bT
Figure 2
Variables used to calculate the surface area of a frustum of a cone and surface area of the
bedding trapezoid
The surface area, thermal resistance of bedding and thickness of the various air spaces formed
adjacent to the 'body' decrease down the length of the bed (y-axis) as diameter of the 'body'
decreases. Thus the length of the body was divided into three sections. The thermal resistance
of section 1 was estimated using the material and air arrangement formed at site 450 mm (xaxis) and section 3 the arrangement at site 100 mm (x-axis) (i.e. based on foot length). Section 2
was estimated as intermediate between sections 1 and 3. The proportions of nude surface area
of the 'body' resulting from each section (Figure 1c) were estimated as:
(8)
" Di + d f i %
Asi =
π lsi $
'
2 &
#
i
∑
where:
Asi
=
surface area of each section of the frustum, i = 1-3 (m2)
Di
=
upper diameter of section i, where i = 1-3 (m)
dfi
=
lower diameter of section i, where i = 1-3 (m)
lsi
=
length of each section of the frustum, where i = 1-3
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
The length of each section was determined using a 1:2:1 ratio and surface area calculated
(Equation 1). The decrease in diameter between the top (D) and bottom (df) of the 'body' was
determined by estimating the Di and dfi for each section as follows (Figure 1c):
(9)
ΔD = (D − d f ) /4
and
df 1 = D − ΔD = D2
d f 2 = D2 − ( ΔD ⋅ 2) = D3
d f = D3 − ( ΔD) = d f
3
and the proportion of the surface area accounted for by each section was calculated according
to:
(10)
As
ysi = i where : A = A s1 + A s2 + As 3
A
(
where:
df1-3
D1-3
=
=
=
=
ΔD
ysi
)
lower diameter of each section of the 'body' (m)
upper diameter of each section of the 'body' (m)
change in diameter between the upper and lower ends of the total 'body'
a constant representing the proportion of surface area attributable to each section of
the 'body', where i = 1-3
'Dry' and 'wet' thermal resistance of bedding during use are thus estimated according to:
-'
0
!
$*
R ct = Rct over x over + . ) R ctadj ys1 + Rct adj ys 2 + # Rct
y s3 & ,x adj 1
s1
s2
adj
"
%+
s3
/(
2
(
)
(
) (
)
(11.1)
(11.2)
(
where:
Ret = Ret
over
Rctadj Si
=
x
over
) + -./ ')(( R
etadj s1
ys
1
) + (R
et adj s2
ys
2
) + !#" R
et adj
s3
0
$*
ys & , x 1
3 % + adj
2
R ct adj = 0. 278 + 0.0127 d − 0. 0024da1 + 0.00226 da 2 + 0.0143 da 3 − 0.0041da 4
− (0. 344if duvet is present)
Retadj Si
=
R et adj = 0. 024 + 0. 0010d − 0. 0002da 1 + 0. 0018da 2 − (0.0346 if duvet is present)
Rct over
=
Rct over i.e. minimal air spaces between layers (m2K/W) where
R ct over = 0.051 + 0. 023d − (0. 469 if duvet is present)
Ret over
=
(Wilson, et al., 1999a)
Ret over where there are minimal air spaces between layers (m2kPa/W) according
to Wilson, et al., (2000):
R etover (if no duvet is present
) = 0.001+ 0.002d
or
R etover (if a duvet is present
) = −0.007 + 0.001d
d
=
thickness of the air spaces dai determined according to Wilson, et al. (1999b))
and total thermal resistance of the material and adherent air layer as:
(10)
RctT = Rct + Rctad
RetT = Ret + Retad
where:
RctT
=
RetT
=
Rctad
=
total 'dry' thermal' resistance of the bedding assembly during use including
resistance of the adherent air layer (m2K/W)
total 'wet' thermal resistance of the bedding assembly during use including
resistance of the adherent air layer (m2kPa/W)
'dry' thermal resistance of the adhering air layer (m2K/W) (Wilson, et al., 1999a):
R ct ad = 0.197 − 000343d ad
Retad
=
'wet' thermal resistance of the adhering air layer (m2kPa/W)(Wilson, et al., 2000):
0.2411
R et ad = 0.0111dad
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
Total heat loss was thus:
QT = Qd + Qe
(13)
where:
" (T − T a ) %
Qd = $ sk
'
# R ctT
&
(13.1)
" (P − Pa ) %
Qe = $ sk
'
RetT
#
&
(13.2)
and
where:
3
QT
Qd
=
=
total heat transfer (W/m2)
'dry' heat transfer (W/m2)
Qe
=
'wet' heat transfer (W/m2)
Application of the model
The application of this model depends on access to information about the infants sleep position
and tucking arrangement (which affect size and distribution of air spaces), and bedding
combinations used. Ambient environment and skin temperature, and vapour pressure data
are also required. Data on infants is required. However, given the age of the infants in
question (<1 year) and the ethical issues surrounding measurement of some sleep and
wrapping combinations (e.g. the prone sleep position and/or duvet use have been identified as
increasing risk of SIDS) alternatives to direct validation of the model such as using manikins,
were investigated. However, while infant manikins exist, they are either partial infant
manikins (e.g. a hip manikin for assessing diapers), too large for the purposes of this study (a
toddler), or simplified premature manikins designed for testing incubators (Bolin, et al., 1989;
Nanameki, et al., 1998; Sarman, et al., 1992). Thus, validation of the model requires laboratory
data from a balance study (similar to that described by Wigfield et al., (1993)) prior to
application of the model to SIDS case and control data. Validation will form Part two of this
series.
To compare resistance and heat loss values calculated using this model with those published
by other researchers (Bolton, et al., 1996; Ponsonby, et al., 1992; Wailoo, et al., 1989; Wigfield, et
al., 1993), the model was applied using 'set' values identified from the published literature.
Four bedding combinations (a sheet (S), a sheet and nine blankets (S+9A), and two of the most
common bedding combinations (a sheet and two air-cell blankets (SAA) and a sheet, two aircell and duvet (SAAD)) commonly used to cover New Zealand infants were used (Wilson, et
al., 1994). Items were:
ii
cotton sheet, plain weave, napped, 18.8 x 16.6 yarns/10mm; thickness X =2.5,
s.d.=0.3 mm;
wool blanket, cellular or air-cell, weft faced, 5.2 x 4.0 yarns/10mm; thickness
iii
X =6.0, s.d.=0.3 mm;
panel quilt or duvet, bulked polyester filling; polyester/cotton, woven plain
i
weave cover, 32.8 x 19.5 yarns/10mm; thickness X =34.8, s.d.=1.8 mm.
The thickness of bedding/air combinations formed during use was measured as previously
described in Wilson, et al., (1999b) and relevant thermal resistances determined (Wilson, et al.,
1999a; Wilson, et al., 2000).
Dimensions of the 'infant' were assumed to be: weight 5100 g; chest circumference 0.37 m;
recumbent length 0.56 m; foot length 0.08 m; surface area of the nude 'body' 0.14 m2 (Snyder, et
al., 1977). An example of surface areas for the lateral sleep position and other variables are
given in Table I a-c.
When estimating total heat loss (Equation 13), temperature, relative humidity and vapour
pressure at the skin surface were assumed to be Tsk = 35.0°C, 20% R. H. and thus Psk =3.17 kPa
with no sensible water loss, and ambient conditions Ta = 16.7°C, 50% R.H. Psk = 0.38 kPa
(Bolton, et al., 1996; Tuohy and Tuohy, 1990).
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
Table I
Surface
areas,
variables
and
thickness
used
to
estimate
integrated
thermal
resistance
of
the
bedding
system
(m,
unless
otherwise
stated)
Tucking and manikin
position
a
cc
bT
aT
Surface areas in the lateral sleep position
Loose
0.66
0.46
Swaddled
0.58
0.41
Firm
0.67
0.46
bover
0.05
0.11
0.05
badj
0.61
0.48
0.62
xover
0.08
0.19
0.08
xadj
Aeff
0.92
0.81
0.92
(m2)
0.24
0.21
0.24
0.19
0.17
0.19
b Section variables
Section 1
Section 2
Diameter (m )
D
df
0.12
0.11
0.11
0.09
0.09
0.08
0.12
0.08
Length (m)
0.11
0.22
0.11
0.44
Surface area (m2)
0.04
0.07
0.03
0.14
Proportions (ysi)
0.29
0.50
0.21
1.00
X
s.d.
c
Thickness of bedding (mm)
S
SAA
SAAD
S+9A
1.65
10.25
60.80
41.00
Aeff
cov
(m2)
Section 3
unc.
Total
0.23
0.25
2.43
0.46
cov. = head covered
unc. = head uncovered
4
Results
The estimated thermal resistance of dry bedding immediately over the manikin with minimal
air spaces between layers ranged from 0.29 to 1.19 m2K/W for 'dry', and from 0.02 to 0.10
m2kPa/W for 'wet' thermal resistance (Figure 3 a). 'Dry' and 'wet' thermal resistance of all
bedding combinations differed significantly (F3,356=23877.55, p≤0.001; F3,356=60440.02, p≤0.001
respectively). Thermal resistance ('dry' and 'wet') of the sheet and nine blankets layers was
310% and 400% (respectively) greater than that of the sheet only.
Thermal resistance of bedding adjacent to the manikin with air spaces between layers ranged
from 0.18 to 1.02 m2K/W for 'dry' and from 0.02 to 0.08 m2kPa/W for 'wet' thermal resistance.
Depending on the tucking and sleep position resistance varied from that with minimal air
spaces between by -17 to 29% and -50 to 30% respectively (Figure 3a). However, when
comparing mean values only, thermal resistances did not vary significantly irrespective of
whether thickness of bedding adjacent to or immediately over the body, was used to estimate
resistance (t3 = 1.61, NS; t3 = 0.52, NS).
The 'dry' and 'wet' thermal resistances of the bedding estimated using the integrated model are shown in
Figure 3b. 'Dry' thermal resistance of the entire bedding assembly ranged from 0.27 to 1.12 m2K/W and
'wet' thermal resistance from 0.02 to 0.10 m2kPa/W. Differences between the thermal resistance of
bedding adjacent to the body and that determined using the integrated model ranged from -50% to 7%
for 'dry' and -25% to 33 for 'wet' thermal resistance.
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
a minimal air spaces between and that with air spaces between
0.12
1.4
1.2
0.10
1.0
0.07
0.8
0.6
0.05
0.4
0.02
0.2
0.00
0.0
S
SAA
SAAD
S+9A
S
Bedding combinations
SAA
SAAD
S+9A
Bedding combinations
b minimal air spaces between and the 'integrated' model
1.4
0.12
1.2
0.10
1.0
0.08
0.8
0.06
0.6
0.04
0.4
0.02
0.2
0.00
0.0
S
SAA
SAAD
S
S+9A
SAAD
S+9A
Bedding combinations
Bedding combinations
Minimal air spaces between
SAA
Sleep positions and tucking arrangement combinations used to
calculate resistance of bedding from thickness of bedding with
air spaces between or using the integrated model
Lateral, loose
Prone, loose
Supine, loose
Lateral, sw/fm
Prone, sw/fm
Supine, sw/fm
Figure 3
Estimated 'dry' and 'wet' thermal resistance of bedding
Differences reflected the effect of tucking and sleep position, and thus the non uniform
thickness of bedding, on thermal resistance of the bedding during use.
Type of bedding combination (F3,359=18845.67, p≤0.001; F3,359=23523.98, p≤0.001), sleep
position (F2,359=2211.96, p≤0.001; F2,359=1944.24, p≤0.001), and tucking arrangements
(F2,359=471.69, p≤0.001; F3,359=4344.22, p≤0.001) significantly affected both 'dry' and 'wet'
thermal resistance respectively when estimated using the integrated model. Sleep position and
tucking arrangement also had a combined effect on thermal resistance of the bedding
(F6,359=97.03, p≤0.001; F6,359=120.54, p≤0.001).
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
The estimated total heat losses ranged from 223.65 to 44.40 W/m2 immediately over the
manikin through bedding with minimal air spaces and from 257.86 to 46.46 W/m2 adjacent to
the manikin through bedding with air spaces (Table II). As expected the most heat was lost
through the sheet and least through the sheet and nine air-cell blankets. Estimating total heat
loss through bedding using thickness of bedding immediately over the manikin only, masked
differences which resulted from the various manikin positions and methods of tucking.
The use of mean total heat loss to represent the losses through bedding adjacent to the body
does not adequately describe the possible range of losses through the various bedding
configurations (Table II b). Estimates of thermal resistance using the integrated model
illustrated differences in resistance over the surface of the bed during use. Thus calculating
heat loss using estimates of thermal resistance derived using the integrated model are likely to
be better representative of what actually occurs.
The predicted thermal resistances using various formulae (Bolton, et al., 1996; Ponsonby, et al.,
1992; Wailoo, et al., 1989; Wigfield, et al., 1993) were compared with those from this study and
are shown in Figure 4.
5
Discussion
Conclusions formed about total heat loss for a specific level of insulation and ambient
conditions are likely to be erroneous if based i) only on thermal resistance of bedding with
minimal air spaces between layers and ii) if the effect of 'wet' thermal resistance is not
accounted for. With the exception of Bolton (1996), the effect of 'wet' thermal resistance of
materials on their insulation has been largely ignored (Fleming, et al., 1990; Nelson, et al., 1989;
Ponsonby, et al., 1992; Wailoo, et al., 1989; Wigfield, et al., 1993). When thermal resistance
estimated using the integrated model is compared with that of other researchers it can be seen
that use of mean values subsumes the effect of differences in the distribution and size of air
spaces among sleep positions and tucking arrangements.
Use of mean values based on
thickness of bedding with minimal air spaces between layers fails to address the question of
how methods of use affect insulation and thus risk of SIDS.
The integrated model proposed in this paper enables the effect of body position and tucking on
the thickness of bedding adjacent to the body to be accommodated by utilising thickness of
bedding with air spaces between layers in the calculation of thermal resistance. Thus the
model accommodates differences in thickness of bedding both across and down the length of
the bed; proportions of the bedding with minimal air spaces and air spaces between layers; and
how these variables affect both 'dry' and 'wet' thermal resistance of the bedding.
Researchers have suggested that SIDS cases have greater thermal insulation for a given room
temperature than matched controls (Ponsonby, et al., 1992); that SIDS is associated with too
little insulation (i.e. when not firmly tucked in infants become more vulnerable to SIDS)
(Williams, et al., 1996); and that thermal resistance of bedding over a prone infant is greater
than that over other sleep positions. However, methods used to estimate thermal insulation do
not appear to have been sufficiently sensitive to differences in resistance to enable the
relationship between SIDS and insulation levels to be satisfactorily assessed. For example,
thermal resistance of loosely tucked bedding estimated using the integrated model were
consistently higher (up to 27%) than firmly tucked bedding or bedding over swaddled infants,
irrespective of sleep position. In addition, the prone sleep position (implicated in risk)
generally resulted in thermal resistance values intermediate between that for the same bedding
over a body in the lateral and supine positions. Re-examination of the relationship between
insulation level and risk of SIDS is required. Part II of this series will address validation and reexamine the relationship between insulation and risk of SIDS.
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
Table II
Estimated total heat loss through bedding (Ta=16.7°C, Pa=0.380; Tsk=35.0°C, Psk=3.172 kPa)
2
(W/m , n=10)
S
X
a
s.d.
X
SAAD
S+9A
s.d.
X
s.d.
X
s.d.
1.62
57.37
2.32
44.40
0.42
75.11 14.36
61.36
9.10
Over the body with minimal air spaces between
223.65
b
SAA
5.27
118.32
Adjacent to the body with air spaces between
Overall mean
155.72
58.77
146.41
31.09
Loose
131.74
1.12
101.66
0.70
68.03
2.90
57.39
0.39
Swaddled
257.86
3.79
168.79
1.78
97.36
5.92
75.74
0.66
257.86
3.79
168.79
1.78
97.36
5.92
75.74
0.66
Loose
115.75
0.76
93.68
0.55
66.56
2.73
55.73
0.36
Swaddled
156.41
1.39
118.68
0.88
78.70
3.86
63.73
0.47
Firm
156.41
1.39
118.68
0.88
78.70
3.86
63.73
0.47
Loose
Swaddled
82.93
121.27
0.40
0.84
70.68
97.13
0.32
0.59
53.37
67.96
1.76
2.85
46.46
56.85
0.25
0.37
Firm
121.27
0.84
97.13
0.59
67.96
2.85
56.85
0.37
Lateral
Firm
Prone
Supine
c
Integrated — both over and adjacent to the body
Lateral
Loose
111.00
0.79
88.63
0.54
61.20
2.38
51.99
0.34
Swaddled
198.22
2.61
134.45
1.32
79.05
4.06
62.53
0.53
Firm
195.62
2.32
137.06
1.26
83.42
4.42
66.21
0.54
Loose
131.21
1.28
97.27
0.77
61.76
2.54
50.55
0.39
Swaddled
170.62
2.33
114.44
1.15
66.17
2.97
52.64
0.45
Firm
171.33
2.36
114.50
1.16
65.98
2.96
52.46
0.45
99.27
0.74
78.25
0.51
52.73
1.86
44.57
0.30
Swaddled
144.64
1.68
102.04
0.92
61.37
2.57
49.71
0.41
Firm
136.18
1.39
99.61
0.82
62.23
2.59
50.82
0.40
Prone
Supine
Loose
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
a
'Dry' thermal resistance
2.0
1.5
1.0
0.5
0.0
S
SAA
SAAD
S+9A
Bedding combination
b
'Wet' thermal resistance
50
40
30
20
10
0
S
SAA
SAAD
S+9A
Bedding combination
c
Heat loss
1000
800
600
Wilson and Laing model
400
Bolton, et al., (1996)
200
Nelson,et al., (1989); Wailoo, et al., (1989)
Fleming, et al., (1990); Wigfield et al., (1993)
0
S
SAA
SAAD
S+9A
Bedding combination
Figure 4
Comparison of estimates of 'dry' and 'wet' thermal resistance and total heat loss derived using the
integrated model of Wilson and Laing with that of selected authors
Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
6
Conclusions
The total thermal resistance of the upper bedding used for infant care is not adequately
described by either the thickness of bedding immediately over or that adjacent to the body. The
model proposed accommodates differences in thickness and thermal resistance across the
bedding and allows their effect on total heat loss to be taken into account. Total heat transfer
through bedding combinations should thus be determined using the integrated method rather
than estimated from thickness of bedding immediately over the infant.
Use of the integrated model to estimate thermal resistance of bedding used to insulate infants
in their homes, assumes that the air layer arrangements documented and ambient and skin
temperature and vapour pressure are representative of those that occur during actual use.
Estimating 'dry' and 'wet' thermal resistance of (Equation 12) and heat loss through (Equation
13) infant bedding used in the home requires measurement of:
i
infant weight, chest circumference and both recumbent and foot length;
ii
classification of bedding composition as either duvet(s) or other;
iii
total thickness of the bedding assembly when arranged flat and with minimal
air spaces between; and
iv
ambient and infant skin temperature and relative humidity under conditions of
use. For example during a nominated sleep or as soon after death as possible.
Acknowledgements
The assistance of J. Anderson, B. Niven, Burston Nuttal, and Alliance Textiles Ltd. is gratefully
acknowledged. When measuring thickness of the bedding C. Wilson was supported partially
by the New Zealand Cot Death Association, a division of the National Child Health Research
Foundation.
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Authors Post-print. The final definitive version of this paper, Wilson, C. A. and Laing, R. M. 2002. Estimating thermal
resistance of dry infant bedding. Part 1: A theoretical mathematical model. International Journal of Clothing Science and
Technology 14 (1): 25-40. is available at
http://www.ingentaconnect.com/content/mcb/058/2002/00000014/00000001;jsessionid=hhp9wpwv0y19.alice
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Cheryl A Wilson