Heat transfer variations of bicycle helmets

Abstract

Bicycle helmets exhibit complex structures so as to combine impact protection with ventilation. A quantitative experimental measure of the state of the art and variations therein is a first step towards establishing principles of bicycle helmet ventilation. A thermal headform mounted in a climate-regulated wind tunnel was used to study the ventilation efficiency of 24 bicycle helmets at two wind speeds. Flow visualization in a water tunnel with a second headform demonstrated the flow patterns involved. The influence of design details such as channel length and vent placement was studied, as well as the impact of hair. Differences in heat transfer among the helmets of up to 30% (scalp) and 10% (face) were observed, with the nude headform showing the highest values. On occasion, a negative role of some vents for forced convection was demonstrated. A weak correlation was found between the projected vent cross-section and heat transfer variations when changing the head tilt angle. A simple analytical model is introduced that facilitates the understanding of forced convection phenomena. A weak correlation between exposed scalp area and heat transfer was deduced. Adding a wig reduces the heat transfer by approximately a factor of 8 in the scalp region and up to one-third for the rest of the head for a selection of the best ventilated helmets. The results suggest that there is significant optimization potential within the basic helmet structure represented in modern bicycle helmets.

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Heat transfer variations of bicycle helmets
P. A. BRU
¨
HWILER
1
, M. BUYAN
1
, R. HUBER
1
, C. P. BOGERD
1
, J. SZNITMAN
2
,
S. F. GRAF
2
, & T. RO
¨
SGEN
2
1
Empa, St. Gallen and
2
Institut fu¨r Fluiddynamik, ETH Zu¨rich, Zu¨rich, Switzerland
(Accepted 4 November 2005)
Abstract
Bicycle helmets exhibit complex structures so as to combine impact protection with ventilation. A quantitative experimental
measure of the state of the art and variations therein is a first step towards establishing principles of bicycle helmet
ventilation. A thermal headform mounted in a climate-regulated wind tunnel was used to study the ventilation efficiency of
24 bicycle helmets at two wind speeds. Flow visualization in a water tunnel with a second headform demonstrated the flow
patterns involved. The influence of design details such as channel length and vent placement was studied, as well as the
impact of hair. Differences in heat transfer among the helmets of up to 30% (scalp) and 10% (face) were observed, with the
nude headform showing the highest values. On occasion, a negative role of some vents for forced convection was
demonstrated. A weak correlation was found between the projected vent cross-section and heat transfer variations when
changing the head tilt angle. A simple analytical model is introduced that facilitates the understanding of forced convection
phenomena. A weak correlation between exposed scalp area and heat transfer was deduced. Adding a wig reduces the heat
transfer by approximately a factor of 8 in the scalp region and up to one-third for the rest of the head for a selection of the best
ventilated helmets. The results suggest that there is significant optimization potential within the basic helmet structure
represented in modern bicycle helmets.
Keywords: Helmet ventilation, bicycle, comfort, heat exchange
Introduction
Bicycle helmets provide effective protection of the
head from impacts (Attewell, Glase, & McFadden,
2001), which is their primary function. However, the
physiological aspects of bicycle helmets are of
increased interest (Bru¨ hwiler, 2003; Bru¨ hwiler,
Ducas, Huber, & Bishop, 2004; Coment, Batsale,
Ladevic, & Caillibotte, 2000; Ellis, Bertolini, &
Thompson, 2000; Gisolfi, Rohlf, Navarude, Hayes,
& Sayeed, 1988; John & Dawson 1989; Quanten
et al., 2004; Reid & Wang 2000; Sheffield-Moore
Nomenclature
A effective heat transfer area (m
2
)
h channel height (m)

h
c
average heat transfer coefficient
(W  m
72
)
k thermal conductivity (W  m
71
)
l channel length (m)
n number of channels
Nu
l
Nusselt number, Nu
l
¼

h
c
l/k
?
Pr Prandtl number, Pr ¼ v
?
/a
?
Q

conv
forced convection heat transfer rate (W)
Q
t

total heat transfer rate (W)
Re
l
Reynolds number, Re
l
¼ V
?
 l/v
?
T temperature (8C)
DT temperature difference (8C)
V velocity (m  s
71
)
w channel width (m)
a thermal diffusivity (m
2
 s
71
)
d momentum boundary layer (m)
(continued)
d
t
thermal boundary layer (m)
 kinematic viscosity (m
2
 s
71
)
lam laminar (subscript)
turb turbulent (subscript)
s scalp (subscript)
? ambient air (subscript)
Correspondence: P. A. Bru¨ hwiler, Empa, Lerchenfeldstrasse 5, CH-9014 St. Gallen, Switzerland. E-mail: paul.bruehwiler@empa.ch
40522 23/1/06 20:53 RJSP_A_145770 (XML)
Journal of Sports Sciences, Month 2006; 24(0): 1 – 13
ISSN 0264-0414 print/ISSN 1466-447X online Ó 2006 Taylor & Francis
DOI: 10.1080/02640410500457877

et al., 1997; Wood, 1986). Many manufacturers have
therefore prioritized wearing comfort, with some of
the most advanced designs touting optimized venti-
lation, including maximum heat transfer. Some
manufacturers have carried out wind tunnel studies
(Ellis et al., 2000), and presumably subject studies as
well. Nevertheless, given the large variation in
designs on the market, there is no widely adopted
systematic approach to designing bicycle helmets for
optimal ventilation. A quantitative survey of a large
number of modern helmets is required to understand
the role of ‘‘common sense’’ parameters, such as the
number of holes in the helmet, since the helmet
geometries are complex. In particular, the impor-
tance of forced, rather than natural, convection
complicates a qualitative a priori analysis.
Subject studies have been a traditional tool for
quantifying helmet heat transfer (Abeysekera &
Shahnavaz, 1988; Davis, Edmisten, Thomas,
Rummer, & Pascoe, 2001; Holland, Laing,
Lemmon, & Niven, 2002; Hsu, Tai, & Chen,
2000; Liu, Abeysekera, & Shahnavaz, 1999; Patel &
Mohan, 1993; Quanten et al., 2004; Wood, 1986),
but generally suffer from higher cost and lower
precision than instrumental studies. Several strate-
gies have been suggested for objectively measuring
the performance of bicycle (Bru¨ hwiler, 2003;
Coment et al., 2000; Ellis, 2001; Reid & Wang,
2000) and other helmets (for a brief review, see
Bru¨ hwiler, 2003). The construction of the helmet
suggests guidelines for a successful measurement. In
particular, openings and air passages must be
constructed through the helmet shell to achieve
forced convection ventilation; these vents and
channels vary in their design and placement, requir-
ing a measurement that is not sensitive to local
variations at the cost of an accurate overall measure.
An exception to this principle would be if portions of
the head covered by the helmet had different
sensitivities to cooling. At present, we are unaware
of established results bearing on this issue. The
average heat transferred from the head is a simple,
robust parameter that satisfies this criterion, and
is accessible to mea- surement using a thermal
headform (Abeysekera, Holme´r, & Dupuis, 1991;
Bru¨ hwiler, 2003; Osczevski, 1995).
We report a study of the heat transfer of an
ensemble of 24 modern bicycle helmets encompass-
ing a broad cross-section of designs. The ensemble
was a mixture of adult models found in the European
market (including North American models), ranging
from typical helmets to those aimed at enthusiasts.
The head angle and wind speed were varied between
two possibilities each, covering a range of typical
cycling situations. Key parameters affecting the
cooling performance were then studied, and in
selected cases strategic modifications were applied
to illustrate basic trends. One helmet was studied in
detail in a flow visualization tunnel, confirming the
results of the heat flow measurements. Finally, a
simple model has been developed to help understand
relevant parameters for bicycle helmet ventilation.
Materials and methods
The headform used for the measurements of heat
transfer is described in detail elsewhere (Bru¨ hwiler,
2003). Its circumference is approximately 57 cm. It
consists of two measurement sections, face and
scalp, as well as a neck section heated to eliminate
conductive heat exchange with the support. The
headform was covered with a slightly elastic synthetic
fabric to aid the dispersion of water during perspira-
tion tests (not reported here). This represented a
noticeable insulation and caused lower heat transfer
than normal; thus the power values determined here
are useful for mutual comparison only. The steady-
state powers were reduced in the presence of the
covering by a factor of 2.2 in the face section and
1.4 in the scalp section in tests with selected helmets
at 6.1 m  s
71
. For the studies of altered helmet
configurations, the fabric was removed to increase
the sensitivity of the apparatus.
The headform was heated to a constant surface
temperature of 358C and placed at the exit of a small
wind tunnel, which in turn was located within a
climate chamber set to 258C and 60% relative
humidity. All values of the required heating power
correspond to steady-state measurements. After
choosing the conditions (helmet, angle, wind speed,
etc.), the experiment was allowed to settle, usually
stabilizing after around 30 min. Then a period of
20 – 30 min was used to determine an average
heating power in each section, as illustrated in
Bru¨ hwiler (2003). This is long compared with the
time-scales of transient changes in the wind speed or
head angle typically encountered in real situations; it
represents an instrumental limitation necessary to
obtain reproducible values. Notably, it yields values
consistent with the (much faster) subjective percep-
tions of humans with regard to the head angle
(Bru¨ hwiler et al., 2004).
The headform was placed so as to be centred in the
wind tunnel. The wind speed was measured as
described elsewhere (Bru¨ hwiler, 2003), and was
varied between two values, 1.6 m  s
71
(6 km  h
71
)
and 6.1 m  s
71
(22 km  h
71
). The angle dependence
of the heating power was studied by setting the head
angle to 08 and 308, giving four measurement
constellations. The headform height was adjusted
to maintain the centring as the angle was varied.
All helmets were studied in the configuration in
which they were sold, which often meant including a
visor – this can have a notable affect on the results for
2 P. A. Bru¨hwiler et al.

a given helmet, but not on the overall trends, and will
be treated in more detail in a later publication. The
soft pads normally included were mounted as
seemed appropriate to ensure at least a minimum
of comfort to a human wearer. The helmets were
placed to have the front brim approximately 3.5 cm
above the bridge of the nose, in accordance with
impact testing standards, using a small mark on the
headform to ensure reproducibility. Three measure-
ments were carried out with each helmet, and the
uncertainties equated to the standard deviation of
these. Further statistical evaluations were carried out
with standard software (SPSS, Version 13.0.1).
Unless otherwise stated, we used one-way analysis
of variance with Tukey-HSD post-hoc analysis of the
differences in mean values.
Results and discussion
Cooling power
The results for the steady-state power, or cooling
power, delivered to the headform are shown for
both measurement sections and for all helmets in
Figure 1. (We will henceforth call this ‘‘cooling
power’’ because it is the power transferred from the
Figure 1. Steady-state heating power required to maintain the headform at 358 in the (a) scalp and (b) face sections, for the indicated
helmets. The helmet numbers are arbitrary; the helmets have been ordered based on the performance in the scalp section for the ‘‘Slow, 308’’
condition. ‘‘N’’ denotes the nude headform.
Heat transfer variations of bicycle helmets 3

head to the environment via forced convection
through the helmet; thus, this quantity is propor-
tional to the ventilation performance of the helmet –
that is, to its cooling potential.) The ordering of the
helmets was referenced to the performance for the
‘‘Slow, 308’’ condition in Figure 1(a). As one would
expect, the overall cooling power increases with the
wind speed. Also, the variations in the face section
are much smaller than those for the scalp, since the
helmets cover only a small fraction of the face. Other
observations are more difficult to explain.
We focus first on the scalp section, for which the
variations are largest. We note that while there are
minor variations in the inter-helmet ranking from
condition to condition, the basic trend for a given
angle is independent of the wind speed over the
measured range. We summarize the statistical
significance of the measured variations as follows,
focusing again on the ‘‘Slow, 308’’ condition:
differences are generally not significant (P 4 0.05)
for helmets which differ by five to seven rankings or
less in either direction; this is true for the other
conditions as well, but with the rankings based on the
condition under consideration. There are stronger
variations in the rankings when changing the angle,
extending the results of a previous study involving
humans (Bru¨ hwiler et al., 2004). In general, cooling
power remains about the same or increases when
changing from 08 to 308. Since a bicycle helmet lets
air flow through, it is natural to consider the scalp
surface as the heat transfer surface, and so the
cooling power can also be considered in terms of a
percentage of that of the nude headform (Bru¨ hwiler,
2003); for the present ensemble, it varies in the
extreme case from about 65% to about 93%,
illustrating the breadth of designs with respect to
ventilation.
The nude headform exhibits the largest cooling
power under all conditions studied here (P 5 0.001),
showing that all helmets tested must be considered
as cooling barriers to some extent, at least in the
tested range of wind speeds. This is in contrast to
the results of Reid and Wang (2000), who found that
the best helmets were indistinguishable at 6.7 m  s
71
from a nude headform, using 13 thermocouples.
The disagreement is difficult to resolve without
testing the same helmets, but the possibility that the
thermocouple placement in the study of Reid and
Wang may have favoured particular helmets must be
considered, as it is unlikely that even the best
helmets of the mid-1990s could outperform those
of the last two years, which are included in the
present ensemble. The fact that Reid and Wang
included an optimization of the thermocouple
placement suggests that the present thermal head-
form is more accurate in determining overall
ventilation performance.
The most notable feature in the data for the face
section is that helmets 7 and 10 have lower cooling
power than all other helmets under all conditions,
although this difference is significant only for about
two-thirds of the helmets. After comparing the
construction of helmets 7 and 10 with that of
the others, we attribute this difference to the fact
that the head bands of these two helmets cover the
face in the temple area relatively tightly, allowing
virtually no airflow. Other helmets have similar
constructions, but the headbands are placed higher,
so limiting the cooling power, primarily in the scalp
region. This important avenue for airflow was noted
by Ellis (2001), and is discussed again later. The
difference found of up to 1 W is in principle
noticeable to the wearer, suggested by facial sensi-
tivity to radiant power differences of this magnitude
found in a recent subject study (Buyan et al., 2006),
but it is premature to draw general conclusions since
the role of sweating and sweat collection, for
example, is not understood. The results in the face
section indicate that the role of ‘‘auxiliary’’ elements
of the helmet, such as the headband and, in
principle, the straps, can have a significant influence
on the ventilation properties.
Air transport into a helmet: Vent cross-section
To begin to elucidate the variations displayed
in Figure 1(a), we measured the cross-sectional
vent area of each helmet for both angles, using
the simple method illustrated in Figure 2. [See
the legend to Figure 2 for a basic description. The
difficulty in this estimate arises due to the three-
dimensional character of the vents. Figure 2(b)
illustrates the most subjective aspect, the selection
of the contributing cross-section of a vent. We
imagine a fluid being pressed against the vent, and
assume that surfaces angled towards the inner
boundary contribute positively; other surfaces are
considered neutral or negative contributors, and are
omitted from the integration. Surfaces outside the
vent (Figure 2b) are neglected. Helmets 10 – 13 and
20 – 22 had netting in the forward vents, which was
ignored.] This extracts an approximate value based
on the frontally projected area likely to contribute to
airflow into the helmet. We compare the values
determined in this manner to the scalp cooling
power at 6.1 m  s
71
(22 km  h
71
) for both angles in
Figure 3.
As indicated by the coefficients shown in Figure 3,
a moderate, significant overall linear correlation is
suggested by the traditional analysis at both angles.
Helmet 3 at 308 constitutes an apparent outlier, with
a forward vent cross-section of over 130 cm
2
; this
in itself indicates that vent cross-section can be
negatively compensated for by other factors, which
4 P. A. Bru¨hwiler et al.

we consider in more detail below. Removing this
point from the regression calculation decreases the
correlation coefficient from 0.49 to 0.42 and reduces
the confidence from 98% to 95%, explaining our
notation in the figure. If one were to examine
helmets that were more uniformly constructed, it is
Figure 2. Schematic of the method to determine projected helmet vent cross-sections. (a) Photograph of a helmet at 308 tilt angle, with
calibration area in white at right. (b) The inner opening is included in its entirety, the outer opening only to the extent that it clearly
augments the flow of air via the intermediate surfaces, as described in the text. (c) The final areas to be counted are marked by hand in the
digital image. (d) The marked pixels are integrated and compared with the calibration to yield the total cross-section in square centimetres.
Figure 3. Comparison of the cooling power of Figure 1 in the scalp section with the frontal vent cross-section at the indicated angles, for the
fast wind setting. The correlation coefficients are indicated, with the approximate result for 308 explained in the text.
Mono
for
print
colour
online
Heat transfer variations of bicycle helmets 5

likely that stronger correlations would emerge.
Finally, we note that the largest cross-sections are
found at 308, as are the highest heat transfer values,
although for similar cross-sections (i.e. between 40
and 50 cm
2
) the heat transfer is higher at 08,
suggesting that helmets are possibly optimized for
ventilation at 08.
The present results can be contrasted with an earlier
subject study of temperature changes under bicycle
helmets (Wood, 1986), which yielded excellent
correlation between front vent cross-section and
ventilation for five helmets of that time. The opposite
conclusions reached there could be explained by a
greater uniformity in helmet designs, with the vent
cross-section being the limiting factor for those
helmets. The small ensemble, with several helmets
from one manufacturer, limits the comparison to the
present study. Thus, the present results show overall
that the vent cross-section alone does not generally
determine the achievable level of ventilation.
Air transport through a helmet: Channel blockage
The helmet channels – that is, the volume between
head and helmet available for airflow – are required
for transport of air under the helmet, but are included
to a varying extent and with varying configurations in
the helmets studied here. To better understand how
these channels are involved in the helmet ventilation,
we first chose four of the best-performing helmets and
compared the cooling power with and without a
blockage of the channels (Figure 4a) at an angle of
308. The results in Figure 4(b) are clear, showing that
air flowing at the back of the scalp is responsible for a
sizeable share of the total scalp cooling. Since smaller
changes in cooling power can be detected by humans
(Bru¨ hwiler et al., 2004), which establishes that
the rear of the helmet can be important for overall
ventilation performance. For Helmet 3 we also
removed a comfort pad that blocked the channels in
the central scalp area when measuring the ‘‘normal’’
configuration, which resulted in a dramatic impro-
vement of the cooling power, confirming this
fundamental principle for a state-of-the-art helmet,
and showing that the designed configuration was not
optimized. Thus forced convection is an effective
cooling mechanism throughout these helmets, due at
least in part to the existence of channels leading from
the front to the rear of the helmet.
Roles of the rear vents
Openings out of the channels in the middle of the
helmet could reduce the cooling power by directing
air inward to counter the flow from the forward
vents, or by directing air out of the helmet before it
has been fully exploited for cooling. Alternatively,
they may enhance the airflow, and thus the cooling
power, by reducing the pressure at the rear as in the
Venturi Effect, or by opening exit channels where the
flow would otherwise be blocked. We examined
some of these possibilities by selectively blocking
vents in such a way that the channels underneath
were unaffected. Figure 5(a) illustrates our chosen
modification for one helmet, which consisted of
covering all vents into which air could not stream
from the forward direction; the other helmets were
modified similarly.
Figure 5(b) displays the effects of the modifica-
tions for a subset of our ensemble at an inclination of
308, including four of the helmets with superior
ventilation (numbers 3, 8, 16, 17). Note that Helmet
3 exhibits a relatively higher cooling power due to the
removal of a comfort pad, as explained in the
previous subsection. For three helmets, there is a
noticeable effect of sealing the rear vents. For
Helmets 8 and 3, this improved the ventilation.
Both have a relatively large air channel volume
towards the rear, suggesting that airflow prematurely
exits the helmet through those vents in the normal
configuration. For Helmet 2, the cooling power
decreased in the closed-vent configuration. We
found that the air channels converge to a single,
narrow channel at the rear of this helmet; hence in
the normal configuration, the rear vents serve as flow
enhancers for this case, compensating for a poorer
channel design. Effects such as these may explain the
higher sensitivity at the back of a headform found in
an earlier study of six helmets (Reid & Wang, 2000).
They serve to illustrate the dependency of forced
Figure 4. (a) Schematic of the test of air flow restrictions under the
helmet. (b) Resultant effects on the measured cooling power at an
angle of 308 (note that the synthetic fabric covering the headform
was removed, and the wind speed set to 3 m  s
71
, increasing the
power values relative to Figures 2 and 3). The symbols are
approximately the size of the measurement uncertainties. The lines
through the points are provided as a visual aid.
6 P. A. Bru¨hwiler et al.

convection in bicycle helmets on the details of the
coupling of the vents and channels.
Effects of hair
Here we consider the influence of hair. Hair
‘‘configuration’’ varies widely among individuals;
nevertheless, although the participants in our study
of perceptions of head angle dependence (Bru¨ hwiler
et al., 2004) exhibited large differences in hairstyle
and hair thickness, they responded similarly on
average, suggesting that hair might represent a
quantitative rather than a qualitative effect on helmet
ventilation. We investigated this by placing a wig on
the headform, as illustrated in Figure 6(a).
Figure 6(b) displays the cooling power at 08
inclination with the wig, using the same helmets as
in Figure 5(b). The power values are markedly
reduced (by factors of about 8) in the scalp section.
The insulation of the wig itself is the dominant effect
in this case, as shown by the ‘‘Wig Only’’ measure-
ment. The post-hoc analysis of the differences
indicated that the ‘‘Wig Only’’ result is significantly
different from that for Helmets 8, 16, and 17
(P 5 0.001), as well as Helmet 3 (P ¼ 0.03). Helmet
3 gave a result significantly different from the other
helmets, which were not mutually significantly
different, as can be seen from Figure 6. Differences
in the scalp area of about 1 W of convection cooling
can be sensed by humans under such conditions
(Bru¨ hwiler et al., 2004), whereas differences of 0.3 W
of radiant heating in the face cannot (Buyan et al.,
2006). This suggests that all helmets measured
would be perceived as cooling barriers in the
presence of hair, and that Helmet 3 could be
perceived as somewhat better than the other three
(i.e. an improvement of this helmet over the others
compared with the case without the wig). Given the
wide variation in human hair (thickness, stiffness,
curliness), and a possible role for perspiration in
determining the hair heat transfer characteristics, a
much broader study involving human participants
would be needed to generally quantify the role of hair
in (lessening the) cooling of the scalp.
The face section cooling is also reduced by the
wig; compared with the nude case, the cooling power
reductions are approximately 10% for the ‘‘Wig
Only’’ condition and 33% when wearing a helmet,
indicating that for the face the effect of a helmet is
significant and noticeable. The intuitively obvious
result of these measurements is that the face will play
a more important role in forced convection cooling
of the head for persons with thick hair than for those
with thin hair. Inter-helmet comparison shows that
only Helmets 3 and 8 are mutually significantly
different. The average difference between these of
1 W is comparable to a change in radiant heating
detectable by humans (Buyan et al., 2006), suggest-
ing that helmets could be partially optimized for
comfort by designing them to minimize the insula-
tion due to hair outside of the helmet itself.
Overall, it is important to realize that the wig may
also bring about an air buffer on the manikin surface
(primarily in the scalp section), creating a level of
Figure 5. (a) Schematic of the test of air flow patterns through the
non-forward-facing vents; selected vents were covered as de-
scribed in the text. (b) Resultant effects on the measured cooling
power at an angle of 308 (note that the synthetic fabric covering the
headform was removed, and the wind speed set to 3 m  s
71
,
increasing the power values relative to Figures 2 and 3). The
symbols are approximately the size of the measurement uncertain-
ties. The lines through the points are provided as a visual aid.
Figure 6. (a) Photograph of the headform capped by a wig, used to
test the effects on airflow in the presence of hair. (b) Resultant
effects on the measured cooling power at an angle of 08 (note that
the synthetic fabric covering the headform was removed, and the
wind speed set to 3 m  s
71
, increasing the power values relative to
Figures 2 and 3).
Heat transfer variations of bicycle helmets 7

insulation above what a natural head of hair would
constitute. For this reason, the present results must
be considered with caution, suggesting that large
amounts of hair will reduce cooling power, as
expected, and that the issue requires further study
if helmet ventilation for such cases is to be optimized.
Flow visualization
Here we report results of a water tunnel study of
Helmet 8. Via Reynolds similarity, the flow char-
acteristics in water can be chosen to correspond to
those in air, and using dye traces details of the flow
patterns between helmet and scalp can be followed.
To accomplish this, the helmet and a head model
were digitized and reproduced at a scale of 1 : 3,
which enabled them to be mounted in the water
tunnel, as shown in Figure 7(a). [The helmet was
produced in white plastic and the head in transparent
silicone (Type RTV615), which was chosen due to
its exceptionally low index of refraction (Hopkins,
2000), which minimizes visual distortions]. A water
speed of 0.38 m  s
71
was selected, which corre-
sponds via Reynolds similarity to the full-size system
in air at a speed of 1.6 m  s
71
. The flow was
visualized by emitting dye into the tunnel upstream
from the helmet (Figure 7b). Further details are
given elsewhere (Graf, 2004).
It is not possible to show photographic images
demonstrating the full flow patterns. Instead, hand-
sketched traces summarizing the observed patterns
are presented in Figure 8, which displays traces
observed at the two head angles, with and without
modifications to the helmet. For this helmet, it was
convenient to divide the vents into regions. The dye
traces are represented in different colours corre-
sponding to their entrance points (see colour in
online version). It is important to bear in mind that
the traces do not represent flux rates.
Several patterns common to both angles are
apparent for the pristine helmet upon inspection of
Figure 8. The dark blue traces, for example,
represent flow entering at the lower edge through a
side vent (Region II), which exits via a lower side/rear
vent (Region V). The dark green trace depicts flow
into Region I, and out of the helmet via several vents
in Regions IV and V. A second aspect of the
ventilation shown only at 308, but common to both
angles, is flow underneath the front rim of the helmet
and then over the scalp; this is suggested to be a
frequent occurrence in a popular report (Ellis, 2001).
Flow into Region I at 308 was, however, difficult to
achieve, suggesting that it provides a relatively minor
contribution to the convection cooling power of the
helmet at this angle. Other characteristics also vary
noticeably as a function of angle; for example, the
vents in Region III act as intake ports at 308 (red
trace). In addition, the side vents in Region II act as
exit ports. Note that the scalp cooling power of this
helmet is a weak function of the angle, illustrating the
complex relationship between details of the flow and
the cooling power.
Blocking the rear vents, as detailed on p. 000 (in
Regions IV and V), is illustrated in the lower part of
Figure 8. An obvious consequence is that flow
emerges in Region III at 08 inclination, or cannot
successfully enter the helmet in Region III at 308
inclination, compared to the pristine case. This
appears to be the consequence of a pressure increase
in Regions IV and/or V for this configuration. At the
same time, much of the flow remains inside the
helmet, emerging beyond the back rim; this strikingly
confirms the deductions to that effect on pp.
000 – 000.
Heat transfer surface
It would be desirable to quantify the channels to
compare helmets as was done with the vent cross-
section. An obvious parameter related to the
channels is the exposed scalp surface, since area
Figure 7. (a) Photograph of the 1 : 3-scale silicone head model
with helmet, mounted in the water tunnel at 308 tilt. (b)
Illustration of a flow visualization measurement, looking from
the underside of the head. A dye trace, manually darkened in the
image, enters the front of the helmet from the right, just below the
helmet symmetry axis, deviates downwards as it passes between
helmet and head, and demonstrates turbulence at the rearward
side, before exiting the helmet as a dispersed trace just below the
symmetry axis.
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8 P. A. Bru¨hwiler et al.

correlates with heat transfer in a simple geometry.
We measured this for the headform by taking the
total scalp area of 554.7 cm
2
(Bru¨ hwiler, 2003), and
subtracting from that the area of all parts of the
helmet that came into contact with the scalp section
of the headform. We estimate the overall uncertainty
in this determination to be about 10 cm
2
. The results
are shown in Figure 9.
The spread of the points in Figure 9 is greater than
the overall uncertainty in the data would justify,
assuming that all helmets should follow a specific
trend; this is also reflected in the correlation
coefficient of 0.60, corresponding to the solid line
shown. As a comparison, we included the dashed line,
which connects the extremes of zero area (zero heat
transfer) to the area and measured heat transfer of the
nude scalp section. This (arbitrary) line passes
centrally through the data, suggesting that the role
of the free scalp surface is broadly reflected in the data
overall, but about half the helmets lie quite far from
this line. The moderate correlation for this compar-
ison is comparable to that found for vent cross-section
(see p. 000). It must partially reflect design weak-
nesses of the channels as discussed earlier for Helmet
2; in addition, a strong correlation would require that
other helmet parameters vary little as a function of the
free scalp surface area, including those that we have
not attempted to define here, such as vent form, local
angles of entry and exit, channel geometry, and so on.
What the data in Figure 9 strongly suggest is that the
ratio of cooling power to free scalp area could be used
as a development criterion, with the bare head value
as a quality guideline for optimization efforts,
especially considering that greater helmet contact
with the scalp (naively) allows better impact distribu-
tion in an accident.
Figure 8. Sketches of the dye traces observed in the water tunnel experiment for the indicated angles and helmet modifications. The upper
left sub-figure indicates how the vents were categorized using Roman numerals according to their approximate placement in rows, moving
from front to back; the first row is not visible, since it consists of a single horizontal vent in the front rim. Some possible flow paths are not
shown (see the text for further details).
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Heat transfer variations of bicycle helmets 9

Model calculation of the wind speed dependence
Here we develop a simple analytical model to explain
basic cycling helmet ventilation aspects, which can
help in conceptualizing the principles behind the
present observations and support future modelling
efforts. The complexity of the helmet interior has thus
far limited sophisticated modelling work, such as
computational fluid dynamics (Ellis, Wong, Bertolini,
& Thompson, 2001). Indeed, our experimental results
underscore the importance of taking that complexity
into account for absolute accuracy. We limit ourselves
here to a study of the variation of cooling power with
wind speed, and investigate the extent to which the
basic geometrical aspects are important.
The scalp is approximated as a dry, smooth surface
at a constant temperature T
s
¼ 358C, with the
surrounding air at a lower temperature T
?
, so that
DT ¼ T
s
7 T
?
4 0. The total rate of heat trans-
fer, Q
t

, between the scalp and the environment is
generally the sum of the radiant, conductive, con-
vective and evaporative rates. Forced convection is
nevertheless the only cooling mechanism included in
the model, since it dominates over all others in the
experiments.
An important issue is the choice of geometry. As a
general simplification, we assume that the inner
surface of a helmet can be considered to consist of n
identical straight channels oriented parallel to the
direction of motion, as sketched in the inset of
Figure 10. Indeed, some of the best-ventilated
helmets exhibit roughly this construction. Each
channel has one inlet and one outlet vent at the
ends, and the length l is determined by the covered
scalp surface. The channel width w and height h are
assumed to be constant, with h assumed large
enough not to affect the results.
In the Appendix, we show that the model with the
given approximations corresponds to the intuitive
picture of a heated plate. We note that, for typical
cycling velocities, one may assume that turbulence
develops along the channels, described by the
boundary layer thicknesses d
t
¼ d ¼ 0.16  l  Re
l
71/7
(Lienhard & Lienhard, 2003). This is supported by
the observation in Figure 7(b) of turbulence occur-
ring well before the flow exits the helmet.
Figure 10 presents a number of experimental
measurements at 6 and 22 km  h
71
(covering a
representative range of cooling power) as well as
the model prediction using the following parameters:
n ¼ 5, w ¼ 25 mm, which correspond to typical
values for the helmets studied here, and l ¼ 200 mm,
which is close to the length of the scalp section of the
headform. T
?
was set to 258C, as in the experiments.
Qualitatively, the prediction matches the cooling
power variations well, slightly underestimating the
average absolute values.
The boundary layer thicknesses reach d  d
t

6mm at x ¼ l; this suggests that the value of h must
be explicitly included in the computations in some
cases, since such channels are commonly from a few
millimetres up to about 2 cm in height in real
helmets. The results reported on pp. 000 – 000 sug-
gest that the rear of the helmet contributes about
one-quarter of the scalp heat transfer in the absence
of hair, implying that the simple model should be
Figure 9. Comparison of the measured cooling power of Figure 1(a) for the ‘‘Fast, 308’’ condition to the estimated non-covered scalp surface
area for the helmet ensemble. The dashed line is defined by the points (0, 0) and that of the nude scalp (see the text for further details).
10 P. A. Bru¨hwiler et al.

valid to the extent that the assumptions hold. The
total heat transfer rate roughly follows Q
t

/ Re
0:8
l
.
An important weakness of the present model is
that it assumes a channel air speed of V
?
. The true
speed can be influenced by several factors, in
addition to the complex channel shapes and branch-
ings found in real helmets, or hair. For instance,
vents along the channel may locally change the flow,
as suggested on pp. 000 – 000. The calculation also
omits flow resistance, which would reduce the air
speed. Thermal radiation has also been neglected;
under the experimental conditions studied here, it
will contribute a constant factor of the order of 1.5 W
to the heat transfer, which would fit the measure-
ments better. The observed experimental variations
are assumed to be a consequence of varying
geometries; hence, for a detailed understanding and
quantitatively accurate calculations, one will need to
employ realistic geometries and more sophisticated
algorithms, such as finite element modelling. The
present model and associated discussion of its
limitations has nevertheless met the goal of illustrat-
ing important principles involved in bicycle helmet
ventilation, and suggests an explanation, for exam-
ple, for the observation of turbulence between scalp
and helmet reported earlier. The role of air resistance
in the channels emerges as an important open
question.
Summary and outlook
The wide variation in ventilation performance in the
present ensemble serves to emphasize the lack of
systematic understanding of the principles behind
bicycle helmet ventilation. We have shown that
intuitively important factors such as vent cross-
section or exposed scalp surface are often limited in
their impact by other parameters. This and the wide
variability in helmet performance indicate that
suboptimal combinations of relevant factors reduce
the ventilation of most helmets under the conditions
studied. A key result of the present study is the
negative role of at least some of the vents in the
cooling power of several helmets, suggesting that
helmet structure could in many cases be better
optimized for protection and ventilation simulta-
neously; effects of airflow onto the back of the neck
should be included in such efforts. The role of hair is
a non-trivial issue, with no obvious methods of
controlling its influence when present.
An important future development will be the
comparison of the measured cooling power with
finite-element calculations of steady-state heat trans-
fer. Such sophisticated calculations are needed for a
more realistic study of the role of vent form and
dimension, channel form and dimension, and so on,
and particularly the interaction of these aspects, on
the cooling power. These issues are common to
forced-ventilation problems as well (Luo, Leung,
Chan, & Wong, 2005); the possibility for the air flow
to deviate around the helmet and a desire, for
example, to limit wind resistance and noise are
peculiarities of the bicycle helmet problem. More
precise visualization studies will help to quantify the
flow characteristics. The coupling of ventilation
development work to studies of impact properties
Figure 10. Comparison of the calculated heat transfer to the data of several helmets at the two velocities studied. The experimental data were
selected to illustrate the range of cooling power measured in the present helmet ensemble. Inset: Illustration of the model used in the heat
transfer calculations. The parameters are defined in the text.
Heat transfer variation s of bicycle helmets 11

forms a desirable longer-term goal, so that improve-
ments in ventilation do not come at the expense of
the level of impact protection.
The constant temperature method of measuring
helmet ventilation gives an accurate comparison
among helmets and a guiding value for the absolute
heat transfer, but ignores the temperature shifts or
fluctuations that will occur (Quanten et al., 2004;
Wood, 1986), especially in the presence of perspira-
tion (Quanten et al., 2004). These could be important
for wearing comfort. The role of perspiration in the
presence of hair introduces new channels of cooling
(i.e. conduction) that are not trivially related to the
present study of forced convection cooling. Local
cooling sensitivities of the human head under realistic
conditions are also a long-term point of concern that
will be non-trivial to address. Ultimately, one could
also ask whether helmets should be optimized for
ventilation in different circumstances, such as profes-
sional racing, casual riding and mountain-biking,
which has a bearing on the importance of the balance
between aerodynamics and airflow through the hel-
met, as well as the typical head angles to be considered.
Acknowledgements
We thank S. Aemisegger and C. Simon of the Institute
for Rapid Product Development, Hochschule fu¨r
Technik, Wirtschaft und Soziale Arbeit St.Gallen, for
their work in constructing the miniature helmet and
headform for the water tunnel measurements, as well
as R. Swart for sending a copy of the Wood thesis.
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Appendix
Given the assumptions on pp. 000 – 000, the total
rate of heat transfer is reduced to Q
t

 Q

conv
, where
forced convection is described as usual using
Newton’s law of cooling, Q

conv
¼ h
c
ADT. A ¼ n  l  w
is the surface area over which forced convection
occurs; we assume that heat is transferred solely from
the bottom surface of the channels, consistent with
the fact that the liners used in typical helmets are
excellent insulators. Thus, the model reduces to that
of forced convection over a flat plate of length l and
width w. This analogy may be used under the
condition that the respective thermal and momen-
tum boundary layer thicknesses over each flat
plate are much smaller than the channel height – that
is, d
t
 h and d
t
 h, respectively (Lienhard &
Lienhard, 2003).
The average convective heat transfer coefficient
over the length l is Nu
l
¼

h
c
l=k
1
; where k
?
is the
thermal conductivity of the air. For forced convec-
tion over a flat plate, assuming a laminar-turbulent
transition and constant wall temperature, the
Nusselt number can be approximated as
Nu
l
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Nu
2
l;lam
þ Nu
2
l;turb
q
(Gnielinski, 1975), where
the laminar Nusselt number correlation is given by
Nu
l;lam
¼ 0:664Re
1=2
l
Pr
1=3
(Polhausen, 1921), and
the turbulent Nusselt number correlation by
Nu
l;turb
¼ð0:037Re
0:8
l
PrÞ=ð1þ2:443Re
0:1
l
ðPr
2=3
1ÞÞ
(Petukhov, 1970). The Prandtl number Pr ¼ n
?
/a
?
,
where n
?
is the kinematic viscosity of air and
a
?
is thermal diffusivity. The Reynolds number
Re
l
¼ (V
?
 l)/n
?
, for which the air is assumed
to maintain the free stream air speed V
?
. Com-
bining the above equations, the total rate of
heat transfer through the helmet with n channels
is Q

t
¼ Nu
l
k
?
 n  w  DT. Given the aggregate chan-
nel width nw, the total rate of heat transfer
depends only on the wind speed and channel length
via Re
l
.
Heat transfer variation s of bicycle helmets 13