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Thermal comfort responses to ankle-level draft under winter clothing conditions

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Authors
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Affiliations
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Tobias Kramer

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- Center for the Built Environment, University of California, Berkeley, USA -

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Junmeng Lyu

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- Center for the Built Environment, University of California, Berkeley, USA -

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- Department of Architecture, School of Design, Shanghai Jiao Tong University, Shanghai, China -

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Stefano Schiavon

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- Center for the Built Environment, University of California, Berkeley, USA -

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- Department of Architecture, College of Environmental Design, University of California, Berkeley, USA -

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- Department of Civil and Environmental Engineering, College of Engineering, University of California, Berkeley, USA -

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Published
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April 30, 2026

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1 Center for the Built Environment, University of California, Berkeley, USA
-2 Department of Architecture, College of Environmental Design, University of California, Berkeley, USA
-3 Department of Civil and Environmental Engineering, College of Engineering, University of California, Berkeley, USA
-4 Department of Architecture, School of Design, Shanghai Jiao Tong University, Shanghai, China

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Correspondence: Tobias Kramer <t.kramer@berkeley.edu>

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Abstract

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The ankle draft model incorporated in ASHRAE Standard 55 was derived from studies in which participants wore summer clothing with exposed ankles (~0.5 clo), potentially leading to overly conservative perimeter heating requirements in winter conditions where office occupants typically wear long trousers, socks, and closed-toe shoes (~0.75 clo). This study evaluated thermal comfort responses to ankle-level draft under such winter clothing conditions through controlled laboratory experiments with 51 participants. Using a within-subjects repeated-measures design, we exposed participants to nine conditions varying supply air temperature (15°C, 17°C, 19°C) and ankle-level air speed (0.1–0.7 m/s) simulating window downdraft while they wore clothing ensembles targeting 0.75 clo.

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The existing ankle draft model systematically overpredicted dissatisfaction across all conditions. While prior studies with exposed ankles reported dissatisfaction rates of 23–57%, we observed rates of only 6–20%, with the existing model overestimating dissatisfaction by an average of 2.8 times and by as much as 39 percentage points at high air speeds. We fit generalized linear mixed-effects models to data from this study and prior research, developing separate prediction equations for ankle-covered and ankle-uncovered conditions. The covered-ankle model exhibited both a lower baseline dissatisfaction risk and reduced sensitivity to air speed. Whole-body thermal sensation and ankle-level air speed were the only significant predictors; ankle air temperature and room temperature were not significant within the tested ranges.

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These findings support differentiating ASHRAE Standard 55 ankle draft criteria by clothing insulation level. Adopting a covered-ankle criterion for winter heating scenarios will enable meaningful reductions in perimeter heating requirements without compromising occupant comfort, with associated benefits for installation costs, energy consumption, and carbon emissions.

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1 Introduction

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Cold downdraft near windows is a common source of local thermal discomfort in buildings during winter. When outdoor temperatures drop, the interior surface of windows, particularly large or poorly insulated glazing, becomes significantly cooler than the surrounding air. This temperature differential causes nearby air to cool, increase in density, and descend, creating a localized airflow pattern that can cause discomfort at the lower extremities of seated occupants (Heiselberg, 1994 ). Building designers typically address this issue by installing perimeter heating systems, such as radiators or in-floor heating, to counteract the downdraft effect and to prevent thermal discomfort in the ankle region.

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The current approach to evaluating ankle draft risk relies on a predictive model presented in Liu et al. (2017), which estimates the predicted percentage dissatisfied (PPD) with ankle draft as a function of air speed and temperature at ankle level, as well as whole-body thermal sensation. This model, now incorporated into ASHRAE Standard 55 (ASHRAE, 2023), was derived from laboratory experiments conducted under cooling conditions typical of underfloor air distribution (UFAD) and displacement ventilation systems. Importantly, participants in these foundational studies, including an earlier investigation by Schiavon et al. (2016), wore summer clothing with exposed ankles, resulting in clothing insulation levels of approximately 0.5 clo.

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However, building occupants in winter typically wear substantially different attire. Analysis of the ASHRAE Global Thermal Comfort Database II (Földváry Ličina et al., 2018) indicates that median clothing insulation in office environments during heating seasons is approximately 0.75 clo, with occupants commonly wearing long trousers, closed-toe shoes and socks that cover the ankle region. This discrepancy raises an important question: does the existing ankle draft model, calibrated for summer conditions with exposed skin, accurately predict discomfort when ankles are covered by clothing?

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If the current model overestimates draft risk under winter clothing conditions, the practical implications are significant. Designers may be specifying perimeter heating systems that are larger than necessary, or installing them in situations where they could be avoided entirely. This has consequences for both first costs and operational energy consumption, as perimeter heating systems contribute to building energy use and associated carbon emissions. Conversely, if the model underestimates risk, occupants may experience discomfort that compromises satisfaction and productivity.

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The objective of this study is to evaluate thermal comfort responses to ankle-level draft under typical winter clothing conditions through controlled laboratory experiments. Specifically, we aim to: (1) characterize whole-body and local thermal perception across a range of supply air temperatures and air speeds representative of window downdraft conditions; (2) compare observed dissatisfaction rates with predictions from the existing ankle draft model; and (3) assess whether the current ASHRAE 55 criteria require adjustment for winter scenarios. The findings are intended to inform guidance on perimeter heating requirements and support more energy-efficient building design without compromising occupant comfort.

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2 Methods

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2.1 Experimental design

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We conducted a controlled laboratory experiment using a within-subjects repeated-measures design. Each participant was exposed to nine experimental conditions in a 3×3 factorial arrangement, varying supply air temperature (SAT) at three levels (15°C, 17°C, 19°C) and air speed at ankle level at three levels (low, medium, high; ranging between 0.1–0.7 m/s). The SAT and air speeds were selected to represent the range of conditions associated with window downdraft under typical winter conditions, informed by computational fluid dynamics simulations conducted as part of a broader research collaboration.

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Participants attended four sessions: an introductory session for explaining the experiment and obtaining consent, followed by three experimental sessions of approximately two hours each. Each experimental session corresponded to one SAT level, with participants experiencing all three air speed conditions within that session in a counterbalanced order. We scheduled sessions on separate days to minimize carryover effects and subjects were allowed to attend the three sessions in their preferred order.

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2.2 Climate chamber and apparatus

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We conducted the experiment in a climate-controlled chamber at the Center for the Built Environment, UC Berkeley. The chamber floor area is approximately 25 m². We set up three workstations to allow simultaneous testing of multiple participants and three seats for reacclimatization during breaks in the back of the room. Ambient room conditions were maintained at approximately 22°C operative temperature, 50% relative humidity, and background air velocity below 0.1 m/s, targeting a whole-body thermal sensation of approximately −0.5 (slightly cool) on the ASHRAE seven-point scale as calculated using the CBE Comfort Tool (Tartarini et al., 2020).

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-Figure 1: Experimental configuration and temporal protocol: (a) Seated occupant positioned 0.7 m from the custom displacement diffuser, which simulates window downdraft by directing conditioned air toward the ankle region from behind; (b) Timeline of the 120-minute experimental sessions featuring overlapping participant groups and synchronized questionnaire intervals to characterize the progression of local and whole-body thermal perception. -
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We used custom displacement diffusers to deliver conditioned air to the ankle region of participants seated at the three workstations. The diffuser was positioned 0.7 m behind each workstation, directing airflow toward the participants’ lower legs from behind and simulating the approach direction of window downdraft. The diffuser was connected to an independent air handling unit capable of delivering supply air at the target temperatures and flow rates. The three supply air temperatures (15°C, 17°C, 19°C) represent temperatures at the VAV outlet and we controlled air flow rates by damper adjustment. Turbulence intensity at the measurement location was approximately 30% (see Table 3), consistent with values reported in prior ankle draft studies (Liu et al., 2017). The three seats in the back of the room were not affected by the diffusers targeting the three workstations only.

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2.3 Monitoring

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2.3.1 Environmental

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We measured head-level air temperature (1.1 m) at each workstation using calibrated Atmocube monitors (Atmotech Inc., United States; air temperature: -40 to +125°C, ± 0.5°C, relative humidity: 0 to 100%RH, ± 2 %RH, CO2: 0 to 5000 ppm, ± 50 ppm + 2.5% of reading at standard room levels) positioned within 0.5 m of participants. To measure air velocity and air temperature at ankle level (0.1 m) we used the AirDistSys 5000 omnidirectional hot-wire anemometers (Sensor Electronic, Poland, air velocity: 0.05-5 m/s, accuracy: ±0.02 m/s ±2% of reading; temperature: -10 to +50°C, accuracy: ±0.2°C, sampling interval: 1 s). Room-level measurements of relative humidity and CO2 concentration were recorded throughout each session.

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2.3.2 Physiological

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In addition, we recorded continuously participants skin temperature on the lateral lower leg (mid-calf) and feet using iButton sensors (Thermochron, Maxim Integrated, USA, Type DS1923; measurement range: 20°C to 85°C; accuracy: ±0.5°C; resolution: 0.0625°C) attached with medical-grade hypoallergenic tape. We used the skin temperature data to assess local cooling responses and as physiological correlates of subjective thermal sensation.

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2.3.3 Subjective feedback

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To assess the perception of the thermal environment we used validated scales consistent with prior ankle draft research and ASHRAE Standard 55 requirements. Constructs and their scales used in the questionnaires are summarized in Table 1 below. We administered the questions electronically via a custom survey tool written in Java. Participants were not required to respond to any individual question, though completion rates were monitored.

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-Table 1: Survey constructs and measurement scales -
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ConstructQuestionScale typeLevels
Thermal sensationHow do you feel right now?7-point continuous−3 (cold) −2 (cool) −1 (slightly cool) 0 (neutral) +1 (slightly warm) +2 (warm) +3 (hot)
Thermal comfortRight now do you find this environment…?6-point continuous−3 (very uncomfortable) −2 (uncomfortable) −1 (just uncomfortable) +1 (just comfortable) +2 (comfortable) +3 (very comfortable)
Thermal preferenceRight now would you prefer to be…?3-point ordinal−1 (warmer) | 0 (no change) | +1 (cooler)
Thermal acceptabilityPlease rate your acceptance of the current thermal environment4-point continuous−2 (clearly unacceptable) −1 (just unacceptable) +1 (just acceptable) +2 (clearly acceptable)
Air movement acceptability at anklesPlease rate your acceptance of air movement at your ankles4-point continuous−2 (clearly unacceptable) −1 (just unacceptable) +1 (just acceptable) +2 (clearly acceptable)
Air movement preference at anklesRight now around my ankles I would prefer…?3-point ordinal−1 (less air movement) | 0 (no change) | +1 (more air movement)
Clothing changeDid you adjust your upper body clothing?binary
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2.4 Participants

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We recruited 51 participants from the university community and local area through the Experimental Social Science Laboratory (Xlab) platform and email outreach to individuals who had participated in previous studies and consented to future contact. Eligible participants were between 21 and 55 years of age, fluent in English, and free from chronic cardiorespiratory conditions or recent major surgery. Pregnant individuals were excluded. Demographic details of the cohort are summarized in Table 2.

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2.5 Experimental protocol

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Upon arrival for each experimental session, we checked participants for elevated temperature and fitted them with skin temperature sensors. Participants then entered the climate chamber and completed a 20-minute adaptation period in the acclimatization zone under baseline conditions.

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To simulate typical winter office attire, we instructed participants to wear a long-sleeve top, long trousers (ending just above the ankle), thin socks, and closed-toe shoes. This ensemble targets a clothing insulation of approximately 0.75 clo, consistent with the median value observed in office buildings during heating seasons (Földváry Ličina et al., 2018). Participants were permitted to make minor clothing adjustments during sessions (e.g., rolling sleeves), and any changes were recorded.

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Following adaptation, participants were exposed to three consecutive 20-minute conditions at different air speed levels, with 20-minute rest periods between conditions (see PROTOCOL GRAPHIC REFERENCE). The sequence of air speed conditions was counterbalanced across participants and sessions. During each exposure period, participants completed standardized questionnaires at the end of each interval.

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2.6 Statistical analysis

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2.6.1 Variable processing

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Thermal sensation votes were collected on a continuous scale. For descriptive analyses, we mapped these values to the corresponding categorical sensation levels, whereas the original continuous values were retained for statistical modeling. We dichotomized ankle airflow acceptability as acceptable or unacceptable for subsequent analyses. The original recorded votes for thermal acceptability, thermal preference, ankle thermal preference, and ankle airflow preference were retained without further processing. Consistent with the definition used by Liu et al. (2017), we defined ankle draft dissatisfaction as an ankle thermal sensation vote below 0 (neutral) together with an ankle airflow acceptability vote below 0.

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2.6.2 Within-subject comparisons

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We used a within-subject repeated-measures design and conducted comparisons between experimental conditions within participants. We analyzed continuous variables using paired-samples t-tests and reported paired Cohen’s d as the effect size. We analyzed ordinal variables using the paired Wilcoxon signed-rank test, reporting the test statistic based on the normal approximation and the effect size r. For multiple pairwise comparisons within each family of tests, we adjusted p-values using the Benjamini-Hochberg method (Benjamini & Hochberg, 1995).

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2.6.3 Evaluation of the existing ankle draft model

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Applying it to the experimental data, we calculated the predicted percentage of dissatisfaction with ankle draft at each observation point. Predictions were then averaged by experimental condition and compared with the observed dissatisfaction percentages. We used calibration curves to quantitatively assess the model’s predictive performance in this study’s dataset (Van Calster et al., 2016) and report the calibration intercept and slope, AUC, and Brier score. All analyses were implemented using the R package CalibrationCurves (De Cock et al., 2025).

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2.6.4 Development of the new ankle draft model

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We modeled ankle draft dissatisfaction using a generalized linear mixed model with a binomial distribution and logit link, as the outcome was binary and repeated observations were correlated within subjects. We included the subject as a random intercept to account for between-subject heterogeneity and within-subject dependence arising from repeated measurements. To enable an integrated analysis of the effects of different clothing conditions on ankle draft dissatisfaction, we also included data from Liu et al. (2017) in the modeling dataset. Continuous predictors were mean-centered using the overall means of the combined dataset before model fitting.

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In this generalized linear mixed model, the inverse-logit transformation is nonlinear. As a result, direct back-transformation of the fixed-effects linear predictor yields a conditional probability, representing an individual-level prediction when the random effect is set to zero, rather than a population-averaged probability. To characterize the average risk of dissatisfaction at the population level, we therefore use marginal probabilities instead of conditional probabilities (Neuhaus et al., 1991). Specifically, we extracted fixed-effect estimates and the variance of the random intercept from the fitted model, assuming that the random intercept followed a normal distribution with mean zero. We then approximated integration over the random effects using Monte Carlo simulation (K = 10,000, random seed = 1), and calculated the marginal predicted probability for each combination of predictor values.

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Because these marginal probabilities generally cannot be written as a simple closed-form equation, we used the Monte Carlo-simulated marginal probabilities to fit an approximate linear equation for logit(P). Applying the inverse-logit transformation to the fitted equation yielded a closed-form prediction equation. We evaluated the accuracy of this approximation using coefficient of determination (R2).

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2.7 Software

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We performed all data processing, statistical analyses, and model fitting in R (version 4.4.1). The main packages we used were tidyverse (version 2.0.0), lme4 (version 2.0.1), rstatix (version 0.7.3), and CalibrationCurves (version 3.0.0).

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3 Results

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3.1 Participants and environmental conditions

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-Table 2: Summary of demographic information (mean ± SD) on study participants. -
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SexNo. SubjectsAge [a]Height [m]Weight [kg]Body Mass Index (BMI)
All5123.5 (+/- 5.9)1.70 (+/- 0.10)69.0 (+/- 11.8)23.9 (+/- 4.1)
Female2823.5 (+/- 6.4)1.65 (+/- 0.06)65.6 (+/- 11.5)24.3 (+/- 4.7)
Male2023.9 (+/- 5.6)1.79 (+/- 0.09)74.8 (+/- 9.6)23.4 (+/- 3.0)
Third Gender / Other322.0 (+/- 1.0)1.61 (+/- 0.02)62.0 (+/- 14.9)23.9 (+/- 5.7)
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Table 2 summarizes the demographic information of the study subjects. A total of 51 subjects participated in the study (28 female, 20 male, 3 other), with a mean age of 23.5 (+/- 5.9) years.

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-Table 3: Summary of environmental measurements. -
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Measurement15C17C19C
Air temperature, head level (°C)21.9 ( +/- 0.2)21.9 ( +/- 0.3)21.9 ( +/- 0.2)
Relative humidity (%)54.9 ( +/- 5.5)52.3 ( +/- 5)51.2 ( +/- 4.8)
Air temperature, ankle level (°C)17.6 ( +/- 0.2)18.3 ( +/- 0.2)19.7 ( +/- 0.2)
Air speed, low (m/s)0.14 ( +/- 0.02)0.16 ( +/- 0.01)0.18 ( +/- 0.01)
Air speed, medium (m/s)0.37 ( +/- 0.02)0.39 ( +/- 0.03)0.42 ( +/- 0.03)
Air speed, high (m/s)0.64 ( +/- 0.04)0.62 ( +/- 0.01)0.65 ( +/- 0.03)
Turbulence, low (%)0.36 ( +/- 0.02)0.34 ( +/- 0.01)0.3 ( +/- 0.01)
Turbulence, medium (%)0.26 ( +/- 0.02)0.23 ( +/- 0.01)0.23 ( +/- 0.02)
Turbulence, high (%)0.24 ( +/- 0.01)0.24 ( +/- 0.01)0.23 ( +/- 0.01)
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Table 3 provides an overview of the measured environmental conditions. Across all three sessions, head-level air temperature remained stable at 21.9 ( +/- 0.2) °C, 21.9 ( +/- 0.3) °C, and 21.9 ( +/- 0.2) °C, and relative humidity was comparable across sessions, confirming stable background thermal conditions and establishing baseline in line with the PMV target level of ~ -0.5 (slightly cool).

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As the primary experimental manipulation, we set supply air temperatures to 15°C, 17°C, and 19°C to simulate the effect of window downdraft. Ankle-level temperatures were slightly higher than the supply temperature due to mixing with the warmer ambient air, but remained stable across all sessions. Within each session, we exposed subjects to three airspeed levels at separate workstations. We measured consistent air speeds across all three workstations and sessions, confirming reliable reproduction of the low, medium, and high airspeed conditions. Turbulence intensities remained low throughout, indicating stable and controlled airflow.

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3.2 Whole body thermal perception

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Figure 2 presents whole-body thermal sensation and preference responses across all experimental conditions. Thermal sensation votes were predominantly in the Neutral to Slightly cool range, with 81%–92% of participants reporting sensations between Cool and Neutral across conditions. At the lowest supply air temperature (15°C), 43% of participants reported feeling Slightly cool at the highest air speed, compared to 28% at the lowest air speed. This pattern was less pronounced at warmer supply temperatures.

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Thermal preference responses indicated that participants were generally satisfied with the thermal conditions. Across all conditions, 47%–65% of participants preferred No change to the thermal environment. The proportion preferring Warmer conditions ranged from 25% to 45%, with the highest values observed during the 15°C supply air temperature sessions.

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-Figure 2: Whole body thermal sensation (a) and thermal preference (b) votes: Participants predominantly reported neutral to cool sensations and mostly a preference for no change, though cooler supply air temperatures increased the desire for warmer conditions. -
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Figure 3 shows thermal acceptability responses for whole-body conditions. Overall, acceptability was high across all conditions, ranging from 85% to 98%. Acceptability rates were highest during the 19°C supply air temperature sessions (90%–98%) and lowest at 15°C (85%–91%). Within each supply air temperature condition, air speed had minimal effect on whole-body thermal acceptability.

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-Figure 3: Whole body thermal acceptability: Participants reported high overall acceptability across all sessions, with minimal variation driven by air speed. -
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3.3 Ankle level observations

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3.3.1 Thermal perception

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Figure 4 presents thermal sensation and preference responses at the ankle level. Compared to whole-body responses, participants overall reported cooler sensations at the ankles. The proportion reporting sensations on the cool side of neutral (Cold, Cool, or Slightly cool) ranged from 38% to 66% across conditions (compared to 27% to 54% for whole-body thermal sensation). At the coldest supply air temperature (15°C) with high air speed, 66% of participants reported Cool sensations at the ankles, compared to 39% at 19°C with low air speed.

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Thermal preference at the ankle level reflected this cooling effect. The proportion of participants preferring Warmer ankles ranged from 28% to 53%. At the most demanding condition (15°C, high air speed), 53% preferred Warmer ankles, while at the mildest condition (19°C, low air speed), this proportion decreased to 31%.

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-Figure 4: Ankle-level thermal sensation (a) and thermal preference (b): Participants reported cooler sensations at the ankles than the whole body, with cooler supply air and higher air speeds slightly increasing both cool sensations and the preference for warmer conditions. -
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3.3.2 Air movement perception

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Figure 5 shows air movement acceptability and preference at the ankle level. Despite the localized cooling, air movement at the ankles was rated Acceptable by 80%–94% of participants across all conditions. Acceptability was highest at 19°C (83%–94%) and lowest at 17°C (80%–92%). Within each supply air temperature, acceptability tended to decrease slightly with increasing air speed.

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Air movement preference responses indicated that a substantial proportion of participants would prefer less air movement at the ankles, particularly at higher air speeds. The proportion preferring less air movement ranged from 12% to 41%. At 17°C with high air speed, 41% preferred less air movement, compared to only 12% at 19°C with low air speed. The majority of participants (43%–75%) preferred no change to the air movement across conditions.

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-Figure 5: Ankle-level air movement acceptability (a) and preference (b): Most participants found ankle air movement acceptable (80%–94%), though higher air speeds increased the preference for less air movement, particularly at cooler supply temperatures. -
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3.3.3 Skin temperature

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Figure 6 illustrates the progression of ankle skin temperatures throughout the exposure period. Using the pre-exposure adaptation period as a baseline, ankle skin temperatures dropped under all conditions, with final reductions ranging from -1.7°C to -0.8°C. In general, the magnitude of this skin temperature reduction increased with air speed, as medium and high air speeds produced greater local cooling than low air speed across all three supply air temperatures.

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Statistical analysis using BH correction confirmed that the cooling differences between low and medium air speeds, as well as between low and high air speeds, were significant at all supply temperatures (p_adj < 0.05 and p_adj < 0.001, respectively). In contrast, the difference between medium and high air speeds reached significance only at 19C (p_adj = 0.012). These findings indicate that increasing local airflow increases the short-term cooling response of the ankle skin and most noticeable temperature drops occur when shifting away from the lowest air speed setting.

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-Figure 6: Time course of ankle skin temperature during the formal exposure phase across the nine experimental conditions for (a) absolute skin temperature and (b) change relative to the adaptation-period baseline ( Shaded bands denote the between-subject mean ± 1 SD): Local cooling intensified as air speed increased, with the most significant temperature drops occurring when moving from low to medium airflow. -
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3.4 Dissatisfaction with ankle draft

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Figure 7(a) compares the dissatisfaction rates predicted by the Liu model against our experimental observations. Across all conditions, the existing model consistently overpredicted local thermal dissatisfaction. At a 15°C ankle temperature, the discrepancy between predicted and observed rates widened as air speed increased: the model overpredicted dissatisfaction by 8 percentage points (pp), rising to 39 pp at high flow (0.6 m/s).

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We observed similar trends at 17°C and 19°C. Notably, for the 19°C condition at high air speed (0.6 m/s), the model predicted a PPD of 50%, while the actual dissatisfied rate was only 17%, resulting in a mean overestimation of 34 pp. Across all experimental sessions, the model overpredicted dissatisfaction by an average of 23 pp.

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-Figure 7: Performance and calibration of the Liu local dissatisfaction model: (a) The model consistently overpredicted ankle-level dissatisfaction across all conditions, with discrepancies widening at higher air speeds (points represent mean values, with the segment length indicating the magnitude of model overestimation); (b) while maintaining acceptable discrimination (AUC = 0.85), the calibration curve confirms a systematic overestimation of dissatisfaction in winter conditions. -
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In addition, as shown in Figure 7(b), the model retained acceptable discrimination on this dataset (AUC = 0.847), the calibration results indicated a systematic overestimation under winter conditions. Across the nine experimental conditions, the mean observed dissatisfaction rate was 13%, whereas the Liu model predicted an average of 36%, corresponding to an overestimation of approximately 2.8 times. The discrepancy was greatest at high air speed and smaller, but still evident, at low air speed.

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3.5 Updated model for winter conditions

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As shown in Table 4, in the mixed-effects model including all candidate predictors, air speed at ankle, whole-body thermal sensation, and ankle condition were significantly associated with draft dissatisfaction at the ankle, whereas room air temperature, air temperature at ankle, and turbulence intensity were not significant within the range investigated in this study. Based on these results, separate mixed-effects models for ankle draft dissatisfaction were developed for the ankle-uncovered and ankle-covered conditions, using air speed at ankle and whole-body thermal sensation as predictors.

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-Table 4: Results of the generalized linear mixed-effects model used for predictor screening. -
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PredictorEstimateSEzp
Air speed at ankle3.200.575.57<0.001
Room air temperature-0.120.25-0.510.612
Air temperature at ankle-0.080.07-1.140.254
Whole-body thermal sensation-1.440.13-11.32<0.001
Turbulence intensity0.391.360.290.776
Ankle condition (uncovered vs. covered)1.220.442.790.005
Season-1.590.85-1.860.063
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-Table 5: Generalized linear mixed-effects models for the ankle-uncovered and ankle-covered conditions. -
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ConditionPredictorEstimateSEzp
Ankle uncoveredIntercept-1.640.32-5.16<0.001
Air speed at ankle3.510.615.75<0.001
Whole-body thermal sensation-1.460.16-9.35<0.001
Ankle coveredIntercept-3.550.45-7.97<0.001
Air speed at ankle2.740.913.010.003
Whole-body thermal sensation-1.460.22-6.62<0.001
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As shown in Table 5, the two final models exhibited the same structure but different coefficients. The intercept of the covered model was 1.91 units lower than that of the uncovered model, indicating a substantially lower baseline risk of ankle draft dissatisfaction when the ankle was covered by clothing. In addition, the air speed coefficient was smaller in the covered model than in the uncovered model, indicating reduced sensitivity of dissatisfaction to air velocity under ankle-covered conditions.

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For the ankle-uncovered condition, the approximate closed-form equation derived from the marginal predictions of the mixed-effects model can be written as:

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\[ -PPD_{AD} = \frac{\exp\left(-2.087 + 2.255V - 0.915TS\right)}{1 + \exp\left(-2.087 + 2.255V - 0.915TS\right)} -\]

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For the ankle-covered condition, the corresponding approximate closed-form equation is:

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\[ -PPD_{AD} = \frac{\exp\left(-3.222 + 1.878V - 0.983TS\right)}{1 + \exp\left(-3.222 + 1.878V - 0.983TS\right)} -\]

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Where, \(PPD_{AD}\) is the predicted percentage dissatisfied with ankle draft, \(V\) is air speed at ankle (m/s), and \(TS\) is whole-body thermal sensation.

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These linear approximations reproduced the marginal predictions of the mixed-effects models with high accuracy. The corresponding \(R^2\) values were 0.9989 for the uncovered condition and 0.9967 for the covered condition, indicating that the approximate equations preserved the predictive behavior of the original mixed-effects models well. The resulting model predictions are shown in Figure 8.

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-Figure 8: Updated ankle draft dissatisfaction model under exposed and covered conditions. (a) ankle-uncovered conditions, and (b) ankle-covered conditions. -
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4 Discussion

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4.1 Comparison with prior research

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The central finding of this study is that ankle-level dissatisfaction under winter clothing conditions (≥0.75 clo) is substantially lower than predicted by the existing model of Liu et al. (2017) and than observed in prior studies with exposed ankles. In the experiments of Schiavon et al. (2016), where participants wore summer clothing (~0.6 clo) with exposed ankles and lower legs, unacceptability rates ranged from 23% to 57%. Under the ankle-covered conditions in this study, airflow unacceptability ranged from only 6% to 20% across comparable air speed and temperature conditions.

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These findings align with other research on the protective effects of lower-body coverage. Zhou et al. (2022) reported that high-top shoes increased ankle airflow acceptability by approximately 15% in stratified heating environments, demonstrating that even partial ankle coverage meaningfully reduces sensitivity to local airflow. Similarly, Toftum & Nielsen (1996) found that occupants with cooler overall thermal sensations are more likely to perceive airflow as uncomfortable, and that higher clothing insulation attenuates the interaction between ambient temperature and airflow-induced discomfort.

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Regarding predictor selection, only whole-body thermal sensation and air speed were significant predictors of dissatisfaction in our models, consistent with the structures reported by Toftum & Nielsen (1996) and Liu et al. (2017). Cheng et al. (2023) similarly identified a relationship between overall thermal sensation and draft rate thresholds, further supporting its inclusion as a predictor.

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Although the dataset used by Liu et al. (2017) included both exposed and covered ankle conditions, no significant clothing effect was identified in their analysis. This discrepancy likely stems from their use of standard logistic regression, which pooled observations across subjects without accounting for the non-independence introduced by repeated measures. This approach may have masked the clothing effect as a between-subject variable due to inter-individual variability, which is a limitation addressed in our study through the use of mixed-effects models.

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4.2 Mechanisms

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Two complementary pathways, physiological and psychological, may explain the reduced sensitivity to ankle draft under winter clothing conditions.

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From a physiological perspective, the skin temperature results indicate that winter clothing attenuates, though does not eliminate, the local cooling effect of airflow. During the final steady-state period, significant reductions in ankle skin temperature occurred only at the coldest supply temperature (15°C), where medium and high air speeds produced lower skin temperatures than the low-speed condition. At 17°C and 19°C, variations in air speed did not yield significant differences in steady-state skin temperature, and no significant differences were observed between medium and high air speeds at any supply temperature. These findings suggest that detectable local cooling requires a sufficiently large environmental contrast.

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Thermal sensation changes are more closely associated with rapid variations in skin temperature than with absolute values (Choi & Loftness, 2012; Kenshalo et al., 1968). In this study, ankle \(\Delta T_{\text{sk}}\) relative to the baseline adaptation period showed significant differences between low and medium/high air speed conditions across all supply temperatures (effect size \(d \approx 0.6\text{-}0.9\)). Consistent with this, local ankle thermal sensation at medium and high speeds was significantly lower than at low speed under the 15°C condition. However, air movement acceptability did not differ significantly across conditions, indicating that while air speed produced measurable shifts in skin temperature and local thermal sensation, the magnitude of these changes was insufficient to generate distinguishable differences in dissatisfaction within the tested range. From a heat transfer perspective, clothing coverage increases local thermal resistance and reduces convective heat exchange (Lee et al., 2007), suppressing both the magnitude and variability of skin temperature changes and making it less likely that occupants cross discomfort thresholds.

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Psychological factors may also contribute to the observed tolerance. Occupants wearing thicker lower-body clothing may perceive themselves as “protected,” increasing their tolerance to local airflow. Prior research has demonstrated that thermal perception is not solely determined by physical stimuli but is modulated by expectations and informational cues. Providing occupants with temperature information or group perception feedback can improve thermal comfort evaluations (Zhang et al., 2022), and thermal expectations themselves influence perception (Schweiker et al., 2020). Field studies have also identified associations between perceived control and thermal satisfaction in winter conditions (Xu & Li, 2021). These findings suggest that the subjective sense of being protected by clothing may enhance tolerance to ankle draft, though this psychological pathway was not directly measured in the present study and warrants further investigation.

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Together, these physiological and psychological mechanisms likely act in concert: clothing reduces the physical cooling stimulus while simultaneously altering occupants’ expectations and perceived vulnerability to draft.

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4.3 Implications for building design and standards

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The ankle draft model of Liu et al. (2017), now incorporated into ASHRAE Standard 55, does not distinguish between covered and uncovered ankle conditions. Given the standard’s acceptable thermal sensation range of PMV = −0.5 to +0.5, the current criterion requires ankle-level air speed below 0.22 m/s to achieve less than 20% dissatisfied when TS = −0.5. This constraint may be overly conservative for typical winter office environments where occupants wear clothing that covers the ankle.

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The findings of this study support a differentiated approach. For winter conditions with ankle coverage (≥0.75 clo), the covered-ankle model developed here indicates that dissatisfaction remains within acceptable limits at air speeds that would exceed the current threshold. Empirical predictions of window downdraft suggest that maximum velocities at approximately 1 m from the façade are around 0.25 m/s, with peak velocities often falling within 0.1–0.2 m/s under milder outdoor conditions or with smaller window areas (Lyons et al., 1999). Many of these scenarios would be acceptable under the covered-ankle model but flagged as problematic under the current single-threshold approach.

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For practitioners, this suggests a two-criteria framework: apply the existing model (or the uncovered-ankle model from this study) when evaluating spaces where occupants are likely to have exposed ankles, and apply the covered-ankle model for winter heating scenarios where long trousers, socks, and closed-toe shoes are expected. Within the near-neutral thermal range where ASHRAE Standard 55 applies, PMV provides a reasonable proxy for whole-body thermal sensation during design evaluation.

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The practical benefits are significant. Perimeter heating systems represent non-trivial costs in both installation and operation. If covered and uncovered conditions are evaluated separately, designers may be able to reduce perimeter heating capacity or, in some cases, eliminate it entirely for spaces with favorable glazing and winter-clothed occupants. This approach could yield meaningful reductions in first costs, energy consumption, and associated carbon emissions while maintaining occupant comfort.

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4.4 Limitations

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Several limitations should be considered when interpreting these findings.

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First, this study was conducted in a controlled laboratory environment with standardized clothing, which differs from real office settings where occupants exhibit considerable variability in attire even during winter months. While we targeted 0.75 clo to represent median winter office clothing, actual insulation levels vary with individual preferences, building temperatures, and cultural norms. The protective effect of ankle coverage may differ with clothing types not tested here, such as ankle-length skirts, cropped trousers, or low-cut shoes.

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Second, the participant sample consisted primarily of university-affiliated individuals within a limited age range. Thermal sensitivity varies with age, and older occupants may respond differently to ankle draft. The generalizability of these findings to broader occupant populations warrants further investigation.

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Third, the experimental protocol involved 20-minute exposure periods, whereas real office occupants experience sustained exposure over hours. Whether dissatisfaction accumulates or diminishes with prolonged exposure was not assessed. Similarly, participants remained seated throughout; standing or walking occupants may have different thermal experiences at the ankle level.

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Fourth, the experimental conditions covered supply air temperatures of 15–19°C and air speeds of 0.1–0.7 m/s. While these ranges were selected to represent typical window downdraft conditions, more extreme scenarios (colder supply temperatures or higher velocities) were not tested. The model predictions should be applied with caution outside the tested parameter space.

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Fifth, airflow was delivered from behind the participants to simulate window downdraft approaching from the façade. Other airflow directions (lateral or frontal) may produce different perceptual responses, particularly given potential differences in skin exposure and attention to the stimulus source.

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Finally, the experimental setup simulated the convective component of window downdraft but did not include radiant asymmetry from a cold window surface. In real buildings, occupants near poorly insulated glazing experience both convective cooling from downdraft and radiant heat loss to the cold surface. The combined effect of these two mechanisms on ankle-level comfort was beyond the scope of this study.

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5 Conclusions

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This study evaluated thermal comfort responses to ankle-level draft under winter clothing conditions representative of typical office environments. Through controlled laboratory experiments with participants wearing approximately 0.75 clo ensembles that covered the ankle, we characterized local and whole-body thermal perception across a range of supply air temperatures (15-19°C) and air speeds (0.1–0.7m/s) simulating window downdraft.

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The principal findings indicate that the existing ankle draft model systematically overpredicts dissatisfaction under winter clothing conditions. While prior studies with exposed ankles reported dissatisfaction rates between 23% and 57% under similar air speeds, our observations with covered ankles ranged from only 6% to 20%. This suggests that ankle coverage substantially reduces sensitivity to local draft, a conclusion supported by the covered-ankle model developed in this study; the model demonstrates both a lower baseline risk and a reduced response to air speed compared to uncovered-ankle models, with an intercept difference of approximately 1.5 units on the logit scale.

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Consistent with prior model structures, we found that whole-body thermal sensation and air speed at the ankle are the primary predictors of dissatisfaction, whereas ankle air temperature, room temperature, and turbulence intensity were not significant within the tested ranges. This reduced sensitivity under winter clothing appears to stem from a combination of physiological mechanisms, specifically attenuated skin cooling due to increased thermal resistance, and potentially psychological factors, such as a perceived sense of protection provided by the clothing coverage.

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These findings support a differentiated approach to ankle draft assessment in building standards. For winter heating scenarios where occupants typically wear clothing that covers the ankle (≥0.75 clo), the covered-ankle model provides more accurate predictions than the current ASHRAE Standard 55 criterion. Adopting separate criteria for covered and uncovered conditions could enable significant reductions in perimeter heating requirements without compromising occupant comfort, yielding benefits in installation costs, energy consumption, and carbon emissions.

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Future research should validate these findings in field settings with diverse occupant populations and clothing practices, examine prolonged exposure effects, and investigate the combined influence of convective draft and radiant asymmetry from cold window surfaces.

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CRediT authorship contribution statement

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Tobias Kramer: Conceptualization, Data curation, Formal analysis, Methodology, Investigation, Project administration, Software, Writing - original draft, Writing - review & editing. Junmeng Lyu: Data curation, Formal analysis, Methodology, Investigation, Software, Writing - original draft, Writing - review & editing. Stefano Schiavon: Conceptualization, Funding acquisition, Methodology, Project administration, Supervision, Writing - review & editing.

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Declaration of competing interest

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All authors declare no competing interest. The Center for the Built Environment (CBE) at the University of California, Berkeley, with which the authors are affiliated, is advised and funded in part by approximately 50 partners that represent a diversity of organizations from the building industry, including manufacturers, building owners, facility managers, contractors, architects, engineers, government agencies, and utilities.

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Data availability

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The datasets generated and analyzed during the current study as well as the full source code of the data analysis workflow are available in the following GitHub repository: https://github.com/CenterForTheBuiltEnvironment/ankle-draft-II

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Declaration of Generative AI and AI-assisted technologies in the writing process

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During the preparation of this work, the authors utilized the chatbot Claude to enhance the language and readability of the content. Subsequently, they reviewed and edited the material as required, while maintaining full accountability for the publication’s content.

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Acknowledgements

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Schüco and the Center for the Built Environment at the University of California, Berkeley supported this research.

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References

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- - - - - \ No newline at end of file diff --git a/manuscript/index.qmd b/manuscript/index.qmd index 254a3e6..6c43382 100644 --- a/manuscript/index.qmd +++ b/manuscript/index.qmd @@ -296,14 +296,31 @@ Benjamini-Hochberg method [@benjaminiHighberg1995]. ### Evaluation of the existing ankle draft model Applying it to the experimental data, we calculated the predicted -percentage of dissatisfaction with ankle draft at each observation -point. Predictions were then averaged by experimental condition and -compared with the observed dissatisfaction percentages. We used -calibration curves to quantitatively assess the model's predictive -performance in this study's dataset [@vancalster2016] and report the -calibration intercept and slope, AUC, and Brier score. All analyses were -implemented using the R package CalibrationCurves -[@deCockCalibrationCurves2023]. +percentage of dissatisfaction with ankle draft using the existing ankle +draft model at each observation point. For each observation, a logistic +regression model was fitted with the individual-level predicted +probability as the independent variable and the observed binary outcome +(ankle draft dissatisfaction (1) or satisfaction (0)) as the dependent +variable to form a calibration curve to assess the agreement between +predicted probabilities and observed proportions [@vancalster2016]. +Model performance was further evaluated using the C (ROC) and the Brier +score. The C (ROC) quantifies the model's discriminative ability, +defined as the probability that a randomly selected dissatisfied +observation receives a higher predicted probability than a randomly +selected satisfied observation [@AlbaCROC2017]. The Brier score measures +the overall accuracy of probabilistic predictions [@GLENNBrier1950] and +is defined as: + +$$ +\mathrm{Brier\ score} = \frac{1}{N}\sum_{i=1}^{N}(p_i - y_i)^2, +$$ + +where $p_i$ is the predicted probability from the existing model for +the $i$-th observation, and $y_i$ is the corresponding binary outcome +indicating ankle draft dissatisfaction (1) or satisfaction (0). In +addition, predictions were averaged by experimental condition and +compared with the observed dissatisfaction percentages to examine +differences in prediction accuracy across conditions. ### Development of the new ankle draft model @@ -312,11 +329,8 @@ model with a binomial distribution and logit link, as the outcome was binary and repeated observations were correlated within subjects. We included the subject as a random intercept to account for between-subject heterogeneity and within-subject dependence arising from -repeated measurements. To enable an integrated analysis of the effects -of different clothing conditions on ankle draft dissatisfaction, we also -included data from @liuPredictedPercentageDissatisfied2017 in the -modeling dataset. Continuous predictors were mean-centered using the -overall means of the combined dataset before model fitting. +repeated measurements. Continuous predictors were mean-centered using +the overall means of the dataset before model fitting. In this generalized linear mixed model, the inverse-logit transformation is nonlinear. As a result, direct back-transformation of the @@ -759,44 +773,46 @@ liu_max_diff_speed <- liu_diff_by_speed %>% dplyr::slice(1) %>% dplyr::pull(sess liu_min_diff_speed <- liu_diff_by_speed %>% dplyr::slice(n()) %>% dplyr::pull(session_air_flow) ``` -@fig-model-comp(a) compares the dissatisfaction rates predicted by the -Liu model against our experimental observations. Across all conditions, -the existing model consistently overpredicted local thermal -dissatisfaction. At a 15°C ankle temperature, the discrepancy between -predicted and observed rates widened as air speed increased: the model -overpredicted dissatisfaction by `r res$diff[1]` percentage points (pp), -rising to `r res$diff[3]` pp at high flow (0.6 m/s). - -We observed similar trends at 17°C and 19°C. Notably, for the 19°C -condition at high air speed (0.6 m/s), the model predicted a PPD of -`r res$ppd_liu_mean[9]`%, while the actual dissatisfied rate was only -`r res$dissatisfied_rate[9]`%, resulting in a mean overestimation of -`r res$diff[9]` pp. Across all experimental sessions, the model -overpredicted dissatisfaction by an average of `r round(mean(res$diff))` -pp. - -![Performance and calibration of the Liu local dissatisfaction model: -(a) The model consistently overpredicted ankle-level dissatisfaction -across all conditions, with discrepancies widening at higher air speeds -(points represent mean values, with the segment length indicating the -magnitude of model overestimation); (b) while maintaining acceptable -discrimination (AUC = -`r sprintf("%.2f", liu_calibration_stats["C (ROC)"])`), the calibration -curve confirms a systematic overestimation of dissatisfaction in winter -conditions.](figs/model_error_combined.png){#fig-model-comp width="90%"} - -In addition, as shown in @fig-model-comp(b), the model retained -acceptable discrimination on this dataset (AUC = -`r sprintf("%.3f", liu_calibration_stats["C (ROC)"])`), the calibration -results indicated a systematic overestimation under winter conditions. -Across the nine experimental conditions, the mean observed -dissatisfaction rate was `r liu_model_summary$mean_observed`%, whereas -the Liu model predicted an average of -`r liu_model_summary$mean_predicted`%, corresponding to an +For each observation sample, the predicted percentage of +dissatisfaction with ankle draft using the existing ankle draft model +based on ankle-level air speed and whole-body thermal sensation was +fitted against the observed binary outcome of ankle draft +satisfaction/dissatisfaction using logistic regression. The resulting +curve is shown in @fig-model-comp(a). If the model were well +calibrated, the curve would be expected to closely follow the 45° ideal +line. Overall, the existing model retained acceptable discriminative +ability in the present dataset (C (ROC) = +`r sprintf("%.3f", liu_calibration_stats["C (ROC)"])`), indicating that +it could generally distinguish observations with higher versus lower +likelihood of ankle draft dissatisfaction. However, the curve was +located predominantly below the ideal line, and the Brier score was +`r sprintf("%.3f", liu_calibration_stats["Brier"])`, suggesting that the +existing model systematically overestimated the probability of ankle +draft dissatisfaction under winter conditions. + +@fig-model-comp(b) compares the dissatisfaction rates predicted by the +existing model against our experimental observations under each +experimental condition. Across all conditions, the existing model +consistently overpredicted local thermal dissatisfaction. At a 15°C +ankle temperature, the discrepancy between predicted and observed rates +widened as air speed increased: the model overpredicted dissatisfaction +by `r res$diff[1]` percentage points (pp), rising to `r res$diff[3]` pp +at high flow (0.6 m/s). We observed similar trends at 17°C and 19°C. +Notably, for the 19°C condition at high air speed (0.6 m/s), the model +predicted a PPD of `r res$ppd_liu_mean[9]`%, while the actual +dissatisfied rate was only `r res$dissatisfied_rate[9]`%, resulting in a +mean overestimation of `r res$diff[9]` pp. Across the nine experimental +conditions, the mean observed dissatisfaction rate was +`r liu_model_summary$mean_observed`%, whereas the Liu model predicted an +average of `r liu_model_summary$mean_predicted`%, corresponding to an overestimation of approximately -`r liu_model_summary$overprediction_ratio` times. The discrepancy was -greatest at `r liu_max_diff_speed` air speed and smaller, but still -evident, at `r liu_min_diff_speed` air speed. +`r liu_model_summary$overprediction_ratio` times. + +![Performance of the existing ankle draft model: (a) calibration curve +of the existing model on this study dataset, and (b) predicted and +observed dissatisfaction under each experimental conditions (points +represent mean values, with the segment length indicating the magnitude +of model overestimation)](figs/model_performance_combined_raw.png){#fig-model-comp width="90%"} ## Updated model for winter conditions @@ -902,15 +918,24 @@ model_final_table <- dplyr::bind_rows( dplyr::select(model_display, term_label, estimate_fmt, std_error_fmt, z_value_fmt, p_value_fmt) ``` -As shown in @tbl-updated-model-screening, in the mixed-effects model -including all candidate predictors, air speed at ankle, whole-body -thermal sensation, and ankle condition were significantly associated -with draft dissatisfaction at the ankle, whereas room air temperature, -air temperature at ankle, and turbulence intensity were not significant -within the range investigated in this study. Based on these results, -separate mixed-effects models for ankle draft dissatisfaction were -developed for the ankle-uncovered and ankle-covered conditions, using -air speed at ankle and whole-body thermal sensation as predictors. +As shown in Section 3.4, the existing model showed limited accuracy in +predicting ankle draft dissatisfaction under winter conditions. This +highlights the need for a revised model that accounts for differences in +application contexts. To enable an integrated analysis of the effects of +different factors on ankle draft dissatisfaction, we combined data from +@liuPredictedPercentageDissatisfied2017 and collected in this study in +the modeling dataset. + +To identify significant predictors, a model including all candidate +predictors was first fitted following the methods described in Section +2.6.4. Given that both datasets were obtained from repeated +measurements, subject-level dependence was accounted for in the +analysis. The result of the screening model is shown in +@tbl-updated-model-screening, ankle-level air speed, whole-body thermal +sensation, and ankle condition were significantly correlated with ankle +draft dissatisfaction, whereas room air temperature, ankle-level air +temperature, and turbulence intensity were not significant within the +range investigated in this study. ```{r} #| label: tbl-updated-model-screening @@ -923,6 +948,19 @@ knitr::kable( ) ``` +Based on these results, separate mixed-effects models for ankle draft +dissatisfaction were developed for the ankle-uncovered and +ankle-covered conditions, using ankle-level air speed and whole-body +thermal sensation as predictors. As shown in @tbl-updated-model-final, +the two final models exhibited the same structure but different +coefficients. The intercept of the covered model was +`r sprintf("%.2f", abs(glmm_delta_intercept))` units lower than that of +the uncovered model, indicating a lower baseline risk of ankle draft +dissatisfaction when the ankle was covered by clothing. In addition, +the air speed coefficient was smaller in the covered model than in the +uncovered model, indicating reduced sensitivity of dissatisfaction to +air speed under ankle-covered conditions. + ```{r} #| label: tbl-updated-model-final #| tbl-cap: "Generalized linear mixed-effects models for the ankle-uncovered and ankle-covered conditions." @@ -934,16 +972,6 @@ knitr::kable( ) ``` -As shown in @tbl-updated-model-final, the two final models exhibited the -same structure but different coefficients. The intercept of the covered -model was `r sprintf("%.2f", abs(glmm_delta_intercept))` units lower -than that of the uncovered model, indicating a substantially lower -baseline risk of ankle draft dissatisfaction when the ankle was covered -by clothing. In addition, the air speed coefficient was smaller in the -covered model than in the uncovered model, indicating reduced -sensitivity of dissatisfaction to air velocity under ankle-covered -conditions. - For the ankle-uncovered condition, the approximate closed-form equation derived from the marginal predictions of the mixed-effects model can be written as: diff --git a/manuscript/refs.bib b/manuscript/refs.bib index 9f5b731..25cfbc2 100644 --- a/manuscript/refs.bib +++ b/manuscript/refs.bib @@ -536,3 +536,31 @@ @article{ author={Tartarini, Federico and Schiavon, Stefano and Cheung, Toby and Hoyt, Tyler}, year={2020}, pages={100563} } +@article{AlbaCROC2017, + author = {Alba, Ana Carolina and Agoritsas, Thomas and Walsh, Michael and Hanna, Steven and Iorio, Alfonso and Devereaux, P. J. and McGinn, Thomas and Guyatt, Gordon}, + title = {Discrimination and Calibration of Clinical Prediction Models: Users’ Guides to the Medical Literature}, + journal = {JAMA}, + volume = {318}, + number = {14}, + pages = {1377-1384}, + year = {2017}, + month = {10}, + abstract = {Accurate information regarding prognosis is fundamental to optimal clinical care. The best approach to assess patient prognosis relies on prediction models that simultaneously consider a number of prognostic factors and provide an estimate of patients’ absolute risk of an event. Such prediction models should be characterized by adequately discriminating between patients who will have an event and those who will not and by adequate calibration ensuring accurate prediction of absolute risk. This Users’ Guide will help clinicians understand the available metrics for assessing discrimination, calibration, and the relative performance of different prediction models. This article complements existing Users’ Guides that address the development and validation of prediction models. Together, these guides will help clinicians to make optimal use of existing prediction models.}, + issn = {0098-7484}, + doi = {10.1001/jama.2017.12126}, + url = {https://doi.org/10.1001/jama.2017.12126}, + eprint = {https://jamanetwork.com/journals/jama/articlepdf/2656816/jama_alba_2017_ug_170001.pdf}, +} +@article {GLENNBrier1950, + author = "GLENN W. BRIER", + title = "VERIFICATION OF FORECASTS EXPRESSED IN TERMS OF PROBABILITY", + journal = "Monthly Weather Review", + year = "1950", + publisher = "American Meteorological Society", + address = "Boston MA, USA", + volume = "78", + number = "1", + doi = "10.1175/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2", + pages= "1 - 3", + url = "https://journals.ametsoc.org/view/journals/mwre/78/1/1520-0493_1950_078_0001_vofeit_2_0_co_2.xml" +} diff --git a/src/R/x_analysis.R b/src/R/x_analysis.R index 284f097..fb21b4a 100644 --- a/src/R/x_analysis.R +++ b/src/R/x_analysis.R @@ -661,7 +661,7 @@ ggsave( dissatisfied_with_draft_ankles <- analysis %>% dplyr::filter( - question %in% c("thermal_sensation_ankles", "air_movement_acceptability_ankles", "dissatisfied_with_draft_ankles"), + question %in% c("thermal_sensation", "thermal_sensation_ankles", "air_movement_acceptability_ankles", "dissatisfied_with_draft_ankles"), is_open_text == FALSE ) %>% dplyr::filter(workstation != "adaptation") %>% @@ -669,6 +669,7 @@ dissatisfied_with_draft_ankles <- analysis %>% dplyr::group_by(session_sat,t_air_c, t_supply_c, v_air_m_s, session_id, subject_id, workstation) %>% dplyr::summarise( + thermal_sensation = response_value[question == "thermal_sensation"], thermal_sensation_ankles = response_value[question == "thermal_sensation_ankles"], air_movement_acceptability_ankles = response_value[question == "air_movement_acceptability_ankles"], dissatisfied_with_draft_ankles = response_value[question == "dissatisfied_with_draft_ankles"], @@ -679,7 +680,7 @@ dissatisfied_with_draft_ankles <- analysis %>% dissatisfied_with_draft_ankles <- dissatisfied_with_draft_ankles %>% dplyr::mutate( - ppd_liu = plogis(-2.58 + 3.05 * v_air_m_s - 1.06 * thermal_sensation_ankles) + ppd_liu = plogis(-2.58 + 3.05 * v_air_m_s - 1.06 * thermal_sensation) ) @@ -893,8 +894,8 @@ ggsave( # Combined figure -model_performance_p <- (model_error_p | Liumodel_calibrationcurve) + - plot_layout(widths = c(2, 1)) + +model_performance_p <- (Liumodel_calibrationcurve | model_error_p ) + + plot_layout(widths = c(1, 2)) + plot_annotation(tag_levels = "a", tag_suffix = ".") & theme( plot.subtitle = element_text(hjust = 0.05, margin = margin(b = 3, unit = "mm")),