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@@ -62,11 +62,38 @@ source(here::here("src", "R", "x_analysis.R"))
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# Abstract {.unnumbered}
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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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The ankle draft model incorporated in ASHRAE Standard 55 was derived
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from studies in which participants wore summer clothing with exposed
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ankles (\~0.5 clo), potentially leading to overly conservative perimeter
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heating requirements in winter conditions where office occupants
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typically wear long trousers, socks, and closed-toe shoes (\~0.75 clo).
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This study evaluated thermal comfort responses to ankle-level draft
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under such winter clothing conditions through controlled laboratory
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experiments with 51 participants. Using a within-subjects
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repeated-measures design, we exposed participants to nine conditions
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varying supply air temperature (15°C, 17°C, 19°C) and ankle-level air
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speed (0.1–0.7 m/s) simulating window downdraft while they wore clothing
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ensembles targeting 0.75 clo.
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The existing ankle draft model systematically overpredicted
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dissatisfaction across all conditions. While prior studies with exposed
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ankles reported dissatisfaction rates of 23–57%, we observed rates of
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only 6–20%, with the existing model overestimating dissatisfaction by an
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average of 2.8 times and by as much as 39 percentage points at high air
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speeds. We fit generalized linear mixed-effects models to data from this
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study and prior research, developing separate prediction equations for
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ankle-covered and ankle-uncovered conditions. The covered-ankle model
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exhibited both a lower baseline dissatisfaction risk and reduced
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sensitivity to air speed. Whole-body thermal sensation and ankle-level
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air speed were the only significant predictors; ankle air temperature
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and room temperature were not significant within the tested ranges.
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These findings support differentiating ASHRAE Standard 55 ankle draft
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criteria by clothing insulation level. Adopting a covered-ankle
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criterion for winter heating scenarios will enable meaningful reductions
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in perimeter heating requirements without compromising occupant comfort,
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with associated benefits for installation costs, energy consumption, and
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carbon emissions.
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# Introduction
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the ASHRAE seven-point scale as calculated using the CBE Comfort Tool
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[@tartariniCBEThermalComfort2020].
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![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.](figs/experimental_setup.png){#fig-setup
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![Experimental configuration and temporal protocol: (a) Seated occupant
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positioned 0.7 m from the custom displacement diffuser, which simulates
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window downdraft by directing conditioned air toward the ankle region
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from behind; (b) Timeline of the 120-minute experimental sessions
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featuring overlapping participant groups and synchronized questionnaire
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intervals to characterize the progression of local and whole-body
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thermal perception.](figs/experimental_setup.png){#fig-setup
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width="75%"}
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We used custom displacement diffusers to deliver conditioned air to the
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implemented using the R package CalibrationCurves
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[@deCockCalibrationCurves2023].
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### Development of the new ankle draft model
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### Development of the new ankle draft model {#sec-method-new-model}
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We modeled ankle draft dissatisfaction using a generalized linear mixed
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model with a binomial distribution and logit link, as the outcome was
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temperature drops occurring when moving from low to medium
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airflow.](figs/tsk_p.png){#fig-tsk width="90%"}
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## Dissatisfaction with ankle draft
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## Dissatisfaction with ankle draft {#sec-model-comp}
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```{r}
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#| label: setup-results-data
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(a) The model consistently overpredicted ankle-level dissatisfaction
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across all conditions, with discrepancies widening at higher air speeds
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(points represent mean values, with the segment length indicating the
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magnitude of model overestimation); (b) while maintaining acceptable
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discrimination (AUC =
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`r sprintf("%.2f", liu_calibration_stats["C (ROC)"])`), the calibration
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curve confirms a systematic overestimation of dissatisfaction in winter
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conditions.](figs/model_error_combined.png){#fig-model-comp width="90%"}
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In addition, as shown in @fig-model-comp(b), the model retained
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acceptable discrimination on this dataset (AUC =
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`r sprintf("%.3f", liu_calibration_stats["C (ROC)"])`), the calibration
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results indicated a systematic overestimation under winter conditions.
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Across the nine experimental conditions, the mean observed
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dissatisfaction rate was `r liu_model_summary$mean_observed`%, whereas
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the Liu model predicted an average of
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`r liu_model_summary$mean_predicted`%, corresponding to an
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overestimation of approximately
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`r liu_model_summary$overprediction_ratio` times. The discrepancy was
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greatest at `r liu_max_diff_speed` air speed and smaller, but still
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evident, at `r liu_min_diff_speed` air speed.
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magnitude of model overestimation); (b) calibration curve of the existing model on this study dataset.](figs/model_error_combined.png){#fig-model-comp width="90%"}
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In addition, we evaluated the performance of the existing ankle draft model by fitting its predictions—based on local air speed and whole-body thermal sensation—against our observed binary satisfaction outcomes using logistic regression. The resulting calibration curve is shown in @fig-model-comp(b). In a well-calibrated model, the curve should closely follow the 45° ideal line; however, our results show the curve located predominantly below this line.
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While the model maintained acceptable discriminative ability (AUC = 0.77), meaning it can effectively rank which conditions are more likely to cause discomfort, the calibration statistics reveal significant inaccuracy in the magnitude of its predictions. With a Brier score of 0.14 and a systematic shift away from the ideal line, the results confirm that the existing model consistently overestimates the probability of ankle draft dissatisfaction under winter conditions.
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## Updated model for winter conditions
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dplyr::select(model_display, term_label, estimate_fmt, std_error_fmt, z_value_fmt, p_value_fmt)
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```
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As shown in @tbl-updated-model-screening, in the mixed-effects model
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including all candidate predictors, air speed at ankle, whole-body
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thermal sensation, and ankle condition were significantly associated
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with draft dissatisfaction at the ankle, whereas room air temperature,
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air temperature at ankle, and turbulence intensity were not significant
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within the range investigated in this study. Based on these results,
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separate mixed-effects models for ankle draft dissatisfaction were
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developed for the ankle-uncovered and ankle-covered conditions, using
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air speed at ankle and whole-body thermal sensation as predictors.
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As shown in @sec-model-comp, the existing model showed limited accuracy
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in predicting ankle draft dissatisfaction under winter conditions. This
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highlights the need for a revised model that accounts for differences in
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application contexts. To enable an integrated analysis of the effects of
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different factors on ankle draft dissatisfaction, we combined data from
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@liuPredictedPercentageDissatisfied2017 and collected in this study
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in the modeling dataset. To identify significant predictors, a model
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including all candidate predictors was first fitted following the
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methods described in @sec-method-new-model. Given that both datasets
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were obtained from repeated measurements, subject-level dependence was
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accounted for in the analysis. The result of the screening model is
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shown in @tbl-updated-model-screening. Ankle-level air speed, whole-body
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thermal sensation, and ankle condition were significantly correlated
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with ankle draft dissatisfaction, whereas room air temperature,
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ankle-level air temperature, and turbulence intensity were not
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significant within the range investigated in this study.
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```{r}
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#| label: tbl-updated-model-screening
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)
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```
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As shown in @tbl-updated-model-final, the two final models exhibited the
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same structure but different coefficients. The intercept of the covered
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model was `r sprintf("%.2f", abs(glmm_delta_intercept))` units lower
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than that of the uncovered model, indicating a substantially lower
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baseline risk of ankle draft dissatisfaction when the ankle was covered
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by clothing. In addition, the air speed coefficient was smaller in the
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covered model than in the uncovered model, indicating reduced
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sensitivity of dissatisfaction to air velocity under ankle-covered
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conditions.
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Based on these results, separate mixed-effects models for ankle draft
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dissatisfaction were developed for the ankle-uncovered and ankle-covered
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conditions, using ankle-level air speed and whole-body thermal sensation
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as predictors. As shown in @tbl-updated-model-final, the two final
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models exhibited the same structure but different coefficients. The
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intercept of the covered model was 1.91 units lower than that of the
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uncovered model, indicating a lower baseline risk of ankle draft
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dissatisfaction when the ankle was covered by clothing. In addition, the
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air speed coefficient was smaller in the covered model than in the
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uncovered model, indicating reduced sensitivity of dissatisfaction to
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air speed under ankle-covered conditions.
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For the ankle-uncovered condition, the approximate closed-form equation
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derived from the marginal predictions of the mixed-effects model can be

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