|
| 1 | +""" pyplots.ai |
| 2 | +psychrometric-basic: Psychrometric Chart for HVAC |
| 3 | +Library: altair 6.0.0 | Python 3.14.3 |
| 4 | +Quality: 86/100 | Created: 2026-03-15 |
| 5 | +""" |
| 6 | + |
| 7 | +import altair as alt |
| 8 | +import numpy as np |
| 9 | +import pandas as pd |
| 10 | + |
| 11 | + |
| 12 | +# Constants |
| 13 | +P_ATM = 101325 # Pa, standard atmospheric pressure |
| 14 | + |
| 15 | +# Precompute saturation pressure over a fine grid (ASHRAE formula, computed once) |
| 16 | +_t_grid = np.linspace(-10, 50, 500) |
| 17 | +_t_grid_k = _t_grid + 273.15 |
| 18 | +_p_sat_grid = np.where( |
| 19 | + _t_grid >= 0, |
| 20 | + np.exp( |
| 21 | + -5.8002206e3 / _t_grid_k |
| 22 | + + 1.3914993 |
| 23 | + - 4.8640239e-2 * _t_grid_k |
| 24 | + + 4.1764768e-5 * _t_grid_k**2 |
| 25 | + - 1.4452093e-8 * _t_grid_k**3 |
| 26 | + + 6.5459673 * np.log(_t_grid_k) |
| 27 | + ), |
| 28 | + np.exp( |
| 29 | + -5.6745359e3 / _t_grid_k |
| 30 | + + 6.3925247 |
| 31 | + - 9.677843e-3 * _t_grid_k |
| 32 | + + 6.2215701e-7 * _t_grid_k**2 |
| 33 | + + 2.0747825e-9 * _t_grid_k**3 |
| 34 | + - 9.484024e-13 * _t_grid_k**4 |
| 35 | + + 4.1635019 * np.log(_t_grid_k) |
| 36 | + ), |
| 37 | +) |
| 38 | + |
| 39 | +# Interpolation-based saturation pressure lookup (replaces 6x formula repetition) |
| 40 | +p_sat_at = lambda t: np.interp(t, _t_grid, _p_sat_grid) # noqa: E731 |
| 41 | + |
| 42 | +# Data - Generate psychrometric curves |
| 43 | +t_range = np.linspace(-10, 50, 200) |
| 44 | +p_sat = p_sat_at(t_range) |
| 45 | + |
| 46 | +# Relative humidity curves (10% to 100%) |
| 47 | +rh_curves = [] |
| 48 | +for rh_pct in range(10, 110, 10): |
| 49 | + rh_frac = rh_pct / 100 |
| 50 | + p_w = rh_frac * p_sat |
| 51 | + w_vals = 0.621945 * p_w / (P_ATM - p_w) * 1000 # g/kg |
| 52 | + w_vals = np.clip(w_vals, 0, 30) |
| 53 | + for t, w in zip(t_range, w_vals, strict=True): |
| 54 | + if 0 < w <= 30: |
| 55 | + rh_curves.append({"t_db": float(t), "w": float(w), "rh": f"{rh_pct}%"}) |
| 56 | + |
| 57 | +rh_df = pd.DataFrame(rh_curves) |
| 58 | + |
| 59 | +# Wet-bulb temperature lines |
| 60 | +wb_lines = [] |
| 61 | +for t_wb_val in range(0, 36, 5): |
| 62 | + p_sat_wb = float(p_sat_at(t_wb_val)) |
| 63 | + w_s_wb = 0.621945 * p_sat_wb / (P_ATM - p_sat_wb) |
| 64 | + for t_db in np.linspace(max(-10, t_wb_val), 50, 80): |
| 65 | + w = (2501 * w_s_wb - 1.006 * (t_db - t_wb_val)) / (2501 + 1.86 * t_db - 4.186 * t_wb_val) |
| 66 | + w_gkg = w * 1000 |
| 67 | + if 0 <= w_gkg <= 30: |
| 68 | + wb_lines.append({"t_db": float(t_db), "w": float(w_gkg), "wb": f"{t_wb_val}°C"}) |
| 69 | + |
| 70 | +wb_df = pd.DataFrame(wb_lines) |
| 71 | + |
| 72 | +# Enthalpy lines (h = 1.006*t + w*(2501 + 1.86*t), solve for w) |
| 73 | +enthalpy_lines = [] |
| 74 | +for h_val in range(10, 120, 10): |
| 75 | + for t_db in np.linspace(-10, 50, 80): |
| 76 | + w_gkg = (h_val - 1.006 * t_db) / (2.501 + 0.00186 * t_db) |
| 77 | + if 0 <= w_gkg <= 30: |
| 78 | + enthalpy_lines.append({"t_db": float(t_db), "w": float(w_gkg), "h": f"{h_val} kJ/kg"}) |
| 79 | + |
| 80 | +enthalpy_df = pd.DataFrame(enthalpy_lines) |
| 81 | + |
| 82 | +# Specific volume lines (v = 0.287042*T_k*(1+1.6078*w)/P, solve for w) |
| 83 | +vol_lines = [] |
| 84 | +for v_val in [0.75, 0.80, 0.85, 0.90, 0.95]: |
| 85 | + for t_db in np.linspace(-10, 50, 80): |
| 86 | + w = (v_val * P_ATM / 1000 / (0.287042 * (t_db + 273.15)) - 1) / 1.6078 |
| 87 | + w_gkg = w * 1000 |
| 88 | + if 0 <= w_gkg <= 30: |
| 89 | + vol_lines.append({"t_db": float(t_db), "w": float(w_gkg), "v": f"{v_val} m³/kg"}) |
| 90 | + |
| 91 | +vol_df = pd.DataFrame(vol_lines) |
| 92 | + |
| 93 | +# Comfort zone (20-26°C, 30-60% RH) |
| 94 | +comfort_temps = np.linspace(20, 26, 30) |
| 95 | +comfort_psat = p_sat_at(comfort_temps) |
| 96 | +comfort_w_lo = 0.621945 * 0.30 * comfort_psat / (P_ATM - 0.30 * comfort_psat) * 1000 |
| 97 | +comfort_w_hi = 0.621945 * 0.60 * comfort_psat / (P_ATM - 0.60 * comfort_psat) * 1000 |
| 98 | +comfort_df = pd.DataFrame({"t_db": comfort_temps, "w": comfort_w_lo, "w2": comfort_w_hi}) |
| 99 | + |
| 100 | +# HVAC process path: cooling and dehumidification (35°C/50%RH -> 13°C/sat) |
| 101 | +t1, t2 = 35.0, 13.0 |
| 102 | +p_sat_t1, p_sat_t2 = float(p_sat_at(t1)), float(p_sat_at(t2)) |
| 103 | +w1 = 0.621945 * 0.50 * p_sat_t1 / (P_ATM - 0.50 * p_sat_t1) * 1000 |
| 104 | +w2 = 0.621945 * 1.00 * p_sat_t2 / (P_ATM - 1.00 * p_sat_t2) * 1000 |
| 105 | + |
| 106 | +process_points = pd.DataFrame( |
| 107 | + { |
| 108 | + "t_db": [t1, t2], |
| 109 | + "w": [float(w1), float(w2)], |
| 110 | + "label": ["Outdoor Air (35°C, 50% RH)", "Supply Air (13°C, 100% RH)"], |
| 111 | + "rh_pct": ["50%", "100%"], |
| 112 | + "order": [0, 1], |
| 113 | + } |
| 114 | +) |
| 115 | + |
| 116 | +# RH label positions (staggered to avoid overlap) |
| 117 | +rh_labels = [] |
| 118 | +for rh_pct in range(10, 110, 10): |
| 119 | + rh_frac = rh_pct / 100 |
| 120 | + # Stagger label temperatures to reduce convergence overlap |
| 121 | + if rh_pct == 100: |
| 122 | + t_label = 33 |
| 123 | + elif rh_pct >= 80: |
| 124 | + t_label = 36 |
| 125 | + elif rh_pct >= 60: |
| 126 | + t_label = 40 |
| 127 | + elif rh_pct >= 40: |
| 128 | + t_label = 44 |
| 129 | + else: |
| 130 | + t_label = 47 |
| 131 | + p_sat_label = float(p_sat_at(t_label)) |
| 132 | + w_label = 0.621945 * rh_frac * p_sat_label / (P_ATM - rh_frac * p_sat_label) * 1000 |
| 133 | + if w_label <= 30: |
| 134 | + rh_labels.append({"t_db": float(t_label), "w": float(w_label), "label": f"{rh_pct}%"}) |
| 135 | + |
| 136 | +rh_label_df = pd.DataFrame(rh_labels) |
| 137 | + |
| 138 | +# Wet-bulb labels (offset from saturation curve to avoid overlap with enthalpy labels) |
| 139 | +wb_labels_data = [] |
| 140 | +for t_wb_val in range(0, 36, 5): |
| 141 | + p_sat_wb = float(p_sat_at(t_wb_val)) |
| 142 | + w_wb_label = 0.621945 * p_sat_wb / (P_ATM - p_sat_wb) * 1000 |
| 143 | + if w_wb_label <= 28: |
| 144 | + wb_labels_data.append({"t_db": float(t_wb_val) + 1.5, "w": float(w_wb_label) + 0.8, "label": f"{t_wb_val}°C"}) |
| 145 | + |
| 146 | +wb_label_df = pd.DataFrame(wb_labels_data) |
| 147 | + |
| 148 | +# Enthalpy labels (along left edge, skip values that would overlap with wet-bulb labels) |
| 149 | +enthalpy_labels = [] |
| 150 | +for h_val in range(20, 120, 20): |
| 151 | + w_at_left = (h_val - 1.006 * (-10)) / (2.501 + 0.00186 * (-10)) |
| 152 | + if 0 <= w_at_left <= 30: |
| 153 | + enthalpy_labels.append({"t_db": -9.5, "w": float(w_at_left), "label": f"{h_val} kJ/kg"}) |
| 154 | + else: |
| 155 | + t_at_top = (h_val - 2.501 * 30) / (1.006 + 0.00186 * 30) |
| 156 | + if -10 <= t_at_top <= 50: |
| 157 | + enthalpy_labels.append({"t_db": float(t_at_top), "w": 30.0, "label": f"{h_val} kJ/kg"}) |
| 158 | + |
| 159 | +enthalpy_label_df = pd.DataFrame(enthalpy_labels) |
| 160 | + |
| 161 | +# Volume labels (along bottom-right) |
| 162 | +vol_labels = [] |
| 163 | +for v_val in [0.75, 0.80, 0.85, 0.90, 0.95]: |
| 164 | + w_at_bot = (v_val * P_ATM / 1000 / (0.287042 * (45 + 273.15)) - 1) / 1.6078 * 1000 |
| 165 | + if 0 <= w_at_bot <= 30: |
| 166 | + vol_labels.append({"t_db": 45.0, "w": float(w_at_bot), "label": f"{v_val} m³/kg"}) |
| 167 | + |
| 168 | +vol_label_df = pd.DataFrame(vol_labels) |
| 169 | + |
| 170 | +# Colorblind-safe palette: blue (RH), orange (wet-bulb), teal (enthalpy), purple (volume) |
| 171 | +CLR_RH = "#306998" |
| 172 | +CLR_WB = "#d97b0e" |
| 173 | +CLR_ENTHALPY = "#17becf" |
| 174 | +CLR_VOL = "#9467bd" |
| 175 | +CLR_COMFORT = "#2ecc71" |
| 176 | +CLR_PROCESS = "#c0392b" |
| 177 | +CLR_BG = "#fafbfc" |
| 178 | + |
| 179 | +# Plot |
| 180 | +x_scale = alt.Scale(domain=[-10, 50]) |
| 181 | +y_scale = alt.Scale(domain=[0, 30]) |
| 182 | + |
| 183 | +# Saturation curve (100% RH) - visually prominent |
| 184 | +sat_df = rh_df[rh_df["rh"] == "100%"] |
| 185 | +saturation = ( |
| 186 | + alt.Chart(sat_df) |
| 187 | + .mark_line(strokeWidth=3.5, color=CLR_RH) |
| 188 | + .encode( |
| 189 | + x=alt.X("t_db:Q", scale=x_scale, title="Dry-Bulb Temperature (°C)"), |
| 190 | + y=alt.Y("w:Q", scale=y_scale, title="Humidity Ratio (g/kg)"), |
| 191 | + ) |
| 192 | +) |
| 193 | + |
| 194 | +# Other RH curves with tooltips |
| 195 | +other_rh_df = rh_df[rh_df["rh"] != "100%"] |
| 196 | +rh_chart = ( |
| 197 | + alt.Chart(other_rh_df) |
| 198 | + .mark_line(strokeWidth=1.5, opacity=0.55) |
| 199 | + .encode( |
| 200 | + x=alt.X("t_db:Q", scale=x_scale), |
| 201 | + y=alt.Y("w:Q", scale=y_scale), |
| 202 | + color=alt.Color("rh:N", scale=alt.Scale(scheme="blues"), legend=None), |
| 203 | + detail="rh:N", |
| 204 | + tooltip=[ |
| 205 | + alt.Tooltip("t_db:Q", title="Dry-Bulb (°C)", format=".1f"), |
| 206 | + alt.Tooltip("w:Q", title="Humidity (g/kg)", format=".1f"), |
| 207 | + alt.Tooltip("rh:N", title="Relative Humidity"), |
| 208 | + ], |
| 209 | + ) |
| 210 | +) |
| 211 | + |
| 212 | +# RH labels |
| 213 | +rh_text = ( |
| 214 | + alt.Chart(rh_label_df) |
| 215 | + .mark_text(fontSize=13, color="#4a7fb5", fontWeight="bold") |
| 216 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N") |
| 217 | +) |
| 218 | + |
| 219 | +# Wet-bulb lines (orange, colorblind-safe) |
| 220 | +wb_chart = ( |
| 221 | + alt.Chart(wb_df) |
| 222 | + .mark_line(strokeWidth=1, strokeDash=[6, 4], opacity=0.5, color=CLR_WB) |
| 223 | + .encode( |
| 224 | + x=alt.X("t_db:Q", scale=x_scale), |
| 225 | + y=alt.Y("w:Q", scale=y_scale), |
| 226 | + detail="wb:N", |
| 227 | + tooltip=[ |
| 228 | + alt.Tooltip("t_db:Q", title="Dry-Bulb (°C)", format=".1f"), |
| 229 | + alt.Tooltip("w:Q", title="Humidity (g/kg)", format=".1f"), |
| 230 | + alt.Tooltip("wb:N", title="Wet-Bulb Temp"), |
| 231 | + ], |
| 232 | + ) |
| 233 | +) |
| 234 | + |
| 235 | +# Wet-bulb labels (offset to avoid overlap) |
| 236 | +wb_text = ( |
| 237 | + alt.Chart(wb_label_df) |
| 238 | + .mark_text(fontSize=12, color=CLR_WB, align="left", dx=2, dy=-6, fontWeight="bold") |
| 239 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N") |
| 240 | +) |
| 241 | + |
| 242 | +# Enthalpy lines (teal, colorblind-safe) |
| 243 | +enthalpy_chart = ( |
| 244 | + alt.Chart(enthalpy_df) |
| 245 | + .mark_line(strokeWidth=1, strokeDash=[4, 6], opacity=0.45, color=CLR_ENTHALPY) |
| 246 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), detail="h:N") |
| 247 | +) |
| 248 | + |
| 249 | +# Enthalpy labels |
| 250 | +enthalpy_text = ( |
| 251 | + alt.Chart(enthalpy_label_df) |
| 252 | + .mark_text(fontSize=11, color=CLR_ENTHALPY, align="left", dx=2, dy=-4, fontWeight="bold") |
| 253 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N") |
| 254 | +) |
| 255 | + |
| 256 | +# Specific volume lines |
| 257 | +vol_chart = ( |
| 258 | + alt.Chart(vol_df) |
| 259 | + .mark_line(strokeWidth=1, strokeDash=[2, 4], opacity=0.4, color=CLR_VOL) |
| 260 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), detail="v:N") |
| 261 | +) |
| 262 | + |
| 263 | +# Volume labels |
| 264 | +vol_text = ( |
| 265 | + alt.Chart(vol_label_df) |
| 266 | + .mark_text(fontSize=11, color=CLR_VOL, align="left", dx=3, dy=-5, fontWeight="bold") |
| 267 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N") |
| 268 | +) |
| 269 | + |
| 270 | +# Comfort zone shaded area |
| 271 | +comfort = ( |
| 272 | + alt.Chart(comfort_df) |
| 273 | + .mark_area(opacity=0.12, color=CLR_COMFORT) |
| 274 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), y2="w2:Q") |
| 275 | +) |
| 276 | + |
| 277 | +comfort_label = ( |
| 278 | + alt.Chart(pd.DataFrame({"t_db": [23.0], "w": [10.5], "label": ["Comfort Zone"]})) |
| 279 | + .mark_text(fontSize=14, color="#27ae60", fontWeight="bold", fontStyle="italic") |
| 280 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N") |
| 281 | +) |
| 282 | + |
| 283 | +# Interactive selection for HVAC process points |
| 284 | +point_selection = alt.selection_point(on="pointerover", nearest=True, fields=["t_db"]) |
| 285 | + |
| 286 | +# HVAC process path with tooltips |
| 287 | +process_line = ( |
| 288 | + alt.Chart(process_points) |
| 289 | + .mark_line(strokeWidth=3.5, color=CLR_PROCESS, point=alt.OverlayMarkDef(size=140, filled=True, color=CLR_PROCESS)) |
| 290 | + .encode( |
| 291 | + x=alt.X("t_db:Q", scale=x_scale), |
| 292 | + y=alt.Y("w:Q", scale=y_scale), |
| 293 | + order="order:Q", |
| 294 | + tooltip=[ |
| 295 | + alt.Tooltip("label:N", title="State Point"), |
| 296 | + alt.Tooltip("t_db:Q", title="Dry-Bulb (°C)", format=".1f"), |
| 297 | + alt.Tooltip("w:Q", title="Humidity (g/kg)", format=".1f"), |
| 298 | + alt.Tooltip("rh_pct:N", title="RH"), |
| 299 | + ], |
| 300 | + ) |
| 301 | + .add_params(point_selection) |
| 302 | +) |
| 303 | + |
| 304 | +# Process labels (adjusted positions to avoid overlap) |
| 305 | +outdoor_label = ( |
| 306 | + alt.Chart(process_points[process_points["order"] == 0]) |
| 307 | + .mark_text(fontSize=12, fontWeight="bold", color=CLR_PROCESS, align="right", dx=-12, dy=-14) |
| 308 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N") |
| 309 | +) |
| 310 | + |
| 311 | +supply_label = ( |
| 312 | + alt.Chart(process_points[process_points["order"] == 1]) |
| 313 | + .mark_text(fontSize=12, fontWeight="bold", color=CLR_PROCESS, align="left", dx=12, dy=14) |
| 314 | + .encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N") |
| 315 | +) |
| 316 | + |
| 317 | +# Layer all elements |
| 318 | +chart = ( |
| 319 | + alt.layer( |
| 320 | + comfort, |
| 321 | + rh_chart, |
| 322 | + saturation, |
| 323 | + wb_chart, |
| 324 | + enthalpy_chart, |
| 325 | + vol_chart, |
| 326 | + rh_text, |
| 327 | + wb_text, |
| 328 | + enthalpy_text, |
| 329 | + vol_text, |
| 330 | + comfort_label, |
| 331 | + process_line, |
| 332 | + outdoor_label, |
| 333 | + supply_label, |
| 334 | + ) |
| 335 | + .properties( |
| 336 | + width=1600, |
| 337 | + height=900, |
| 338 | + title=alt.Title( |
| 339 | + text="psychrometric-basic · altair · pyplots.ai", |
| 340 | + fontSize=28, |
| 341 | + anchor="middle", |
| 342 | + subtitle="Standard Atmosphere (101.325 kPa) · HVAC Air Properties", |
| 343 | + subtitleFontSize=18, |
| 344 | + subtitleColor="#888888", |
| 345 | + offset=12, |
| 346 | + ), |
| 347 | + ) |
| 348 | + .configure_axis( |
| 349 | + labelFontSize=18, |
| 350 | + titleFontSize=22, |
| 351 | + titleColor="#444444", |
| 352 | + labelColor="#555555", |
| 353 | + grid=True, |
| 354 | + gridOpacity=0.12, |
| 355 | + gridColor="#cccccc", |
| 356 | + domainColor="#999999", |
| 357 | + ) |
| 358 | + .configure_view(strokeWidth=0, fill=CLR_BG) |
| 359 | +) |
| 360 | + |
| 361 | +# Save |
| 362 | +chart.save("plot.png", scale_factor=3.0) |
| 363 | +chart.save("plot.html") |
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