A psychrometric chart plots dry-bulb temperature against humidity ratio, overlaid with curves for relative humidity, wet-bulb temperature, enthalpy, and specific volume. It is the fundamental tool for HVAC system design and air conditioning process analysis. The chart reveals the thermodynamic properties of moist air at a glance, enabling engineers to trace heating, cooling, humidification, and dehumidification processes as paths on the diagram.
""" anyplot.ai
psychrometric-basic: Psychrometric Chart for HVAC
Library: altair 6.2.1 | Python 3.13.13
Quality: 86/100 | Updated: 2026-06-16
"""
import os
import sys
# Strip the script directory from sys.path so `import altair` resolves to the
# installed package, not this file (which is named altair.py).
_script_dir = os.path.dirname(os.path.abspath(__file__))
sys.path[:] = [p for p in sys.path if os.path.abspath(p or ".") != _script_dir]
import altair as alt
import numpy as np
import pandas as pd
from PIL import Image
# Theme tokens (see prompts/default-style-guide.md "Theme-adaptive Chrome")
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
# Imprint palette — each moist-air property family gets one canonical hue.
CLR_RH = "#009E73" # brand green — relative humidity + saturation (first series)
CLR_WB = "#C475FD" # lavender — wet-bulb temperature lines
CLR_ENTHALPY = "#4467A3" # blue — constant enthalpy lines
CLR_VOL = "#BD8233" # ochre — constant specific-volume lines
CLR_PROCESS = "#AE3030" # matte red (semantic emphasis) — HVAC process path
CLR_COMFORT = "#2ABCCD" # cyan — thermal comfort zone
# Constants
P_ATM = 101325 # Pa, standard sea-level atmospheric pressure
# Saturation pressure over a fine grid (ASHRAE 2017 formula), computed once.
_t_grid = np.linspace(-10, 50, 500)
_t_grid_k = _t_grid + 273.15
_p_sat_grid = np.where(
_t_grid >= 0,
np.exp(
-5.8002206e3 / _t_grid_k
+ 1.3914993
- 4.8640239e-2 * _t_grid_k
+ 4.1764768e-5 * _t_grid_k**2
- 1.4452093e-8 * _t_grid_k**3
+ 6.5459673 * np.log(_t_grid_k)
),
np.exp(
-5.6745359e3 / _t_grid_k
+ 6.3925247
- 9.677843e-3 * _t_grid_k
+ 6.2215701e-7 * _t_grid_k**2
+ 2.0747825e-9 * _t_grid_k**3
- 9.484024e-13 * _t_grid_k**4
+ 4.1635019 * np.log(_t_grid_k)
),
)
# Data — psychrometric property curves over the -10..50 °C dry-bulb range.
t_range = np.linspace(-10, 50, 200)
p_sat = np.interp(t_range, _t_grid, _p_sat_grid)
# Relative-humidity curves (10% to 100%)
rh_curves = []
for rh_pct in range(10, 110, 10):
p_w = (rh_pct / 100) * p_sat
w_vals = 0.621945 * p_w / (P_ATM - p_w) * 1000 # g/kg
for t, w in zip(t_range, w_vals, strict=True):
if 0 < w <= 30:
rh_curves.append({"t_db": float(t), "w": float(w), "rh": f"{rh_pct}%"})
rh_df = pd.DataFrame(rh_curves)
# Wet-bulb temperature lines (constant t_wb)
wb_lines = []
for t_wb_val in range(0, 36, 5):
p_sat_wb = float(np.interp(t_wb_val, _t_grid, _p_sat_grid))
w_s_wb = 0.621945 * p_sat_wb / (P_ATM - p_sat_wb)
for t_db in np.linspace(t_wb_val, 50, 80):
w = (2501 * w_s_wb - 1.006 * (t_db - t_wb_val)) / (2501 + 1.86 * t_db - 4.186 * t_wb_val)
w_gkg = w * 1000
if 0 <= w_gkg <= 30:
wb_lines.append({"t_db": float(t_db), "w": float(w_gkg), "wb": f"{t_wb_val}°C"})
wb_df = pd.DataFrame(wb_lines)
# Constant-enthalpy lines (h = 1.006*t + w*(2501 + 1.86*t), solved for w)
enthalpy_lines = []
for h_val in range(10, 120, 10):
for t_db in np.linspace(-10, 50, 80):
w_gkg = (h_val - 1.006 * t_db) / (2.501 + 0.00186 * t_db)
if 0 <= w_gkg <= 30:
enthalpy_lines.append({"t_db": float(t_db), "w": float(w_gkg), "h": f"{h_val} kJ/kg"})
enthalpy_df = pd.DataFrame(enthalpy_lines)
# Constant specific-volume lines (v = 0.287042*T_k*(1+1.6078*w)/P, solved for w)
vol_lines = []
for v_val in [0.78, 0.82, 0.86, 0.90, 0.94]:
for t_db in np.linspace(-10, 50, 80):
w = (v_val * P_ATM / 1000 / (0.287042 * (t_db + 273.15)) - 1) / 1.6078
w_gkg = w * 1000
if 0 <= w_gkg <= 30:
vol_lines.append({"t_db": float(t_db), "w": float(w_gkg), "v": f"{v_val} m³/kg"})
vol_df = pd.DataFrame(vol_lines)
# Comfort zone (20-26 °C, 30-60% RH)
comfort_temps = np.linspace(20, 26, 30)
comfort_psat = np.interp(comfort_temps, _t_grid, _p_sat_grid)
comfort_w_lo = 0.621945 * 0.30 * comfort_psat / (P_ATM - 0.30 * comfort_psat) * 1000
comfort_w_hi = 0.621945 * 0.60 * comfort_psat / (P_ATM - 0.60 * comfort_psat) * 1000
comfort_df = pd.DataFrame({"t_db": comfort_temps, "w": comfort_w_lo, "w2": comfort_w_hi})
# HVAC process path: cooling + dehumidification (35 °C/50% RH -> 13 °C/saturated)
t1, t2 = 35.0, 13.0
p_sat_t1, p_sat_t2 = float(np.interp(t1, _t_grid, _p_sat_grid)), float(np.interp(t2, _t_grid, _p_sat_grid))
w1 = 0.621945 * 0.50 * p_sat_t1 / (P_ATM - 0.50 * p_sat_t1) * 1000
w2 = 0.621945 * 1.00 * p_sat_t2 / (P_ATM - 1.00 * p_sat_t2) * 1000
process_points = pd.DataFrame(
{
"t_db": [t1, t2],
"w": [float(w1), float(w2)],
"label": ["Outdoor Air (35°C, 50% RH)", "Supply Air (13°C, 100% RH)"],
"rh_pct": ["50%", "100%"],
"order": [0, 1],
}
)
# RH labels — staggered along the curves to avoid convergence overlap near saturation
rh_labels = []
for rh_pct in range(10, 110, 10):
if rh_pct == 100:
t_label = 31
elif rh_pct >= 80:
t_label = 35
elif rh_pct >= 60:
t_label = 39
elif rh_pct >= 40:
t_label = 43
else:
t_label = 47
p_sat_label = float(np.interp(t_label, _t_grid, _p_sat_grid))
w_label = 0.621945 * (rh_pct / 100) * p_sat_label / (P_ATM - (rh_pct / 100) * p_sat_label) * 1000
if w_label <= 30:
rh_labels.append({"t_db": float(t_label), "w": float(w_label), "label": f"{rh_pct}%"})
rh_label_df = pd.DataFrame(rh_labels)
# Wet-bulb labels — placed in the interior along each line, away from the saturation crowd.
# Per-line anchor offsets: 25 °C steps left to clear the red process marker (~35 °C, 17.8 g/kg);
# 30 °C steps right to descend out of the crowded saturation apex.
wb_label_offset = {25: 4, 30: 11}
wb_labels_data = []
for t_wb_val in range(0, 36, 5):
p_sat_wb = float(np.interp(t_wb_val, _t_grid, _p_sat_grid))
w_s_wb = 0.621945 * p_sat_wb / (P_ATM - p_sat_wb)
t_at = t_wb_val + wb_label_offset.get(t_wb_val, 7)
w_at = (2501 * w_s_wb - 1.006 * (t_at - t_wb_val)) / (2501 + 1.86 * t_at - 4.186 * t_wb_val) * 1000
if 0 < w_at <= 28:
wb_labels_data.append({"t_db": float(t_at), "w": float(w_at), "label": f"{t_wb_val}°C WB"})
wb_label_df = pd.DataFrame(wb_labels_data)
# Enthalpy labels — anchored on the left/top edges where wet-bulb labels are absent
enthalpy_labels = []
for h_val in range(20, 120, 20):
w_at_left = (h_val - 1.006 * (-10)) / (2.501 + 0.00186 * (-10))
if 0 <= w_at_left <= 30:
enthalpy_labels.append({"t_db": -9.0, "w": float(w_at_left), "label": f"{h_val} kJ/kg"})
else:
t_at_top = (h_val - 2.501 * 30) / (1.006 + 0.00186 * 30)
if -10 <= t_at_top <= 50:
enthalpy_labels.append({"t_db": float(t_at_top), "w": 29.4, "label": f"{h_val} kJ/kg"})
enthalpy_label_df = pd.DataFrame(enthalpy_labels)
# Volume labels — along the lower-right where the volume lines exit the frame
vol_labels = []
for v_val in [0.78, 0.82, 0.86, 0.90, 0.94]:
w_at = (v_val * P_ATM / 1000 / (0.287042 * (44 + 273.15)) - 1) / 1.6078 * 1000
if 0 <= w_at <= 30:
vol_labels.append({"t_db": 44.0, "w": float(w_at), "label": f"{v_val} m³/kg"})
vol_label_df = pd.DataFrame(vol_labels)
# Plot
x_scale = alt.Scale(domain=[-10, 50])
y_scale = alt.Scale(domain=[0, 30])
# Comfort zone shaded band
comfort = (
alt.Chart(comfort_df)
.mark_area(opacity=0.18, color=CLR_COMFORT)
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), y2="w2:Q")
)
comfort_label = (
alt.Chart(pd.DataFrame({"t_db": [23.0], "w": [10.8], "label": ["Comfort Zone"]}))
.mark_text(fontSize=12, color=CLR_COMFORT, fontWeight="bold", fontStyle="italic")
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N")
)
# Specific-volume lines (ochre)
vol_chart = (
alt.Chart(vol_df)
.mark_line(strokeWidth=1.2, strokeDash=[2, 4], opacity=0.65, color=CLR_VOL)
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), detail="v:N")
)
vol_text = (
alt.Chart(vol_label_df)
.mark_text(fontSize=10, color=CLR_VOL, align="left", dx=3, dy=-4, fontWeight="bold")
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N")
)
# Constant-enthalpy lines (blue)
enthalpy_chart = (
alt.Chart(enthalpy_df)
.mark_line(strokeWidth=1.2, strokeDash=[4, 5], opacity=0.7, color=CLR_ENTHALPY)
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), detail="h:N")
)
enthalpy_text = (
alt.Chart(enthalpy_label_df)
.mark_text(fontSize=10, color=CLR_ENTHALPY, align="left", dx=2, dy=-4, fontWeight="bold")
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N")
)
# Wet-bulb lines (lavender)
wb_chart = (
alt.Chart(wb_df)
.mark_line(strokeWidth=1.2, strokeDash=[6, 4], opacity=0.7, color=CLR_WB)
.encode(
x=alt.X("t_db:Q", scale=x_scale),
y=alt.Y("w:Q", scale=y_scale),
detail="wb:N",
tooltip=[
alt.Tooltip("t_db:Q", title="Dry-Bulb (°C)", format=".1f"),
alt.Tooltip("w:Q", title="Humidity (g/kg)", format=".1f"),
alt.Tooltip("wb:N", title="Wet-Bulb Temp"),
],
)
)
wb_text = (
alt.Chart(wb_label_df)
.mark_text(fontSize=10, color=CLR_WB, align="left", dx=2, dy=-5, fontWeight="bold")
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N")
)
# Relative-humidity curves (10%-90%, brand green, lighter than saturation)
other_rh_df = rh_df[rh_df["rh"] != "100%"]
rh_chart = (
alt.Chart(other_rh_df)
.mark_line(strokeWidth=1.5, opacity=0.5, color=CLR_RH)
.encode(
x=alt.X("t_db:Q", scale=x_scale),
y=alt.Y("w:Q", scale=y_scale),
detail="rh:N",
tooltip=[
alt.Tooltip("t_db:Q", title="Dry-Bulb (°C)", format=".1f"),
alt.Tooltip("w:Q", title="Humidity (g/kg)", format=".1f"),
alt.Tooltip("rh:N", title="Relative Humidity"),
],
)
)
# Saturation curve (100% RH) — the prominent upper boundary
sat_df = rh_df[rh_df["rh"] == "100%"]
saturation = (
alt.Chart(sat_df)
.mark_line(strokeWidth=3.5, color=CLR_RH)
.encode(
x=alt.X("t_db:Q", scale=x_scale, title="Dry-Bulb Temperature (°C)"),
y=alt.Y("w:Q", scale=y_scale, title="Humidity Ratio (g/kg)"),
)
)
rh_text = (
alt.Chart(rh_label_df)
.mark_text(fontSize=12, color=CLR_RH, fontWeight="bold")
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N")
)
# HVAC process path (matte red) — focal point with state-point markers
process_line = (
alt.Chart(process_points)
.mark_line(strokeWidth=3.5, color=CLR_PROCESS, point=alt.OverlayMarkDef(size=130, filled=True, color=CLR_PROCESS))
.encode(
x=alt.X("t_db:Q", scale=x_scale),
y=alt.Y("w:Q", scale=y_scale),
order="order:Q",
tooltip=[
alt.Tooltip("label:N", title="State Point"),
alt.Tooltip("t_db:Q", title="Dry-Bulb (°C)", format=".1f"),
alt.Tooltip("w:Q", title="Humidity (g/kg)", format=".1f"),
alt.Tooltip("rh_pct:N", title="RH"),
],
)
)
outdoor_label = (
alt.Chart(process_points[process_points["order"] == 0])
.mark_text(fontSize=11, fontWeight="bold", color=CLR_PROCESS, align="right", dx=-14, dy=-16)
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N")
)
supply_label = (
alt.Chart(process_points[process_points["order"] == 1])
.mark_text(fontSize=11, fontWeight="bold", color=CLR_PROCESS, align="right", dx=-14, dy=16)
.encode(x=alt.X("t_db:Q", scale=x_scale), y=alt.Y("w:Q", scale=y_scale), text="label:N")
)
# Layer all elements (faint property grids first, prominent features last)
chart = (
alt.layer(
comfort,
vol_chart,
enthalpy_chart,
wb_chart,
rh_chart,
saturation,
vol_text,
enthalpy_text,
wb_text,
rh_text,
comfort_label,
process_line,
outdoor_label,
supply_label,
)
.properties(
width=640,
height=330,
background=PAGE_BG,
title=alt.Title(
text="psychrometric-basic · python · altair · anyplot.ai",
fontSize=16,
anchor="middle",
color=INK,
subtitle="Standard Atmosphere (101.325 kPa) · Moist-Air Properties for HVAC",
subtitleFontSize=11,
subtitleColor=INK_SOFT,
offset=10,
),
)
.configure_view(strokeWidth=0, fill=PAGE_BG)
.configure_axis(
labelFontSize=10,
titleFontSize=12,
titleColor=INK,
labelColor=INK_SOFT,
grid=True,
gridOpacity=0.15,
gridColor=INK,
domainColor=INK_SOFT,
tickColor=INK_SOFT,
)
)
# Save — interactive HTML untouched; PNG padded to the exact canonical target.
chart.save(f"plot-{THEME}.html")
chart.save(f"plot-{THEME}.png", scale_factor=4.0)
TW, TH = 3200, 1800
_img = Image.open(f"plot-{THEME}.png").convert("RGB")
_w, _h = _img.size
if _w > TW or _h > TH:
raise SystemExit(
f"altair vl-convert produced {_w}×{_h}, exceeds target {TW}×{TH}. "
f"Shrink chart .properties(width=, height=) values and re-render."
)
if _w < TW or _h < TH:
_canvas = Image.new("RGB", (TW, TH), PAGE_BG)
_canvas.paste(_img, ((TW - _w) // 2, (TH - _h) // 2))
_canvas.save(f"plot-{THEME}.png")
Part of Psychrometric Chart for HVAC on anyplot.ai.