A power duration curve plots an athlete's best mean-maximal power output (watts) against effort duration on a logarithmic time axis spanning roughly 1 second to several hours. Each point answers "what is the highest average power this rider could sustain for exactly this long?", producing a characteristic monotonically decreasing decay curve. A critical power (CP) model is fitted and overlaid, decomposing performance into an aerobic asymptote (CP) and a finite anaerobic work capacity (W′). The chart is a cornerstone of cycling and endurance sports analytics for profiling rider strengths, tracking fitness, and setting training zones.
""" anyplot.ai
curve-power-duration: Mean-Maximal Power Duration Curve
Library: plotly 6.8.0 | Python 3.13.13
Quality: 89/100 | Created: 2026-06-13
"""
import os
import numpy as np
import plotly.graph_objects as go
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
# Imprint palette — first series always #009E73
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
# Data — synthetic well-trained cyclist
np.random.seed(42)
CP = 280 # Critical Power in watts (aerobic asymptote)
W_PRIME = 22000 # Anaerobic work capacity in joules
P_1SEC = 1100 # Neuromuscular peak power at 1 s
# Log-spaced test durations: 1 s to 5 hours (50 points)
durations = np.logspace(0, np.log10(18000), 50)
# CP model: P(t) = CP + W′/t (valid mainly for 2–60 min)
model_power = CP + W_PRIME / durations
# Empirical curve bounded by neuromuscular capacity at short durations
neuro_cap = P_1SEC * (durations**-0.15)
empirical_raw = np.minimum(model_power, neuro_cap)
empirical_raw += np.random.normal(0, 8, len(durations))
# Enforce monotonically non-increasing; keep power above CP floor
empirical_power = np.minimum.accumulate(np.maximum(empirical_raw, CP + 1))
# Smooth model display line
model_t = np.logspace(0, np.log10(18000), 300)
model_display = CP + W_PRIME / model_t
# Reference durations: data values for interpolated empirical power
references = {"5 s": 5, "1 min": 60, "5 min": 300, "20 min": 1200}
# Log10 range for the x-axis (1 s → 18000 s)
LOG_MIN = 0.0
LOG_MAX = float(np.log10(18000)) # ≈ 4.255
# Paper x-coordinate constants (accounts for l=80, r=40 margins on width=800)
_LEFT_FRAC = 80 / 800
_DATA_FRAC = 1.0 - _LEFT_FRAC - 40 / 800
# Title — 49 chars < 67-char baseline, no scaling needed
title = "curve-power-duration · python · plotly · anyplot.ai"
title_fontsize = round(16 * min(1.0, 67 / len(title)))
# X-axis ticks: 7 well-spaced values, no overlap
tick_vals = [1, 10, 60, 300, 1200, 3600, 18000]
tick_text = ["1s", "10s", "1min", "5min", "20min", "1h", "5h"]
# Plot
fig = go.Figure()
# Subtle aerobic zone fill: area between the empirical curve and the CP floor
fig.add_trace(
go.Scatter(
x=np.concatenate([durations, durations[::-1]]),
y=np.concatenate([empirical_power, np.full(len(durations), CP)]),
fill="toself",
fillcolor="rgba(0,158,115,0.07)",
line={"width": 0},
showlegend=False,
hoverinfo="skip",
)
)
# Empirical mean-maximal power curve (primary series — Imprint position 1)
fig.add_trace(
go.Scatter(
x=durations,
y=empirical_power,
mode="lines+markers",
name="Mean-Maximal Power",
line={"color": IMPRINT_PALETTE[0], "width": 3},
marker={"size": 10, "color": IMPRINT_PALETTE[0], "opacity": 0.85, "line": {"color": PAGE_BG, "width": 1.5}},
)
)
# CP model fit — dashed (Imprint position 2)
fig.add_trace(
go.Scatter(
x=model_t,
y=model_display,
mode="lines",
name=f"CP Model (CP = {CP} W, W′ = {W_PRIME // 1000} kJ)",
line={"color": IMPRINT_PALETTE[1], "width": 2.5, "dash": "dash"},
)
)
# CP asymptote horizontal dotted line
fig.add_hline(y=CP, line={"color": INK_MUTED, "width": 1.5, "dash": "dot"})
# CP label near the right where the curve flattens (paper coords for robustness)
fig.add_annotation(
x=0.86,
y=CP + 25,
xref="paper",
yref="y",
text=f"CP = {CP} W",
showarrow=False,
font={"size": 10, "color": INK_MUTED},
bgcolor=ELEVATED_BG,
borderpad=3,
xanchor="left",
)
# Reference vertical dotted lines
for dur in references.values():
fig.add_vline(x=dur, line={"color": INK_MUTED, "width": 1.2, "dash": "dot"})
# Reference annotations using paper x-coordinates to avoid log-axis positioning issues
for label, dur in references.items():
ref_power = int(np.interp(dur, durations, empirical_power))
x_paper = _LEFT_FRAC + (np.log10(dur) - LOG_MIN) / (LOG_MAX - LOG_MIN) * _DATA_FRAC
fig.add_annotation(
x=x_paper,
y=0.97,
xref="paper",
yref="paper",
text=f"<b>{label}</b><br>{ref_power} W",
showarrow=False,
font={"size": 11, "color": INK},
bgcolor=ELEVATED_BG,
bordercolor=INK_SOFT,
borderwidth=1,
borderpad=3,
xanchor="center",
yanchor="top",
)
# Layout
fig.update_layout(
autosize=False,
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
title={"text": title, "font": {"size": title_fontsize, "color": INK}, "x": 0.5, "xanchor": "center"},
xaxis={
"type": "log",
"range": [LOG_MIN, LOG_MAX],
"title": {"text": "Duration", "font": {"size": 12, "color": INK}},
"tickvals": tick_vals,
"ticktext": tick_text,
"tickfont": {"size": 10, "color": INK_SOFT},
"tickangle": 0,
"gridcolor": GRID,
"showgrid": True,
"showline": False,
"zeroline": False,
},
yaxis={
"range": [220, 1250],
"title": {"text": "Power (W)", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"gridcolor": GRID,
"showgrid": True,
"showline": False,
"zeroline": False,
},
legend={
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
"font": {"size": 10, "color": INK_SOFT},
"x": 0.98,
"xanchor": "right",
"y": 0.50,
"yanchor": "top",
},
margin={"l": 80, "r": 40, "t": 80, "b": 60},
)
# Save — landscape 3200 × 1800 (width=800, height=450, scale=4)
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Mean-Maximal Power Duration Curve on anyplot.ai.