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: plotnine 0.15.7 | Python 3.13.13
Quality: 87/100 | Created: 2026-06-13
"""
import os
import sys
sys.path = [p for p in sys.path if os.path.abspath(p) != os.getcwd()]
import numpy as np
import pandas as pd
from plotnine import (
aes,
annotate,
coord_cartesian,
element_blank,
element_line,
element_rect,
element_text,
geom_hline,
geom_line,
geom_vline,
ggplot,
labs,
scale_color_manual,
scale_linetype_manual,
scale_x_log10,
theme,
)
from scipy.interpolate import PchipInterpolator
# 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"
# Imprint palette — position 1 always first series
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
BRAND = IMPRINT_PALETTE[0]
# Data: well-trained cyclist power-duration profile
np.random.seed(42)
CP = 280 # Critical Power in watts (aerobic asymptote)
W_PRIME = 20000 # Anaerobic work capacity in joules
# Anchor points for realistic empirical mean-maximal power curve
anchor_dur = np.array([1, 5, 15, 30, 60, 120, 300, 600, 1200, 3600, 7200, 18000])
anchor_pwr = np.array([1050, 820, 620, 520, 430, 365, 350, 316, 298, 287, 283, 278])
# 50 empirical points, log-spaced, via monotone cubic interpolation
log_interp = PchipInterpolator(np.log10(anchor_dur), anchor_pwr)
durations = np.logspace(0, np.log10(18000), 50)
empirical_power = log_interp(np.log10(durations))
# Realistic noise — stronger at short neuromuscular efforts
noise_scale = np.where(durations < 120, 0.025, 0.012)
empirical_power = empirical_power + np.random.normal(0, empirical_power * noise_scale)
# Enforce monotonically non-increasing (MMP is always the BEST effort at each duration)
for i in range(1, len(empirical_power)):
empirical_power[i] = min(empirical_power[i], empirical_power[i - 1])
# CP model: P(t) = CP + W′/t, shown from 5 min (valid aerobic-anaerobic range)
model_dur = np.logspace(np.log10(300), np.log10(18000), 200)
model_pwr = CP + W_PRIME / model_dur
# Build tidy DataFrames
SERIES_EMP = "Mean-maximal power"
SERIES_MOD = "CP model (P = CP + W′/t)"
df_emp = pd.DataFrame({"duration_s": durations, "power_w": empirical_power, "series": SERIES_EMP})
df_mod = pd.DataFrame({"duration_s": model_dur, "power_w": model_pwr, "series": SERIES_MOD})
df_all = pd.concat([df_emp, df_mod], ignore_index=True)
# Title length scaling
title = "curve-power-duration · python · plotnine · anyplot.ai"
n = len(title)
ratio = 67 / n if n > 67 else 1.0
title_fontsize = max(8, round(12 * ratio))
# Series color and linetype mappings
color_map = {SERIES_EMP: BRAND, SERIES_MOD: IMPRINT_PALETTE[1]}
linetype_map = {SERIES_EMP: "solid", SERIES_MOD: "dashed"}
# X-axis: human-readable log ticks
x_breaks = [1, 5, 30, 60, 300, 1200, 3600, 18000]
x_labels = ["1 s", "5 s", "30 s", "1 min", "5 min", "20 min", "1 h", "5 h"]
# Theme
anyplot_theme = theme(
figure_size=(8, 4.5),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG),
panel_grid_major_y=element_line(color=INK, size=0.3, alpha=0.15),
panel_grid_major_x=element_blank(),
panel_grid_minor=element_blank(),
panel_border=element_blank(),
axis_line=element_line(color=INK_SOFT, size=0.5),
axis_title=element_text(color=INK, size=10),
axis_text=element_text(color=INK_SOFT, size=8),
plot_title=element_text(color=INK, size=title_fontsize, weight="medium"),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
legend_text=element_text(color=INK_SOFT, size=8),
legend_title=element_blank(),
legend_key=element_rect(fill=PAGE_BG),
legend_position="top",
legend_direction="horizontal",
)
# Plot
plot = (
ggplot(df_all, aes("duration_s", "power_w", color="series", linetype="series"))
+ geom_line(size=1.1)
# Reference duration markers
+ geom_vline(xintercept=[5, 60, 300, 1200], color=INK_MUTED, linetype="dotted", size=0.5)
# CP asymptote
+ geom_hline(yintercept=CP, color=INK_MUTED, linetype="dotted", size=0.4)
# Duration annotation labels
+ annotate("text", x=5, y=1000, label="5 s", color=INK_MUTED, size=3.5, ha="center")
+ annotate("text", x=60, y=1000, label="1 min", color=INK_MUTED, size=3.5, ha="center")
+ annotate("text", x=300, y=1000, label="5 min", color=INK_MUTED, size=3.5, ha="center")
+ annotate("text", x=1200, y=1000, label="20 min\n(FTP proxy)", color=INK_MUTED, size=3.5, ha="center")
# CP label
+ annotate("text", x=1.5, y=CP + 16, label=f"CP = {CP} W", color=INK_MUTED, size=3.2, ha="left")
# Scales
+ scale_x_log10(breaks=x_breaks, labels=x_labels)
+ scale_color_manual(values=color_map, name="")
+ scale_linetype_manual(values=linetype_map, name="")
+ labs(x="Duration", y="Power (W)", title=title)
+ coord_cartesian(ylim=(220, 1120))
+ anyplot_theme
)
# Save
plot.save(f"plot-{THEME}.png", dpi=400, width=8, height=4.5, units="in")
Part of Mean-Maximal Power Duration Curve on anyplot.ai.