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: makie 0.22.10 | Julia 1.11.9
# Quality: 90/100 | Created: 2026-06-13
using CairoMakie
using Colors
using Random
Random.seed!(42)
# Theme tokens
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const INK_MUTED = THEME == "light" ? colorant"#6B6A63" : colorant"#A8A79F"
const IMPRINT_PALETTE = [
colorant"#009E73", # 1 — brand green (Imprint palette — always first series)
colorant"#C475FD", # 2 — lavender
colorant"#4467A3", # 3 — blue
colorant"#BD8233", # 4 — ochre
colorant"#AE3030", # 5 — matte red
colorant"#2ABCCD", # 6 — cyan
colorant"#954477", # 7 — rose
colorant"#99B314", # 8 — lime
]
# Critical power parameters — well-trained cyclist
const CP = 280.0 # W — aerobic asymptote (critical power)
const W_PRIME = 20_000.0 # J — anaerobic work capacity (W′)
const P_MAX = 1_100.0 # W — neuromuscular peak at 1 s
# Empirical mean-maximal power: 45 log-spaced efforts from 1 s to 5 h
const n_emp = 45
const dur_emp = exp.(range(log(1.0), log(18_000.0); length = n_emp))
# At short durations the neuromuscular cap (P_MAX) limits power below the CP model;
# from ~32 s onwards the CP model governs. Use min() to model this crossover.
base_emp = [min(P_MAX * t^(-0.05), CP + W_PRIME / t) for t in dur_emp]
scatter_weights = [exp(-((log(t) - log(300.0))^2) / (2.0 * log(8.0)^2)) for t in dur_emp]
empirical_mmp = base_emp .+ abs.(randn(n_emp)) .* 12.0 .* scatter_weights
# CP model line — dense curve (300 points) for smooth rendering
const n_model = 300
const dur_model = exp.(range(log(1.0), log(18_000.0); length = n_model))
const model_power = [CP + W_PRIME / t for t in dur_model]
# Display range — clip the model's off-chart divergence at very short durations
const Y_MIN = 200.0
const Y_MAX = 1_250.0
model_mask = model_power .<= Y_MAX
mt = dur_model[model_mask]
mp = model_power[model_mask]
# Reference durations specified in the spec
const ref_dur = [5.0, 60.0, 300.0, 1_200.0]
const ref_labels = ["5 s", "1 min", "5 min", "20 min (FTP)"]
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "curve-power-duration · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Duration",
ylabel = "Power (W)",
xlabelsize = 14,
ylabelsize = 14,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelsize = 12,
yticklabelsize = 12,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xscale = log10,
xgridvisible = false,
ygridvisible = true,
ygridcolor = (INK, 0.12),
xminorgridvisible = false,
yminorgridvisible = false,
)
xlims!(ax, 1.0, 18_000.0)
ylims!(ax, Y_MIN, Y_MAX)
# Reference duration vertical lines (drawn first so data layers render on top)
for dur in ref_dur
vlines!(ax, [dur]; color = (INK_SOFT, 0.45), linewidth = 1.0, linestyle = :dash)
end
# W′ reserve zone — band! fill between CP asymptote and model line (Makie-native primitive)
band!(ax, mt, fill(CP, length(mt)), mp;
color = (IMPRINT_PALETTE[3], 0.08),
)
# Area fill under MMP curve — band! adds depth and makes the primary data the focal point
band!(ax, dur_emp, fill(Y_MIN, n_emp), empirical_mmp;
color = (IMPRINT_PALETTE[1], 0.08),
)
# CP model overlay (dashed, Imprint position 3 — blue)
lines!(ax, mt, mp;
color = IMPRINT_PALETTE[3],
linewidth = 2.5,
linestyle = :dash,
label = "CP model: P = CP + W′/t",
)
# Empirical MMP curve (solid, Imprint position 1 — brand green)
lines!(ax, dur_emp, empirical_mmp;
color = IMPRINT_PALETTE[1],
linewidth = 3.0,
label = "Mean-maximal power (empirical)",
)
scatter!(ax, dur_emp, empirical_mmp;
color = IMPRINT_PALETTE[1],
markersize = 8,
strokewidth = 1,
strokecolor = PAGE_BG,
)
# CP asymptote horizontal line (dotted, muted)
hlines!(ax, [CP]; color = (INK_MUTED, 0.85), linewidth = 1.5, linestyle = :dot)
# CP asymptote label
text!(ax, 150.0, CP + 14;
text = "CP = $(Int(CP)) W",
color = INK_MUTED,
fontsize = 12,
align = (:left, :bottom),
)
# Reference duration labels at the top of each vertical marker
for (dur, lbl) in zip(ref_dur, ref_labels)
text!(ax, dur, Y_MAX - 30;
text = lbl,
color = INK_SOFT,
fontsize = 12,
align = (:center, :top),
)
end
# Human-readable x-axis tick labels (log scale, data-space positions)
ax.xticks = (
[1.0, 5.0, 30.0, 60.0, 300.0, 1_200.0, 3_600.0, 18_000.0],
["1 s", "5 s", "30 s", "1 min", "5 min", "20 min", "1 h", "5 h"],
)
axislegend(ax;
position = :rt,
framevisible = true,
framecolor = (INK_SOFT, 0.4),
backgroundcolor = ELEVATED_BG,
labelcolor = INK,
padding = (10, 10, 8, 8),
labelsize = 12,
patchsize = (24, 8),
rowgap = 4,
)
save("plot-$(THEME).png", fig; px_per_unit = 2)
Part of Mean-Maximal Power Duration Curve on anyplot.ai.