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: ggplot2 3.5.1 | R 4.4.1
#' Quality: 88/100 | Created: 2026-06-13
library(ggplot2)
library(ragg)
set.seed(42)
# Theme tokens (Imprint palette — see prompts/default-style-guide.md)
THEME <- Sys.getenv("ANYPLOT_THEME", "light")
PAGE_BG <- if (THEME == "light") "#FAF8F1" else "#1A1A17"
ELEVATED_BG <- if (THEME == "light") "#FFFDF6" else "#242420"
INK <- if (THEME == "light") "#1A1A17" else "#F0EFE8"
INK_SOFT <- if (THEME == "light") "#4A4A44" else "#B8B7B0"
INK_MUTED <- if (THEME == "light") "#6B6A63" else "#A8A79F"
IMPRINT_PALETTE <- c(
"#009E73", # 1 - brand green (empirical MMP curve)
"#C475FD", # 2 - lavender (CP model overlay)
"#4467A3", # 3 - blue
"#BD8233", # 4 - ochre
"#AE3030", # 5 - matte red
"#2ABCCD", # 6 - cyan
"#954477", # 7 - rose
"#99B314" # 8 - lime
)
# Grid color: INK with alpha embedded for subtlety (ggplot2 has no alpha on element_line)
GRID_COLOR <- grDevices::adjustcolor(INK, alpha.f = 0.12)
# --- Data -------------------------------------------------------------------
# Well-trained cyclist parameters
CP <- 280 # Critical Power (watts) — aerobic asymptote
Wp <- 20000 # W' anaerobic work capacity (joules)
Pmax <- 1100 # Neuromuscular peak power at 1 s (watts)
# Empirical mean-maximal power: 45 log-spaced durations from 1 s to 5 h
n_emp <- 45
dur_emp <- exp(seq(log(1), log(18000), length.out = n_emp))
# Power-law decay: P(t) = CP + (Pmax - CP) / sqrt(t)
# Gives realistic MMP shape: 1100 W at 1 s, converging to ~286 W at 5 h
W_eff <- Pmax - CP # 820 W effective surplus above CP at t = 1 s
emp_power <- CP + W_eff / sqrt(dur_emp)
# Add ~2% noise and enforce monotonicity (MMP is always non-increasing)
noise <- rnorm(n_emp, 0, sd = 5)
emp_final <- cummin(emp_power + noise)
df_emp <- data.frame(
duration_s = dur_emp,
power_w = emp_final,
series = "Mean-Maximal Power"
)
# CP model P(t) = CP + W'/t — shown from 2 min onward where it is physically valid
# (at < 2 min the model overestimates vs. neuromuscular-bounded empirical efforts)
dur_mod <- exp(seq(log(120), log(18000), length.out = 200))
mod_power <- CP + Wp / dur_mod
df_mod <- data.frame(
duration_s = dur_mod,
power_w = mod_power,
series = "Critical Power Model"
)
# Reference durations for vertical annotation guides
ref_dur <- c(5, 60, 300, 1200)
ref_labels <- c("5 s", "1 min", "5 min", "20 min")
# Title (46 chars < 67 baseline — no fontsize scaling needed)
plot_title <- "curve-power-duration · r · ggplot2 · anyplot.ai"
# --- Plot -------------------------------------------------------------------
p <- ggplot() +
# CP asymptote — horizontal guide at CP = 280 W
geom_hline(
yintercept = CP,
color = INK_SOFT,
linewidth = 0.5,
linetype = "dotted"
) +
# Reference duration vertical guides (5 s sprint, 1 min, 5 min, 20 min FTP)
geom_vline(
xintercept = ref_dur,
color = INK_MUTED,
linewidth = 0.35,
linetype = "dashed",
alpha = 0.55
) +
# CP model — dashed lavender line (from 2 min to 5 h)
geom_line(
data = df_mod,
aes(x = duration_s, y = power_w, color = series, linetype = series),
linewidth = 1.0
) +
# Empirical MMP — solid green line
geom_line(
data = df_emp,
aes(x = duration_s, y = power_w, color = series, linetype = series),
linewidth = 1.3
) +
# Empirical data points (every 3rd for clarity at this density)
geom_point(
data = df_emp[seq(1, n_emp, by = 3), ],
aes(x = duration_s, y = power_w),
color = IMPRINT_PALETTE[1],
size = 1.8,
alpha = 0.75,
show.legend = FALSE
) +
# Reference duration labels at top of chart
annotate(
"text",
x = ref_dur,
y = 1120,
label = ref_labels,
color = INK_MUTED,
size = 2.4,
hjust = 0.5,
vjust = 1,
fontface = "plain"
) +
# CP label next to the asymptote line
annotate(
"text",
x = 160,
y = CP + 24,
label = "CP = 280 W",
color = INK_SOFT,
size = 2.6,
hjust = 0,
fontface = "italic"
) +
# Color scale — Imprint positions 1 (green) and 2 (lavender), canonical order
# limits forces legend order: MMP first (primary), CP Model second
scale_color_manual(
values = c(
"Mean-Maximal Power" = IMPRINT_PALETTE[1],
"Critical Power Model" = IMPRINT_PALETTE[2]
),
limits = c("Mean-Maximal Power", "Critical Power Model"),
name = NULL
) +
# Linetype scale — suppress redundant guide, handled via override in color guide
scale_linetype_manual(
values = c(
"Mean-Maximal Power" = "solid",
"Critical Power Model" = "dashed"
),
limits = c("Mean-Maximal Power", "Critical Power Model"),
name = NULL,
guide = "none"
) +
# Legend icons match actual styles: MMP = solid green, CP Model = dashed lavender
guides(color = guide_legend(
override.aes = list(
linetype = c("solid", "dashed"),
linewidth = c(1.3, 1.0)
)
)) +
# Log-scale x axis: 1 s to 5 h with human-readable labels
scale_x_log10(
limits = c(1, 18000),
breaks = c(1, 5, 30, 60, 300, 1200, 3600, 18000),
labels = c("1 s", "5 s", "30 s", "1 min", "5 min", "20 min", "1 h", "5 h"),
expand = expansion(mult = c(0.02, 0.04))
) +
# Y axis: power in watts, 200–1150 W shows full curve and CP asymptote
scale_y_continuous(
limits = c(200, 1150),
breaks = c(200, 400, 600, 800, 1000),
labels = function(x) paste0(x, " W"),
expand = expansion(mult = c(0.02, 0.08))
) +
labs(
title = plot_title,
x = "Duration (log scale, s)",
y = "Mean-Maximal Power (W)"
) +
theme_minimal(base_size = 8) +
theme(
plot.background = element_rect(fill = PAGE_BG, color = PAGE_BG),
panel.background = element_rect(fill = PAGE_BG, color = NA),
panel.grid.major = element_line(color = GRID_COLOR, linewidth = 0.35),
panel.grid.minor = element_blank(),
panel.border = element_blank(),
axis.line = element_line(color = INK_SOFT, linewidth = 0.4),
axis.ticks = element_line(color = INK_SOFT, linewidth = 0.3),
axis.ticks.length = unit(3, "pt"),
axis.title = element_text(color = INK, size = 10),
axis.text = element_text(color = INK_SOFT, size = 8),
plot.title = element_text(color = INK, size = 12, face = "bold",
margin = margin(b = 8)),
legend.background = element_rect(fill = ELEVATED_BG, color = INK_SOFT,
linewidth = 0.3),
legend.text = element_text(color = INK_SOFT, size = 8),
legend.key.width = unit(1.4, "cm"),
legend.position = "bottom",
legend.margin = margin(t = 4, b = 4, l = 6, r = 6),
plot.margin = margin(t = 12, r = 20, b = 8, l = 10)
)
# --- Save -------------------------------------------------------------------
ggsave(
filename = sprintf("plot-%s.png", THEME),
plot = p,
device = ragg::agg_png,
width = 8,
height = 4.5,
units = "in",
dpi = 400
)
Part of Mean-Maximal Power Duration Curve on anyplot.ai.