Monte Carlo: Getting Wet — Running vs Walking in Rain
10
Simple model comparing expected 'wetness' when covering a distance in rain. Wetness = (top rain exposure + front/splash exposure) × time. Running reduces time b
NOTEInterpretation
This is a **toy physics-inspired** model that captures the classic tradeoff:
- **Walking**: longer time under rain from above.
- **Running**: shorter time, but more rain impacts the front because you move faster (and wind matters).
If `delta_wet > 0`, running tends to keep you drier for that set of conditions.
To tailor it: set distance, typical speeds, and widen/narrow the rain/wind ranges.
VARIABLETrip distance (m)
triangular(300, 800, 1500)
How far you need to go in the rain.
distance_m
VARIABLEWalking speed (m/s)
triangular(1, 1.4, 1.8)
Typical walking speed.
v_walk
VARIABLERunning speed (m/s)
triangular(2.2, 3, 4.2)
Easy jog to moderate run.
v_run
VARIABLERainfall rate (mm/hr)
triangular(1, 4, 12)
Light to moderate/heavy rain.
rain_mm_hr
VARIABLEWind speed (m/s)
triangular(0, 2, 8)
Wind makes rain more horizontal.
wind_m_s
VARIABLEBody top area factor
triangular(0.8, 1, 1.2)
Relative 'catch' from above (umbrella/clothing posture).
top_area_factor
VARIABLEBody frontal area factor
triangular(0.8, 1, 1.2)
Relative 'catch' from the front.
front_area_factor
VARIABLEFront exposure sensitivity
triangular(0.4, 0.7, 1.1)
How strongly wind + speed adds to front wetting (dimensionless).
k_front
CONSTANTBaseline top wetting scale
1
Normalization constant (wetness units per (mm/hr)*min).
k_top
CONSTANTMinutes per hour
60
Unit conversion helper.
min_per_hr
FORMULATime walking (min)
(distance_m / v_walk) / 60
Time = distance / speed; convert seconds to minutes.
distance_m
v_walk
t_walk_min
FORMULATime running (min)
(distance_m / v_run) / 60
Time = distance / speed; convert seconds to minutes.
distance_m
v_run
t_run_min
FORMULAEffective front rain multiplier (dimensionless)
1 + k_front * (wind_m_s / 5)
More wind -> more horizontal rain hitting the front.
k_front
wind_m_s
front_multiplier
FORMULAWetness walking (units)
(k_top * top_area_factor + front_area_factor * front_multiplier * (v_walk/2)) * (rain_mm_hr / min_per_hr) * t_walk_min
Wetness = (top + front) × rain × time. Front term grows with speed.
k_top
top_area_factor
front_area_factor
front_multiplier
v_walk
rain_mm_hr
min_per_hr
t_walk_min
wet_walk
FORMULAWetness running (units)
(k_top * top_area_factor + front_area_factor * front_multiplier * (v_run/2)) * (rain_mm_hr / min_per_hr) * t_run_min
Same wetness model, but with running speed and time.
k_top
top_area_factor
front_area_factor
front_multiplier
v_run
rain_mm_hr
min_per_hr
t_run_min
wet_run
FORMULARunning advantage (units)
wet_walk - wet_run
Positive => running gets you less wet than walking.
wet_walk
wet_run
delta_wet
OUTPUTWetness running
Wetness (run)
Relative wetness if you run.
OUTPUTWetness walking
Wetness (walk)
Relative wetness if you walk.
OUTPUTDifference
Walk − Run (positive favors running)
How much wetter walking is vs running (relative units).
What is Carlo?
Carlo is a visual tool for Monte Carlo simulation. Model uncertainty by dragging probability distributions, connecting them visually, and running thousands of scenarios instantly.