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Running in the Rain

Running in the rain approximates how wet a person would get from running in the rain.

The total wetness increases with width shoulder to shoulder, width front to back, height, rain speed and rain density. It decreases with speed. The amount of rain that strikes every side depends on the angle the rain makes with the direction of movement. Rain density equals the rain rate divided by the rain velocity.

Formula

{QuantityVariable["t", "Time"] == QuantityVariable["d", "Distance"]/QuantityVariable["v", "Speed"], QuantityVariable[Subscript["v", "x"], "Speed"] == -(Cos[QuantityVariable["θ", "Angle"]]*Cos[QuantityVariable["ϕ", "Angle"]]*QuantityVariable[Subscript["v", "r"], "Speed"]), QuantityVariable[Subscript["v", "y"], "Speed"] == -(Cos[QuantityVariable["θ", "Angle"]]*QuantityVariable[Subscript["v", "r"], "Speed"]*Sin[QuantityVariable["ϕ", "Angle"]]), QuantityVariable[Subscript["v", "z"], "Speed"] == -(QuantityVariable[Subscript["v", "r"], "Speed"]*Sin[QuantityVariable["θ", "Angle"]]), QuantityVariable["ρ", "Unitless"] == QuantityVariable["i", "RainfallRate"]/Abs[QuantityVariable[Subscript["v", "r"], "Speed"]], QuantityVariable[Subscript["w", "x"], "Volume"] == (Abs[-QuantityVariable["v", "Speed"] + QuantityVariable[Subscript["v", "x"], "Speed"]]*QuantityVariable["d", "Distance"]*QuantityVariable["H", "Height"]*QuantityVariable["W", "Length"]*QuantityVariable["ρ", "Unitless"])/QuantityVariable["v", "Speed"], QuantityVariable[Subscript["w", "y"], "Volume"] == (Abs[QuantityVariable[Subscript["v", "y"], "Speed"]]*QuantityVariable["d", "Distance"]*QuantityVariable["D", "Length"]*QuantityVariable["H", "Height"]*QuantityVariable["ρ", "Unitless"])/QuantityVariable["v", "Speed"], QuantityVariable[Subscript["w", "z"], "Volume"] == (Abs[QuantityVariable[Subscript["v", "z"], "Speed"]]*QuantityVariable["d", "Distance"]*QuantityVariable["D", "Length"]*QuantityVariable["W", "Length"]*QuantityVariable["ρ", "Unitless"])/QuantityVariable["v", "Speed"], QuantityVariable[Subscript["w", "T"], "Volume"] == QuantityVariable[Subscript["w", "x"], "Volume"] + QuantityVariable[Subscript["w", "y"], "Volume"] + QuantityVariable[Subscript["w", "z"], "Volume"]}

symbol description physical quantity
t time spent in the rain "Time"
d distance to travel "Distance"
v speed "Speed"
vx rain speed in x direction "Speed"
θ angle of rain to the direction of motion "Angle"
ϕ angle of rain to the side of the person "Angle"
vr rain speed "Speed"
vy rain speed in y direction "Speed"
vz rain speed in z direction "Speed"
ρ rain density "Unitless"
i rain rate "RainfallRate"
wx wetness for front and back "Volume"
H height "Height"
W width shoulder to shoulder "Length"
wy wetness for sides "Volume"
D width front to back "Length"
wz wetness for top "Volume"
wT total wetness "Volume"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Running in the Rain"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Running in the Rain"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Running in the Rain"], {QuantityVariable["d","Distance"] -> Quantity[100, "Yards"], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("x"\)]\),"Speed"] -> Quantity[2, ("Miles")/("Hours")]}]
Out[3]=

Publisher Information