Re: [Phys-L] raining
Richard,
I like to think of it as the volume with a human-shaped cross section that
is cut from the starting location through the volume of "future rain."
It's a prism from the starting location upwards into the clouds. You're
trying to minimize the volume of that prism. The equations you gave
calculate exactly that.
It raises some related questions:
1. Can you be completely soaked at some point where more rain doesn't
matter?
2. Will you be happier getting out of the rain sooner even if you get
wetter?
3. Why didn't you take your umbrella like your mother reminded you?
Paul
On Wed, Dec 20, 2023 at 10:50 AM Richard Tarara via Phys-l <
phys-l@mail.phys-l.org> wrote:
> Seems to me, always has, that there is nothing (that HAS to get)
> complicated
> about this question. Just consider the limits. Move at zero speed and you
> get infinitely wet from the top down. Let the Flash run through the rain
> and his head is essentially dry, but he did have to run through the volume
> of rain in the 3 dimensional path cut out of the essentially stationary
> rain
> in his way. But that amount in finite and as David has pointed out, fast
> or
> slow you will intercept that amount of water to your front. Running will
> always collect the least amount of moisture on the person.
>
> Richard W. Tarara
> Professor of Physics, emeritus
> Saint Mary’s College
> Notre Dame, Indiana
>
> Free Physics Instructional Software
> Windows and Mac
> sites.saintmarys.edu/~rtarara/software.html
>
> -----Original Message-----
> From: Phys-l <phys-l-bounces@mail.phys-l.org> On Behalf Of David Bowman
> via
> Phys-l
> Sent: Wednesday, December 20, 2023 8:29 AM
> To: Phys-L@Phys-L.org
> Cc: David Bowman <David_Bowman@georgetowncollege.edu>
> Subject: Re: [Phys-L] raining
>
> Weird. Each Greek [rho] in my previous post got translated into a tilded n
> after passing through the Phys-l list. I trust the readers can cope with
> that. It's a good thing I didn't use more than one Greek letter.
>
> David Bowman
>
> ________________________________________
> From: Phys-l <phys-l-bounces@mail.phys-l.org> on behalf of David Bowman
> via
> Phys-l <phys-l@mail.phys-l.org>
> Sent: Wednesday, December 20, 2023 8:16 AM
> To: Phys-L@Phys-L.org
> Cc: David Bowman
> Subject: Re: [Phys-L] raining
>
>
> Elaborating further on my previous post.
>
> Assume the walking/running direction is horizontal/perpendicular to the
> vertically falling rain & assuming the falling rain has a uniform
> distribution in space and time.
>
> Let ñ = mass density of falling rain (per unit volume of air + rain).
> Let L = horizontal distance walked/ran through in the rain.
> Let v_t = (mass weighted) mean terminal velocity of falling raindrops Let v
> = speed of walking/running Let A_th = body's projected top facing
> horizontal
> cross section area.
> Let A_fv = body's projected front facing vertical cross section area.
> Let W = mass of water intercepted by moving body.
>
> Then W = ñ*L*(A_fv + (v_t/v)*A_th) .
>
> This is just the projected gross rain interception rate due to simple
> kinematics. It obviously neglects the hydrodynamics of tiny deflected air
> motions partially carrying drops in the immediate vicinity of body
> collisions with drops causing altered localized trajectories of drops that
> could affect the collision rate by a tiny amount.
>
> But a much bigger neglected effect is due to wind. Wind causes a number of
> complications. Here are 4 of them off the top of my head. First, wind
> tends to be gusty & quite time dependent and thus hard to model. Second,
> wind changes the direction of the falling rain so the direction of the
> projected area perpendicular to it must also change. Third, because of the
> poly-disperse distribution of drop sizes there is a distribution of
> different terminal velocities of the drops and this causes different sized
> drops to fall/move in different directions at different speeds. Fourth,
> there is a Galilean transformation involved for the effective walking speed
> due to any component of wind which may be parallel the walking direction,
> and this changes the effective walking speed for those drops which are
> carried with that horizontal component of velocity by the wind.
>
> I suspect there are even more complications from wind, but I'm not in the
> mood to try to think of them.
>
> David Bowman
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