re:raindrop drop

[David J Heritage <DHeritage@compuserve.com>]

charset=ISO-8859-1
Content-Disposition: inline
Content-Transfer-Encoding: 8bit
X-MIME-Autoconverted: from quoted-printable to 8bit by secure.crest.net id
SAA30908
X-Sender: <DHeritage@compuserve.com>
Sender: owner-strawbale@crest.org
Precedence: bulk

Prof waterloo said-
>snip
The speed of falling rain drops is proportional to their diameter.  Most

rain drops are of the 1-2 mm diameter size, although heavy thuderbursts and

tropical storms can result in drop diamters to 6 mm or so (after which the

shape becomes unstable and they split)  Light rainfall is composed of
pretty
small drops, less than 1 mm.
An accurate (+/-2.5%) equation that describes the speed as a function of

dimater is:

Vt(Ø) = -.166033 + 4.91844Ø - .888016Ø2 + .054888Ø3 £ 9.20


where, Vt(Ø) is the terminal velocity of a raindrop with diamter Ø in still

air (m/s).

This shows that normal drops fall at about 5 m/s, but the speed can vary

from less than 1m/s to almost 9 m/s.
Hence, if the wind speed is the same as the drop speed, the rain angle will

be 45 degrees and other angles can be calculated.
>snip

If I translated your formula correctly then:

Vt(drop-diameter)=-0.166033+4.91844*drop.diameter-0.88016*drop.diameter^2+0
.054888*drop.diameter^3/9.2

Where:
Vt = terminal velocity
drop.diameter = drop diameter in mm
* means times or multiplied by
^ means raised to the power of
/ means divided by

Drop diameter   Drop diameter   Speed (m/s)     Speed (mi/hr)
mm                               inch
1.0                            0.0394                      3.88
       8.59
1.5                            0.0591                      5.25
     11.64
2.0                            0.0787
6.20                          13.73
3.0                            0.1181                      6.83
  15.13
4.0                            0.1575                      5.81
  12.87
5.0                            0.1969                      3.17
    7.02
5.5                            0.2165                      1.25
    2.78
6.0                            0.2362                     -1.05
   -2.33

For Reference:
1/16 inch =     0.0625


This seems a lot slower than I would have thought. But, assuming my math is
right(big assumption) with a 1.5mm raindrop it would only take a 12mph
crosswind for the drop to fall at a 45 degree angle.

A 25mph crosswind would cause the drop to fall at a 65 degree angle and
would require an 11 1/2 ft overhang to completely protect an 8 ft wall. Not
to mention all the other factors that make things more complex.  I think I
like the porch idea.

Question?- Do raindrops have the shape of a teardrop when they fall or are
they constantly changing shape depending on the wind pressure(aerodymanic
drag). Why does the speed increase, then decrease. Weight vs drag?

Dave Heritage
St. Louis, Mo