 The magazine of the Melbourne PC User Group "Just walking in the rain" "Getting not so wet" Ken Holmes |
Indulging in this pursuit recently brought to mind the oft-raised question -
How fast should you walk to minimise the hydration of the person? Maybe that's a suitable subject to help the
team fill the magazine!
Let us simplify the problem by considering you, not as a biped, but as a parallelopiped, orthogonal of
course, just in from the planet Geometrica. You are 1.5 m high, 0.5 m wide and 0.25 m thick ("'ere, 'o you
callin' thick?") Your frontal area is six times your plan area (= height / thickness); this ratio (RF) is
really the only figure we need. We will assume that one unit of rain is falling on your (top) plan area each
second and that the vertical speed (VS) of the raindrops is 10 m/s. This depends on the size of the drops -
the bigger they are, the faster they fall. Pity this didn't apply to more of the entrepreneurs! Normal
walking speed (WS) is about 2 m/s and we will consider a range of headwind speeds (HW) up to 6 m/s and down
to -6 m/s (tailwind). We'll look at side winds later.
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'rainwalk.bas SCREEN 9: CLS 'EGA screen WINDOW (0, -.4)-(9, 3.6) RF = 6 'ratio front/top RS = 3 'ratio side/top VS = 10 'rain fall speed r1 = RF/VS 'calculate once r2 = RS/VS SW = 0 'side wind FOR HW = -6 TO 6 'headwind FOR WS = 1 TO 6.5 STEP .01 'wetting rate per sec, wr wr = 1 + ABS(r1 *(WS+HW)) wr = wr + ABS(r2 * SW) wet = wr / WS 'per metre 'for HW=0 use col. 7(grey) PSET (WS, wet), HW + 7 NEXT WS 'walking speed NEXT HW DO: LOOP WHILE INKEY$ = "" |
Firstly, the top surface will receive rain at
the same rate irrespective of HW or WS. To determine the amount on the front, or back, surface, we need the
apparent angle at which the drops approach. The horizontal component equals (WS + HW) and the vertical
component is of course VS; the ratio of these gives the tangent of the angle (tan = (WS + HW) / VS). If we,
notionally, extend the top surface forward to intercept the rain that will hit the front face, we can
estimate the amount easily. The ratio (VR) of the "veranda" area to that of the top surface is RF times the
above tangent (sketch a side view if you don't believe me) and the total incident rain will be (1 + VR). The
time taken to walk one metre is (1 / WS) and you will receive (1 + RF * (WS + HW) / VS) / WS units of
refreshing rain water for each metre progress to your goal.
The QBasic code calculates and plots the wetting (per metre) against walking speed for various head/tailwind
speeds. General conclusions can be drawn, which agree with instinctive beliefs. With headwinds, it is best to
run as fast as you can since minimising exposure time outweighs greater wetting each second. With tailwinds
of 2 m/s or more, it is best to walk at the wind speed so that you only receive one unit on the top surface,
since walking faster will cause a small increase due to rain on the front and slower will wet the back more
quickly since time exposure increases. From calm to 2 m/s tailwind, maintain normal walking pace as the
benefits of running are marginal and slowing will increase exposure time and saturation.
A proviso should be put on running as it increases the risks of falling, colliding or having a heart attack.
Either be prepared with an umbrella, or have another beer. With the program written, it is easy to
investigate the effects of finer drops (lower VS) or a greater ratio of frontal area to plan area, both of
which accentuate the amount hitting the front when running into it. With rain falling at 5 m/s, there is a
small advantage, in a 1 m/s tail wind, in slowing down to this but it doesn't affect the general conclusions.
With side wind (SW) components, the side will be constantly bombarded, independent of walking speed. The
ratio of side area to top area (RS) is less at 3:1, but we need to add (RS * SW / VS) to the time rate of
wetting and running faster to minimise exposure time will still be desirable. However, examining plots for
side winds up to 6 m/s doesn't provide any basis to change the general conclusions.
Purists might wish to deal with a more normally shaped individual but would need the silhouette area of the
body for all possible apparent angles of rain approach and would need to calculate the apparent rain
velocity. I doubt it would alter the conclusions. I hope this illustrates, albeit in a fairly simple way, the
value of a graphical presentation of results in a situation where a number of factors are variously
influencing an outcome. The more complex the problem, the more useful are graphics in getting a balanced
overall view. With more challenging problems it is worth looping the program and getting keyboard input to
increment or decrement any of the variables, clear the screen and re-plot instantly. If you print the
variables on screen, you can run through all combinations in rapid order and select an optimal solution to
the particular problem.
Reprinted from the November 1998 issue of PC Update, the
magazine of Melbourne PC User Group, Australia
