Scale time.

[William and Melissa Johns <gizmology-at-gizmology.net>]

At 03:37 PM 7/8/2004, you wrote:
>The Hetzer was recently upgraded to 24V Makita drill
>motors and has regained its title as the fastest tank
>in RC Tank Combat   http://www.rctankcombat.com


That gets me thinking.  At what speed should my Mk V run?  The real thing 
roared along at the breakneck speed of 4 mph.  If I aim for an accurate 
scale speed, the model would move at a mere 1 foot per second, take a month 
to reach the battlefield, and stop every paintball in the country.  On the 
other hand, if I made it go really fast, it would look pretty absurd.   I 
figure 2.4 feet per second is about right.  (That way it would only take 
two weeks to reach the battle field.)

I've always been fascinated by the effects of scale.  My theory is that 
since we can't scale gravity down, we have to compensate by scaling time up.

An object falls 16 feet in one second, during which the real Mk V moved six 
feet.  16 scale feet is 2.67 real feet, which would take a falling object 
0.41 seconds to travel, during which the model should move 6 scale feet, or 
one real foot.  one foot divided by 0.41 seconds is 2.4 feet per second.

An object would fall 1600 feet in ten seconds, during which the tank would 
move 60 feet.  1600 scale feet is 266 real feet, and a falling object would 
cover that in 4.1 real seconds.  In that time, the model would have to move 
60 scale feet, or 10 real feet ... or 2.4 feet per second.  (Repeatability 
is nice.)

Scale time works out to the inverse of the square root of scale 
distance.  (6" = 1" for linear dimensions, 1 second = 2.45 seconds for time 
dimensions.)

I think I think too much.  Or maybe I have 2.4 times too much time on my hands.


Bill "What time is it?" Johns


--

"Ocean: A body of water occupying about two-thirds of a world made by God 
specifically for man - who has no gills." - Ambrose Bierce