me and my shadow

[thinktank]

Are you Questioning the validity of the Extrapolation ?

What are those 8 values and the hours at which they were taken ?

[Guv]

I think that Starman is asking if it can be proven that the shadow graph results in a straight line, as implied by his empirical data.

This looks like a tricky question to answer.

[Starman]

Yes thinktank, I am questioning the validity of my guesses, but Guv has rephrased my meanderings into a proper question. Is it a straight line?

I wonder if it’s as simple as marking the end of the shadow on the ground throughout the day? – I would try this myself but the sun here is almost permanently obscured by cloud at this time of year and I am rarely in a place where I can mark a shadow through a whole day.

I’ve tried drawing an inverted cone with an inclined plane cutting it, but I can’t properly visualise or draw the projected path – it seems to be a conic section with a much more pronounced curve than our measurements indicated.

[Starman]

Well I've had a dig around and found the values.

The measurements were made mostly on grass so there is obviously plenty of inaccuracy - it's hard to tell where the end of the shadow is, but it's probably within 10cm.
With only these few points and one of those being taken on a different day this may be slightly less than scientific - this was for an eight year olds class homework.

I didn't realise how long ago this was, I can brood about things for ages. Anyway...


Date Time Shadow Length

23/09/2000 09:00 3.50 Metres
23/09/2000 11:30 1.72 Metres
23/09/2000 13:45 1.65 Metres
22/09/2000 16:00 2.93 Mteres
23/09/2000 17:10 4.22 Metres
23/09/2000 17:50 7.60 Metres
23/09/2000 18:00 9.20 Metres
23/09/2000 18:10 10.93 Metres


According to my psion, Sunrise for the 23rd was at 06:47 and Sunset at 18:57.

Plotted on a polar graph as described, the 16:00 stands out, but the other measurements seem to fall on a line nearly parallel to the sunrise-sunset line.

My guesses were that the distance between these lines in some way represents the height of my daughter (which I didn't record), and that the 16:00 does not fit the line as this was taken a day earlier.

Any thoughts or comments please.

[Starman]

Just playing around with POV and I made this picture, the codes a mess and the pictures too dark, it looks like a straight line but I'm not sure.

global_settings { assumed_gamma 2.2 }
#include "colors.inc"

camera {
location <0, 60, -70>
direction <0, 1, 0>
up <0, 1, 0>
right <4/3, 0, 0>
look_at <0, 0, 0>
}

#declare inclination=60

union{
//ground and gnomon
union{
plane {y,0
pigment{
color rgb <0.5, 1.0, 0.5>
}
}
cylinder{<0,0,0>,<0,10,0>,.2}

rotate z*inclination
}


#declare sol=50
#declare Count=24

#while (Count>=0)
#declare degs=15*Count*pi/180
//the spheres
#declare X=sol*cos(degs)
#declare Y=2
#declare Z=sol*sin(degs)
//bring the light source inside the spheres
#declare Xl=(sol-1)*cos(degs)
#declare Yl=1.8
#declare Zl=(sol-1)*sin(degs)

sphere { <X, Y, Z>, 1
texture {pigment { color <1,1,0> }
finish {ambient 0.5}
}
}

light_source {
<Xl,Yl,Zl>
color <.2,.2,.2>
spotlight
point_at <0,1,0>
radius 2
falloff 50
tightness 5
}

#declare Count=Count-1
#end


rotate z*-inclination

}