Go to Fun_Math Content Table Earth Moon & Sun
"Eratosthenes of Cyrene was a man of great distinction in all branches of knowledge...Thus he was called an all around athlete. ... Eratosthenes' most famous achievement was his measurement of the earth."
**************** Eratosthenes_base_model.dwg ****************
Latitude | Longitude | |
---|---|---|
Alexandria,Egypt | 31.2 N | 29.9 E |
Syene(Aswan),Egypt | 24.088 N | 32.899 E |
The longitude value for Syene differs slightly from that of Alexandria (difference is almost 3 degrees), and since one degree is about 69 miles apart, Syene must be about 200 miles west of the present day Aswan. Here in our model, longitude value of Syene is assumed to be 29.4 E, so that Alexandria and Syene are on the same meridian. At Alexandria a sundial is erected to measure the inclination angle on the summer solstice. The pole is 3 meters high and its radius is 10 cm(0.1 m). At Syene, a Well is drilled to show that when the Sun is on The Tropic of Cancer, the Sun does not cast any shadow on the bottom of the well. The dimension of the well is 5 meters deep from the ground, and its inner radius is 1 meter. Also added here is a body of water at the bottom of the well.This is how the model looks.
*************************************** Eratosthenes_model_2.dwg ***************************************
To create this drawing :
Load Eratosthenes_model2.lsp (load "Eratosthenes_model2")
Then from command line, type measure_earth
Author's Note:
When the original model was created,the height of the sundial's pole length was set to 3 meters,with its diameter 0.2 meter.
But the shadow making rendering process did not work well for this scale difference(compared to the Earth's diameter). So the scale of pole and well are
bumped up 3 orders of magnitude. If the earth is erased before the rendering process, maybe the original scale would be OK,
but author have not verified it yet. Just for the viewing purpose , the author should have treated both sundial and well independently
of the earth.
Following four different light directions are selected. The angles are inclination to the equatorial plane:
Season | Angle | cosine | sine |
---|---|---|---|
Summer Solstice | 23.5 | 0.91706 | 0.39875 |
Angle 12 deg | 12.0 | 0.97815 | 0.20791 |
Vernal and Autumnal Equinox | 0.00 | 1.00000 | 0.00000 |
Winter Solstice | -23.5 | 0.91706 | -0.39875 |
**** earthsize_win_id.dwg ****
********************** sundial_at_Alexandria.dwg **********************
Animation is now being prepared.
To create this drawing :
Load Eratosthenes_model2.lsp (load "Eratosthenes_model2")
Then from command line, type measure_earth
At this stage, AutoCAD displays Eratosthenes_model_2.dwg.
In order to get rendering image, additional steps are required.
The following steps are specific to AutoCAD.
(1) Select the upper left viewport, and using VPORTS command, make a single viewport.
Erase the blue line representing the earth.
(2) Using 3DORBITS command , rotate the sundial as shown in the drawing above.
(3) Using VPORTS command , split into 4 viewports.
(4) For each viewport, specify the direction of the distant sunlight.
Here it is importan to select SHADOWS ON and Volumetric/Raytraced shadows option.
(5) Use RENDER command to render the drawing.
**** earthsize_win_id.dwg ****
**************************** well_at_Syene.dwg ****************************
Animation is now being prepared.
To create this drawing :
Load Eratosthenes_model2.lsp (load "Eratosthenes_model2")
Then from command line, type measure_earth
At this stage, AutoCAD displays Eratosthenes_model_2.dwg.
In order to get rendering image, additional steps are required.
The following steps are specific to AutoCAD.
(1) Select the lower left viewport, and using VPORTS command, make a single viewport.
Erase the blue line representing the earth.
(2) Using VPOINT command , input !pnt_syen to specify the viewing direction.
(3) Using VPORTS command , split into 4 viewports.
(4) For each viewport, specify the direction of the distant sunlight.
Here it is importan to select SHADOWS ON and Volumetric/Raytraced shadows option.
(5) Use RENDER command to render the drawing.
All comments should be sent to Takaya Iwamoto
Last Updated July 9-th, 2006
Copyright 2006 Takaya Iwamoto All rights reserved.
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