I made some simple calculation about deformation of a window.
The drawing represents the two pieces of a double glazing window. (The glass thickness of each panes is not represented).
- bend.GIF (15.33 KiB) Viewed 2885 times
Considering the very large radius of curvature, we can make the approximation of parabolic shape y = x^2/(2R)
The local slope is given by : y’ = dy/dx = x/R
The angle between the two panes is : alpha = 2*atan y', so : alpha ~= 2*y' for small angles (in radians !)
For a deformation 'a' at the center of the window, and total size L of the window, we can calculate the value of R.
R = x^2/(2y) with x = L/2 and y = a
R = L^2/(8a)
1) The slope at the center is zero. The local tilt angle between panes is also zero.
2) if the beam goes through the window at x = L/4 :
y' = L/(4R) = 2a/L => alpha = 4a/L (radians)
L = 1 m, a = 1 mm => alpha = 0.23 deg
3) if the beam goes through the window at x = L/2 (close to the edge) :
y' = L/(2R) = 4a/L => alpha = 8a/L (radians)
same values => alpha = 0.46 deg
All these calculations to say that : 1mm central bending is much easier to produce than a 6.5mm gap variation from one edge to opposite.
If the window is 1m wide, the gap variation is about 6.5mm which is quite big indeed, compared to typical value of gap (16 mm) inside double glazing.
Glass is a very "flexible" material. While taking the pictures I posted yesterday, I tried to push by hand at the center of the window, the effect was to increase the deviation of the ghosts (first ghost was visible with unaided eye) whatever the initial sign of the deviation.
That means I increased the deformation of the surface which was already concave.