After hearing the show where in a woman questioned the ability of a bird splat to crack her windshield I laughed and thought that she was crazy. Then I saw a piece on wired.com by Rhett Allain saying it was possible based on some hair brained physics math and I thought he is nuts. I am a engineer so I never trust a physicist. I did the hair brained math myself and turns out I am a whacko too! The pressure of the poop could crack the glass. However Rhett was right only because he got lucky which is the usually case with physicists. He compared an impact pressure to the compressive strength of the glass. This is crazy, as any mild mannered mechanics professor would tell you, the actual mode of failure of glass would be cracking in the glass due to tensile stress in plate bending. Utilizing some numbers and math I cite below I found that the tensile stress in the glass under the impact pressure of descending dove detritus was 132 MPa, greater than the estimated stress capacity of the glass at 105 MPa. Now his estimate for the impact pressure may be bo o o o gus, but at least his bogus conclusion is supported by my bogus calculations as well.
The Glass has a tensile strength according to some germans as 105 MPa. Lets assume the impact area functions as a fixed plate giving us established formulas to work from.
Uniform Pressure on Flat Circular Plate
(Reference: Roark’s Formulas for Stress and Strain, 7th Edition, Table 11.2 Case 10)
Radius of plate: a = 50 mm (The size of the poop)
Thickness of plate: t = 6.72 mm (Properties of Auto Glass According to Germans)
Poisson’s ratio: u = 0.22 (Properties of Auto Glass According to Germans)
Modulus of elasticity: Es = 70000 MPa (Properties of Auto Glass According to Germans)
Specified uniform pressure: q = 3180 kPa (Rhett’s Impact Pressure)
D = Es. t3 / [12(1 - u2)] = 70,000 x 6.73 / [12(1 - 0.222)] =1.86e+06 N.mm
Deflection at the center: yc = -q . a4 / (64 D) = -1 x 3,180.0 x 10-3 x 504 / (64 x 1.86e+06) =-0.2 mm
Bending moment at the center: Mc = q . a2(1 + u)/16 = 3,180.0 x 10-3 x 502 x (1 + 0.22) / 16 =606.2 N.mm/mm
Normal stress at the center: (≤ 0.6 Fy): s = 6 Mc / t2 = 6 x 606.2 / 6.72 =80.5 MPa
Bending moment at the support: Mra = -q . a2/8 = -1 x 3,180.0 x 10-3 x 502 / 8 =-993.8 N.mm/mm
Normal stress at the support: (≤ 0.6 Fy): s = 6 Mra / t2 = 6 x -993.8 / 6.72 =-132.0 MPa
THIS IS THE BIG ONE 132 MPa AT THE EDGE OF THE PLATE > 105 MPa STRENGTH THUS THE CRACK!
Maximum shear: Qa = -q . a / 2 = -1 x 3,180.0 x 10-3 x 50 / 2 =-79.5 N/mm
Maximum shear stress: t = 1.5 Qa / t = 1.5 x -79.5 / 6.7 =-17.7 MPa
M. Timmel, S. Kolling, P. Osterrieder, P.A. Du Bois, A finite element model for impact simulation with laminated glass, International Journal of Impact Engineering, Volume 34, Issue 8, August 2007, Pages 1465-1478, ISSN 0734-743X, 10.1016/j.ijimpeng.2006.07.008.
The Wired Piece