David Wolfson
EF5
The design considerations are fun to ponder and right up the alley for physics and engineering students, which I'm not. But with that big disclaimer, here are some observations and suggestions.
First, you must decide what combination of hail size and horizontal wind you want to guard for. But it's not "how big" but rather "how small" a stone for the specified horizontal wind. This is because for a given overhang and horizontal wind any guard that catches the small stone will catch any bigger one, since the bigger one falls faster, hence more vertically. This is an empirical question, but 4cm and 30m/s might be a good start.
The terminal velocity of hail varies with geometry and surface characteristics, but my Googling comes up with a reasonable estimate to be V = 1.5d^0.75, where V is m/s and d is diameter in mm. For the above, V is around 24m/s. This makes for a vector triangle with a "30" horizontal leg and a "24" vertical leg. This proportion gives up the answer without messing with angles. If you want to fully guard a window extending 18" below the guard then the guard must extend 22 1/2" beyond the plane of the window.
Now for a given horizontal (strike) velocity the impulse is linearly proportional to the mass, if my physics is right -- or proportional to the cube of the diameter. So to protect the same window against 8cm stones a plastic sheet cover must increase the smash resistance by a factor of 8 relative to the glass alone. I think suitably thick polycarbonate is good for a factor of 50 or more. FWIW.
First, you must decide what combination of hail size and horizontal wind you want to guard for. But it's not "how big" but rather "how small" a stone for the specified horizontal wind. This is because for a given overhang and horizontal wind any guard that catches the small stone will catch any bigger one, since the bigger one falls faster, hence more vertically. This is an empirical question, but 4cm and 30m/s might be a good start.
The terminal velocity of hail varies with geometry and surface characteristics, but my Googling comes up with a reasonable estimate to be V = 1.5d^0.75, where V is m/s and d is diameter in mm. For the above, V is around 24m/s. This makes for a vector triangle with a "30" horizontal leg and a "24" vertical leg. This proportion gives up the answer without messing with angles. If you want to fully guard a window extending 18" below the guard then the guard must extend 22 1/2" beyond the plane of the window.
Now for a given horizontal (strike) velocity the impulse is linearly proportional to the mass, if my physics is right -- or proportional to the cube of the diameter. So to protect the same window against 8cm stones a plastic sheet cover must increase the smash resistance by a factor of 8 relative to the glass alone. I think suitably thick polycarbonate is good for a factor of 50 or more. FWIW.
