Hi All. I'm curious if anyone else did some back of the envelope calculations? I read through this thread and didn't see any guesses to the properties of the impact object. I decided to work the problem with two different sets of assumptions.
Firstly i assumed the object was a bullet-type and based my assumptions on data for a 7.62 NATO bullet (11g, terminal velocity of 90 m/s both from wikipedia). I also assumed the glass has a shattering pressure limit of 70MPa (pulled from a random technical presentation of nominal tempered glass). I also assumed an impact duration of 1ms before the object bounced away at the end of the impact event. I also assumed the tip of the bullet hits first and deforms until the diameter of the impact surface is 7.62 mm. Using all of these values, and the formula for net force during an impact (Fnet = delta momentum / delta time), I calculated that the pressure imparted by the impact object was around 17.37 MPa. The lower bound i found for shatter pressure of tempered glass was 7 Mpa, so this number is in the right ballpark i think. This tells me that my assumptions are close. I also assumed a relatively low-velocity impact from essentially a vector normal to the surface of the glass after reading this summary of glass shattering forensics on the FBI's website:
https://www.fbi.gov/about-us/lab/forensic-science-communications/fsc/jan2005/index.htm/standards/2005standards7.htmI thought about this all so more, and i decided to also work the problem with the assumption that the impact event imparted a pressure 70MPa, and then figure the mass of the object based on that. This made more sense to me because we know at least a minimum amount of pressure was imparted, so it is a safer assumption. In this case, i assumed a spheroid object, which gives a drag coefficiant of 0.47 through air. I also assumed 70% relative humidity, 70 deg F (21 C), and an altitude of 19 feet (about 6m) EGM96 MSL. I also assumed the object's radius to be 0.5 inches this time around (about 1.27 cm). I also assumed an impact duration of 0.7 ms this time because wolfram alpha informed me that the average impact duration of a baseball hitting a bat is 0.7 ms. I could be way off here on the duration.
I should point out, that i read this thread after i assumed the radius, and there is a post in this thread that explains how the radius of the object is likely greater than the white crushed area on the glass. Even so, i think my numbers are still the right magnitude. Given all of the above assumptions, i now calculated the impact object's mass to be around 387.018 grams (or about 13 ounces, or 0.85 lbs). 13 ounces sounds right to me (it agrees somewhat with my first calculation), and i think it really points to a meteorite type object.
I could take this even further and calculate a probable radius for the final resting place of the object. It seems we could use the concentric ring pattern to extrapolate the impact angle, and then we can simply figure the angle relative to the earth. Then it would be a matter of figuring a range for momentum transfers to the glass (there would be an upper bound less than 100% transfer because the object was not embedded and is not sitting right next to the panel). At any rate, this would give us a range of trajectories that should draw a line on the ground. Treat this line as a diameter of a circle, and then you have a grid for Dave to search for a meteorite type object. I think it would be very cool if we predicted where the object would be, and then Dave actually found it.
Feel free to tear my calculations apart and make them better (or just point out what is wrong). It is all back of the envelope, so i'm not pretending any of it is accurate beyond magnitude level analysis. Does anyone else have any values? I'm very curious.
This was a very entertaining way to spend my morning when i'm feeling sick. Thank you for reading this far!
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