Ballistic’s ballistic equations

I promise I’ll let this go at some point. But not today.

In my little mishap from this past Tuesday, I estimate that I got tossed about 6-8 feet. 

Well. That’s enough to calculate a trajectory!

If we assume that I was launched at the most effective and efficient launch angle of 45 degrees for simplicity, that means that my initial velocity imparted by the explosion was something like 4.3m/s.

If we treat the Gaming Ballistic author as a spherical frictionless brainless cow massing 81 kg, we can see that the blast imparted to me roughly 350 kg-m/s of momentum and 750J of energy. That’s about the same energy as in a 10mmAuto, for comparison, but far more momentum.

Let’s assume that the combustion/explosion took place over a roughly 0.005 second period (5 milliseconds). That seems to be on the order of what some brief searching shows is on the upper end of how long it takes for the fuel-air mixture in an automobile cylinder to combust.

If that’s the case, it means that since Impulse = Momentum (F x delta t) = MV, that I was thrown with roughly 70,000 N of force! Roughly seven tons.

Is that reasonable? If half my body was exposed to the blast, that’s about 0.8 square meters. So a pressure requirement of 70,000N per 0.8 square meters, or 87,500 Pascals – 0.85 atmospheres.

According to the Wiki page on blast overpressure, 85 kPa is more than enough to cause severe heart and lung damage, and rip off limbs. Since that didn’t happen, my estimate is off somewhere. 

I suspect that the real problem is my estimation of initial velocity, since my mass is what it is. But I did travel that far (I measured!), so we’ll leave it as is.

It could also be that the velocity was fine, but if the overpressure effect lasted for much longer than 5ms. The force would drop by at least an order of magnitude, and the overpressure is lower and more in the “not turned to instant pulp” zone. Since I’m sitting here typing, that seems much more reasonable, and a discussion here of typical results and levels of overpressure suggest that since my house did not suffer any major damage (nor did I, really), that I was probably subjected to 0.04 to 0.4 psi of overpressure – let’s assume 0.3, giving me more credit for robustness and getting lucky a bit.

So that’s more like 2.1kPa rather than a ridiculous 87kPa. That implies about 1700N of force, which is about a 200ms pressure wave duration.

I don’t know if it’s real or valid, but that’s what the math suggests!

Edit: My wife thinks she’s funny (she’s right)

  • She complained that I hadn’t replaced the drawing of the circle with a little stick figure going “aaaaahhhhh!”
  • Also, today when she was helping me get dressed, she says “Hmm. What should you wear? How about a T-shirt?” And she tosses me this one –>

2 thoughts on “Ballistic’s ballistic equations

  1. One more thing thing. If you were standing when it happened, but were not, 45 deg is not the ideal angle and your falling side of the arc is greater then the 'up' side. If you could use a rough approximation of half your height for the starting height for your frictionless sphere.

Leave a Reply

Your email address will not be published. Required fields are marked *