What Happens to Bullets When They Hit Auto Glass?

[Hambo]

I’ve done a lot of training in and around vehicles. Quite often shooting through windshields is like a box of chocolates. But generally speaking with a lot of caveats, outside/in goes downward and inside/out goes upward. The exact amount of deflection changes depending on a variety of factors.

Same here; same story. Training ammo would deflect the same, get shredded sometimes (or not depending on caliber), sometimes the core still hit the target.

[the Schwartz]

I'll admit, it took me way too long to understand the WHY behind this.

But I finally realized it's basically a function of "braking". The part of the bullet that hits first is suddenly and rather abruptly slowed down. Causing the bullet to yaw in the direction of the braking. Now I see how larger caliber/higher mass bullets can help mitigate this problem a bit. And how bonded and monolithic rounds avoid the secondary problems of the jacket shearing off or beginning to flatten/mushroom.

I failed kinematics twice in college, but physics is pretty cool. Still prefer electricity, light, and magnetism though (I made an A in that course...).

Your explanation is a pretty good one for someone who admits to having struggled with kinematics.

The turning moment, more correctly defined as ''moment of force'', induced by the asymmetric contact projectile/target interface is dependent upon the angle of the impact face. There is also a critical angle, ß, at which the projectile cannot overcome the dynamic strength, R_T, of the target being struck which results in the projectile being fully deflected (ricochet) from the target face, failing to defeat it.

In the AT model, Tate (of Alekseeskii and Tate) computes the deflection vector as being perpendicular to the axis of the rod multiplied by one-half the length of the rod, to obtain the moment of force about the projectile's center of gravity. This moment induces a longitudinal rotation in the projectile body—which is treated as being rigid—that results in the critical ricochet condition.



In later work, Rosenberg et al. go about the process of determining the critical deflection angle differently. In their approach, the asymmetric force assumed in Tate’s model is assumed to act only upon the mass located at the tip of the projectile which is engaged by direct contact at the nose-target interface. This alteration was made in order to account for the plastic hinge that occurs as the forward portion of the rod bends during its deflection from the target face. Rosenberg's model is also dependent upon the dynamic target strength, R_T, which is velocity-dependent in that as impact velocity increases R_T decreases, which requires iterative computational steps to correctly represent the extent of the elastic-plastic zone formed in the target ahead of the projectile's nose.



ETA: in the equations cited above, U is velocity of the projectile's nose at the point of contact with the target and V is the projectile's impact velocity.

[farscott]

The (V+U)/(V-U) ratio also shows up in the reflection coefficient for electromagnetic waves when the impedance of the medium changes. The models are remarkably similar.

[the Schwartz]

The (V+U)/(V-U) ratio also shows up in the reflection coefficient for electromagnetic waves when the impedance of the medium changes. The models are remarkably similar.

Yep. It does. I'll be damned!

Just as the speed of light decreases in mediums denser than air, so too does the velocity of the nose of a penetrator when it strikes a target medium.

As you might expect, the value of U (penetration velocity) is related to the ratio of the density of the projectile and target material as in this equation—



It is amazing that two phenomena (electromagnetic waves and non-linear impact response mechanics) so different from one another could have such commonality.




Although I prefer the Rosenberg methodology over the AT model's methodology for the determination of a target-projectile pair's critical angle, solving for R_T—



is where the real difficulty exists since it requires α_p be determined iteratively through the solution of the following transcendental equation—

[LockedBreech]

Y'all are going full Good Will Hunting and I'm still sitting here murmuring "inside up, outside down" to try and memorize it.

[Hambo]

Y'all are going full Good Will Hunting and I'm still sitting here murmuring "inside up, outside down" to try and memorize it.

C'mon, man. If you can't run those numbers like Rainman in a gunfight, you're dead in the streetz.

[PrideAmmunitionComponents]

I’ve done a lot of training in and around vehicles. Quite often shooting through windshields is like a box of chocolates. But generally speaking with a lot of caveats, outside/in goes downward and inside/out goes upward. The exact amount of deflection changes depending on a variety of factors.

I've heard the same exact thing from many combat veterans. That's right on the money.

[blues]

transcendental equation

"Wait...did I carry the nine or...? My mind's a blank."

[the Schwartz]

Transcendental equations are no big deal.

The trick is to find the value(s) of the variable being investigated that satisfies both sides of the equation.

So, for example, look at the simple linear transcendental equation 2a = a + 1

We just graph the two sides of the equation after we set each side to 0.



Where both lines intersect, we get the solution of a = 1.



Or, we can do it ''by hand''...

2a = a + 1

Solve for 'a'

2a - a = (a - a) + 1

Eliminating excess terms, we get...

a = (a - a) + 1

a = 0 + 1

a = 1

Substituting

2a = a + 1 where a = 1

2 x 1 = 1 + 1

2 = 2




ETA: For anyone with the burning desire to know the solution for the transcendental equation in post #14, it is—

[Half Moon]

Y'all are going full Good Will Hunting and I'm still sitting here murmuring "inside up, outside down" to try and memorize it.