In the US, terrorist is not synonymous with suicide bomber.

Compare the number of suicide bombers and attempts in the US versus the run of the mill domestic terrorist armed with a gun or using explosives, vehicles or other weapons without an intent to commit suicide.

The most recent attempt was on NWA flight 253 was in 2009
and it was unsuccessful.

There was the University of Oklahoma bombing in 2005, where the bomber blew him self up but managed to no kill anyone else.

Then we have a bit of a dry spell before these 4 events between 1927 and 1962:

Continental Airlines flight 11 in 1962
National Airlines flight 2511 in 1960
Poe Elementary school in 1959
Bath Township school in 1927

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Lots of people have suggested that worrying about body armor is pointless as the bomber will have a dead man switch and suggest that at handgun engagement ranges, you are better off running.

I'll posit that advice is only good advice if you see an actual explosive vest.

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What you can do is practice failure to stop drills.

The basic concept is that if you've hit an assailant in the chest 2-3 times already and he's not going down, you need to suspect that he's either wearing body armor or he's on something.

In either case, the response is to transition to a head shot. It's not a precision sniper shot, so I would not worry about the angles and avenues needed to hit the cerebellum and get an instantaneous no twitch stop. Just aim for the center of the head squeeze it off as accurately as you can under the circumstances. Hopefully the hits to the torso will have slowed him down so it's not a moving target, and/or he's moving directly at you so the aspect and lead angles are not a factor.

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Most LEOs don't use their sights at all in a gun fight. The undertrained take that as proof that no one uses their sights in a gun fight and thus they view training to use them as a waste of time. Those folks probably can't make a head shot much past 7 yards on a stationary target even on a good day at the range.

Don't be those guys.

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Ideally, you'll train to use the sights slowly at first, practicing your draw, grip and presentation so that the sights are naturally aligned as the firearm rises into your line of sight. They won't be at first, but just pause, align the sights and then squeeze off the shot. As your skills improve and you develop a consistent grip and establish the eye motor loop, you'll find the rear sights are already aligned with the front sight and the major task is just to place the front sight on target, then pause and verify the sight alignment and make the shot. That's the point where you start working on improving your speed.

Once again over time, as your speed increases while maintaining good combat accuracy, that pause becomes extremely short, to the point where you're talking about maybe .1 to .2 seconds to verify sight alignment. At that point you are primarily verifying that you still need to take the shot.

Once you start working on speed, you'll also start practicing controlled pairs where you shoot the first shot as described above, then take the next shot as soon as the pistol or revolver recovers and the front sight is back on target. You will again rely on that well trained grip to ensure the rear sights are sufficiently aligned for an accurate shot.

Once you have that down, you put the two together, putting a controlled pair center of mass and then transitioning your eyes upward for a head shot. In this case, the brief pause is primarily used to determine if the head shot is still needed, and if he's sagging to the ground the head won't be needed.

With either a semi auto pistol or a revolver, I'm inclined to put 4 shots center of mass, then transition to a head shot for the fifth shot. If he's still active after that, I'm going to be focused leaving the AO while I reload a 5 shot revolver.

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Which brings us to the very important point that you also want to practice shooting and moving. You're much harder to hit if you're moving and in a gun fight you should be moving laterally towards suitable cover.

If the assailant has a knife or blunt weapon you want to get off the X before he gets there, moving laterally to force a rushing assailant to overcome momentum to try to follow you. That momentum will put him on the outside of what ends up being a spiral as you keep moving 90 degrees away from his line of advance, giving you 3-4 seconds to fil him full of holes, even if the incident starts at a range as short as 20 feet.

Even if you can't shoot at move at your local range, you can practice your foot work as well as drawing and moving with blue gun or a positively known by you to be cleared firearm that is always pointed in a safe direction.

You want to move laterally by stepping out with one foot then bringing the other foot over to meet it, so that you never cross your feet. If you cross your feet, the odds are good that under stress you'll trip your self, and that makes you much more vulnerable in an attack.