# How fast would a person need to be to cross a gap and prevent a gunman from shooting someone?

I was reading one of the recent questions involving a fast-moving superhero, and it reminded me of something I've been wondering about for a while, so I decide to create a spinoff scenario question.

Speedster Bob is a superhero, so he likes rescuing people. Damsel Jane is being threatened by Jerkface Joe, who is holding a standard handgun. Joe decides to point his gun at Jane. He isn't planning on shooting her, yet, just pointing it, but Bob doesn't know this. Bob doesn't want to allow this, because he doesn't want Jane shot. Bob is standing approximately 15 feet away from Joe, who is aware of his presence but currently focused on Jane.

Given this scenario, these things need to occur to achieve Bob's goal of preventing Jane's death (or injury). 1) he needs to recognize Joe's intended movement and 2) he needs to cross the space between them and grab/push Joe's arm before Joe can recognize he has begun to move, change his intention from simply pointing to shooting Jane, finish his initial motion, and pull the trigger.

Now, for an average human, this is extremely risky. You'd be more likely to get yourself shot (no matter what the movies say), and have to be super lucky to pull it off. But Bob isn't super lucky, just super. So he is pretty sure he can pull it off with a relatively high chance of success.

Assuming that Bob's top speed is not limited, then I think it comes down to his reaction time and rate of acceleration from a stopped position.

If Joe's reaction time is that of an average healthy adult, what are the minimum estimates of what Bob's super reaction time and acceleration would need to be in order to successfully pull off this move?

• @JBH sorry, I wasn't trying to change the question, just make more clear what I was asking. If you look at the actual original question as phrased in the post, it asks about Bob's reaction speed and acceleration, not just the flat speed it takes to get one object (Bob) from one point to another in a certain timeframe, which is the only thing most of the answers really addressed. I thought editing the original post in response to clarify the question would be better than just leaving comments asking for consideration of these factors beneath all the (very well thought and explained) answers. Mar 30 '19 at 1:24
• @JBH So, you think I should post a new, nearly identical question with specifically stated limitations on Bob's reaction time and so on, as opposed to editing this one in order to avoid near duplicates? Mar 30 '19 at 1:35
• @JBH given some consideration, I think it might actually be better to ask a question (not sure if Worldbuilding would be the right place for it?) specifically about what factors affect an animal or human's maximum muscle-powered acceleration speed, and how those could be altered (possibly with pseudo-science, since Bob isn't likely to be actually scientifically possible) to give Bob an unnaturally high acceleration speed. Because you're right, as far as this specific scenario is concerned, they answered what I initially asked. Thanks for clarifying. I'll edit my post to revert it to original Mar 30 '19 at 1:44
• @Agrajag, No problem. Thanks for following up. I've deleted my previous comments to clean up the comment chain and to remove any evidence that I jumped to a conclusion. 😉 Mar 30 '19 at 14:25

Given that Bob only has to deflect the gun by about 4 degrees in order to make a formerly-well-aimed shot miss Jane at a range of 15 ft, the time it'll take Bob to shove the gun off target is likely comparable to the time it'll take Joe to pull the trigger. This means the question really boils down to whether Bob can close the gap before Joe can react to his movement.

Human reaction time to visual stimuli averages around a quarter of a second, but there are outliers. Bob shouldn't underestimate his opponent, so he should probably aim to get there in 200ms or less. Covering 15 feet in 200ms has Bob traveling at 75 ft/s, or about 51 mph. To achieve this, Bob has to significantly outpace Usain Bolt (whose record is 27.8 mph), but doesn't need to come anywhere near the speed of sound (767 mph at sea level, slower at higher altitudes).

Incidentally, were Bob to accelerate at a constant rate such that he hit the speed of sound just as he arrived at Joe's position, he'd get there in a bit under 27ms, leaving him plenty of time to turn to the camera and make a face for the slow-mo shot before pushing the gun's barrel an inch to the side in time to beat even the fastest human reflexes.

• Does the question actually say how far Joe is from Jane? It says that Joe and Bob are 15 feet apart, but I don't see anything about where Jane is positioned. Mar 29 '19 at 21:59
• Good catch, although probably immaterial -- in a 75+ ft/s collision, the extra time necessary to deflect the gun 7 inches vs. 1 inch isn't going to make much difference unless Joe's got his trigger set up for competition shooting. Mar 29 '19 at 22:06
• If you factor both time to pull and time to register, you are looking at ~450ms. That is actually within Usain Bolt's record if you exclude acceleration time. Mar 29 '19 at 22:07
• I was going to make an answer relating to human reaction, but you already did, but I have some comments. Once Joe visually recognize Bob. Joe's brain must then process the threat and devise a course of action. This could take some time as perception and bias may cloud his mind. That's where you get the freeze moment. Also, in law enforcement, anyone within 20 feet is considered an immediate threat as the "Joe" could quickly close the gap before the "Bob" can recognize the threat and devise a course of action. That is where you get inadvertent police shootings Mar 29 '19 at 22:14
• I should add, just because Joe is pointing the gun at Jane, once presented with the threat of Bob, Joe wont necessarily shoot Jane. Natural threat response would tend to make Joe address the imminent threat as Jane does not necessarily pose a threat. Mar 29 '19 at 22:18

A person can pull (and release) a trigger about three times per second. A rare person might be able to pull four times per second. (source)

That tells us Bob must complete his action in 0.25 second to guarantee Jane's safety.

• Bob's 15 feet away.
• The gun is presumably pointed midway between Jane's arms (at the vertical bisection point).

Survey data taken in the early 1960s calculated that 3,581 American women over the age of 17 had an average shoulder width of 13.9 inches (35.3 cm). (Source)

• So Bob needs to move the arm 7 inches to save Jane.
• Bob can raise his arms while in motion, but they cut down the distance he needs to travel. The average man's arm length is 25 inches.

So Bob needs to move 162 inches in 0.25 seconds to successfully save Jane. That's 54 fps or 36.8 miles per hour.

Bonus: It takes 4,000 Newtons of force to break the average human femur. Using this as a baseline, and assuming Bob is the human average of 196.9 pounds or 89 kg, and using the equation...

$$F = \frac{mv}{\Delta t}$$

We get 5,856 Newtons and Joe gets a broken arm/wrist as a reward for trying to shoot Jane.

• Per your calculation, 5856 N is the force required to get Bob moving fast enough. But this is not the same as the force he then applies to Joe, which is also not the same as the force applied to Joe's femur or his wrist. Mar 29 '19 at 21:40
• @GeoffreyBrent, I dropped in a "wait..." edit because I thought that was true, but as I worked through the math, it appears they're the same thing (so I removed it). It's Newton's 3rd law. If it takes Z force to get X mass up to Y speed, it takes the same Z force to stop it (upon impact with the arm). There are details I'm ignoring (e.g., some force is dissipated into the compressiblity of flesh), but I've enough newtons to ignore that. Mar 29 '19 at 21:42
• Only if you assume that Bob stops dead in the collision with Joe's arm, which is a very peculiar thing to assume. If I'm holding my arm out and you charge into it at full speed, you're not going to suddenly stop dead. You're going to knock my arm aside and slow by a fraction of your speed. Mar 29 '19 at 21:49
• (also, it never ever takes "Z force to get X mass up to Y speed" - the force required depends on the delta-t, which is unlikely to be the same in deceleration as in acceleration.) Mar 29 '19 at 21:54
• The fire rate is not the same as reaction time (time to make first shot), though they both are in the same ballpark. Mar 29 '19 at 21:55

The answers are markedly varied.

If he has to watch the trigger, he may have no more than quarter second to act. However, realistically speaking, he doesn't need to do that.

Your brain makes up its mind up to ten seconds before you realize it, according to researchers. - https://www.nature.com/news/2008/080411/full/news.2008.751.html

In this case, he has quite a lot of time, if he can read the tells. Now the really hard question to answer is how good can he read the tells. This depends on nuances of both Bob and Joe which are well beyond the paragraphs in the question. Does Joe play poker? How good is his poker face? How angry is Joe (your tells show differently when you're angry)

Regradless, your specific answer about breaking the sound barrier is the same for all cases. 15 feet is about 4.5 m. Covering that in a quarter second is 18m/s. The speed of sound is roughly 330m/s, so Bob is not only not breaking the sound barrier, but substantially below it. He'll have much more of a challenge accelerating to those speeds.

For Bob to have trouble with the sound barrier, he would need to be responding to something in 0.013 seconds. For perspective, that 13 milliseconds is 10 times faster than our eye blink reflex.

Now the more interesting question is what is Bob made of? At these speeds, propagation of neural impulses start to matter. Signals down the fastest neurons travel at 120m/s. That's fast, but the 2m of spinal cord and nerves the signal has to travel down adds 16ms -- more than our entire time budget! So hopefully Bob has some unspecified hacks to boost his neurons too!

• You're right. It is partly Bob's acceleration that I am interested in, actually. Mar 30 '19 at 0:13