Finding a bullet's velocity over time

[l2aizou]

Hi, I engage in physics as a hobby, and I'm not extremely familiar with things reaching into calculus levels of math. That said, how would I find the velocity of a bullet at a given time or distance, taking wind/humidity/etc. out of the equation?

I know the muzzle velocity only applies to the bullet leaving the barrel, but given I know that, how would I attempt to find the decrease in velocity with a given time, or distance? For example, a 700m/s bullet velocity being decreased down to 683m/s at a distance of 10 meters. I can find the acceleration within the barrel given the final velocity = muzzle velocity. I also have the dimensions of the bullet, weight, and bullet coefficient.

This thread seemed like it was what I needed, but I am unsure if it is what I'm looking for.

Eventually, I want to be able to make a graph like this.

 

[boneh3ad]

You aren't going to get very far on this without calculus.

 

[l2aizou]

You aren't going to get very far on this without calculus.

I can do it, I'm just not as familiar with it as other levels of math.

 

[Mister T]

Hi, I engage in physics as a hobby, and I'm not extremely familiar with things reaching into calculus levels of math. That said, how would I find the velocity of a bullet at a given time or distance, taking wind/humidity/etc. out of the equation?

If you ignore everything, the bullet maintains its muzzle velocity as it moves. Add gravity into the picture and the horizontal component remains unchanged but the vertical component changes by 32.2 ft/s every second. If you want to account for air resistance then you need to look at the effects of air drag. The Wikipedia article seems accurate and accessible:

https://en.wikipedia.org/wiki/Drag_(physics)

 

[JRMichler]

An excellent book on the subject is Modern Practical Ballistics by Arthur J. Pejsa. No calculus required.

 

[l2aizou]

If you ignore everything, the bullet maintains its muzzle velocity as it moves. Add gravity into the picture and the horizontal component remains unchanged but the vertical component changes by 32.2 ft/s every second. If you want to account for air resistance then you need to look at the effects of air drag. The Wikipedia article seems accurate and accessible:

https://en.wikipedia.org/wiki/Drag_(physics)

Yeah, I meant just weather conditions, not gravity and stuff.

But with one of the calculators I used to find speed over time, I needed the ballistic coefficient, muzzle velocity, and diameter and weight of the bullet, so I don't know how that'll help.

I found a few Pejsa things, but this is really starting to frustrate me. I've been attempting this since almost 12 hours ago.

 

[Mister T]

But with one of the calculators I used to find speed over time, I needed the ballistic coefficient, muzzle velocity, and diameter and weight of the bullet, so I don't know how that'll help.

Sorry, you lost me there. You said you have all that information. If all you want is that graph you mentioned you just use that calculator to find the values and plot them on a graph.

 

[l2aizou]

Sorry, you lost me there. You said you have all that information. If all you want is that graph you mentioned you just use that calculator to find the values and plot them on a graph.

I do, but I want to learn how to do those calculations on my own.

 

[Mister T]

I do, but I want to learn how to do those calculations on my own.

Okay. You can see from the Wiki article I referenced that it's a complicated problem. The best place to start might be a textbook for a junior-level course in dynamics. A forum like this is a good place to ask questions when you get stuck.

The best approach might be to use numerical methods and start with spreadsheet software. If you're already proficient with computer programming this a really simple programming task. You just use something like Euler's method.

 

[l2aizou]

Yeah with that last suggestion it really helped, I was able to make sense of the formulas linked above, the only thing I need to check is if my bullet measurements were correct.