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So after some fruitless searching I need to know the equations to get FPS from the distance and time traveling of a projectile. I normally look down apon people doing what I am, but damn I really need these equations and I could of swore I saw them somewhere...
have you googled it.
I doubt there is a single person on this site that knows them.
they are very complicated.
what is the data you have? some distance over some time? and you need to convert it to feet per second? wait a second, feet is a distance and seconds are time. does my sarcastic tone help any? maybe this might... google uconeer. it's just a conversion tool that converts everything to everything.
I think I'm missing something here....
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V=dx/dt only gives the average velocity, not incredibly helpful if you want muzzle velocity. that said, if you're using a chrono near the barrel rather than entire flight time, it shouldn't be a problem.
pizlo, do you mean the equations of motion; V^2=U^2+2as, etc? i can't see it being difficult to find those on the internet though.
i can't think of any other equations that might be pertinent to chrono-ing.
Using a set distance away from the muzzle will only give you an average velocity anyway. You would have to use a very very short distance to get the rough muzzle velocity.
You can use a sound recording over say 10m between target and cannon and multiply that by whatever to get fps.
You won't get muzzle fps but if the cannon is high powered enough and the projectile isn't tissue paper there won't be a significant speed loss at that distance.
Theres a thread somewhere on how to do it... *rummages*
All chrono's give an average velocity over a distance. Usually, the distance is short enough so the drop in velocity can be ignored.
The average velocity is just (delta distance)/(delta time).
To try to extract the instantaneous velocity at a particular distance (or time) you need the equations of motion, the parameters of the ammo (mass, area, Cd ...). A google search with "equation of motion" or just "ballistic equation" will return hundreds of thousands of pages. The first page for each query (a wiki and NASA pages respectively) would be a good starting point for a noob.
"FPS" = feet per second
"per" means divide
"FPS" = feet divided by seconds = feet/seconds
Perhaps you shouldn't look down on people with IQs of more than 80.
I have used soft chrono (with quite good results), and for my science fair I was hoping to say what equations it most likely performed. Maybe I'm mistaken but it just seems that it did more than feet divided by seconds, but it does seem to make sense. Well thanks for the replys, I guess I wasn't thinking quite as clear last night. Now I'm wondering why some of you also think it should be more complicated. and softChrono only gave me "muzzle velocity". it was a set shot from 2o feet.
A few ways it would be more complicated would be if you are accounting for the speed of sound with a microphone not midway between the muzzle and target, or if you wanted to account for air drag to find the actual muzzle velocity rather than average velocity. I could be wrong, but I don't believe soft chrono accounts for either of those and it is most likely just doing distance/time.
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To actually find the velocity using drag you need math physics and science that is way above high school level, and you would need matlab and know how to program in it. To do drag correctly it is very complicated and technically impossible to solve because to find the drag you need the velocity, but you don't have it. But it's a science fair you could do graphs of acceleration or velocity, jerk, position, stuff like that. or create a "program" in excel for a simple cannon in which you change dimensions of the tank, barrel, and pressure to show how you can change the range of the cannon based on different variables
It is fairly easy to use what I would consider "high school" level math (some of the physics is probably university level, but I'm sure they teach things like force, acceleration, velocity, and displacement in high school physics classes) to very accurately estimate the change in velocity between 2 points. The process is not exact (as you said, the problem turns into a loop when you try to solve it exactly) because it does assume that deceleration is constant during each time step, but it is damn close. It involves calculating acceleration due to air resistance during very small time steps (0.001 seconds usually), then calculating a final velocity at the end of the time step, and using the resulting value as the initial velocity in the next time step. The math would look a bit like this;
Drag force in vector form is -(1/2*Cd*d*A*V<sup>2</sup>), where Cd = drag coefficient, d = density of the atmosphere, A = frontal area of the projectile, and V = velocity.
Acceleration is F/m, where F = force, and m = mass.
Final velocity is v<sub>initial</sub> + a*t, where v<sub>initial</sub> = initial velocity, a = acceleration, and t = time.
The velocity at the end of the time step would thus be v<sub>initial</sub> + -(1/2*Cd*d*A*V<sup>2</sup>)/m*t
You can figure out the distance the projectile has traveled during each time step using d = v<sub>initial</sub> + 1/2*a*t<sup>2</sup>, and at this point you have basically covered the main algorithm of my projectile range calculator (aside from the trig ratios and pythagorean theorem required to separate, then recombine the horizontal and vertical components of the velocity when modeling a projectile launched at an angle).
Considering 99% of what I know about physics is self taught, I don't really see why anyone with even a high school level physics education should have trouble with estimating drag, unless I am severely overestimating high school physics classes.
Oh crap... I seem to have forgotten what this thread is about. Anyway, the above process could be rearranged to figure out the actual muzzle velocity of a cannon that is placed several feet from a chronograph, but in reality, air drag at that distance is not going to have much of an effect.
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well the loop i was thinking of was you need the reynolds number to calculate the Cd of the object, and you need velocity for the reynolds number and then each shape has a graph that has no equation (it's based solely on experimental data) that needs to be examined by hand each time, for every increment of time. none of this information is available online or anything. and in order to do it correctly you need to know fluid mechanics and numerical modeling. your not under estimating highschool physics, just the drag portion of it. i think the thread was about him trying to do something fancy for his highschool physics show or something.
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