math figures?

[NoltaiR]

Hey guys, tomorrow (if I have enough time after work) I plan on making a crude cannon/mortor that will made of a stainless steel pipe (3' long by 4" ID). I will be shooting both 'grape shot' (just a bunch of peices of scrap metal, nuts, and bolts) as well as well as cement spheres (made by filling spherical glass ornaments with an ID of slightly smaller than 4" with cement and allowing them to dry). I will be using my electrical ignitor for the initiation so it will be fairly well controlled.

Also, rather than just shooting aimlessly, I am going to be shooting at a target made of plywood that will be set at different distances for different tests.

I was just wondering if any of you knew any mathematical formulas I could use to figure out theoretically how fast my shot is going to fire out.

[mrloud]

On a related note, does anyone know how ammunition and firearm manufacturers determine the velocity of a projectile? I suspect that it is not determined until after the product is tried out. They could use RADAR in modern times or they could have used high speed film in old times.

[DBSP]

The VOD is determined with a chronograf. Its a box similar to a brick in shape filled with electronics. On the top there's two sensors wich measure the time it takes for the bullet to pass both sensors.

[Ctrl_C]

I will bring my physics notes home tomorrow...they contain all the projectile motion equations you will ever need.

[SATANIC]

If you are going to be really simple about it, you could take a measurement of the distance it flies, (fire one at a set charge) estimate the height, measure the angle of the barrel, and record the time. From that you can work out the actual distance it flew, then the average speed. from those you could at least make a rough estimation of the launch speed. just use your simple trig rules, and possibly pythagoras's theorem, (sp). It's year 10 science stuff ( i did advanced science but).

i'd post diagrams, but i have none. if you really can't do it your self, post the data and i'll work it out. i can't explain how to do it, i haven't got the patience.

[NoltaiR]

Well today I shot off a few and with a little work made it quite accurate (I shot a small branch off a tree that was about 100 feet away).

My homemade BP doesn't burn fast enough to shoot any kind of projectile off well, so I mixed it 50/50 with industrial FFG grade BP and it worked just fine with my electrical ignitor.

I went through my old physics notes and found a formula if I was to shoot the mortar off straigh up in the air.

To measure using time, you can time the amount of seconds it takes for the projectile to leave the barrel to the point in which it stops (reaches 0m/s).
VI = VF - GT (where g = -9.81 gravity)

Therefore if it took my projectile 7 seconds before it reached 0m/s, then
VI = 0 - (-9.81)(7) = 68.67m/s

Also you can calulate the maximum height it achieved by using:
D = (VF² - VI²)/(2G)
= (0² - 68.67²) / (2)(-9.81)
= 240m
(of coarse this is its theoretical value, not including the factor of wind causing it to slow down)

[zaibatsu]

To measure speed of a bullet in an easy way just use a ballistic pendulum.
http://www.frontiernet.net/~jlkeefer/ball_pen.htm or do a search on it a find a load of different pages.

[vulture]

The distance where your projectile hits the ground(so not a tree in the middle!) is equal to:
Vo x Vo x sin 2y / 9,81
Vo = muzzle velocity
y = angle with the ground

so if you want to know the muzzle velocity you have to take the square root of:

9,81 x d / sin 2y

d = distance

I hope this is clear to you, if not, send me a mail.

[Ctrl_C]

you also have to take into account the height of the barrel from the ground. in reality, you should find the distance to where it hit, calculate the trajectory, and calculate where the "landing poing" is at the same height as the muzzle.

i forgot my notes...tomorrow perhaps

[NoltaiR]

Vulture's formula seem to be a formula made for 2 dimensional (where Vox and Voy are both accounted for) analysis of distance and hieght and he just translated it to be made for a vertical measurement.. sounds like making it a lot harder than it really is but I guess if your the technical type, then that's the way to go. BTW, for you people that don't know your physics all that well, Vo and Vi are the same.. they both represent the initial velocity.

Anyways the formulas I gave earlier were to measure from the time that the projectile left the barrel and was far enough away that the BP no longer had an accelerating effect on it (about 6-8 inches I should think from the end of the barrel) to the point in which its vertical hieght is at its maximum point (when V = 0m/s). You could also (theoretically because the real acceleration would not be uniform) calculate the acceleration from when the projectile is at rest inside the barrel to the point outside the barrel when it is no longer accelerating. I forget what this formula is but I am pretty sure it works.

[vulture]

Actually, it's the simplest formula that exists for this!
Of course it's a 2-dimensional movement, it has a vertical and a horizontal velocity.

And i don't see where you get that Vo and Voy from, it's just the square of Vo, but i don't know how to type superscript.
My x stands for multiply BTW.

2x barrel lenght / square of time in barrel = acceleration

[Ctrl_C]

heres all projectile motion equations from my physics notes.



g = -9.80 m/s²

V_f = V_i + at

d = 1/2 (V_f + V_i)t

d = V_it = 1/2 at²

V_f² = V_i² + 2ad

d_x = V_i_xt

d_y = V_i_yt + 1/2 gt²

where
V_i = Initial velocity (muzzle velocity)
V_f = Final velocity
d = displacement (distance)
t = time in s
a = accel due to gravity (g)



Furthermore, you can seperate the projectile into an x and y component using:



V_i_x = V_icos(angle)

V_i_y = V_isin(angle)



[ 27 February 2002: Message edited by: ctrl_c ]

[xoo1246]

When a projectile reaches higher speed than aprox 60km/h air resistance becomes important.

[Bignutsami]

The older chronographs just used two sheets of paper with wires running through them set at a defined distance apart.

As the bullet passed through the wires were cut, which started and stopped a timer which shows how long the projectile took to go that distance, the math is simple from there.

[A-BOMB]

I'll scan you some pages for a old gun book I have that tells you pretty much every way to register velocity of your projectile.
I'll put it on the FTP in the uploads It name will be "chronographs scanned pages.pdf"