Weight and Balistics...

[Jared Haehnel]

Ok there's alot of smart guys in the forum who know alot about balistics... I hope you don't mind if I pick your brians for a moment....

I'm doing a paper on comparing the weights of an object luanched from a given cannon with the same CD.

Basicaly my constants are the gun. A 1000 cubic inch chamber with a ten foot barrel (120 inches). The chambers contian 120 PSI of compressed air.

The whole point of this is to show how weight plays into distance. Too of an light object will have high muzzle vilocities but won't go far. Too heavy an object will just plop out of the barrel. So I'm trying to see what the best wieght will be. I'm starting with a CD of 0.5.

I hope to be able to do the math and graph my results then compare them with GGDT to see how I faired. Given the GGDT will be much more accurate since it includes more variables then mine will.

Here where I need a bit of help...I'm looking at the math and I'm realizing that some of it is pretty foriegn to me... If a few of you wouldn't mind giving me a hand with some of the balistic equations and explaining how to work the math...perhaps I'm a bit over my head...Any help would be appreciated...

(I just realized its kind of a help me post...Mods, forgive me )

[jackssmirkingrevenge]

It's not just a question of weight but the shape and size come into it too, here's a helpful definition:

Ballistic Coefficient - Measure of the ability of a projectile to overcome air resistance. Ballistic coefficient (BC) = SD / F, where SD is the sectional density of the projectile and F is a form factor for the shape of the projectile. Sectional density is calculated from the mass (M) of the projectile divided by the square of its diameter. The value of F decreases with as the pointedness of the projectile increases. A projectile shaped like a sphere would have the highest F value while one in the shape of a long needle would have the lowest F value

If it's distance you want, then it's a good ballistic coefficient you should be after. It's the science that leads to streamlined high density projectiles with a low frontal area like these:



Of course, in the barrel you need maximum frontal area for good energy transfer and minimum weight for good acceleration, which is where the sabot comes in. This gives you the best of both worlds in terms of external and internal ballistics, at the cost of a more complex build.

[Jared Haehnel]

Ok so what I get from this is that wight is already a factor in the CD equation... am I right?

But still I'm hoping to figure out with the given constants what is the best weight of a projectile fired from a specific spud gun...

[jackssmirkingrevenge]

With all other factors being constant (ie projectile size and shape) then weight will be the determining factor in terms of range.

In terms of muzzle energy, the heavier the projectile the more energy it will gain from a pneumatic, there is no ideal weight after which the energy tapers off. Penetration on the other hand does have a "sweet spot", because even though a heavy projectile might have a higher energy, it will have a lower velocity if fired from the same cannon, and speed is a factor when it comes to penetration because low speed gives the target time to deform and absorb the blow.

The same logic applies to the way the projectile travels, because it is effectively "penetrating" the air - therefore there is a balance between weight and velocity to be reached. I'm sure there are programs available online that will calculate the ballistic coefficient of a given projectile for you and allow you to determine what this ideal weight is, if you combine it with GGDT's muzzle velocity estimates for a projectile of given weight.

[Jared Haehnel]

I was defiantly planning on using GGDT to check and figure the results....

Do you happen to know any of the equations to figure trajectory?

Its funny my teacher wants me to demonstrate a spud gun in my presentation

[jackssmirkingrevenge]

Use GGDT to model your launcher, increase the weight in incrememnts (say 10 grams every time) and build up a table of weight with its corresponding velocity.

Then find something similar to this, keep all values standard except weight, velocity corresponding to that weight from GGDT, and the ballstic coefficient - which is also changing, because by altering the weight but keeping the same projectile shape and size, you're changing the sectional density.

This will allow you to come up with a table that gives an arbitrary measure of how range varies with weight.

[THUNDERLORD]

It looks to me like JSR covered it as far as a math formula goes.
You physics guys are cool. I tend to be more mechanical myself for example if I want to compare chamber volume to barrel volume I'm more likely to fill one with water and pour it into the other, rather than use mathmatics. But the mathmatic thinkers will win out in the long run I guess.
My old science teacher said velocity is speed and direction combined. Like knautical miles, for example, if an airplane is going 200 mph but there are mountains below it would be covering mountains a car would have to drive over at maybe 250 mph to go the same distance. Trajectory may be similar. there are factors to consider in projectile shape that I haven't read about here.
Such as if the front is pointed sure it will be more aerodynamic, but weight retains velocity better so weight at the front , although being less aerodynamic, will keep a projectile straighter.
Also there is muzzle blast though and if the back end is too light, the muzzle blast will send the back end towards the front creating unstability.
Then you have principals of supersonic velocity which don't concern spud type technology, such as boat tail bullet shape for the vacuum vortexs or eddys at the back.
I was just thinking there is a balance between mechanical and mathmatical principals there that can best be studied through actual application. Which is also the reason you are asked to physically demonstrate for your "teacher" that's funny a little right?

-----------Spudding, the new sport of kings!!!-------------------

[jackssmirkingrevenge]

It looks to me like JSR covered it as far as a math formula goes.
You physics guys are cool. I tend to be more mechanical myself for example if I want to compare chamber volume to barrel volume I'm more likely to fill one with water and pour it into the other, rather than use mathmatics. But the mathmatic thinkers will win out in the long run I guess.

You have to be a bit of both, all theory and no practice gets you nowhere. I've always been a practical hands-on sort of person, but tools like GGDT (Which EVERYONE should use, D_Hall has my eternal gratitude ) are an extremely simple way of playing with parameters before you even get to the workbench stage, saving a lot of time, effort and materials with trial-and-error testing. The advantages of computer modelling are being applied to industry the world over, spudding shouldn't be left out

Then you have principals of supersonic velocity which don't concern spud type technology, such as boat tail bullet shape for the vacuum vortexs or eddys at the back.

Small correction, as far as I know boat tails mostly provide an aerodynamic advantage when bullets have entered the region of subsonic speeds. A historical example of this would be the British introduction of the Mk.VIII boat tailed bullet for the 0.303 cartridge for use in machineguns firing at long range, not an issue at normal ranges but machineguns fired far enough for the bullet to slow down to subsonic speeds, and the idea was not to have it slow down as much in this region of flight.

[THUNDERLORD]

I feel honored to have you reply JSR,and once again you made valid points.
Maybe this is a dumb question, but it will help other guys reading this as well, I am wondering where do go to use GGDT? thank you

[jackssmirkingrevenge]

GGDT can be found here, click on >>this link<< for instructions on how to download and install it - make sure you follow the instructions and you shouldn't have any trouble using it. If you have any questions on how to tune it to your specific needs, just ask on the forum, someone will be able and happy to assist you

[boilingleadbath]

You want to calculate your own trajectories?

Ok, I can help you with the more basic stuff.
We are writing for a teacher who probably scarcely remembers that F=CdAV², not the department of defense, so that's fine.

First off, there are two ways to calculate drag-inclusive ballistics:
1) Calculus
2) Iterations

I can't help you with #1, so we go with number 2. I expect that its easier to explain and understand anyways... plus, its hard teach computers calc.

1) As you should know, the force of drag is equal to Cd*A*V². Well, pretty much. We ignore the fact that Cd changes with velocity and that there is a type of drag, important at low velocities, equal to A*V. (IIRC)

You could use BC, but it seems to be somewhat "unstandard" outside of the bullets industry. Besides, it's derived from Cd, A, and mass anyways.

2) This force of drag is calculated using the actual velocity of the projectile. You can't calculate X-axis drag and Y-axis drag separately and then combine them.

3) Remember to include gravity.

So, basically, you calculate the path of the projectile by doing the following:

1) Apply drag
2) Apply gravity
3) Find new velocity
4) Repeat the above, unless the projectile has hit the ground

The tricky part is mostly the trig work; the conceptual and calculated physics is actually pretty simple.

You can do this in excel, JavaScript, C++...

[Jared Haehnel]

Thanks...that helps a lot to point me in the right direction...thank you. 8)

I'll post what I come up with I doubt its going to be revolutionary but I think it may be interesting....