New Ballistics Program for Graphing Calculators

[Ragnarok]

I don't know, it depends whether you want to compensate for atmospheric pressure losses at different altitudes and the curvature of the earth. Both of which should not be a factor in designing a humble poatato gun.

I do actually consider those factors in the latest LRC build. It's fairly inconsquential... but I'm a spudgunner. I specialise in overkill.

Well, it's not just that, as I did need some pretty good results for a simulation I was doing... but overkill is part of it, yeah.

I was a little surprised at the difference the atmospheric thinning, even over a relatively small range of a few hundred feet in height over the course of a projectiles flight. Depending on conditions, it can affect range by as much as a few feet.

[rcman50166]

Ill put it up as soon as I figure out how make it a text document

But how would I put the text on my calculator?

On a TI-83 plus, you press [PRGM] then go over to the right where it says new program and press [ENTER]. Name the program and then start typing away. The Majority of the program commands are under the [PRGM] button when your editing the code. Anything else is under [2ND] [0]. That is the catalog of all the commands for a calculator. But if you browse around on the calculator, you will find shortcuts to the keys that aren't under the [PRGM] key.

I do actually consider those factors in the latest LRC build. It's fairly inconsquential... but I'm a spudgunner. I specialise in overkill.

Well, it's not just that, as I did need some pretty good results for a simulation I was doing... but overkill is part of it, yeah.

I was a little surprised at the difference the atmospheric thinning, even over a relatively small range of a few hundred feet in height over the course of a projectiles flight. Depending on conditions, it can affect range by as much as a few feet.

Well those are surprising results. But i think temperature changes atmospheric pressure more than altitude does at those distances. Perhaps that's another I'll add. Oh and compensation for gravity changes at specific altitudes.

[Ragnarok]

Oh and compensation for gravity changes at specific altitudes.

That however, is redundant. The miniscule changes are completely inconsquential - at sea level, Gravity is 9.80665 N/kg by definition.

At 1000 metres up, it's then 9.802 N/kg - a difference of just 0.004 N/kg.

I did consider the inclusion of the effect in the LRC, but given the amount of processing time that was added for a difference in gravity of less than 0.05% even in exceptionally extreme cases, I disregarded it - the range results were changed by even less, maybe 0.01%, even when I was zealous with the other figures.
The curvature of the Earth is also getting axed, given the extra time added for that - the results are changed by just micrometres, even under pretty extreme circumstances.

The fact is, that when there is a relatively high uncertainty in even basic figures like muzzle velocity, projectile mass, and most notably, drag coefficient, it is ridiculous to include effects that change results less than even a change of 1% to the drag coefficient.

Given that you can't be that precise on measuring the Cd (although the LRC will include a Cd calculator), I don't think that for a modest spudgun ballistics modeller, you need to be concerned about effects like that.

Of the three, the only effect that will remain in the final build is the surprisingly significant atmospheric thinning.

[Blitz]

I need to find my data cable, and see if this will work on a TI-86. I don't see why not.

[rcman50166]

That however, is redundant. The miniscule changes are completely inconsquential - at sea level, Gravity is 9.80665 N/kg by definition.

At 1000 metres up, it's then 9.802 N/kg - a difference of just 0.004 N/kg.

I did consider the inclusion of the effect in the LRC, but given the amount of processing time that was added for a difference in gravity of less than 0.05% even in exceptionally extreme cases, I disregarded it - the range results were changed by even less, maybe 0.01%, even when I was zealous with the other figures.
The curvature of the Earth is also getting axed, given the extra time added for that - the results are changed by just micrometres, even under pretty extreme circumstances.

The fact is, that when there is a relatively high uncertainty in even basic figures like muzzle velocity, projectile mass, and most notably, drag coefficient, it is ridiculous to include effects that change results less than even a change of 1% to the drag coefficient.

Given that you can't be that precise on measuring the Cd (although the LRC will include a Cd calculator), I don't think that for a modest spudgun ballistics modeller, you need to be concerned about effects like that.

Of the three, the only effect that will remain in the final build is the surprisingly significant atmospheric thinning.

Well those extreme cases is what I want to compensate for. It's just I need to know whether anyone would ever need such a feature. Curvature of the earth is a factor when meters turn into kilometers. The same applies for gravity. If someone shoots a projectile straight up for 5 miles well then gravity is a significant factor in flight time. The same goes with atmospheric thinning. However, for spuds your right many won't need such accuracy. But the program is a ballistics calulator, not a spudgun calculator, so I may need to program it one day. Also something I didn't think of until know is terminal velocity, right now, if given enough time a projectile will fall at an increasing velocity all the way to the speed of light and beyond.

[koolaidman]

nice, this should be pretty freakin genius. i might be able to get a cord from someone, but could you try and post the code?

[Ragnarok]

Terminal velocity is an essential. It was missed from LRC v2.2, and is probably the main source of error in the old sheet.

The other thing you might not have considered is transonic and supersonic ballistic effects, which are a considerable mess, and require a large number of data tables to work from. Drag co-efficent is not a constant, it changes with Mach number.

The tables I'm using for the LRC cover 11 conventional ballistic models (to cover as many projectile geometries as possible), and a 12th composite model created from the conventional models.
This last model is created by matching the drag co-coefficient of the projectile to the coefficients of the basic models, then combining the models in varying proportions decided by an algorithm.

To get the results I want, each of these 12 models has nearly 200 items of data connected to it, for a total of almost 2400 data entries.
I don't imagine you want to try and program in a data table of that magnitude. It took me many hours to find and process the data into a suitable form for the spreadsheet to use it.

Now, let's see... Actually, looking at it, I made an error in the Earth curvature equation.

Over a quarter mile (not inconceivable for a powerful enough launcher), it seems like the earth's surface curves down around 4 feet, which is far more significant than I thought was, although still not worryingly large.

I'll try programming the correct equation in and see what difference it makes - hmm, quite some change. Although in the end, it depends on whether the launch is decided on angle to target or to the ground.

That's something I will have to think about...

Still as for the other problem, at 5 miles up, gravity is still 9.77 N/kg - that's still less than 0.5% difference, and given the error in Cd remains far greater than that, I would deem it a waste of what precious little processing power the calculator has.

That's not to mention that you need to worry about latitude as well if you're being that pedantic, as gravity varies with latitude.
I'm not even going near how you'd cope with that kettle of fish.

[rcman50166]

That is very informative. I'll make some changes as well as add some new things. Terminal Velocity will be added as well as earth's curvature. Wow, 4 feet every quarter mile... Very significant. Anyway do you mind sharing the equation for air resistance & the drag coefficient. I realized the coefficient I used is kinetic resistance, not aerodynamic resistance. This will mean I will need to fix the program, and remove these versions. For all those who already have the program, it is still be accurate to a certian point. Just do not try to calculate the distance of a projectile using rediculous values. (such as the speed of light!)

[Ragnarok]

Wow, 4 feet every quarter mile... Very significant.

More so than I thought, but it seems I made another error. I accidentally had a factor of 100 in the equation by mistake, and it would seem to be just half an inch, not 4 feet.
BTW, it's not "every quarter mile" - it's "at a quarter mile", and you can't just extrapolate that out.
For example, at one mile, it would appear to be around 8 inches - which is far more than you would expect from extending out 1/2" per 1/4 mile.

Hmm, it's still more significant than I originally thought, but can I really justify the extra processor cycles?

Anyway do you mind sharing the equation for air resistance & the drag coefficient.

http://en.wikipedia.org/wiki/Drag_equation

[boilingleadbath]

The earth isn't a sphere, and even in relatively flat areas (widwest USA, for instance) the topography of the landscape is far more important than the standard curvature. At sea, I suppose it might be significant once one starts considering distances of a couple miles... but at that point, the curvature is rather swamped by the other variables one doesn't know.

[rcman50166]

Well at the point where you need to compenstate for the curvature of the earth, you can assume the planet is perfectly spherical. At a point you'll be able to orbit it. But making those kind of compenstations would require one to know the topograpgy of the earth. That is a feature no ballistics program compenates for except one. But unless your computer's run speed is measured in teraflops, you can't run it.

[jimmy101]

Ragnarok, it sounds like you've gotten to the point where the simulation is "more accurate" than the actual guns. Shot-to-shot variability is probably at least an order of magnitude greater than several of the affects you are considering.

Heck, even a high power rifle isn't accurate (reproducable) to 1/2" at 1/4 mile. IIRC, an M-16 will do 3"~4" groupings at 300 feet.

[rcman50166]

This is true. Perhaps it isn't necessary to have such factors when the round doesn't even leave the barrel straight. Air resistance seems to be the only needed determinig factor in a simulator.

[Blitz]

Yeah, you guys are just overanalyzing the project here. The KISS princple is starting to show favor!

That being said, I wouldn't worry about much, it's not like we're firing several miles (yet... insert evil laugh).

[Ragnarok]

it's not like we're firing several miles (yet... insert evil laugh).

*Inserts a really evil laugh*
I've just started the very early stages of building something that will have a maximum range of about 2.5 miles.

There's no way it could be used at those ranges (as if I tried, I'm at a risk of hitting something living or valuable, as that's well out of my visual range) - but at short range, imagine the potential.

Bear in mind, before you get excited, it is going to take a very long time to complete the build. It's barely started, and in the later stages, a single part of the setup - and a relatively simple part at that - I have allotted 2 or 3 weeks on the build time table to do to sufficient standards. This thing requires precision engineering on a scale as of yet unknown to spudgunning, and it can't be rushed.
Even then I'm going to be hesitant about starting that part. The thing as a whole is going to take months, as there are parts that ideally would be machined, but because of prohibitive costs, will have to be made via other methods.