looking for calc based physics for real world projectiles

[Squid]

Not the college Physics 101 where they pretend air resistance doesn't exist, and hence everything from temp to wind to humidity doesn't either.

I remember my bother in Jr High brought home a few pages of how "they" can actually totally calculate projectiles, with all sorts of calculus about air resistance including things like how it decreases towards top of arc and decreases as speed of bullet decreases, etc.

How wind drift increases toward top of arc, how gravity decreases at top of arc(professional surveyors will tell you about how they need to compensate for how LIGHT RAYS are bent by the gravity of a large building)....how windage decreases as bullet's rotation slows with air resistance etc.

This was mostly for artillery but still all applies(even though might not make a real world diff).

I thought it was fascinating how calc was able to tie all this stuff together into one not TOO big of an equation.

Anyone got a good reference for a Mother of All Ballistic Equations, hopefully with explanations.

I'd like to program a common graphing calculator like ti-83+ to do that, instead of buying a dedicated unit, and somewhat understand what is really going on with a long range shot.

PS-I remember my brother telling me the special presentation was the only time during the year when the kids perked up in math class and really tried.

[Peter.Steele]

Hm.

I seeeeeem to recall - but I might be sadly mistaken - that most (all?) of this was covered in one of my textbooks from college ... you can still find copies of it out there.


I can't recall for sure, and the book is packed away pretty thoroughly at the moment. I do remember for positive that it's got all the calculations you need for lead / lag pursuit courses for missiles, calculations for determining the dwell points for phased array radars, signal strength, antenna size requirements, sonar, etc. I'm pretty sure that all the ballistics stuff was in there too. It's pretty cheap to get a used copy.

[WolfInSheeple'sClothing]

I actually did my senior seminar on ballistics (physics degree). First, I'm assuming you're comfortable with differential equations. If not, pick up an ODE's book to get familiar with them. It can get pretty complicated when you take into account such things as yaw, spin drift, the rotation of the earth, etc. There is actually one differential equation that can be solved (only by computer btw, not gonna happen on a TI-83/89). It involves 30 different coefficients that can be reduced to ten by symmetry. It takes computers a long time to solve the equation, so don't think you are going to do this by hand. This is why they have ballistics apps and calculators, which are based on various models. To get you started, check out The Mathematics of Projectiles in Sport by Neville De Mestre. This is a great little book and will walk you through the calculation involving different parameters. If you just want to know how to solve for drag, that is a simple ordinary differential equation and is covered in any introductory ODEs book. Also, google the various ballistics models to give you an idea of how this problem is dealt with in the real world. Have fun.

[HotRails]

I actually did my senior seminar on ballistics (physics degree). First, I'm assuming you're comfortable with differential equations. If not, pick up an ODE's book to get familiar with them. It can get pretty complicated when you take into account such things as yaw, spin drift, the rotation of the earth, etc. There is actually one differential equation that can be solved (only by computer btw, not gonna happen on a TI-83/89). It involves 30 different coefficients that can be reduced to ten by symmetry. It takes computers a long time to solve the equation, so don't think you are going to do this by hand. This is why they have ballistics apps and calculators, which are based on various models. To get you started, check out The Mathematics of Projectiles in Sport by Neville De Mestre. This is a great little book and will walk you through the calculation involving different parameters. If you just want to know how to solve for drag, that is a simple ordinary differential equation and is covered in any introductory ODEs book. Also, google the various ballistics models to give you an idea of how this problem is dealt with in the real world. Have fun.

wow. The hidden technical expertise of calguns never ceases to amaze!

[Pinto]

Bryan Litz also wrote a little - with extensive practical application

Applied Ballistics for Long Range Shooting

Here's a little light reading for part of the mathmatics aspect: How External Ballistics Programs Work

Quote: " If I were to write a ballistics program for small arms that’s intended to surpass the existing available packages, I would use a point mass solver (3-DOF numeric solver) for the following reasons:
1. Modern computers, even field deployable devices like palm pilots and cell phones have fast enough processors these days to solve a numerical solution in a reasonable amount of run time.
2. The program does not require you to store large tables (S, T and V functions) like the Siacci method.
3. You can make use of multiple standards (G1, G7, etc) depending on whichever one is best suited to the bullet you’re modeling. (Siacci also has this feature).
4. If you have access to a 6-DOF simulation, you can investigate trends like gyroscopic drift as a function of flight time for certain classes of projectiles, and then apply the trends as corrections to the point mass solution (Ref article: Extending Max Effective Range of Small Arms on this website). Applying the 6-DOF corrections won’t significantly affect computer run time."

[Rusty Scabbard]

sort of related, although the ballistics calculators may not be using it yet...
This spring, a 16 yr old German, Shourrya Ray, came up with an analytical solution to the problem of calculating trajectory with gravity and atmospheric drag. The problem was originally proposed by Isaac Newton over 300 yr ago.

[WolfInSheeple'sClothing]

There are many different forces to take into account if you want to straight up solve for the trajectory of a real world projectile. If you want to calculate trajectories at distances less than 1000yds, most of these forces can be ignored. However, at real long distances, there are all sorts of things to take into account, not just gravity and atmospheric drag. That's why I suggested the book I did in my first post as it introduces many of these forces one by one and shows how the equation changes. Also, remember that the individual projectile causes huge differences in the trajectory/calculation. Another thing to look up is spin stabilization/destabilization, as funny things start to happen at long ranges. In preparing my seminar I poured over and studied numerous naval ordnance documents, but that is a grueling route to go. Check out the book I recommended as well as naval ordnance docs or the book Peter.Steele recommended. There is no pretty answer to this, and it is the reason we use ballistics calculators as they are more than accurate enough. Many of the forces involved only make a tiny difference at extreme ranges.

[theicecreamdan]

Hm.

I seeeeeem to recall - but I might be sadly mistaken - that most (all?) of this was covered in one of my textbooks from college ... you can still find copies of it out there.

Its also really easy to find a PDF of that one.