Trajectory,Trigonometry,Ballistics?

Hello all, now this post is a bit odd and doesnt really have everything to do with sl, rather than types of math and calculations, I posted here in hopes that somone could help me out here.
I have been researching on how to calculate cannon fire by angle, power distance and also calculate wind into the equation, but I can not seem to find the correct equation, i'm not even toataly sure i'm useing the right catalyst to go about solving this i'm not sure if it would be classified as either trajectory,trigonometry or ballistics, I was also looking at a triangulator calculator but alas no wind entry, does anyone know of any type of calculator or anythign to help me solve this? any help and or feedback is higly appreciated

There is a good page about the physics equations of such matters at http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

Foolish Frost's SL forum website SLDrama.com has a forum called Scripting and Physics, which I believe is where I got that link from.

thanks that super helpful! i'v seen some things like this in my research but not quite like that, however, it doesnt have one that calculates wind into the equation thus my search continues, but again thats a great link!

Hi there,

I saw your query and checked with someone I know who is into gunsmithing and paintballing. He says to check out the Tinker's Guild tech Forum, and there should be someone there who can help you.

thanks mik! i was searching for a calculator forum earler to post in and couldnt find an active one, thats why i took a shot in the dark and posted here, i have seen some sites on gunsmithing and reloaders/ballistic software in my search also, so i think this may be just what i need, thank you much for your help!

Maybe this might be helpful.
http://www.phy.davidson.edu/StuHome/jocampbell/projectile/projectile.ProjectileControl.html

also I forgot to mention that what i'm looking for is the end position of the ballistic target, where exactly it will land when calculated against angle, power, distance and wind

I was particularly bad at physics, but as I recall, trajectories of projectiles involve understanding simple kinematics and dynamics first. Some of which are explained in the links people have suggested. However, most of these equations simplified the calculation by assuming that the projectile is travelling through a vacuum.

To factor in in wind, you need to understand the fluid dynamics part of physics. Particularly, the calculation of drag (not the crossdressing kind). Specifically, you need to find your projectile's drag coefficient so that you can find the force applied by wind using the traditional drag force formula for non-laminar flow.

F=-1/2 AC pv2 (have no idea how to write this in equations)

F=force from drag
A=cross sectional area of the projectile
C=drag coefficient
p=density of air
v=wind velocity

the 2 is a squared

theres a minus there because its a reverse force applied dragging the projectile
The drag coefficient for a typical sphere is 0.1 I think. Crappy boxy things are about 2.0.

When you have obtained the force from wind and wind drag, you can them pump the value into the regular F=ma calculations from kinematics/dynamics.

thanks cotton this may be just what I need, I didnt relise that drag=wind, I guess thats what I get for staying up days racking my brain on a simulation haha.

Unfortunately the skills necessary to calculate the effects of drag on a moving projectile without resorting to numerical approximation methods (not that there's anything wrong with that) are quite beyond even most people who aren't particularly bad at physics.

The relevant wind velocity is the apparent wind velocity, which is dependent on the projectile velocity (even if there is zero "wind" there is still air resistance as soon as the projectile is moving), which turns the whole mess into a nasty differential equation.

If the projectile is nonspherical, it gets worse, because both the apparent cross-sectional area and the drag coefficient change over time depending on its profile toward the direction of motion.

It's really, really, really hard to get right, which is why all the intro books pretend it doesn't exist.

well this is not for a real life situation but a computer simulation, so i dont think that would be the case because no areodynamic friction, just a number accounting for drag-wind

In that case there are generally all sorts of corners you can cut to simplify it and make it run faster. Just tweak the simple ballistic formula so that you get peak range at a cannon inclination of about 25-30 degrees and nobody will ever notice the difference.

For calculating the effects of wind in that scenario, you'd have to explain more about your model and what you're interested in:

- only where it lands
- the positions it travels through (without regard to time)
- the position as a function of time
- velocity as a function of time

I tried to simulate lift and drag for my paper aeroplane thrower, but it was a pain in the backside. For a simple projectile I'd advise just factoring in a force proportional to the square of the velocity, acting in the opposite direction, for drag, with the co-efficient being whatever seems to produce a projectile that moves correctly Proper aerodynamics are hideous to deal with.

(The paper aeroplane is free and the script is open, by the way - if anyone wants to see it, it's in my freebie box in Caledon.)

this is what i need, and this isnt for secondlife by the way

so for example I need to be able to have power distance angle and wind as the variables then have a calculation of where the trajectory will land

Oh, missed that. End position is dead easy to approximate, as long as the ground is flat.

Just do it the regular way (assuming no wind, d=sin(2*theta)*(v^2)/g ) and treat that as the magnitude of a vector in the firing direction. Then create a second vector representing the wind direction and velocity, multiply it by a tweakable variable between 0 and 1 that you can call CoD "coefficient of drag."

Add the two vectors, look at the results, and tweak the CoD variable until you get results you like.

what if your dealing with non flat lands/mountains valleys ect..

At a minimum, you'd have to construct the flight parabola and either solve for the intersection with the function representing the ground, or, if you don't have a continuous function for the ground, step through the flight parabola until there's a collision.

You can still tack the wind modification on at the end without complicating too much, with the caveat that by applying the wind effect at the end of flight, you'd miss hypothetical cases like a narrow ledge where the wind would have blown the cannonball around (or onto) it.

If you want to cover those edge cases, then it's no longer really true that you only want an end position, and you're back to differential equations and/or numerical approximations.

I'm sure you're using some spreadsheet to some extent, but if you're a student constantly doing projects like these, I suggest trying some software to help with the calculations like Mathematica that assists with plots of all kinds of equations. I think they have a student edition.

There is also a software called 'Working Model' from here

http://www.design-simulation.com/

It helps with simulating dynamics as well as mechanical models that involve springs, pulleys, weights, etc. Its kind of fun to play with.

This shouldn't be too difficult actually. Use F=ma in conjunction with some basic aero equations. For drag effects, while it's true that crosswind would have effects on different shapes in RL, you could use approximations. You could also have the projectile calculate altitude and run a simple calculation on air density (similar to the real atmosphere) which then plugs into Bernoulli's Equation which modifies the Drag (you just set the Cd which is unchanging).

Stuff from the top of my head now (been years)...

start off with the explosive Force and the projectile Mass. You get Acceleration. From that you have initial velocity at an angle Theta. You use trig to get components for both Force and Velocity (F horiz and F vert; V horiz and V vert). You know one condition which is that the vertical velocity will eventually be 0.00 at the top of the arc. You also know that the Force component at that point related to Potential Energy is maximized (in other words, at the highest point, the project's vertical Force component is max'd). You also know the end conditions (I'll let you figure those out). From those you get probably 3 or 4 related equations. Solve them. Assume no Drag for your first pass to make it easier. Then plug in the Drag. Drag is related to shape which is related to Pressure. Pressure is defined as Force/Area. Concern yourself with Dynamic Pressure (not Total Pressure, unnecessary). You should find stuff online explaining how that works (usually just treated as P = 0.5(rho)V**2 where rho is atmospheric density and V is the velocity). You have the projective cross sectional area so you have Force. Some online resources should get you through the rest. Have fun.