Ballistic apps and potential energy via gravity

[Scotchmo]

Igor replied to my request and said "I will think how it can be done"....because (in my opinion) integrating such effects is not straightforward and the current apps that achieve this calculation probably relied on Doppler data to work out a expression or equation that lines up with their data. Wish I had the answers for him because it's not that he isn't willing, rather the solution isn't known or widespread knowledge, and heck, I'd like to integrate it into my personal one but...math is hard.

-Matt

I don’t see why it would take a Doppler data.

There is a gain or loss in projectile energy as the target elevation is raised or lowered. Very easy to calculate that. Since I would be hard pressed to do the analytics, I would be using numerical integration, probably every inch (or cm).

Over the entire distance of 600yds, when compared to a level shot, the 171gr projectile loses about 11.4 additional FPE on a +15 degree shot and gains that amount on a -15 degree shot. Those losses or gains can be factored in incrementally along the trajectory path, and the corresponding velocity adjusted accordingly.

There is also the air density changes that must be accounted for as the projectile rises or falls. That can also be accounted for incrementally via numerical integration.

It’s not an exact solution, but probably better than ignoring it.

 

[Stubbers]

I don’t see why it would take a Doppler data.

There is a gain or loss in projectile energy as the target elevation is raised or lowered. Very easy to calculate that. Since I would be hard pressed to do the analytics, I would be using numerical integration, probably every inch (or cm).

Over the entire distance of 600yds, when compared to a level shot, the 171gr projectile loses about 11.4 additional FPE on a +15 degree shot and gains that amount on a -15 degree shot. Those losses or gains can be factored in incrementally along the trajectory path, and the corresponding velocity adjusted accordingly.

There is also the air density changes that must be accounted for as the projectile rises or falls. That can also be accounted for incrementally via numerical integration.

It’s not an exact solution, but probably better than ignoring it.

If you don't see why, please provide the math needed here mate. Otherwise, maybe you don't see why because you don't comprehend why...

A lot of math is derived from data collected by instruments such as Doppler radar, which many modern ballistic formulas are based on...

-Matt

 

[Scotchmo]

If you don't see why, please provide the math needed here mate. Otherwise, maybe you don't see why because you don't comprehend why...

A lot of math is derived from data collected by instruments such as Doppler radar, which many modern ballistic formulas are based on...

-Matt

I comprehend it and I see why some might think they need that data.

As I said, I would not attempt to do the analytical integration, because as you said “math is hard”. Well, at least calculus is hard. That’s why I would use numerical integration. So instead of solving for some complex integral, it only requires a relatively simple formula that can be more easily implemented using a numerical solution of sufficiently small increments.

delta(FPE)=sin(angle) x grains/7000 x increment

Here is a simplified example for a single segment where the trajectory angle is 15 degree. For further simplification, I’ll use 1 foot for the increment, rather than 1in (or 1cm).

delta(FPE)=sin(15) x 171gr/(7000gr/pound) x 1foot

So for every foot of travel closer to the target, 0.063fpe is added (or subtracted) to/from the energy balance of the projectile.

The result is that the projectile will slow down a little faster on an inclined shot. And just the opposite for a decline shot.

As pointed out earlier, this will be partially counteracted by the changing density, which should also be included in the numerical integration. But I would guess, for most cases, that over half of that potential energy to/from kinetic energy conversion would show up as a corresponding increase or decrease in projectile velocity at the target.

 

[Stubbers]

I did the math...my ballistic solver now includes this effect. I also added in spin drift (active in below calcs), Coriolis and Eotvos effect (disabled), and magnus effect (disabled). However I am not currently calculating density change along the trajectory because you'd have to shoot at very steep angles, nearly like a rocket, to get substantial density change, however that is my next step...because I like challenges.

*Edit* Added tracker to density changes over the trajectory for every 50 feet, which effects which reference law is taken from the drag tables.

I even allow you to include the wind in your zero in case you're zeroing in the wind at your zero, which I don't think most ballistic solvers allow you to include. Took me about 3 days to convert my old ballistic solver that used constant cD to one that uses current cD values provided by Ballistic Boy.

Shown below is -10degree, 0 degree, and +10 degree with a 33.95 traveling 876 fps, 500 yards, 10 yard zero.

Even predicts the changes in FPE just as well.

-Matt

 

[JungleShooter]

I did the math...my ballistic solver now includes this effect. I also added in spin drift (active in below calcs), Coriolis and Eotvos effect (disabled), and magnus effect (disabled). However I am not currently calculating density change along the trajectory because you'd have to shoot at very steep angles, nearly like a rocket, to get substantial density change, however that is my next step...because I like challenges.

*Edit* Added tracker to density changes over the trajectory for every 50 feet, which effects which reference law is taken from the drag tables.

I even allow you to include the wind in your zero in case you're zeroing in the wind at your zero, which I don't think most ballistic solvers allow you to include. Took me about 3 days to convert my old ballistic solver that used constant cD to one that uses current cD values provided by Ballistic Boy.

View attachment 501442

Shown below is -10degree, 0 degree, and +10 degree with a 33.95 traveling 876 fps, 500 yards, 10 yard zero.

View attachment 501432


View attachment 501434
View attachment 501436
View attachment 501438


Even predicts the changes in FPE just as well.

-Matt

Wow!
Matt, that is a loud, approving WOW that's coming from my airgunner's soul....!

So glad there are people who are not like me (they did not flunk physics and are able to do mental miracles like you)!


Of course, now we all want your program/app!!
For iPhone, Android, Mac, and Windows. Linux maybe, too.
We can never get enough! (n + 1 applies to everything....)


Matt, rock on, calculate on, shoot on!

Matthias

 

[Scotchmo]

I did the math...my ballistic solver now includes this effect….

-Matt

That’s good. I’m curious what approach you took. Solving for the integral or numerical integration as I would do? And did you use the potential energy conversion to/from kinetic energy?

 

[Stubbers]

That’s good. I’m curious what approach you took. Solving for the integral or numerical integration as I would do? And did you use the potential energy conversion to/from kinetic energy?

Gy = GRAVITY * Math.cos(DegtoRad(ShootingAngle + ZeroAngle))
Gx = GRAVITY * Math.sin(DegtoRad(ShootingAngle + ZeroAngle))


-Matt

 

[Scotchmo]

Gy = GRAVITY * Math.cos(DegtoRad(ShootingAngle + ZeroAngle))
Gx = GRAVITY * Math.sin(DegtoRad(ShootingAngle + ZeroAngle))


-Matt

Ok. I think I see where you are going with that.

 

[Stubbers]

Ok. I think I see where you are going with that.

vx = velocity on the x-axis
vy = velocity on the y-axis
dv = drag value for the current velocity
dt = time component

dvx = -(vx / v) * dv
dvy = -(vy / v) * dv

vx += dt * dvx + dt * Gx
vy += dt * dvy + dt * Gy

-Matt