Excellent.

I have been meaning to get some actual ballistic coefficients for some of my favourite ammo's since although you can find them posted for musket round balls they are obviously in a much different drag regime. Not got round to it yet since the leaves on the trees are in the way of me using the chronograph down my normal shooting lane. Guessing since round balls are simple projectiles modelling might get pretty close anyway.

My main question isn't "effective range" but the "Hazardous" range essentially just the maximum range the ball will still be in the air over fairly flat ground and the retained energy since until it hits the ground it could hit something. I believe it's likely approximately 300m with some of my setup's and to take the .395 lead as an example I believe it may still have a damaging amount of energy when it comes back to land. (Yes I'm already mixing units)

Will stay posted it's interesting.

 

Yeah, I think ballistic coefficient is pretty easy to get from here, since I already have all of the parameters. Now the actual coefficient is going to depend on the pellet speed, because the air resistance changes. Do you have:

• A particular set of ammo you want me to calculate coefficients for?
• A particular set of speeds you want me to calculate coefficients for? Maybe speeds between 100 and 300 ft / sec in 10 ft / sec intervals?

 

Great work bool,

Currently Iam using Hawkes chair gun pro (free download) to work out the ballistics coefficeint for steel balls.

I had found this equation that works with lead balls.

B.C. = Ball Wt. in grains divided by (10640 x ball dia. x ball dia.)

B.C. standing for ballistics coefficient. All data in the math is in Imperial. Example, 8mm steel.
32.25 / ( 10640 x 0.314 x 0.314) = BC 0.0307

Ballistic Coefficient of the round ball.

I guess this belongs under the " for what it's worth " catagory, but I personally find such things interesting. I have said before, and I will say it again, that energy figures, as computed today by using velocity squared, is practically useless in the real world of hunting with muzzleloaders...

www.muzzleloadingforum.com

However this equation does not seem to work for steel balls, lead being a different mass than steel. If you could give me the equation (as above) that works for steel balls it would be very much appreciated and a great contribution to the community. Thankyou.

https://www.slingshotforum.com/threads/ballistics-coefficients-for-steel-round-balls.127600/?post_id=1467120#post-1467120

 

Thanks for posting this. First I'll try to check if my code can reproduce the equation for lead balls. If that works it's a great independent validation. Then I can calculate some new coefficients that might work for steel and clay.

 

Thanks bool

I will follow your posts.

 

Outstanding bool,

I might be wrong, probably. It might be the minutes per angle / clicks with my scope rail that was not calibrated. My shooting range is flooded and I cant redo the measurements with the chronograph and ammo drop at ranges at this time. What ever I wrote down is long gone and just save the calculated BC into a chairgun profile.

Thankyou, if you are correct you made my day. Great work. Good luck with you shooting.

 

Thanks. I do not have a chronograph, nor do I have a bunch of different types of ammo (I literally started 14 days ago), so I cant take any measurements to check. But maybe you have or can collect some data that we can use to validate this.

Does anyone have any recommendations on a decently accurate and affordable chronograph? I was thinking about just marking out 10 m and timing the flight time with my phone (marking the start / stop with the sound of the bands snapping and hitting the target), then back-calculating to get the launch speed, but that might not be as accurate.

Next post I am making some drop tables!

 

very cool discussion. I m not sure I can help. But I think a slingshot would be OK under 30 meters max range. Bcause you need a shot that is able to do a flat trajectory, which is not going to happen if you shoot 11mm balls longer than 10 meters. 8mm balls wlil probly go better for longer distance. I personally try to target things under 10 meters while im practicing. And when I will be able to do hit after hit after hit, consistently, I will then move on to target moving things. And then target things at 15 meters and so on.

 

The ones on Aliexpress. I have used one of those for years and it has worked just fine.

 

Introduction

Whats up slingshot people!

I bought my first slingshot (Scout LT) a couple weeks ago, and whatever I lack in slingshot skill I can make up for in modeling ability. So while I still can't build a catch box big enough to catch my stray shots, I can tell you very precisely where those shots would end up or how I should have fired them in order to have a direct hit.

I saw this video on YouTube where Fowler hit a 6" target from 100 yards in about 20 shots. I've also seen Chinese style slingshots with adjustable "sights" that supposedly help hit targets at range. This all got me asking: what is the maximum effective range of a slingshot, and what are the factors (human, equipment, or environmental) that limit it?

So for my first posts on the forum, I am going to focus on slingshot ballistics where I'll calculate all kinds of things about how slingshot ammo flies through the air. Because there is a lot to talk about, I am going to break this up into a series of posts:

1. Introduction and methodology (this post)
2. Maximum ranges of various slingshot ammo and sighting tables
3. How steady does your arm need to be?
4. Energy loss from drag and the maximum effective hunting range
5. Wind, temperature, and air pressure effects

I have no idea if this is interesting to any of you. I am just some nerd that's nerding out about slingshots. But if it is interesting or useful, give me some feedback. I've written some good code for this, and it's probably easy for me to look into other ammo types, environmental conditions, and other scenarios than the ones I cover here.

The code is publicly available on Github. Follow the repo here and I'll keep it up to date as I add new features. If you can code Python I am open to contributions. Just fork and pull request.

Methodology

Slingshot ballistics is very similar to the physics you learned in high school. Ammo moves in a parabolic arc that starts at the firing position and ends at the impact point. We are going to be slightly more sophisticated than high-school physics by including air resistance. As ammo travels through the air it "drags" the air behind it, creating eddy currents. Because it takes energy to move the air, this energy comes from the kinetic energy of the ammunition. As a result, your shot slows down as it flies through the air. From the shooter's perspective, the ammo drops faster towards the end of it's flight. These effects are super important for long range shots.

Alright, this next section is probably the most technical of everything I am going to cover in this series. I am putting it here so that the people who know this stuff can check my work, but you don't really need to understand it in order to understand what follows. The take away is I was very careful to calculate drag forces accurately.

For those in the know, this is what I did:

• I am only considering smooth, spherical ammunition.
• The drag force on the ammunition is modeled with the drag equation. The reference area is the cross-section of the sphere.
• The mass-density of air calculated using the ideal gas law. This lets me consider effects that change the density of air, such as shooting on a cold day or shooting at high altitude where the air is thinner.
• The mass of the ammunition is calculated from the ammunition diameter and material density (steel, lead, clay, etc.).
• The drag coefficient is tricky to model (more on that below).
• I solved the ODE for F = ma numerically using the RK45 algorithm. The solver I am using lets me hone in on specific points in the trajectory, such as the exact moment when the ammunition passes through a paper target.

The drag coefficient

I promise, this is the only fluid mechanics. The drag coefficient is actually not a constant, and actually depends on the speed of ammunition relative to the air (the flow speed). More precisely, the drag coefficient is a function of the Reynolds number. If you've never heard of the Reynolds number, just know it's proportional to the flow speed and it allows us to model the flow regardless of the fluid viscosity. Flow through air and oil are modeled with the same sets of equations, but you might have a different Reynolds number describing the flow.

The graph below plots the drag coefficient of a smooth sphere versus the Reynolds number.

• The black points are experimental data that I extracted from a plot from Munson, Young, and Okiishi 'Fundamentals of Fluid Mechanics', Wiley, 1990.
• I smoothed the logarithms of the experimental data using Locally Weighted Scatterplot Smoothing (Lowess). I then converted the smoothed logarithms back to linear space. These points are plotted in red.

• Introduction
  
  Whats up slingshot people!
  
  I bought my first slingshot (Scout LT) a couple weeks ago, and whatever I lack in slingshot skill I can make up for in modeling ability. So while I still can't build a catch box big enough to catch my stray shots, I can tell you very precisely where those shots would end up or how I should have fired them in order to have a direct hit.
  
  I saw this video on YouTube where Fowler hit a 6" target from 100 yards in about 20 shots. I've also seen Chinese style slingshots with adjustable "sights" that supposedly help hit targets at range. This all got me asking: what is the maximum effective range of a slingshot, and what are the factors (human, equipment, or environmental) that limit it?
  
  So for my first posts on the forum, I am going to focus on slingshot ballistics where I'll calculate all kinds of things about how slingshot ammo flies through the air. Because there is a lot to talk about, I am going to break this up into a series of posts:
  
  1. Introduction and methodology (this post)
  2. Maximum ranges of various slingshot ammo and sighting tables
  3. How steady does your arm need to be?
  4. Energy loss from drag and the maximum effective hunting range
  5. Wind, temperature, and air pressure effects
  
  I have no idea if this is interesting to any of you. I am just some nerd that's nerding out about slingshots. But if it is interesting or useful, give me some feedback. I've written some good code for this, and it's probably easy for me to look into other ammo types, environmental conditions, and other scenarios than the ones I cover here.
  
  The code is publicly available on Github. Follow the repo here and I'll keep it up to date as I add new features. If you can code Python I am open to contributions. Just fork and pull request.
  
  Methodology
  
  Slingshot ballistics is very similar to the physics you learned in high school. Ammo moves in a parabolic arc that starts at the firing position and ends at the impact point. We are going to be slightly more sophisticated than high-school physics by including air resistance. As ammo travels through the air it "drags" the air behind it, creating eddy currents. Because it takes energy to move the air, this energy comes from the kinetic energy of the ammunition. As a result, your shot slows down as it flies through the air. From the shooter's perspective, the ammo drops faster towards the end of it's flight. These effects are super important for long range shots.
  
  Alright, this next section is probably the most technical of everything I am going to cover in this series. I am putting it here so that the people who know this stuff can check my work, but you don't really need to understand it in order to understand what follows. The take away is I was very careful to calculate drag forces accurately.
  
  For those in the know, this is what I did:
  

  • I am only considering smooth, spherical ammunition.
  • The drag force on the ammunition is modeled with the drag equation. The reference area is the cross-section of the sphere.
  • The mass-density of air calculated using the ideal gas law. This lets me consider effects that change the density of air, such as shooting on a cold day or shooting at high altitude where the air is thinner.
  • The mass of the ammunition is calculated from the ammunition diameter and material density (steel, lead, clay, etc.).
  • The drag coefficient is tricky to model (more on that below).
  • I solved the ODE for F = ma numerically using the RK45 algorithm. The solver I am using lets me hone in on specific points in the trajectory, such as the exact moment when the ammunition passes through a paper target.

  [*]
  The drag coefficient
  
  I promise, this is the only fluid mechanics. The drag coefficient is actually not a constant, and actually depends on the speed of ammunition relative to the air (the flow speed). More precisely, the drag coefficient is a function of the Reynolds number. If you've never heard of the Reynolds number, just know it's proportional to the flow speed and it allows us to model the flow regardless of the fluid viscosity. Flow through air and oil are modeled with the same sets of equations, but you might have a different Reynolds number describing the flow.
  
  The graph below plots the drag coefficient of a smooth sphere versus the Reynolds number.
  
  

  
  
  

  • The black points are experimental data that I extracted from a plot from Munson, Young, and Okiishi 'Fundamentals of Fluid Mechanics', Wiley, 1990.
  • I smoothed the logarithms of the experimental data using Locally Weighted Scatterplot Smoothing (Lowess). I then converted the smoothed logarithms back to linear space. These points are plotted in red.
  • I use cubic interpolation to interpolate between smoothed points. The interpolated curve is in blue.
  • Later, I found a good empirical approximation by Cheng that fit the experimental data all the way to the drag crisis which occurs above Re ~ 1e5. The Cheng model is plotted in green.

  [*]
  Since all of the slingshot problems I've seen so far operate below the drag crisis, I just use the Cheng model in most of my calculations. It tends to be more numerically stable and gives effectively the same results as the interpolated model.
  
  TL;DR
  

  • I am new here. I am a terrible shot, but I'm good at math.
  • I am writing a series of posts about how slingshot ammo flies through the air.
  • Feedback welcome. Tell me what you want me to calculate.

  [*]

  Appears to be boo-lean to me, that's my calculus of it all ... ; ) ; )
• Later, I found a good empirical approximation by Cheng that fit the experimental data all the way to the drag crisis which occurs above Re ~ 1e5. The Cheng model is plotted in green.I use cubic interpolation to interpolate between smoothed points. The interpolated curve is in blue.

Since all of the slingshot problems I've seen so far operate below the drag crisis, I just use the Cheng model in most of my calculations. It tends to be more numerically stable and gives effectively the same results as the interpolated model.

TL;DR

• I am new here. I am a terrible shot, but I'm good at math.
• I am writing a series of posts about how slingshot ammo flies through the air.
• Feedback welcome. Tell me what you want me to calculate.

"Back in the day" I was a photographer for a magazine known as "Models Showcase". I photographed "Runway" models in scant attire.

 

Introduction

Whats up slingshot people!

I bought my first slingshot (Scout LT) a couple weeks ago, and whatever I lack in slingshot skill I can make up for in modeling ability. So while I still can't build a catch box big enough to catch my stray shots, I can tell you very precisely where those shots would end up or how I should have fired them in order to have a direct hit.

I saw this video on YouTube where Fowler hit a 6" target from 100 yards in about 20 shots. I've also seen Chinese style slingshots with adjustable "sights" that supposedly help hit targets at range. This all got me asking: what is the maximum effective range of a slingshot, and what are the factors (human, equipment, or environmental) that limit it?

So for my first posts on the forum, I am going to focus on slingshot ballistics where I'll calculate all kinds of things about how slingshot ammo flies through the air. Because there is a lot to talk about, I am going to break this up into a series of posts:

1. Introduction and methodology (this post)
2. Maximum ranges of various slingshot ammo and sighting tables
3. How steady does your arm need to be?
4. Energy loss from drag and the maximum effective hunting range
5. Wind, temperature, and air pressure effects

I have no idea if this is interesting to any of you. I am just some nerd that's nerding out about slingshots. But if it is interesting or useful, give me some feedback. I've written some good code for this, and it's probably easy for me to look into other ammo types, environmental conditions, and other scenarios than the ones I cover here.

The code is publicly available on Github. Follow the repo here and I'll keep it up to date as I add new features. If you can code Python I am open to contributions. Just fork and pull request.

Methodology

Slingshot ballistics is very similar to the physics you learned in high school. Ammo moves in a parabolic arc that starts at the firing position and ends at the impact point. We are going to be slightly more sophisticated than high-school physics by including air resistance. As ammo travels through the air it "drags" the air behind it, creating eddy currents. Because it takes energy to move the air, this energy comes from the kinetic energy of the ammunition. As a result, your shot slows down as it flies through the air. From the shooter's perspective, the ammo drops faster towards the end of it's flight. These effects are super important for long range shots.

Alright, this next section is probably the most technical of everything I am going to cover in this series. I am putting it here so that the people who know this stuff can check my work, but you don't really need to understand it in order to understand what follows. The take away is I was very careful to calculate drag forces accurately.

For those in the know, this is what I did:

• I am only considering smooth, spherical ammunition.
• The drag force on the ammunition is modeled with the drag equation. The reference area is the cross-section of the sphere.
• The mass-density of air calculated using the ideal gas law. This lets me consider effects that change the density of air, such as shooting on a cold day or shooting at high altitude where the air is thinner.
• The mass of the ammunition is calculated from the ammunition diameter and material density (steel, lead, clay, etc.).
• The drag coefficient is tricky to model (more on that below).
• I solved the ODE for F = ma numerically using the RK45 algorithm. The solver I am using lets me hone in on specific points in the trajectory, such as the exact moment when the ammunition passes through a paper target.

The drag coefficient

I promise, this is the only fluid mechanics. The drag coefficient is actually not a constant, and actually depends on the speed of ammunition relative to the air (the flow speed). More precisely, the drag coefficient is a function of the Reynolds number. If you've never heard of the Reynolds number, just know it's proportional to the flow speed and it allows us to model the flow regardless of the fluid viscosity. Flow through air and oil are modeled with the same sets of equations, but you might have a different Reynolds number describing the flow.

The graph below plots the drag coefficient of a smooth sphere versus the Reynolds number.

• The black points are experimental data that I extracted from a plot from Munson, Young, and Okiishi 'Fundamentals of Fluid Mechanics', Wiley, 1990.
• I smoothed the logarithms of the experimental data using Locally Weighted Scatterplot Smoothing (Lowess). I then converted the smoothed logarithms back to linear space. These points are plotted in red.
• I use cubic interpolation to interpolate between smoothed points. The interpolated curve is in blue.
• Later, I found a good empirical approximation by Cheng that fit the experimental data all the way to the drag crisis which occurs above Re ~ 1e5. The Cheng model is plotted in green.

Since all of the slingshot problems I've seen so far operate below the drag crisis, I just use the Cheng model in most of my calculations. It tends to be more numerically stable and gives effectively the same results as the interpolated model.

TL;DR

• I am new here. I am a terrible shot, but I'm good at math.
• I am writing a series of posts about how slingshot ammo flies through the air.
• Feedback welcome. Tell me what you want me to calculate.

Were you a runway model?

THWACK!

 

um could you do this with darts?