Need suggestions for second book

[Photobug]

I am just finishing up Ryan Cleckner's book Long Range Shooting Handbook. It all was simple and easy to understand so far. I have a background that makes it fairly easy for me to get this. I feel the need to also understand some of the more advanced calculations regarding adjustments needed for temperatures and air density. However a multiple page book on heavy calculations or anything involving calculus might cause my brain to shut down. Is there an intermediate book that will help me move on from this book or a good advanced book that does not get too technical?

Also wanted to double check this graph from the book. The math on the mils at 25 yards seems wrong, either that or I don't understand what i have read so far as well as i thought I did.

 

[KnowNothing256]

The chart is correct. At 100 yards, 1 MOA is 1.047”. At a quarter of the distance, it’s a quarter of the movement on the target.

Wish I could help you on the book, I’m an engineer and have no interest in going down that rabbit hole when there are plenty of programs and apps to do it for you haha.

ETA: Whoops, only looked at the MOA. My bad. Agreed that 1 Mil at 25 yards is 0.9”.

 

[Photobug]

I was thinking about the source of error in the graph and could find no reasoning behind it but then realized the adjustment would make sense at 10 yards?

 

[6.5SH]

It is wrong, that result would be 0.1 Mil at 100 yards.

1 full Mil would be 0.9" at 25 yards

 

[Photobug]

The chart is correct. At 100 yards, 1 MOA is 1.047”. At a quarter of the distance, it’s a quarter of the movement on the target.

Wish I could help you on the book, I’m an engineer and have no interest in going down that rabbit hole when there are plenty of programs and apps to do it for you haha.

I plan on using an app someday but feel you need to be able to do the math or at least understand what is happening under the hood of the app. I used to teach navigation and feel you shouldn't use a GPS until you can navigate on paper.

 

[6.5SH]

I'd suggest Frank's book as well as the many articles here on the site.

 

[KnowNothing256]

I plan on using an app someday but feel you need to be able to do the math or at least understand what is happening under the hood of the app. I used to teach navigation and feel you shouldn't use a GPS until you can navigate on paper.

The problem is that pen-and-paper navigation is 7th-grade geometry, so it’s reasonable to expect a person new to the subject to grasp it reasonably quickly. External ballistics is the purview of PhD theses and DoD grants. I don’t know how air density is mathematically related to ballistic drag, but I can tell you that air density changes with temperature according to the following equation:

Density = Pressure / [Gas Constant * Temperature]

This is a derivation of the ideal gas law, that states PV = nRT where P is pressure, V is volume, n is number of moles of gas, R is the universal gas constant, and T is absolute temperature (Kelvin or Rankine, you can’t use Fahrenheit or Celsius). Density is moles per volume (moles and mass are proportional to each other assuming constant chemical composition), so n/V = P/RT. Even more simply, you can manipulate the ideal gas law to show that density at T2 can be calculated from density at T1 by the equation Den2 = Den1 * T1 / T2. So if temp goes up, density goes down.

Relative humidity’s effects are harder to show with an equation, but put simply, water vapor weighs less than dry air. So for every bit of water that is evaporated into dry air at a given pressure, the density of that air at the same pressure will go down, leading to less drag. Sorry, don’t have a great book reference for this either, but Google should get you a better explanation. For now, a graph:

External ballistics is freaking complicated at a mathematical level, but I hope I explained the temp and humidity effects well enough to at least get you a gut feel for which direction they move the ballistics: if either temp or humidity go up, drag goes down (same story for altitude/pressure).

 

[Newbie2020]

1. Frank Galli’s @lowlight book should be required reading for anyone shooting long range.

2. Brian Litz’s books should be read after you finish Frank and Ryan’s books.

 

[Photobug]

The problem is that pen-and-paper navigation is 7th-grade geometry, so it’s reasonable to expect a person new to the subject to grasp it reasonably quickly. External ballistics is the purview of PhD theses and DoD grants. I don’t know how air density is mathematically related to ballistic drag, but I can tell you that air density changes with temperature according to the following equation:

Density = Pressure / [Gas Constant * Temperature]

This is a derivation of the ideal gas law, that states PV = nRT where P is pressure, V is volume, n is number of moles of gas, R is the universal gas constant, and T is absolute temperature (Kelvin or Rankine, you can’t use Fahrenheit or Celsius). Density is moles per volume (moles and mass are proportional to each other assuming constant chemical composition), so n/V = P/RT. Even more simply, you can manipulate the ideal gas law to show that density at T2 can be calculated from density at T1 by the equation Den2 = Den1 * T1 / T2. So if temp goes up, density goes down.

Relative humidity’s effects are harder to show with an equation, but put simply, water vapor weighs less than dry air. So for every bit of water that is evaporated into dry air at a given pressure, the density of that air at the same pressure will go down, leading to less drag. Sorry, don’t have a great book reference for this either, but Google should get you a better explanation. For now, a graph:
View attachment 7607617

External ballistics is freaking complicated at a mathematical level, but I hope I explained the temp and humidity effects well enough to at least get you a gut feel for which direction they move the ballistics: if either temp or humidity go up, drag goes down (same story for altitude/pressure).

You explained it perfectly well. Now that i have the formulas and the graphs, I don't need any books I can derive my own calculation.

As a professional pilot and as a flight instructor, I had to work with air density calculations so figure I could get it. At least all the theories and how it relates to ballistics so far are easily understood. The level of complexity in calculating a landing or takeoff distance at a given weight is a whole lot easier than some of the math you are showing me. When done posting this, I will be shopping for my next book and a ballistic calculator app.

 

[308pirate]

You explained it perfectly well. Now that i have the formulas and the graphs, I don't need any books I can derive my own calculation.

As a professional pilot and as a flight instructor, I had to work with air density calculations so figure I could get it. At least all the theories and how it relates to ballistics so far are easily understood. The level of complexity in calculating a landing or takeoff distance at a given weight is a whole lot easier than some of the math you are showing me. When done posting this, I will be shopping for my next book and a ballistic calculator app.

As you get deeper into the practical applications of long range rifle marksmanship, you'll realize that the time you wasted studying theory would have been better spent learning how to build effective shooting positions, learning how to flawlessly execute the fundamentals of marksmanship, and learning how to read clues around you to come up with an effective estimate of what the wind will do to the bullet.

I say this from the point of view of someone who has the educational and professional background to delve into the minutia but has the wisdom to know better.