Category Archives: Ballistics

Pejsa Formula for Midpoint as a Function of Zero Range

This post will cover Pejsa's formula for the trajectory midpoint as a function of the rifle's zero range. Shooters often have a preferred zero range, like 100 yards or 200 yards. This formula allows the shooter to determine his midpoint range directly from the zero range. The midpoint range can then be used to determine the maximum bullet height above the line of sight, which can be used to determine the maximum bullet placement error. Continue reading

 
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Pejsa Trajectory Midpoint Formula Given a Maximum Projectile Height

Pejsa defines the trajectory midpoint as the range at which the projectile height reaches its maximum (Figure 1). Pejsa's midpoint formula allows you to compute the midpoint given a specific maximum height (Hm). The derivation is straightforward and I will not provide much additional commentary beyond the mathematics itself. Continue reading

 
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Pejsa Bullet Height Versus Distance Formula For a Zeroed Rifle

In this post, I will review Pejsa's development of a formula for the height of a bullet relative to the shooter's line of sight, assuming that the rifle is adjusted to have zero drop at a known range (referred to as the rifle's "zeroed" range). Figure 1 illustrates the trajectory of a bullet fired from a rifle zeroed at a given range. Continue reading

 
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Pejsa's Projectile Drop Versus Distance Formula (Part 3 of 3)

In this post (part 3), I will work an example from Pejsa's "Modern Practical Ballistics 2nd ed." and show that the exact and approximate solutions to the drop differential equation give nearly the same answers. Continue reading

 
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Pejsa's Projectile Drop Versus Distance Formula (Part 2 of 3)

In our previous post, we developed an expression for y' (=dy/dx, Newton's notation) expressed as differential equation in terms of x. We will now solve this equation through the use of an integrating factor. Having solved for y' in terms of x, we can integrate that expression to obtain y(x). Continue reading

 
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Pejsa's Projectile Drop Versus Distance Formula (Part 1 of 3)

I recently have had a number of readers ask me to continue my review of Pejsa's "Modern Practical Ballistics". The last major topic I have left to cover is his formula for the drop of a horizontally‑fired projectile as a function of distance. My plan is to derive the formula and present an example of its use. The derivation is not difficult, but it is a bit long and I will divide my presentation into a couple of posts. Continue reading

 
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Air Rifle Math

Introduction I received an email this weekend from a dad struggling to help his son with a project involving aerodynamic drag and BB gun. I did some quick calculations which I document here. I will try to look at pellets … Continue reading

 
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Ballistic Coefficient Rule of Thumb Example

Quote of the Day Wisdom and experience are built from bricks made from the mud of failure. — Mike Blue I am working on a ballistic simulator and I was looking for some test data. While hunting up some data, … Continue reading

 
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A Problem Solved in Excel and Mathcad

I use both Excel and Mathcad in my daily work. Most people would consider me very proficient in both. I frequently get asked, "Which tool is better?" Like all other interesting questions in Engineering, the answer is "it depends".

As an example, I decided to work a simple problem in both Excel and Mathcad. A number of the advantages and disadvantages of both tools can be seen in this example. The key problem with Excel is its cell-oriented approach. While the cell-oriented approach works for small problems, it has major issue with large problem Continue reading

 
Posted in Ballistics, History of Science and Technology, Military History, Naval History | 2 Comments

Fire Control Formulas from World War 1

Quote of the Day When fascism comes to America, it will be wrapped in the flag carrying the Cross. — Sinclair Lewis Introduction I am reading the book "Dreadnought Gunnery and the Battle of Jutland: The Question of Fire Control". … Continue reading

 
Posted in Ballistics, History of Science and Technology, Military History | 11 Comments