Category Archives: Ballistics

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

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

Another Interpretation of the Ballistic Coefficient

Introduction I love to look for physical interpretations of various constants. Sometimes it is impossible to come up with an interpretation, but such is not the case for the ballistic coefficient. This morning I read a very solid piece of … Continue reading

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16-in Battleship Gun Ballistic Coefficient

A projectile with a large ballistic coefficient is less affected by drag than a projectile with a smaller ballistic coefficient. We can use the the ballistic coefficient to compare the effect of drag on different projectiles. A 16-inch projectile goes so much farther than a rifle bullet because the drag on the 16-inch projectile is relatively small compared to its momentum. Ultimately, this is because mass increases by the cube of the projectile dimensions and drag increases by the square of the projectile dimensions. This means that larger projectiles tend to have higher ballistic coefficients and drag has less effect. Continue reading

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