Category Archives: Ballistics

BB Ballistic Coefficients

Posted on 29-December-2020 by mathscinotes

A number of years ago, I was asked by a father to assist him and his son with a science project that involved calculating the ballistic coefficient of a BB gun projectile. I provide dthis father-son duo with the required calculations (documented here) and the answer I obtained seemed reasonable. Continue reading →

Posted in Ballistics, Excel | Comments Off on BB Ballistic Coefficients

Battleship Shell Size Comparison

Posted on 26-January-2020 by mathscinotes

During some routine research on battleships, I encountered some photos on the web that I thought were worth sharing here. My hope with these photos is to give readers a feel for the size of these guns and their projectiles. Continue reading →

Posted in Ballistics, Naval History | 1 Comment

Earth's Curvature and Battleship Gunnery

Posted on 20-December-2017 by mathscinotes

I must admit that I am a bit of a battleship junkie. I have been reading some old US Navy manuals on battleship fire control, which discuss the various effects that must be corrected for to ensure accurate fire (Figure 1). In this post, I want to examine how the curvature of the Earth affected the gunnery direction. Curvature corrections are only needed for very long-range artillery. Continue reading →

Posted in Ballistics, Naval History | 102 Comments

Recoil Calculation Example

Posted on 21-May-2017 by mathscinotes

I have been reading about the US Air Force's battle to retire the A-10 Warthog (Figure 1). The USAF has never cared for the A-10 and has made a number of attempts to replace it with either the F-16 or the F-35. During my reading, I saw the following statement about the recoil of it 30 mm Gatling gun, and the impact of this recoil on the A-10's speed. Continue reading →

Posted in Ballistics, Military History | 2 Comments

Drag Coefficient From A Ballistic Drop Table

Posted on 8-February-2016 by mathscinotes

I thought it might be interesting show how you can approximate the drag coefficient for a bullet given a standard bullet velocity versus distance table. The folks at Barnes have put together a very nice discussion of how they go about characterizing a projectile using Doppler radar data. They also created an excellent infographic for a common hunting round showing the velocity versus distance table, actual drag coefficient, and G1/G7 reference drag coefficients (Figure 1). I thought I would take their table data and use that data to generate the drag coefficient chart. Since my data is limited, I do not expect a perfect reconstruction, but it should be close. Continue reading →

Posted in Ballistics | 1 Comment

Derivation of Pejsa Point-Blank Range Formula

Posted on 11-January-2016 by mathscinotes

A reader asked me if I could work through Pejsa's formulas related to calculating Point-Blank Range (PBR). During my earlier review of Pejsa's work, I chose not to cover this material just because it was not some of my favorite material – taste is definitely a part of mathematics. However, it is not difficult material to work through, and I like to answer questions when I can. Continue reading →

Posted in Ballistics | 2 Comments

WW2 Reticles

Posted on 5-November-2015 by mathscinotes

I have watched a lot of old WW2 combat footage, and I have noticed that many of the machine guns and fighter planes had similar reticles. A reticle is a fine-grid of lines used in conjunction with an eyepiece to assist in taking measurements or with accurately pointing an instrument. Figure 1 shows a reticle similar to what I have seen in numerous combat scenes. Continue reading →

Posted in Ballistics, Military History | Comments Off on WW2 Reticles

Stadiametric Rangefinding Approaches

Posted on 20-July-2015 by mathscinotes

Recently, I was reading about stadiametric range finding methods being used by hunters and their telescopic sights – I was surprised to find a lot of writing on the topic. As I researched the topic, I saw that there are three common approaches used in telescopic sights: milliradian (mil), Minute Of Angle (MOA), and Inch Of Angle (IOA). I will review these methods here. Continue reading →

Posted in Ballistics, General Mathematics | 2 Comments

Generating Pejsa's F Function

Posted on 1-July-2015 by mathscinotes

I have had several people ask me to review how Pejsa generated his F function. Recall that Pejsa's approach is based on using a parameter called the ballistic coefficient (BC) to scale the performance of a reference projectile – Pejsa used the US military's 30 caliber M2 bullet, which dates back to the Springfield rifle. This effort involves basic curve fitting, and I will illustrate the process for the velocity interval from 1400 feet per second (fps) to 4000 fps. This velocity range is the most important to most folks and it illustrates the basic curve fitting process well. Continue reading →

Posted in Ballistics | 3 Comments

Range Table Construction Using Pejsa's Formulas

Posted on 28-May-2015 by mathscinotes

In the main body of this post, I work through a detailed example from "Modern Practical Ballistics" on how to apply Pejsa's formulas to determine a range table for a projectile moving through a wide range of velocities. In Appendix A, I work through a second example from the text as additional validation of my implementation. In Appendix B, I show how to use an Ordinary Differential Equation (ODE) solver to generate a range table for comparison with Pejsa's algebraic approximations. Continue reading →

Posted in Ballistics | 7 Comments