Days Postings
Blog Series
Copyright Notice
© Mark Biegert and Math Encounters, 2022. Publication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Mark Biegert and Math Encounters with appropriate and specific direction to the original content.
Disclaimer
All content provided on the mathscinotes.com blog is for informational purposes only. The owner of this blog makes no representations as to the accuracy or completeness of any information on this site or found by following any link on this site. The owner of mathscinotes.com will not be liable for any errors or omissions in this information nor for the availability of this information. The owner will not be liable for any losses, injuries, or damages from the display or use of this information.
Monthly Archives: May 2015
Range Table Construction Using Pejsa's Formulas
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
Optical SFP Power Estimation Using Curve Fitting
I was asked today how to use Excel to estimate the power usage of two optical components at case temperatures for which we had no data. I initially solved the problem in Mathcad by fitting an equation of the form $latex c_0 \cdot e^{c_1 \cdot T_{Case}}+e_2 to the data and computing the corresponding power. Continue reading
Posted in Excel, General Mathematics
Comments Off on Optical SFP Power Estimation Using Curve Fitting
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
Posted in Ballistics
1 Comment
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
Posted in Ballistics
2 Comments
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
Posted in Ballistics
5 Comments
Untold ER Story About Tainted Well Water
I sometimes wonder if you can learn anything from television, but I recently saw an article in our local paper about a medical condition threatening a local town that I had first learned about on "Untold Stories of the ER" (USER). Continue reading
Posted in Health
Comments Off on Untold ER Story About Tainted Well Water
Radioactive Paper?
I just read an article article that glossy paper is also slightly radioactive, a fact that I found surprising. As I read about glossy paper, it turns out that glossy paper often contains kaolin, a type of clay. So it is radioactive for the same reason that kitty litter is radioactive, which also contains clay. Continue reading
Posted in General Science
3 Comments
Good Analogy for A VPN
My oldest son is an IT engineer and I find his work very interesting. So that we have more things to talk about, I am trying to become more knowledgeable about IT matters. This means I try try read various blogs about IT topics.
Today, I was reading the Kaspersky blog, and they had a great analogy for a Virtual Private Network (VPN). They said that the WW2 use of Navajo code talkers is analogous to a modern VPN. Continue reading
Posted in Networking
2 Comments
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
Posted in Ballistics
12 Comments
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
Posted in Ballistics
11 Comments