The positioning of both feet is essential to good technique in archery and shooting sports, including rifle and pistol. Stance affects balance before, during, and after release of the string or trigger.
Consider the graph below, excerpted from a book series by Schottenbauer Publishing.
Discussion Questions
- What is the maximum force during the step?
- What is the mass of the person?
- What is the length of time of the step onto the plate?
- What is the length of time of the step off of the plate?
- Write a linear equation approximating the application of force during the step onto the plate.
- Write a linear equation approximating the application of force during the step off of the plate.
- Describe the effect of stance shifts during archery or shooting sports.
Additional Information
Geometry is essential for both archery and rifle sports. Take a moment to write down a few ways in which geometry affects the precision of the sport.
Discussion Questions
- What data is necessary to collect in order to understand the role of geometry in shooting?
- What spatial perspectives and/or mathematical planes are important for precision?
The cover of The Geometry of Summer Olympic Sports, to the right above, features an archer taking aim.
Discussion Questions
- What angles can be measured on the diagram, in order to understand the accuracy of technique? The path of the arrow?
- Is any essential information missing from the picture? What is necessary in order to measure that information?
Geometry diagrams featuring archery and shooting sports are available in the following books from Schottenbauer Publishing:
Geometry Workbooks
Additional Information
The position of a rifle or bow is essential to sport shooting, whether with stationary or moving targets. Graphing the position and movement of a rifle or bow provides an interesting activity for classes in physical education, math, and science.
Consider the graph below, excerpted from The Science of Archery & Shooting Sports: Volume 2 from Schottenbauer Publishing.
Discussion Questions
- Sketch the position of the gun at the following points: (a) Initial Position, (b) Any Intersecting Lines, (c) Final Position.
- How far does the nozzle travel in the x direction? In the y direction?
- How far does the butt travel in the x direction? In the y direction?
- Describe the shape of motion.
- What is the average speed of the nozzle in the x direction? in the y direction?
- What is the average speed of the butt in the x direction? in the y direction?
- Is this most likely a toy rifle or a toy handgun?
Graphs and data on archery and shooting sports can be found in the following science lab manuals from Schottenbauer Publishing:
Graphs & Data for Science Lab: Multi-Volume Series
Anthologies of 28 Graphs
Additional Information
What is the balance point of an arrow, and why does it matter? The data below (Copyright 2014, All Rights Reserved), excerpted from the book series The Science of Archery & Shooting Sports: Volume 1 from Schottenbauer Publishing, describe the balance point of a toy arrow.
Discussion Questions
- How does the arrow sit on the bow? Draw a sketch of the arrow in the bow, in the following positions:
- Bowstring loose
- Bowstring drawn to maximum
- How large is the arrow, proportional to the bow? Describe the following proportions. Are there any other proportions which might be relevant to understanding the bow and arrow?
- Arrow length divided by bow width
- Arrow length divided by bow height
- Arrow mass divided by bow mass
- What is the balance point of the arrow? How does the balance point affect the trajectory of the arrow?
- What would occur if the arrow were weighted towards either end?
Graphs and data on archery can be found in the following science lab manuals from Schottenbauer Publishing:
Graphs & Data for Science Lab: Multi-Volume Series
Anthologies of 28 Graphs
Additional Information
The tension of a bow string provides the force which propels arrows long distances. The bow string acts as a spring, with properties which can be analyzed in a method similar to classical physics experiments.
The graph below (Copyright 2014, All Rights Reserved), excerpted from the book series Gravity, Springs, & Collisions: Graphs from Classical Physics Experiments from Schottenbauer Publishing, shows an experiment which has physical properties very similar to a pull on a bow string.
Discussion Questions
- What is the maximum force on the spring during each of the 3 pulls?
- In what direction(s) do the wireless device accelerate?
- If a bow string were to possess the same tension as this spring, what would be the resulting acceleration of an arrow with 0.03 kg mass? Calculate the acceleration for each of the maximum forces above.
- How is this experiment similar to the pull on a bow string? How is it different?
Additional graphs similar to those above can be found in the following science lab manuals from Schottenbauer Publishing:
Graphs & Data for Science Lab: Multi-Volume Series
Anthologies of 28 Graphs
Additional Information
What occurs when an arrow is shot or a bullet is fired? If the answer were simple, then everyone would be an accurate shot! It is common for individuals participating in archery and shooting sports to use a sight on their instrument, to guide their aim. In order to understand accuracy better, it is necessary to learn some physics.
The graphs below (Copyright 2014, All Rights Reserved), excerpted from the book series The Science of Archery & Shooting Sports from Schottenbauer Publishing, show examples of trajectories from the projectile motion of a foam bullet and a toy arrow.
Discussion Questions
- Describe at least 2 similarities between the graphs.
- Describe at least 2 differences between the graphs.
- What travels higher, the arrow or the bullet? Is this a meaningful comparison?
- What travels further, the arrow or the bullet? Is this a meaningful comparison?
- What is the average velocity of the bullet in the horizontal direction?
- What is the average velocity of the arrow in the horizontal direction?
- What required more force, the trajectory of the arrow or the bullet?
Additional graphs similar to those above can be found in the following science lab manuals from Schottenbauer Publishing:
Graphs & Data for Science Lab: Multi-Volume Series
Anthologies of 28 Graphs
Additional Information
The science and math of archery and shooting sports are topics of new books from Schottenbauer Publishing. Presenting data from real and simulated conditions collected by the science writer and publisher M. Schottenbauer, Ph.D., these books bring the "high tech" end of archery and shooting sports to audiences everywhere!
In these books, students can enjoy learning about common aspects of archery and shooting sports. One series of books, written for elementary school students, focuses on geometry. Another series of science books features graphs and data; these illustrate common mathematical functions, plus a variety of concepts from physics. The science books can be integrated into classes such as math, physical science, physics, physical education, and health, anywhere from 7th grade through high school, as well as some introductory college and university classes.
The books directly pertaining to archery and shooting sports include the following:
Geometry Workbooks
These books are complemented by a series of science books on other popular sports topics, including Olympic sports, athletic training, exercise equipment, gymnastics, yoga, ballet, and more. Most of the books above are available in both English and German translation. The books pertaining to the geometry of Olympic sports are also available in 15 world languages.
The same publisher offers similar books on additional popular topics, including sports, transportation, construction, environment, music, entertainment, and general physics. All of these book series are available in several formats and languages, including the following:
Geometry Workbooks
- Print & E-Book Editions
- Available in English & German
- Olympics Books Available in 15 Languages
Graphs & Data for Science Lab: Multi-Volume Series
- Print Editions
- Available in English & German
Anthologies of 28 Graphs
- Print Editions
- English Only
Additional Information
Unbeatable Specials
With Kindle Unlimited ($9.99/month) at Amazon.com, you can read all e-books from Schottenbauer Publishing for no extra charge! Amazon offers Free 30 Day Trials of Kindle Unlimited. With this deal, trial members can read all Schottenbauer Publishing e-books free! This includes all the geometry workbooks, plus "The World in a Graph," "Alphabets of the World," textbooks on the science of music, all the e-book puzzles, and the educational novels by M. Schottenbauer, Ph.D.
