{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:34:09Z","timestamp":1760240049482,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T00:00:00Z","timestamp":1548720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The \u201csuper-gun\u201d class of weaponry has been around for a long time. However, its unusual physics is largely ignored to this day in mainstream physics. We study an example of such a \u201csuper gun\u201d, the \u201cParis gun\u201d. We first look into the historic accounts of the firing distance of such a gun and try to reconcile it with our physical understanding of ballistics. We do this by looking into the drag component in the equations of motion for ballistic movement, which is usually neglected. The drag component of the equations of motion is the main reason for symmetry breaking in ballistics. We study ballistics for several air density profiles and discuss the results. We then proceed to look into the effects of muzzle velocity as well as mass and ground temperature on the optimal firing angle and firing range. We find that, even in the simplest case of fixed air density, the effects of including drag are far reaching. We also determine that in the \u201csensible\u201d range of projectile mass, the muzzle velocity is the most important factor in determining the maximal firing range. We have found that even the simplest of complications that include air density, shifts the optimal angle from the schoolbook\u2019s 45-degree angle, ground temperature plays a major role. While the optimal angle changes by a mere two degrees in response to a huge change in ground temperature, the maximal distance is largely affected. Muzzle velocity is perhaps the most influential variable when working within a sensible projectile mass range. In the current essay, this principle is described and examples are provided where students can apply them. For each problem, we provide both the force consideration solution approach and the energy consideration solution approach.<\/jats:p>","DOI":"10.3390\/sym11020148","type":"journal-article","created":{"date-parts":[[2019,1,29]],"date-time":"2019-01-29T11:27:52Z","timestamp":1548761272000},"page":"148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Interweaving the Numerical Kinematic Symmetry Principles in School and Introductory University Physics Courses"],"prefix":"10.3390","volume":"11","author":[{"given":"Yuval","family":"Ben-Abu","sequence":"first","affiliation":[{"name":"Department of Physics and Project Unit, Sapir Academic College, Sderot, Hof Ashkelon 79165, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hezi","family":"Yizhaq","sequence":"additional","affiliation":[{"name":"Department of Solar Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of Negev, P.O.B. 653, Beer-Sheva 8410501, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haim","family":"Eshach","sequence":"additional","affiliation":[{"name":"Department of Science and Technology Education, Ben-Gurion University of Negev, P.O.B. 653, Beer-Sheva 8410501, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ira","family":"Wolfson","sequence":"additional","affiliation":[{"name":"Department of physics, Ben Gurion University of the Negev, 84990, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,29]]},"reference":[{"key":"ref_1","unstructured":"Miller, and Paris Gun (1990). The Bombardment of Paris by the German Long-Range Guns and The Great German Offensives Of 1918: Paris Gun. The Bombardment of Paris by the Guns and The Great German Offensives Of 1918, Naval & Military Press. [4th ed.]."},{"key":"ref_2","unstructured":"Steven, J.Z., and Laurier, J. (2018). Superguns 1854\u20131991: Extreme artillery from the Paris Gun and the V-3 to Iraq\u2019s Project Babylon (New Vanguard) Paperback, Osprey Publishing."},{"key":"ref_3","unstructured":"Halliday, D., Resnick, R., and Walker, J. (2015). Fundamentals of Physics Extended, Wiley."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"87","DOI":"10.2307\/3029659","article-title":"Exterior Ballistics","volume":"25","year":"1951","journal-title":"Math. Mag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.dt.2017.04.004","article-title":"Measurement of bullet impact conditions using automated in-flight photography system","volume":"13","author":"Decker","year":"2017","journal-title":"Def. Technol."},{"key":"ref_6","unstructured":"Atkinson, B.W. (1981). Meso-Scale Atmospheric Circulations, Academic Press."},{"key":"ref_7","unstructured":"Battan, L.J. (1984). Fundamentals of Meteorology, 2d ed., Prentice-Hall."},{"key":"ref_8","unstructured":"Brunt, D. (1941). Physical and Dynamic Meteorology, Cambridge University Press."},{"key":"ref_9","first-page":"890","article-title":"The deflecting force and Coriolis","volume":"47","author":"Burstyn","year":"1966","journal-title":"Bull. Amer. Meteor. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.2514\/1.8027","article-title":"Modified Projectile Linear Theory for Rapid Trajectory Prediction","volume":"28","author":"Costello","year":"2005","journal-title":"J. Guidance Control Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ijmst.2015.02.009","article-title":"General formulas for drag coefficient and settling velocity of sphere based on theoretical law","volume":"25","author":"HongliF","year":"2015","journal-title":"Int. J. Min. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ben Abu, Y., Eshach, H., and Yizhaq, H. (2017). Interweaving the Principle of Least Potential Energy in School and Introductory University Physics Courses. Symmetry, 9.","DOI":"10.3390\/sym9030045"},{"key":"ref_13","unstructured":"Seinfeld, J.H., and Pandis, S.N. (2006). Atmospheric Chemistry and Physics: from Air Pollution to Climate Change, John Wiley and Sons, Inc."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ben-Abu, Y. (2018). A Time for Introducing the Principle of Least Potential Energy in High School Physics. Energies, 11.","DOI":"10.3390\/en11010098"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ben-Abu, Y., Wolfson, I., Eshach, H., and Yizhaq, H. (2018). Energy, Christiaan Huygens, and the Wonderful Cycloid\u2014Theory versus Experiment. Symmetry, 10.","DOI":"10.3390\/sym10040111"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/148\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:29:22Z","timestamp":1760185762000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,29]]},"references-count":15,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["sym11020148"],"URL":"https:\/\/doi.org\/10.3390\/sym11020148","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,1,29]]}}}