Distance and height of cannon projectiles
For the mathematical investigation, I want to focus on angles and trigonometry and differentiation, since these areas are the ones interesting me the most in the SL syllabus, and connect it to war history, and weapons used in wars, which are some of my other interests. I take history on higher level in the IB, and war has always been one of my interests.
The cannon has improved over the past 1000 years and has been an effective way for an army to shoot a projectile from a long range into an enemy fortress or behind enemy walls. But did the angle of which the cannons were fired at have any effect on how far the projectile would move, and were the soldiers steering the cannons aware about the angle that would move the projectile the furthest and be the most accurate.
Under the wars that occurred in the 19th and 20th century, there is a high possibility that the soldiers arming and shooting the cannon did not go through the appropriate training in how to optimize their accuracy. An example for this is the American civil war, where the soldiers could have used the “trial and error” methodology i.e. shoot once from a certain angle, see where it lands, and modify the angle according to distance from target. I started thinking about how the awareness of the correlation between speed and shooting angle could affect the efficiency of the army, since they would have to shoot less and by that safe time and money. By that investigate how different cannons with different velocities, could be an advantage for the soldiers. Furthermore, using calculus, I will investigate the maximum distance of various cannons used in the war. The question I want to explore is therefore if applying trigonometry a...
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...r should do is to look at the curve of the cannon they are operating and find out what angle would be optimal for hitting an enemy at a certain distance.
Graph 3: The effect of the angle on the distance, using the equation found earlier shown on three different cannons, with three different velocities
Works Cited
Model 1841 6-Pounder (Gun) Towed Field Gun. Military Factory, n.d. Web. 9 Apr. 2014. .
Poduct Rule for Derivatives. HMC, n.d. Web. 9 Apr. 2014. .
Projectiles. Plymouth University, n.d. Web. 9 Apr. 2014. .
Range of an Artillery Shell. Physics Factbook, n.d. Web. 9 Apr. 2014. .
I have written this science research paper to compare ballistics of a .270 and a .30-06. This paper will also make my decision on which one I will purchase next. If I fire the .270 and the .30-06 rifles into a 2x4, then I will be able to determine from the ballistics which caliber rifle is better. For my experiment, I fired two rounds of ammunition into a 2x4 with each gun. Both rifles were fired at a range of 50 yards away, into the wind, while using 150 grain shells. The rounds for the .270 used soft tips, but the .30-06 used sharp tips.
Melton, Jack W. and Lawrence E. Pawl. “Basic Facts Concerning Artillery.” Civil War Artillery. 2009. 17 January 2010. .
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