DYNAMIC BUCKLING OF FREE RODS IN FLIGHT
Open Access
- Author:
- Full, Steven Joseph
- Area of Honors:
- Physics
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Andrew Leonard Belmonte, Thesis Supervisor
Andrew Leonard Belmonte, Thesis Supervisor
Dr. Richard Wallace Robinett, Thesis Honors Advisor - Keywords:
- dynamic buckling
- Abstract:
- In this thesis we present a study of the buckling of free rods both in flight and undergoing accelerations, specifically in the context of a bow and arrow system. In archery, the phenomenon of an arrow flexing around the bow is more commonly known as Archer’s Paradox, and is a problem of extreme significance to archers. We study the buckling of an arrow experimentally by capturing and analyzing high speed videos and attempt to model the phenomena mathematically. From the high speed videos we are able to track the position of the nock and tip of the arrow as a function of time and use it to indirectly obtain the compression forces and fictitious forces experienced by an accelerating arrow in its non-inertial rest frame. These forces can eventually be used to solve the equations which govern the buckling of an arrow as it is being accelerated. In addition, several images of the buckling of an arrow were obtained which can validate such a mathematical model. The dynamic Euler-Bernoulli buckling equation is modified to model the buckling of an arrow both in flight and as it is being accelerated. The general strategy is model the buckling of the arrow as vibrations about its center of mass in its rest frame. In order to proceed with such a solution the dynamic Euler-Bernoulli buckling equation is derived for a non-inertial reference frame. It is found that the fictitious force acting on the arrow in the rest frame has major consequences on the vibration of the arrow.