# Ballista Case Study

By Hatim Nomani (AU17B1) Kuldeep Pal (AU17B1003) Madhur Chhajed (AU17B1002)

Supervised by Gautam

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Thus, our second design requirement specifies that we will be using Philo’s mathematical model, with a module size of 1 inch, resulting in overall dimensions of approximately 20 inches long by 15 inches wide by 10 inches high.

LITERATURE REVIEW

The objective of this design task is to ensure that two 1‑inch‑diameter torsion springs made of nylon rope will be capable of propelling a golf ball at least 200 feet. To accomplish this task, we will apply the principle of conservation of energy and the projectile range equation.

Our model of the mechanical system consists of the two arms, sling, and projectile, with applied torques at the base of each arm representing the torsion springs.

The two principal forms of energy relevant to this problem are kinetic energy, the energy associated with a mass in motion, and elastic energy, the energy stored though the elastic deformation of a material. The term elastic refers to a material that, when stretched and then released, returns to its original shape. Nylon rope is not perfectly elastic, but its behaviour is sufficiently elastic for our

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(total energy)_1=(total energy)_2 (elastic energy )_█(1 @)+(kinetic energy)_1 =(elastic energy )_2+(kinetic energy )_2

(change in elastic energy)_(1-2)=1/2 mv^2

This formulation incorporates a number of simplifying assumptions. First, it ignores energy losses such as friction and aerodynamic drag that inevitably occur in real‑world mechanical systems. It also ignores the small change in gravitational potential energy that will occur between states 1 and 2 (from figure 2) as the projectile moves up the slider.

Mechanical Efficiency of Ballista

Mechanical efficiency is a quantitative measure of performance that is typically defined as the ratio of useful output to input, expressed as a percentage. For a ballista, the input is the elastic energy imparted to, and stored in, the torsion springs when the machine is cocked. The useful output is the kinetic energy of the projectile.

The ballista is relatively unique in that— subject to a few reasonable simplifying assumptions—it has a maximum theoretical mechanical efficiency of 100%. Most of the machines we encounter in our everyday lives—for example, automobile engines, refrigerators, pumps, and turbines—have inherent limitations in their mechanisms for energy conversion that limit their maximum theoretical efficiency to substantially less than