Aircraft carrier catapult

Problem

A pilot is catapulted from $0$ to $80\;\mathrm{m/s}$ in $90\;\mathrm{m}$. Estimate the average acceleration and express it in units of $g$. Comment on the sensation of being “pinned to the seat”.

Solution

Assume constant acceleration (order-of-magnitude estimate). With zero initial speed, the time-independent kinematic relation is: $v^2 = 2\, a\, s$ Isolating the acceleration: $a = \frac{v^2}{2s} = \frac{80^2}{2 \cdot 90} = \frac{6400}{180} \approx 35{,}6\;\mathrm{m/s^2}$ In units of $g = 9{,}81\;\mathrm{m/s^2}$: $\frac{a}{g} = \frac{35{,}6}{9{,}81} \approx 3{,}6$ Comment. The pilot experiences about $3{,}6\,g$ horizontally. By the principle of action and reaction, the seat back must push them forward with a force equal to about $3{,}6$ times their weight: it is this reaction from the seat that they perceive as being “pinned” to the seat. The launch time is short, $t = v/a \approx 80/35{,}6 \approx 2{,}2\;\mathrm{s}$. $\ev{a = \frac{v^2}{2s} \approx 35{,}6\;\mathrm{m/s^2} \approx 3{,}6\,g}$

Linked items

Topics: Dinamica Concepts: Moto uniformemente accelerato Skills: Stime di Fermi