An aircraft having a total weight of 45 kN lands on the deck of an aircraft carrier and is brought to rest by means of a cable engaged by an arrester hook. If the deceleration indu... An aircraft having a total weight of 45 kN lands on the deck of an aircraft carrier and is brought to rest by means of a cable engaged by an arrester hook. If the deceleration induced by the cable is 3g, determine the tension, T, in the cable, the load on an undercarriage strut, and the shear and axial loads in the fuselage at the section AA; the weight of the aircraft aft of AA is 4.5 kN. Calculate also the length of deck covered by the aircraft before it is brought to rest if the touch-down speed is 25 m/s.
Understand the Problem
The question is asking for several physics-related calculations involving an aircraft landing on a deck. We need to determine the tension in the cable, the load on the undercarriage strut, the shear and axial loads in the fuselage, and the length of the deck covered by the aircraft before it comes to a stop. The calculations will involve concepts of force, deceleration, and motion.
Answer
$T = m(g + a)$, $L = mg + ma$, $F_{axial} = T$, $F_{shear} = mg$, $d = \frac{-v_0^2}{2a}$.
Answer for screen readers
The tension in the cable is given by $T = m(g + a)$, the load on the undercarriage strut is $L = mg + ma$, the axial load is $F_{axial} = T$, the shear load is $F_{shear} = mg$, and the distance covered by the aircraft before stopping is $d = \frac{-v_0^2}{2a}$.
Steps to Solve
- Identify the initial parameters
We need to gather the initial parameters for the calculations, such as the mass $m$ of the aircraft, its initial velocity $v_0$, deceleration $a$, and the gravitational acceleration $g$.
- Calculate the Tension in the Cable
Using Newton's second law, we can express the tension $T$ in the cable while considering the forces at play.
The net force equation is: $$ T - mg = ma $$
So the tension can be found using: $$ T = m(g + a) $$
- Determine the Load on the Undercarriage Strut
The load $L$ on the undercarriage strut also includes the aircraft's weight but needs to factor in any acceleration due to deceleration when landing: $$ L = mg + ma $$
- Calculate Shear and Axial Loads in the Fuselage
Axial load $F_{axial}$ is equal to the tension in the cable: $$ F_{axial} = T $$
Shear load $F_{shear}$ can be understood to be related to the weight of the aircraft: $$ F_{shear} = mg $$
- Determine the Length of the Deck Covered by the Aircraft
Using the kinematic equation for uniformly accelerated motion: $$ v^2 = v_0^2 + 2a d $$
Solving for the distance $d$ gives: $$ d = \frac{v^2 - v_0^2}{2a} $$
Since the final velocity $v$ on landing is 0, we have: $$ d = \frac{-v_0^2}{2a} $$
The tension in the cable is given by $T = m(g + a)$, the load on the undercarriage strut is $L = mg + ma$, the axial load is $F_{axial} = T$, the shear load is $F_{shear} = mg$, and the distance covered by the aircraft before stopping is $d = \frac{-v_0^2}{2a}$.
More Information
These equations derive from fundamental physics principles, including Newton's laws of motion and kinematic equations. When an aircraft lands, these calculations help in understanding the forces acting on the aircraft and ensure safety during landing.
Tips
- Forgetting to include units in calculations, which can lead to confusion or incorrect results.
- Confusing the signs of acceleration (deceleration should be negative).
- Not correctly using initial and final velocities when solving for distances.
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