An aircraft executes a horizontal loop at a speed of $720 k m / h$ with its wings banked at $15^{0}$ . What is the radius of the loop?

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Solution

Speed of the aircraft, $v = 720 k m / h = 720 \times 5 / 18 = 200 m / s$ .
Acceleration due to gravity, $g = 10 m / s^{2}$
Angle of banking = $15^{o}$
For radius, $r$ , of the loop, we have the relation:
$N c o s θ = m g$
$N s i n θ = \frac{m u^{2}}{R}$

$t a n θ = u^{2} / R g$

$r = u^{2} / g t a n$ $θ$

$= 200^{2}$ / ( $10 t a n 15^{o}$ )

$= 4000 / 0.26$

$= 14.92 k m$

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An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 150. What is the radius of the loop?

Speed of the aircraft, v=720 km/h=720×5/18=200 m/s.Acceleration due to gravity, g=10m/s2Angle of banking = 15oFor radius, r, of the loop, we have the relation:Ncosθ=mgNsinθ=mu2Rtanθ=u2/Rgr=u2/g tan θ=2002 / (10 tan15o) =4000/0.26 =14.92 km

An aircraft executes a horizontal loop at a speed of $720 k m / h$ with its wings banked at $15^{0}$ . What is the radius of the loop?