Question
The feasibility of a one-passenger VTOL. (vertical takeoff and landing) craft is under review. The preliminary design calls for a small engine with a high power-to-weight ratio driving an air pump that draws in air through the $70^{\circ}$ ducts with an inlet velocity $v=40 \mathrm{m} / \mathrm{s}$ at a static gage pressure of $-1.8 \mathrm{kPa}$ across the inlet areas totaling $0.1320 \mathrm{m}^{2}$. The air is exhausted vertically down with a velocity $u=$ $420 \mathrm{m} / \mathrm{s}$. For a 90 -kg passenger, calculate the maximum net mass $m$ of the machine for which it cantake off and hover. (See Table D/1 for air density.)
Step 1
Given that $\rho = 1.206 \, \mathrm{kg/m^3}$, $A = 0.1320 \, \mathrm{m^2}$, and $v = 40 \, \mathrm{m/s}$, we find that $m' = 1.206 \cdot 0.1320 \cdot 40 = 6.37 \, \mathrm{kg/s}$. Show more…
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The VTOL (vertical takeoff and landing) military aircraft is capable of rising vertically under the action of its jet exhaust, which can be "vectored" from $\theta \cong 0$ for takeoff and hovering to $\theta=90^{\circ}$ for forward flight. The loaded aircraft has a mass of $8600 \mathrm{kg}$. At full takeoff power, its turbo-fan engine consumes air at the rate of $90 \mathrm{kg} / \mathrm{s}$ and has an air-fuel ratio of $18 .$ Exhaust-gas velocity is $1020 \mathrm{m} / \mathrm{s}$ with essentially atmospheric pressure across the exhaust nozzles. Air with a density of $1.206 \mathrm{kg} / \mathrm{m}^{3}$ is sucked into the intake scoops at a pressure of -2 kPa (gage) over the total inlet area of $1.10 \mathrm{m}^{2}$. Determine the angle $\theta$ for vertical takeoff and the cor responding vertical acceleration $a_{y}$ of the aircraft.
Consider an airplane patterned after the Beechcraft Bonanza V-tailed, singleengine light private airplane. The characteristics of the airplane are as follows: aspect ratio $=6.2$, wing area $=181 \mathrm{ft}^{2}$, Oswald efficiency factor $=0.91$, weight $=$ $3000 \mathrm{lb}$, and zero-lift drag coefficient $=0.027$. The airplane is powered by a single piston engine of $345 \mathrm{hp}$ maximum at sea level. Assume that the power of the engine is proportional to free-stream density. The two-blade propeller has an efficiency of $0.83$. a. Calculate the power required at sea level. b. Calculate the maximum velocity at sea level. c. Calculate the power required at 12,000 -ft altitude. d. Calculate the maximum velocity at $12,000-\mathrm{ft}$ altitude.
A frequently quoted rule of thumb in aircraft design is that wings should produce about 1000 N of lift per square meter of wing. (The fact that a wing has a top and bottom surface does not double its area.) (a) At takeoff, an aircraft travels at 60.0 m/s, so that the air speed relative to the bottom of the wing is 60.0 m/s. Given the sea level density of air to be $1.29 \mathrm{kg} / \mathrm{m}^{3},$ how fast must it move over the upper surface to create the ideal lift? (b) How fast must air move over the upper surface at a cruising speed of 245 m/s and at an altitude where air density is one-fourth that at sea level? (Note that this is not all of the aircraft's lift-some comes from the body of the plane, some from engine thrust, and so on. Furthermore, Bernoulli's principle gives an approximate answer because flow over the wing creates turbulence.)
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