Flight Theory and Aerodynamics. Joseph R. Badick
time for the aircraft to reach takeoff speed.
8 Under no‐wind conditions, what takeoff roll is required for the aircraft in Problem 7?
9 Upon reaching a velocity of 100 fps, the pilot of the airplane in Problem 7 decides to abort the takeoff and applies brakes and stops the airplane in 1000 ft. Find the airplane’s deceleration.
10 An airplane is towing a glider to altitude. The tow rope is 20° below the horizontal and has a tension force of 300 lb exerted on it by the airplane. Find the horizontal drag of the glider and the amount of lift that the rope is providing to the glider. Sin 20° = 0.342; cos 20° = 0.940.
11 A jet airplane is climbing at a constant airspeed in no‐wind conditions. The plane is directly over a point on the ground that is 4 statute miles from the takeoff point and the altimeter reads 15 840 ft. Find the plane’s climb angle and the distance that it has flown through the air.
12 Find the distance s and the force F on the seesaw fulcrum shown in the figure. Assume that the system is in equilibrium.
13 A helicopter has a rotor diameter of 30 ft and it is being operated in a hover at 286.5 rpm. Find the tip speed Vt of the rotor.
14 An airplane weighs 16 000 lb and is flying at 5 000 ft altitude and at an airspeed of 200 fps. Find (a) the potential energy, (b) the kinetic energy, and (c) the total energy. Assuming no extra drag on the airplane, if the pilot drove until the airspeed was 400 fps, what would the altitude be?
15 An aircraft’s turbojet engine produces 10 000 lb of thrust at 162.5 kts. true airspeed. What is the equivalent power that it is producing?
16 An aircraft weighs 24 000 lb and has 75% of its weight on the main (braking) wheels. If the coefficient of friction is 0.7, find the braking force Fb on the airplane.
17 Newton’s third law of motion states:A body at rest will remain at rest and a body in motion will remain in motion, in a straight line, unless acted upon by an unbalanced force.For every action force there is an equal and opposite reaction force.If a body is acted on by an unbalanced force, the body will accelerate in the direction of the force, and the acceleration will be directly proportional to the force and inversely proportional to the mass of the body.
18 An aircraft parked on an airport ramp would be an example of Newton’s _______ law of motion.first.second.fourth.third.
19 An airplane in level flight increases thrust, resulting in an acceleration until once again thrust equals:aerodynamic force.lift.weight.drag.
20 An airplane in straight‐and‐level, unaccelerated flight weighs 2300 lb, what total lift must the aircraft produce to maintain a constant altitude assuming no additional forces are involved:2000 lb2300 lb1150 lb>2300 lb
2 Atmosphere, Altitude, and Airspeed Measurement
CHAPTER OBJECTIVES
After completing this chapter, you should be able to:
Identify the important properties of the atmosphere that influence the aerodynamics of flight.
Define standard pressure and temperature, and calculate pressure and temperature ratios when a standard atmosphere is not encountered.
Summarize the relationship between pressure altitude and density altitude.
Analyze the standard atmosphere table and recognize the change in atmospheric properties with a change in altitude.
Define and compare the definitions for various types of altitude used in aerodynamics and illustrate why each type is important.
Explain the relationship between the continuity equation and Bernoulli’s equation, and show how they apply to an aircraft in flight.
Define and compare the definitions for various types of airspeed used in aerodynamics and illustrate why each type is important.
Determine the true airspeed of an aircraft in flight.
PROPERTIES OF THE ATMOSPHERE
The aerodynamic forces and moments acting on an aircraft in flight are due, in great part, to the properties of the air mass in which the aircraft is flying. By volume, the atmosphere is composed of approximately 78% nitrogen, 21% oxygen, and 1% other gases. The most important properties of air that affect aerodynamic behavior are its static pressure, temperature, density, and viscosity.
It is important to remember at this point that air is a fluid, and like other gases takes on the shape of its container. Just as a liquid can fill a container, air has the capacity to expand and fill the container as well, though the density will differ significantly. Throughout this textbook, we will expand on this introduction to the fluid properties of air, especially as it relates to an airfoil and ultimately the impact on aircraft performance calculations.
Static Pressure
The static pressure of the air, P, is simply the weight per unit area of the air above the level under consideration. Air has mass and as we have discussed thus has weight, which means it exerts a force. For instance, the weight of a column of air with a cross‐sectional area of 1 ft2 and extending upward from sea level through the atmosphere is 2116 lb. The sea level static pressure is, therefore, 2116 pounds per square foot (psf), or 14.7 pounds per square inch (psi). Another commonly used measure of static pressure is inches of mercury. On a standard sea level day, the air’s static pressure will support a column of mercury (Hg) that is 29.92″ high (Figure 2.1). Weather reports express pressure in millibars; standard atmospheric pressure is 1013.2 mb. In addition to these rather confusing systems, there are the metric measurements in use throughout most of the world. For the discussion of performance problems in this textbook, we will primarily use the measurement of static pressure in inches of mercury is the standard used unless stated otherwise.
Static pressure is reduced as altitude is increased because there is less air weight above. At 18 000 ft altitude, the static pressure is about half that at sea level, the higher you go the less air there is above. The accepted standard pressure lapse rate is approximately 1″ Hg decrease in pressure for every 1000 ft gain in altitude from sea level (Figure 2.2). This change in atmospheric pressure with altitude is an important concept during evaluation of aircraft performance as well as the operation of aircraft flight instruments.
Figure 2.1 Standard pressure.
Source: U.S. Department of Transportation Federal Aviation Administration (2008a).
Figure 2.2 Properties of a standard atmosphere.
Source: U.S. Department of Transportation Federal Aviation Administration (2016b).
In aerodynamics, it is convenient to use pressure ratios, rather than actual pressures; thus the units of measurement are canceled out. When at sea level on a standard day, the pressure ratio can be determined using equation:
(2.1)
where P0 is the sea level standard static pressure (2116 psf or 29.92″ Hg). Thus, a pressure ratio