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Flight, Measurements of

Flight, Measurements of

Piloting an aircraft requires constant scanning and verifying of measurements. Pilots develop a sense of reasonable measurements for routine situations. For non-routine situations, pilots practice in simulators so they can quickly make sense of the measurements they see on the aircraft's instrument panel. When necessary, they can make rapid decisions to correct for unanticipated conditions. The U.S. customary system of measurement is used, because that is the system used by most pilots in the United States and worldwide.

Level Flight

On an aircraft, a propeller or jet engine provides thrust, which moves the plane forward through the air. Thrust acts parallel to the direction of flight. The weight of the aircraft is the force of gravity acting toward the center of Earth. The aerodynamic forces of lift and drag result from air pressure. Lift, the vertical component, acts to oppose gravity. Drag acts opposite to the flight path of the aircraft.

An aircraft in level flight must be in a condition of equilibrium, meaning the forces (vector quantities) acting upon the aircraft (thrust, drag, weight, and lift) are in balance. To be in balance, lift must equal weight and engine thrust (power) must equal drag.

During flight, pilots continuously scan the cockpit instrument panel. They pay particular attention to the instruments that display measurements of altitude, speed, attitude, and direction.


Pilots are concerned with three types of altitude: true-altitude, pressure-altitude, and absolute-altitude. They read true-altitude (height above mean sea level) and pressure-altitude (height above a standard reference plane) from a pressure-altimeter, which is an instrument dependent upon air pressure. A pilot uses a radar-altimeter to read absolute altitude, which is the height above the terrain directly below the aircraft.

Prior to takeoff, pilots set local barometric pressure into the pressure-altimeter to monitor true-altitude during takeoff and climb. For flight below 18,000 feet, pilots continue to monitor true-altitude. Every 100 miles, they obtain local pressure from air controllers on the ground and update their altimeter. For flight above 18,000 feet pilots reset their altimeter to the standard pressure of 29.92 inches of mercury and monitor pressure-altitude. Consistent use of standard air-pressure at high altitudes by all aircraft permits maintenance of necessary vertical separation.

Altimeter readings do not provide pilots with information about how high they are above terrain features. Instead, pilots monitor their position using a variety of electronic aids, including the global positioning system (GPS). Below 5,000 feet they can monitor their ground height using a radar altimeter. For example, if the altimeter reads 3,000 feet and the aircraft is over a 2,000-foot plateau, the pilot can "ping" Earth with a radar signal. The radar altimeter translates the return signal to an altitude above ground level of 1,000 feet.


The airspeed indicator converts airflow to an airspeed reading in knots . The airspeed indicator receives information about airflow from a device that is mounted on the outside of the aircraft. Pilots or computers correct for the air density at altitude to determine true airspeed. As altitude increases, air density decreases. At 18,000 feet the air density is about one-half of sea-level density and creates considerably less impact on the aircraft.

To determine true airspeed, pilots must make corrections for the airspeed indicator reading. If an airspeed indicator reads 100 knots in an aircraft that is traveling at an altitude of 5,000 feet with outside air temperature of 10 degrees Celsius, a pilot can consult a conversion chart that shows the indicated airspeed should be multiplied by 1.09 to obtain true airspeed. In this example, the computed true airspeed would be 109 knots using the conversion chart, or 110 knots using a rule of thumb. For quick mental estimations, pilots use a rule of thumb in which they add 2 percent of indicated airspeed for each 1,000 feet of altitude to get true airspeed. Pilots can compute groundspeed, critical for determining flight time and fuel needs, by adding tailwind or subtracting headwind from true airspeed.


Attitude refers to the position of an aircraft with reference to the horizon. Attitude measurements of pitch, roll, and yaw are measured on a right hand, three-dimensional axis system, with the origin representing the center of gravity for the aircraft. Attitude is measured in degrees from level flight.

An attitude indicator on the control panel provides pitch and roll information by displaying a symbol that represents aircraft wings on a "moveable horizon." The moveable horizon is an equator-like horizontal line drawn on the sphere in the horizon indicator. The sphere is attached to a spinning gyroscope , which remains in a vertical position relative to Earth. The hemispherical region above the horizon line represents the sky, and below represents the ground. A symbol of an aircraft is drawn on the clear circular case over the sphere. When the aircraft changes attitude, the aircraft symbol changes position relative to the horizon on the sphere. Pilots can determine the amount of pitch or roll by comparing the position of the wing of the aircraft symbol with the horizon line.

Pitch is rotation about the y-axis or lateral axis. A nose-up aircraft position results in positive degrees of pitch. To determine the pitch of the aircraft, pilots consult the position of the aircraft symbol with respect to the horizon line on the attitude indicator. When an aircraft is climbing, the wings of the symbol in the display are positioned above the horizon line. A nose-down aircraft position results in negative degrees of pitch.

Roll is rotation about the positive x -axis or longitudinal axis. If a pilot causes the left wing to roll downward 30 degrees about the longitudinal axis, the aircraft is said to be in a 30 degree left bank.


Yaw is the term for rotation about the vertical or z -axis. An aircraft is said to yaw when it changes direction. Pilots fly a magnetic heading that they read from the heading indicator. This tool consists of a flat circular card that is mounted underneath a clear cover with an aircraft drawn on it. The circular card is marked with 360 degrees similar to a circular protractor, with 0 degrees representing north.

The heading indicator illustrated above shows the aircraft's heading in degrees from magnetic North. Here the aircraft is headed due North. Note that each number must be multiplied by 10 to yield the actual degree reading.

As an aircraft (and the aircraft symbol) turns and rotates, a gyroscope attached to the circular card keeps the card stabilized and fixed in space. The nose of the aircraft symbol continually points in the direction the aircraft is heading.

A gyroscope does not "know" the direction of magnetic north: therefore, pilots initially read a magnetic heading from a magnetic compass and set the heading indicator. Gyroscopic drift causes heading indicators to become inaccurate during flight. Therefore, heading indicators must be periodically corrected with information from a magnetic compass.


During take-off, engine thrust accelerates the aircraft to the critical velocity necessary for lift to overcome drag, rolling friction, and the weight of the plane. Pilots continually monitor airspeed during take-off, aware that once the aircraft exceeds what is termed "refusal speed" there is no longer enough runway to stop the aircraft and the pilot is committed to take-off.

Gross weight of an aircraft is a critical factor in take-off. Runway distance required for take-off varies with the square of the gross weight of the aircraft. For example, consider a Boeing 707 taking off at sea level at standard temperature and barometric pressure. If the aircraft weighs 172,500 pounds without cargo or passengers, it requires a take-off speed of 112 knots and 1,944 feet of runway distance to take-off. If the aircraft were loaded with 100,000 pounds of cargo and passengers, the aircraft would then weigh 272,500 pounds, require a 156 knot take-off speed, and 5,500 feet of runway to take-off. The 58 percent increase in weight required a 39 percent increase in take-off speed and a 183 percent increase in take-off distance.

At take-off, the pilot guides the aircraft to the intended altitude. To maintain a steady velocity climb, forces must be in equilibrium. During the climb, the weight vector (W) is resolved into a vector perpendicular to the flight path (Wcosγ) and a vector parallel to the flight path (Wsinγ), where γ is the climb angle, and cos and sin are two trigonometric functions.

To balance the forces along the flight path, the thrust force must equal the drag force plus W sin. A reasonable climb angle for a Boeing 707 aircraft is 6 degrees. A take-off weight of 172,500 pounds and a 6-degree angle of climb requires approximately 78,100 pounds of jet engine thrust. The four engines on a Boeing 707 each can supply 22,000 pounds of thrust. The take-off angle is the result of optimizing the pounds of fuel needed for climb and the time and ground distance traveled before the aircraft reaches its desired flight altitude. During take-off the pilot monitors the vertical velocity indicator to assure that the aircraft maintains the climb angle. Ascending at 4,325 feet per minute results in an approximate climb angle of 6 degrees.


When pilots travel, Federal Aviation Agency (FAA) air traffic controllers monitor their flight. Pilots fly between points on airways, which can be thought of as highways in the sky. When an aircraft comes within a specified radius of the airport at which the pilot plans to land, FAA controllers pass the aircraft to an approach controller. Approach controllers "vector the aircraft" for approach and landing. This means they give pilots an airspeed and direction to fly toward the glide slope. The glide slope is an angle, with direction, on which the aircraft descends for its landing. It is generally about 3 degrees.

In a ground directed approach, approach controllers direct pilots with heading corrections and rates of descent in feet per minute so the aircraft will stay on the glide slope. In an instrument landing approach, pilots monitor direction, attitude, and vertical-velocity indicators to maintain the aircraft on the glide slope until touch down.

see also Angles, Measurement of; Global Positioning System; Magnetic and Geographic Poles; Navigation; Vectors.

A. Darien Lauten and

Edward L'Hommedieu


Dole, Charles E. Flight Theory for Pilots, 4th ed. Jeppesen Sanderson Training Products, 1994.

Hurt, H. H., Jr. Aerodynamics for Naval Aviators. Issued by the Office of the Chief of Naval Operations Aviation Training Division, U.S. Navy, 1960, NAVWEPS 00-80T-80. Revised January, 1965.

Machado, Rod. Rod Machado's Private Pilot Handbook. The Aviation Speakers Bureau, 1996.


High school students who plan to attend a college with a strong flight program should complete 4 years of high school mathematics, including trigonometry and pre-calculus. Some students will have taken calculus in high school, but students may take calculus in their first year of college. Good grades in trigonometry and pre-calculus, in which vectors are studied, meet the prerequisites for enrolling in aerodynamics and simultaneously beginning flight training. Soon after beginning, first-year college students in aviation programs become accustomed to the many measurements critical to flying and to using mathematics to make sense of the measurements.


Scalar and vector are two types of measurements important to the study of flight. Scalar quantities have size or magnitude only, whereas vector quantities consist of magnitude and direction. For example, if an aircraft travels 100 miles, the distance is a scalar. If an aircraft travels 100 miles to the east, the displacement is a vector.

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personal watercraft

personal watercraft (PWC), a lightweight vessel usually less than 16 ft (5 m) long that uses an inboard water jet pump, powered by an internal-combustion engine, as its primary source of propulsion. The PWC is operated by a person or persons sitting, standing, or kneeling on it, rather than inside it, as in a conventional boat. The PWC concept originated in the 1960s when a home inventor built a powered water ski that combined the elements of self-power, small size, and a maneuverable, active ride that are distinguishing characteristics of all personal watercraft. The first commercial craft, a sit-down-style PWC, was introduced in the late 1960s, but the PWC did not become commercially successful until the 1970s. Multiperson craft, carrying two, three, or four persons, are now the most common PWCs. Personal watercraft have been criticized for producing noise and air pollution, and tend more than other vessels to be maneuvered in ways that endanger the safety of other boaters. Improved engine designs, increased hull insulation, and water-safety education requirements have resulted in reduced pollution and safety improvements.

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