Figure 11-1. Standard sea level pressure.
Figure 11-2. Properties of standard atmosphere.
Since all aircraft performance is compared and evaluated using the standard atmosphere, all aircraft instruments are calibrated for the standard atmosphere. Thus, certain corrections must apply to the instrumentation, as well as the aircraft performance, if the actual operating conditions do not fit the standard atmosphere. In order to account properly for the nonstandard atmosphere, certain related terms must be defined.
Pressure Altitude
Pressure altitude is the height above the standard datum plane (SDP). The aircraft altimeter is essentially a sensitive barometer calibrated to indicate altitude in the standard atmosphere. If the altimeter is set for 29.92 "Hg SDP, the altitude indicated is the pressure altitude—the altitude in the standard atmosphere corresponding to the sensed pressure.
The SDP is a theoretical level at which the pressure of the atmosphere is 29.92 "Hg and the weight of air is 14.7 psi. As atmospheric pressure changes, the SDP may be below, at, or above sea level. Pressure altitude is important as a basis for determining aircraft performance, as well as for assigning flight levels to aircraft operating at above 18,000 feet.
The pressure altitude can be determined by any of the three following methods:
1. By setting the barometric scale of the altimeter to 29.92 "Hg and reading the indicated altitude,
2. By applying a correction factor to the indicated altitude according to the reported “altimeter setting,” [Figure 11-3]
3. By using a flight computer
Density Altitude
The more appropriate term for correlating aerodynamic performance in the nonstandard atmosphere is density altitude—the altitude in the standard atmosphere corresponding to a particular value of air density.
Figure 11-3. Field elevation versus pressure. The aircraft is located on a field that happens to be at sea level. Set the altimeter to the current altimeter setting (29.7). The difference of 205 feet is added to the elevation or a PA of 205 feet.
Density altitude is pressure altitude corrected for nonstandard temperature. As the density of the air increases (lower density altitude), aircraft performance increases. Conversely, as air density decreases (higher density altitude), aircraft performance decreases. A decrease in air density means a high density altitude; an increase in air density means a lower density altitude. Density altitude is used in calculating aircraft performance. Under standard atmospheric condition, air at each level in the atmosphere has a specific density; under standard conditions, pressure altitude and density altitude identify the same level. Density altitude, then, is the vertical distance above sea level in the standard atmosphere at which a given density is to be found.
Density altitude is computed using pressure altitude and temperature. Since aircraft performance data at any level is based upon air density under standard day conditions, such performance data apply to air density levels that may not be identical to altimeter indications. Under conditions higher or lower than standard, these levels cannot be determined directly from the altimeter.
Density altitude is determined by first finding pressure altitude and then correcting this altitude for nonstandard temperature variations. Since density varies directly with pressure, and inversely with temperature, a given pressure altitude may exist for a wide range of temperature by allowing the density to vary. However, a known density occurs for any one temperature and pressure altitude. The density of the air, of course, has a pronounced effect on aircraft and engine performance. Regardless of the actual altitude at which the aircraft is operating, it will perform as though it were operating at an altitude equal to the existing density altitude.
For example, when set at 29.92 "Hg, the altimeter may indicate a pressure altitude of 5,000 feet. According to the AFM/POH, the ground run on takeoff may require a distance of 790 feet under standard temperature conditions. However, if the temperature is 20 °C above standard, the expansion of air raises the density level. Using temperature correction data from tables or graphs, or by deriving the density altitude with a computer, it may be found that the density level is above 7,000 feet, and the ground run may be closer to 1,000 feet.
Air density is affected by changes in altitude, temperature, and humidity. High density altitude refers to thin air while low density altitude refers to dense air. The conditions that result in a high density altitude are high elevations, low atmospheric pressures, high temperatures, high humidity, or some combination of these factors. Lower elevations, high atmospheric pressure, low temperatures, and low humidity are more indicative of low density altitude.
Using a flight computer, density altitude can be computed by inputting the pressure altitude and outside air temperature at flight level. Density altitude can also be determined by referring to the table and chart in Figures 11-3 and 11-4 respectively.
Figure 11-4. Density altitude chart.
Effects of Pressure on Density
Since air is a gas, it can be compressed or expanded. When air is compressed, a greater amount of air can occupy a given volume. Conversely, when pressure on a given volume of air is decreased, the air expands and occupies a greater space. That is, the original column of air at a lower pressure contains a smaller mass of air. In other words, the density is decreased. In fact, density is directly proportional to pressure. If the pressure is doubled, the density is doubled, and if the pressure is lowered, so is the density. This statement is true only at a constant temperature.
Effects of Temperature on Density
Increasing the temperature of a substance decreases its density. Conversely, decreasing the temperature increases the density. Thus, the density of air varies inversely with temperature. This statement is true only at a constant pressure.
In the atmosphere, both temperature and pressure decrease with altitude and have conflicting effects upon density. However, the fairly rapid drop in pressure as altitude is increased usually has the dominant effect. Hence, pilots can expect the density to decrease with altitude.
Effects of Humidity (Moisture) on Density
The preceding paragraphs are based on the presupposition of perfectly dry air. In reality, it is never completely dry. The small amount of water vapor suspended in the atmosphere may be negligible under certain conditions, but in other conditions humidity may become an important factor in the performance of an aircraft. Water vapor is lighter than air; consequently, moist air is lighter than dry air. Therefore, as the water content of the air increases, the air becomes less dense, increasing density altitude and decreasing performance. It is lightest or least dense when, in a given set of conditions, it contains the maximum amount of water vapor.
Humidity, also called relative humidity, refers to the amount of water vapor contained in the atmosphere and is expressed as a percentage of the maximum amount of water vapor the air can hold. This amount varies with the temperature; warm air can hold more water vapor, while colder air can hold less. Perfectly dry air that contains no water vapor has a relative humidity of zero percent, while saturated air that cannot hold any more water vapor has a relative humidity of 100 percent. Humidity alone is usually not considered an essential factor in calculating density altitude and aircraft performance; however, it does contribute.
The higher the temperature, the greater amount of water vapor that the air can hold. When comparing two separate air masses, the first warm and moist (both qualities making air lighter) and the second cold and dry (both qualities making it heavier), the first must be less dense than the second. Pressure, temperature, and humidity have a great influence on aircraft performance because of their effect upon density. There is no rule-of-thumb or chart used to compute the effects of humidity on density altitude, but it must be taken into consideration. Expect a decrease in overall performance in high humidity conditions.
Performance
Performance is a term used to describe the ability of an aircraft to accomplish certain things that
make it useful for certain purposes. For example, the ability of an aircraft to land and take off in a very short distance is an important factor to the pilot who operates in and out of short, unimproved airfields. The ability to carry heavy loads, fly at high altitudes at fast speeds, and/or travel long distances is essential for the performance of airline and executive type aircraft.
The primary factors most affected by performance are the takeoff and landing distance, rate of climb, ceiling, payload, range, speed, maneuverability, stability, and fuel economy. Some of these factors are often directly opposed: for example, high speed versus short landing distance, long range versus great payload, and high rate of climb versus fuel economy. It is the preeminence of one or more of these factors that dictates differences between aircraft and explains the high degree of specialization found in modern aircraft.
The various items of aircraft performance result from the combination of aircraft and powerplant characteristics. The aerodynamic characteristics of the aircraft generally define the power and thrust requirements at various conditions of flight, while powerplant characteristics generally define the power and thrust available at various conditions of flight. The matching of the aerodynamic configuration with the powerplant is accomplished by the manufacturer to provide maximum performance at the specific design condition (e.g., range, endurance, and climb).
Straight-and-Level Flight
All of the principal components of flight performance involve steady-state flight conditions and equilibrium of the aircraft. For the aircraft to remain in steady, level flight, equilibrium must be obtained by a lift equal to the aircraft weight and a powerplant thrust equal to the aircraft drag. Thus, the aircraft drag defines the thrust required to maintain steady, level flight. As presented in Chapter 4, Aerodynamics of Flight, all parts of an aircraft contribute to the drag, either induced (from lifting surfaces) or parasite drag.
While parasite drag predominates at high speed, induced drag predominates at low speed. [Figure 11-5] For example, if an aircraft in a steady flight condition at 100 knots is then accelerated to 200 knots, the parasite drag becomes four times as great, but the power required to overcome that drag is eight times the original value. Conversely, when the aircraft is operated in steady, level flight at twice as great a speed, the induced drag is one-fourth the original value, and the power required to overcome that drag is only one-half the original value.
Figure 11-5. Drag versus speed.
When an aircraft is in steady, level flight, the condition of equilibrium must prevail. The unaccelerated condition of flight is achieved with the aircraft trimmed for lift equal to weight and the powerplant set for a thrust to equal the aircraft drag.
The maximum level flight speed for the aircraft is obtained when the power or thrust required equals the maximum power or thrust available from the powerplant. [Figure 11-6] The minimum level flight airspeed is not usually defined by thrust or power requirement since conditions of stall or stability and control problems generally predominate.
Figure 11-6. Power versus speed.
Climb Performance
If an aircraft is to move, fly, and perform, work must act upon it. Work involves force moving the aircraft. The aircraft acquires mechanical energy when it moves. Mechanical energy comes in two forms: (1) Kinetic Energy (KE), the energy of speed; (2) Potential Energy (PE), the stored energy of position.
Aircraft motion (KE) is described by its velocity (airspeed). Aircraft position (PE) is described by its height (altitude). Both KE and PE are directly proportional to the object’s mass. KE is directly proportional to the square of the object’s velocity (airspeed). PE is directly proportional to the object’s height (altitude). The formulas below summarize these energy relationships:
KE = ½ × m × v2
m = object mass
v = object velocity
PE = m × g × h
m = object mass
g = gravity field strength
h = object height
We sometimes use the terms “power” and “thrust” interchangeably when discussing climb performance. This erroneously implies the terms are synonymous. It is important to distinguish between these terms. Thrust is a force or pressure exerted on an object. Thrust is measured in pounds (lb) or newtons (N). Power, however, is a measurement of the rate of performing work or transferring energy (KE and PE). Power is typically measured in horsepower (hp) or kilowatts (kw). We can think of power as the motion (KE and PE) a force (thrust) creates when exerted on an object over a period of time.
Positive climb performance occurs when an aircraft gains PE by increasing altitude. Two basic factors, or a combination of the two factors, contribute to positive climb performance in most aircraft:
1. The aircraft climbs (gains PE) using excess power above that required to maintain level flight, or
2. The aircraft climbs by converting airspeed (KE) to altitude (PE).
As an example of factor 1 above, an aircraft with an engine capable of producing 200 horsepower (at a given altitude) is using only 130 horsepower to maintain level flight at that altitude. This leaves 70 horsepower available to climb. The pilot holds airspeed constant and increases power to perform the climb.
As an example of factor 2, an aircraft is flying level at 120 knots. The pilot leaves the engine power setting constant but applies other control inputs to perform a climb. The climb, sometimes called a zoom climb, converts the airspeed (KE) to altitude (PE); the airspeed decreases to something less than 120 knots as the altitude increases.
There are two primary reasons to evaluate climb performance. First, aircraft must climb over obstacles to avoid hitting them. Second, climbing to higher altitudes can provide better weather, fuel economy, and other benefits. Maximum Angle of Climb (AOC), obtained at VX, may provide climb performance to ensure an aircraft will clear obstacles. Maximum Rate of Climb (ROC), obtained at VY, provides climb performance to achieve the greatest altitude gain over time. Maximum ROC may not be sufficient to avoid obstacles in some situations, while maximum AOC may be sufficient to avoid the same obstacles. [Figure 11-7]
Angle of Climb (AOC)
AOC is a comparison of altitude gained relative to distance traveled. AOC is the inclination (angle) of the flight path. For maximum AOC performance, a pilot flies the aircraft at VX so as to achieve maximum altitude increase with minimum horizontal travel over the ground. A good use of maximum AOC is when taking off from a short airfield surrounded by high obstacles, such as trees or power lines. The objective is to gain sufficient altitude to clear the obstacle while traveling the least horizontal distance over the surface.
Figure 11-7. Maximum angle of climb (AOC) versus maximum rate of climb (ROC).
One method to climb (have positive AOC performance) is to have excess thrust available. Essentially, the greater the force that pushes the aircraft upward, the steeper it can climb. Maximum AOC occurs at the airspeed and angle of attack (AOA) combination which allows the maximum excess thrust. The airspeed and AOA combination where excess thrust exists varies amongst aircraft types. As an example, Figure 11-8 provides a comparison between jet and propeller airplanes as to where maximum excess thrust (for maximum AOC) occurs. In a jet, maximum excess thrust normally occurs at the airspeed where the thrust required is at a minimum (approximately L/DMAX). In a propeller airplane, maximum excess thrust normally occurs at an airspeed below L/DMAX and frequently just above stall speed.
Figure 11-8. Comparison of maximum AOC between jet and propeller airplanes.
Rate of Climb (ROC)
ROC is a comparison of altitude gained relative to the time needed to reach that altitude. ROC is simply the vertical component of the aircraft’s flight path velocity vector. For maximum ROC performance, a pilot flies the aircraft at VY so as to achieve a maximum gain in altitude over a given period of time.
Maximum ROC expedites a climb to an assigned altitude. This gains the greatest vertical distance over a period of time. For example, in a maximum AOC profile,
a certain aircraft takes 30 seconds to reach 1,000 feet AGL, but covers only 3,000 feet over the ground. By comparison, using its maximum ROC profile, the same aircraft climbs to 1,500 feet in 30 seconds but covers 6,000 feet across the ground. Note that both ROC and AOC maximum climb profiles use the aircraft’s maximum throttle setting. Any differences between max ROC and max AOC lie primarily in the velocity (airspeed) and AOA combination the aircraft manual specifies. [Figure 11-7]
ROC performance depends upon excess power. Since climbing is work and power is the rate of performing work, a pilot can increase the climb rate by using any power not used to maintain level flight. Maximum ROC occurs at an airspeed and AOA combination that produces the maximum excess power. Therefore, maximum ROC for a typical jet airplane occurs at an airspeed greater than L/DMAX and at an AOA less than L/DMAX AOA. In contrast, maximum ROC for a typical propeller airplane occurs at an airspeed and AOA combination closer to L/DMAX. [Figure 11-9]
Pilot's Handbook of Aeronautical Knowledge (Federal Aviation Administration) Page 46
