Aircraft Performance

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).

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 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 1] 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.

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 2] 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.

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:

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 3]

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.

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 4 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.

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 3]

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 5]

Since weight, altitude and configuration changes affect excess thrust and power, they also affect climb performance. Climb performance is directly dependent upon the ability to produce either excess thrust or excess power. Earlier in the book it was shown that an increase in weight, an increase in altitude, lowering the landing gear, or lowering the flaps all decrease both excess thrust and excess power for all aircraft. Therefore, maximum AOC and maximum ROC performance decreases under any of these conditions.

Weight has a very pronounced effect on aircraft performance. If weight is added to an aircraft, it must fly at a higher AOA to maintain a given altitude and speed. This increases the induced drag of the wings, as well as the parasite drag of the aircraft. Increased drag means that additional thrust is needed to overcome it, which in turn means that less reserve thrust is available for climbing. Aircraft designers go to great lengths to minimize the weight, since it has such a marked effect on the factors pertaining to performance.

A change in an aircraft’s weight produces a twofold effect on climb performance. First, a change in weight changes the drag and the power required. This alters the reserve power available, which in turn, affects both the climb angle and the climb rate. Secondly, an increase in weight reduces the maximum ROC, but the aircraft must be operated at a higher climb speed to achieve the smaller peak climb rate.

An increase in altitude also increases the power required and decreases the power available. Therefore, the climb performance of an aircraft diminishes with altitude. The speeds for maximum ROC, maximum AOC, and maximum and minimum level flight airspeeds vary with altitude. As altitude is increased, these various speeds finally converge at the absolute ceiling of the aircraft. At the absolute ceiling, there is no excess of power and only one speed allows steady, level flight. Consequently, the absolute ceiling of an aircraft produces zero ROC. The service ceiling is the altitude at which the aircraft is unable to climb at a rate greater than 100 feet per minute (fpm). Usually, these specific performance reference points are provided for the aircraft at a specific design configuration. [Figure 6]

The terms “power loading,” “wing loading,” “blade loading,” and “disk loading” are commonly used in reference to performance. Power loading is expressed in pounds per horsepower and is obtained by dividing the total weight of the aircraft by the rated horsepower of the engine. It is a significant factor in an aircraft’s takeoff and climb capabilities. Wing loading is expressed in pounds per square foot and is obtained by dividing the total weight of an airplane in pounds by the wing area (including ailerons) in square feet. It is the airplane’s wing loading that determines the landing speed. Blade loading is expressed in pounds per square foot and is obtained by dividing the total weight of a helicopter by the area of the rotor blades. Blade loading is not to be confused with disk loading, which is the total weight of a helicopter divided by the area of the disk swept by the rotor blades.

The ability of an aircraft to convert fuel energy into flying distance is one of the most important items of aircraft performance. In flying operations, the problem of efficient range operation of an aircraft appears in two general forms:

A common element for each of these operating problems is the specific range; that is, nautical miles (NM) of flying distance versus the amount of fuel consumed. Range must be clearly distinguished from the item of endurance. Range involves consideration of flying distance, while endurance involves consideration of flying time. Thus, it is appropriate to define a separate term, specific endurance.

Fuel flow can be defined in either pounds or gallons. If maximum endurance is desired, the flight condition must provide a minimum fuel flow. In Figure 7 at point A, the airspeed is low and fuel flow is high. This would occur during ground operations or when taking off and climbing. As airspeed is increased, power requirements decrease due to aerodynamic factors, and fuel flow decreases to point B. This is the point of maximum endurance. Beyond this point, increases in airspeed come at a cost. Airspeed increases require additional power and fuel flow increases with additional power.

Cruise flight operations for maximum range should be conducted so that the aircraft obtains maximum specific range throughout the flight. The specific range can be defined by the following relationship.

If maximum specific range is desired, the flight condition must provide a maximum of speed per fuel flow. While the peak value of specific range would provide maximum range operation, long-range cruise operation is generally recommended at a slightly higher airspeed. Most long-range cruise operations are conducted at the flight condition that provides 99 percent of the absolute maximum specific range. The advantage of such operation is that one percent of range is traded for three to five percent higher cruise speed. Since the higher cruise speed has a great number of advantages, the small sacrifice of range is a fair bargain. The values of specific range versus speed are affected by three principal variables:

These are the source of range and endurance operating data included in the performance section of the AFM/POH.

Cruise control of an aircraft implies that the aircraft is operated to maintain the recommended long-range cruise condition throughout the flight. Since fuel is consumed during cruise, the gross weight of the aircraft varies and optimum airspeed, altitude, and power setting can also vary. Cruise control means the control of the optimum airspeed, altitude, and power setting to maintain the 99 percent maximum specific range condition. At the beginning of cruise flight, the relatively high initial weight of the aircraft requires specific values of airspeed, altitude, and power setting to produce the recommended cruise condition. As fuel is consumed and the aircraft’s gross weight decreases, the optimum airspeed and power setting may decrease, or the optimum altitude may increase. In addition, the optimum specific range increases. Therefore, the pilot must provide the proper cruise control procedure to ensure that optimum conditions are maintained.

Total range is dependent on both fuel available and specific range. When range and economy of operation are the principal goals, the pilot must ensure that the aircraft is operated at the recommended long-range cruise condition. By this procedure, the aircraft is capable of its maximum design-operating radius or can achieve flight distances less than the maximum with a maximum of fuel reserve at the destination.

A propeller-driven aircraft combines the propeller with the reciprocating engine for propulsive power. Fuel flow is determined mainly by the shaft power put into the propeller rather than thrust. Thus, the fuel flow can be related directly to the power required to maintain the aircraft in steady, level flight, and on performance charts power can be substituted for fuel flow. This fact allows for the determination of range through analysis of power required versus speed.

The maximum endurance condition would be obtained at the point of minimum power required since this would require the lowest fuel flow to keep the airplane in steady, level flight. Maximum range condition would occur where the ratio of speed to power required is greatest. [Figure 7]

The maximum range condition is obtained at maximum lift/ drag ratio (L/DMAX), and it is important to note that for a given aircraft configuration, the L/DMAX occurs at a particular AOA and lift coefficient and is unaffected by weight or altitude. A variation in weight alters the values of airspeed and power required to obtain the L/DMAX. [Figure 8] Different theories exist on how to achieve max range when there is a headwind or tailwind present. Many say that speeding up in a headwind or slowing down in a tail wind helps to achieve max range. While this theory may be true in a lot of cases, it is not always true as there are different variables to every situation. Each aircraft configuration is different, and there is not a rule of thumb that encompasses all of them as to how to achieve the max range.

The variations of speed and power required must be monitored by the pilot as part of the cruise control procedure to maintain the L/DMAX. When the aircraft’s fuel weight is a small part of the gross weight and the aircraft’s range is small, the cruise control procedure can be simplified to essentially maintaining a constant speed and power setting throughout the time of cruise flight. However, a long-range aircraft has a fuel weight that is a considerable part of the gross weight, and cruise control procedures must employ scheduled airspeed and power changes to maintain optimum range conditions.

The effect of altitude on the range of a propeller-driven aircraft is illustrated in Figure 9. A flight conducted at high altitude has a greater true airspeed (TAS), and the power required is proportionately greater than when conducted at sea level. The drag of the aircraft at altitude is the same as the drag at sea level, but the higher TAS causes a proportionately greater power required.

NOTE: The straight line that is tangent to the sea level power curve is also tangent to the altitude power curve.

The effect of altitude on specific range can also be appreciated from the previous relationships. If a change in altitude causes identical changes in speed and power required, the proportion of speed to power required would be unchanged. The fact implies that the specific range of a propeller-driven aircraft would be unaffected by altitude. Actually, this is true to the extent that specific fuel consumption and propeller efficiency are the principal factors that could cause a variation of specific range with altitude. If compressibility effects are negligible, any variation of specific range with altitude is strictly a function of engine/propeller performance.

An aircraft equipped with a reciprocating engine experiences very little, if any, variation of specific range up to its absolute altitude. There is negligible variation of brake specific fuel consumption for values of brake horsepower below the maximum cruise power rating of the engine that is the lean range of engine operation. Thus, an increase in altitude produces a decrease in specific range only when the increased power requirement exceeds the maximum cruise power rating of the engine. One advantage of supercharging is that the cruise power may be maintained at high altitude, and the aircraft may achieve the range at high altitude with the corresponding increase in TAS. The principal differences in the high altitude cruise and low altitude cruise are the TAS and climb fuel requirements.

The aerodynamic properties of an aircraft generally determine the power requirements at various conditions of flight, while the powerplant capabilities generally determine the power available at various conditions of flight. When an aircraft is in steady, level flight, a condition of equilibrium must prevail. An unaccelerated condition of flight is achieved when lift equals weight, and the powerplant is set for thrust equal to drag. The power required to achieve equilibrium in constant-altitude flight at various airspeeds is depicted on a power required curve. The power required curve illustrates the fact that at low airspeeds near the stall or minimum controllable airspeed, the power setting required for steady, level flight is quite high.

Flight in the region of normal command means that while holding a constant altitude, a higher airspeed requires a higher power setting and a lower airspeed requires a lower power setting. The majority of aircraft flying (climb, cruise, and maneuvers) is conducted in the region of normal command.

Flight in the region of reversed command means flight in which a higher airspeed requires a lower power setting and a lower airspeed requires a higher power setting to hold altitude. It does not imply that a decrease in power produces lower airspeed. The region of reversed command is encountered in the low speed phases of flight. Flight speeds below the speed for maximum endurance (lowest point on the power curve) require higher power settings with a decrease in airspeed. Since the need to increase the required power setting with decreased speed is contrary to the normal command of flight, the regime of flight speeds between the speed for minimum required power setting and the stall speed (or minimum control speed) is termed the region of reversed command. In the region of reversed command, a decrease in airspeed must be accompanied by an increased power setting in order to maintain steady flight.

Figure 10 shows the maximum power available as a curved line. Lower power settings, such as cruise power, would also appear in a similar curve. The lowest point on the power required curve represents the speed at which the lowest brake horsepower sustains level flight. This is termed the best endurance airspeed.

An airplane performing a low airspeed, high pitch attitude power approach for a short-field landing is an example of operating in the region of reversed command. If an unacceptably high sink rate should develop, it may be possible for the pilot to reduce or stop the descent by applying power. But without further use of power, the airplane would probably stall or be incapable of flaring for the landing. Merely lowering the nose of the airplane to regain flying speed in this situation, without the use of power, would result in a rapid sink rate and corresponding loss of altitude.

If during a soft-field takeoff and climb, for example, the pilot attempts to climb out of ground effect without first attaining normal climb pitch attitude and airspeed, the airplane may inadvertently enter the region of reversed command at a dangerously low altitude. Even with full power, the airplane may be incapable of climbing or even maintaining altitude. The pilot’s only recourse in this situation is to lower the pitch attitude in order to increase airspeed, which inevitably results in a loss of altitude.

Airplane pilots must give particular attention to precise control of airspeed when operating in the low flight speeds of the region of reversed command.