Pilot's Handbook of Aeronautical Knowledge
Chapter 11: Aircraft Performance
The performance or operational information section of the Aircraft Flight Manual/Pilot's Operating Handbook (AFM/ POH) contains the operating data pertaining to takeoff, climb, range, endurance, descent, and landing. The use of this data in flying operations is mandatory for safe and efficient operation.
Manufacturers' information and data is not standardized, and performance data may be presented on the basis of standard atmospheric conditions. Pressure and temperature have a major effect on aircraft performance, which pilots should take into account when predicting performance.
Pressure and Density Altitude
Pilots are mainly concerned with atmospheric pressure. Air a fluid substance that has mass, weight, and a force that is exerted equally in all directions. The effect of air on bodies within the air is called pressure. The pressure of the atmosphere varies with altitude and temperature. As air becomes less dense, it reduces power, thrust, and lift.
A standard temperature lapse rate observes the temperature decreasing at the rate of approximately 3.5 degrees F (2 degrees C) per thousand feet, up to 36,000 feet. Above this, the temperature is constant up to 80,000 feet.
A standard pressure lapse rate observes pressure decreasing at a rate of approximately 1"H g per 1,000 feet of altitude gain, up to 10,000 feet. This often is referred to as International Standard Atmosphere (ISA) or ICAO Standard Atmosphere. [11-2]
Any temperature or pressure that differs from the standard lapse rates is considered nonstandard temperature and pressure.
All aircraft instruments are calibrated for the standard atmosphere. Thus, corrections must be applied to the instrumentation and predicted performance if actual operating conditions vary from the standard atmosphere.
The Standard Datum Plane (SDP) is a theoretical level at which atmospheric pressure is 29.92" Hg and the weight of air is 14.7 psi. SDP may be below, at, or above sea level as atmospheric pressure changes.
Pressure altitude is the height above the SDP. Pressure altitude is a basis for determining aircraft performance. It also is used for assigning flight levels to aircraft operating at above 18,000 feet (FL 180).
If the altimeter is set to 29.92", the indicated altitude is pressure altitude. Pressure altitude also can be determined by applying a correction factor to the reported altimeter setting, or by using a flight computer.
Density altitude is pressure altitude corrected for nonstandard temperature. Density altitude is the vertical distance above sea level in the standard atmosphere at which a given density is to be found.
As the density of the air increases (low density altitude), aircraft performance increases. As air density decreases (higher density altitude), aircraft performance decreases
High density altitude refers to thin air while low density altitude refers to dense air. An increase in the air density results in "lower" density altitude, not "higher" density altitude, even though the increased weight of the air has more (a higher amount) of pressure. "High density altitude" refers to a higher altitude with air that is less dense.
Density altitude is determined by first finding pressure altitude and then correcting this altitude for nonstandard temperature variations. A known density occurs for any one temperature and pressure altitude. 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.
Air density is affected by changes in altitude, temperature, and humidity. Contributors to high density altitude are high elevations, low atmospheric pressures, high temperatures, and high humidity.
Density altitude can be computed with a flight computer or a tabular chart.
Air 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.)
Increasing the temperature of a substance decreases its density. (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. With less pressure, the air becomes less dense, while lower temperature will make the air more dense. However, the fairly rapid drop in pressure as altitude is increased usually has the dominant effect. Pilots can expect the density to decrease with altitude.
Air Pressure, Air Density, and Pressure Altitude
When thinking about air pressure, it's best to use a stack of blankets as a metaphor. Imagine 300 blankets, piled high in a column.
Now get under them. You'll feel squished.
The atmosphere is similar to a stack of blankets. Air is matter — it has molecules, and these molecules become compressed if there's a lot of air overhead, because that overhead air is pressing down.
The atmosphere's downward force is easy to measure with a mercury barometer (although these aren't widely used anymore). At sea level, we typically measure about 30 inches of mercury within a sealed tube. An open dish at the base of the tube also contains mercury, and the mercury in this dish is resisting the air that is pressing down on it.
If we take this barometer to a location other than sea level, we'll see that the mercury in the measuring tube will fall, because the mercury in the dish is better able to resist the atmosphere's reduced downward force at higher elevations. The mercury in the dish rises, and the mercury in the measuring tube falls. If we drive up a mountain road, we'll see that (generally speaking) the atmosphere loses one inch of downward force for every 1,000 feet of elevation. As we climb, the mercury in the open dish continues to rise while the mercury in the measuring tube continues to fall.
So if we're looking at a barometer, we might say "Air pressure is 30 inches of mercury." We might even say "Current pressure is 30 inches." But we also could say "three hundred blankets" or "three thousand layers," because what we really care about are the measured layers of air molecules that are piled thousands of feet high.
People at or near sea level exist under about 3,000 layers of air molecules, most of the time. You can think of these as thin layers. In most of the earth's inhabited areas, each measurable layer of atmosphere is about 10 feet tall.
However, people who live at higher elevations, such as Denver, have adjusted to life under 2,500 layers of air molecules. Compared to a coastal atmosphere, the atmosphere in the Rocky Mountains is receiving less downward force, and this somewhat expanded air has fewer available oxygen molecules. That said, almost everyone adjusts to it.
Tibetans in the high Himalayas, above 14,000 feet, live under a mere 1,600 layers of air molecules. That's why visitors to camps at the base of Mount Everest feel a bit light-headed when they first arrive. There isn't as much air above them to press down on the air at the surface. Therefore, the air molecules aren't as squished together compared to a sea-level atmosphere, and this includes oxygen molecules. Up high, the result is "thin air."
Density vs. Pressure
Does the atmosphere at 14,000 feet have less oxygen than a sea-level atmosphere? Yes and no. Because the air isn't being squished down to the same degree as at lower elevations, there aren't as many molecules roaming around in a block of air. The reduction in air pressure results in a reduction in air density. Without question, oxygen becomes scarce at higher elevations.
However, it would be inaccurate to say "The atmosphere has a reduced amount oxygen at higher elevations" — at least, if we are comparing oxygen to other atmospheric matter. About 99% of the tropopause is made up of nitrogen and oxygen. As air density reduces with increased elevation, these molecules become more disperse, which means that there is less oxygen available for organisms that require it. But since both the nitrogen and oxygen molecules become more disperse, it's incorrect to say that the relative amount of oxygen in the atmosphere decreases with altitude. Instead, all atmospheric matter becomes more scarce. (You may come across knowledge test questions on this, which is why it's worth noting.)
It's also important to note that air overhead pressing down on the air below — air pressure — is only one contributing factor when it comes to air density. Air presssure also is affected by changes in temperature, and air density is affected by altitude, temperature, and humidity. So while air pressure and air density are correlated, altitude is not the only variable that creates a specific density within a block of air. Two blocks of air at the same altitude, but with different temperature or humidity characteristics, will have different densities.
So where is pressure altitude?
"Pressure altitude" is the altitude that appears on a barometric altimeter when the pressure is set to 29.92 inches of mercury. On any given day, this probably will be different than the altimeter's physical location, because the current air pressure would have to be exactly 29.92 for pressure altitude to match true altitude. Almost always, pressure altitude is somewhere else.
But it's easy to find, because it's always buried under 2,992 layers of air molecules.
Let's say you listen to a weather broadcast that reports the local altimeter is 29.86. Where is pressure altitude? Your location is buried under 2,986 layers of air, which is fewer than the 2,992 layers that are covering the altimeter at pressure altitude. You are above the pressure altitude. By how much? If we drop one inch of mercury for every 1,000 feet of altitude, then we lose 10 feet for every 1/100th of an inch.
At the location of pressure altitude, the atmosphere has enough downward force to elevate 29.92 inches of mercury.
Thus, if the atmosphere you occupy has enough downward force to elevate 29.86 inches of mercury, your atmosphere is 60 feet above pressure altitude. Or "six ten-foot layers," since each .01 of mercury is about 10 feet tall (in the inhabited troposphere).
Therefore, the pressure altitude is 60 feet below the true altitude.
However, if you enter an air pressure in your altimeter that is heavier than your current air pressure, your altimeter will rise, not fall. Why?
Because you are asking the altimeter a performance question: "If my current air pressure at sea level is 29.82, what altitude would that represent if my current pressure were 29.92? How would my airplane perform in these conditions?"
The airplane will perform as if it were operating from an airport with a field elevation of about 100 feet. And if you are at sea level and change your current altimeter from 29.82 to 29.92, the altimeter will rise, not fall.
Humidity can be an important factor in aircraft performance. A small amount of water vapor suspended in the atmosphere may be negligible under certain conditions, but the air is never completely dry.
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. Warm air can hold more water vapor, while colder air can hold less.
Water vapor is lighter than air. As the water content of the air increases, the air becomes less dense, causing an increase in density altitude, which reduces performance. Air is at its lightest and least dense when it contains the maximum amount of water vapor.
Humidity alone is usually not considered an essential factor in calculating density altitude and aircraft performance, but it does contribute. There is no rule-of-thumb or chart used to compute the effects of humidity on density altitude, but pilots should expect a decrease in overall performance in high humidity conditions.
Performance describes an aircraft's useful abilities. This can include takeoff, landing, rate of climb, payload capacity, altitudes, airspeeds, range, maneuverability, stability, fuel burn, and any other metrics deemed useful. All result from the combination of aircraft and powerplant.
When an aircraft is in straight and level flight, the condition of equilibrium must prevail.
Thrust is a force or pressure exerted on an object, and is measured in pounds or Newtons.
Power is a measurement of the rate of performing work or transferring energy, and is measured in horsepower (hp) or kilowatts (kw).
Mechanical energy can be kinetic or potential. Kinetic energy (KE) comes from speed, while potential energy (PE) is stored.
A climb can be achieved by applying excess horsepower. A climb also can be achieved by an exchange of energy, if the pilot converts the kinetic energy of airspeed (KE) to a gain in altitude (PE). As the altitude increases, airspeed is reduced.
Angle of Climb (AOC) is a comparison of altitude gained relative to distance traveled, i.e. the inclination (angle) of the flight path. Maximum AOC is used to clear obstacles, represented by the performance speed Vx. If excess thrust is available, the greater force can result in a steeper climb.
Rate of Climb (ROC) is a comparison of altitude gained relative to the time needed to reach that altitude, represented by the performance speed Vy, and resulting a maximum gain in altitude over a given period of time. Maximum ROC occurs at an airspeed and AOA combination that produces the maximum excess power.
Climb performance is directly dependent upon the ability to produce either excess thrust or excess power.
A change in weight changes the drag and the power required, affecting both the climb angle and the climb rate. An increase in weight also reduces the maximum ROC.
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 service ceiling is the altitude at which the aircraft is unable to climb at a rate greater than 100 feet per minute (fpm). 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.
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..
Wing loading is obtained by dividing the total weight of an airplane in pounds by the wing area. Wing loading determines the airplane's landing speed.
Endurance involves consideration of flying time, rather than distance traveled. Range is the ability of an aircraft to convert fuel energy into flying distance.
Maximum endurance requires a flight condition with minimum fuel flow.
Maximum specific range requires a flight condition with a maximum of speed per fuel flow.
Maximum endurance occurs at the point of minimum power required, since this requires the lowest fuel flow to keep the airplane in steady, level flight. Maximum range condition occurs where the ratio of speed to power required is greatest. The maximum range condition is obtained at maximum lift/ drag ratio (L/D max).
Long-range aircraft have a fuel weight that is a considerable part of the gross weight. Cruise control procedures employ scheduled airspeed and power changes to maintain optimum range conditions.
A flight conducted in a propeller-driven aircraft at high altitude has a greater true airspeed (TAS), and the power required is proportionately greater than when conducted at sea level because of the higher TAS. The drag of the aircraft at altitude is the same as the drag at sea level.
An aircraft equipped with a reciprocating engine experiences very little, if any, variation of specific range up to its absolute altitude.
Region of Reversed Command
The aerodynamic properties of an aircraft determine the power requirements at various conditions of flight. Powerplant capabilities determine the power available at various conditions of flight.
The power required to achieve equilibrium in constant-altitude flight at various airspeeds is depicted on a power required curve.
At low airspeeds, the power setting required for steady, level flight is high.
In the region of normal command, a higher airspeed requires a higher power setting and a lower airspeed requires a lower power setting to hold altitude. Most flight is conducted in this region.
In the region of reversed command while holding a constant altitude, a higher airspeed requires a lower power setting and a lower airspeed requires a higher power setting to hold altitude. This exists for flight speeds below the speed for maximum endurance, i.e. the lowest point on the power curve. This is often referred to as "flight behind the power curve" or "the backside of the curve." [11-14]
If an unacceptably high sink rate should develop on the backside of the power curve, it may be possible for the pilot to reduce or stop the descent by applying power. If additional power is not available, the airplane may stall or be incapable of flaring for landing. The only recourse is to lower the pitch attitude in order to increase airspeed, which inevitably results in a loss of altitude. If sufficient altitude does not exist, impact is possible.
Takeoff and Landing Performance
The most critical conditions of takeoff performance are the result of some combination of high gross weight, altitude, temperature, and unfavorable wind. An accurate prediction of takeoff distance can be determined from the performance data of the AFM/POH.
An airplane on the runway moving at 80 knots has four times the energy it has traveling at 40 knots. Thus, an airplane requires four times as much distance to stop as required at half the speed.
Any runway surface that is not hard and smooth increases the ground roll during takeoff. Runways can be concrete, asphalt, gravel, dirt, or grass.
The amount of power that is applied to the brakes without skidding the tires is referred to as braking effectiveness. Water on the runway can reduce braking effectiveness.
The gradient or slope of the runway is the amount of change in runway height over the length of the runway. The gradient is expressed as a percentage, such as a 3 percent gradient. This means that for every 100 feet of runway length, the runway height changes by 3 feet. A positive gradient indicates the runway height increases, and a negative gradient indicates the runway decreases in height. Up-sloping and down-sloping runways affect takeoff performance.
Dynamic hydroplaning is a condition in which the aircraft tires ride on a thin sheet of water rather than on the runway's surface. The minimum hydroplaning speed (in knots) is determined by multiplying the square root of the main gear tire pressure in psi by nine. (If the tire pressure is 36 psi, the square root is 6, and thus the hydroplaning speed is 54 knots.) Once hydroplaning starts, it can continue well below the minimum initial hydroplaning speed.
The lift-off speed is a fixed percentage of the stall speed or minimum control speed for the aircraft in the takeoff configuration. It can be anywhere from 1.05% to 1.25% the stall speed or minimum control speed.
Any item that alters the takeoff speed or acceleration rate during the takeoff roll affects the takeoff distance. Increased gross weight creates a higher lift-off speed, because there is a greater mass to accelerate and an in increase in drag and ground friction. For example, a 21% increase in takeoff weight requires a 10% increase in lift-off speed to support the greater weight.
The effect of a headwind is to allow the aircraft to reach the lift-off speed at a lower groundspeed, while the effect of a tailwind is to require the aircraft to achieve a greater groundspeed to attain the lift-off speed. The effect of wind on landing distance is identical to its effect on takeoff distance.
An increase in density altitude can produce a greater takeoff speed, as well as decreased thrust and reduced net accelerating force.
Proper accounting of pressure altitude and temperature is mandatory for accurate prediction of takeoff roll distance.
If an aircraft of given weight and configuration is operated at a pressure altitude above standard sea level, the aircraft requires the same dynamic pressure to become airborne at the takeoff lift coefficient. Thus, the aircraft at altitude takes off at the same indicated airspeed (IAS) as at sea level, but because of the reduced air density, the TAS is greater.
An increase in altitude above standard sea level brings an immediate decrease in power output for the unsupercharged reciprocating engine.
The most critical conditions of landing performance are combinations of high gross weight, high density altitude, and unfavorable wind.
The landing speed is some fixed percentage of the stall speed or minimum control speed for the aircraft in the landing configuration. Runway slope and condition are additional factors.
Minimum landing distance is obtained with extensive use of the brakes for maximum deceleration. An ordinary landing roll may allow use of aerodynamic drag to minimize wear on the tires and brakes. Aerodynamic drag is applicable only for deceleration to 60 or 70 percent of the touchdown speed.
Wind alters the groundspeed at which the aircraft touches down.
An increase in density altitude increases the landing speed. An aircraft at altitude lands at the same IAS as at sea level but, because of the reduced density, the TAS is greater. Deceleration is the same as with the landing at sea level, but the TAS will affect the landing distance.
The approximate increase in landing distance with altitude is approximately three and one-half percent for each 1,000 feet. At 5,000 feet, the minimum landing distance is 16 percent greater than the minimum landing distance at sea level.
A ten percent excess landing speed causes at least a 21 percent increase in landing distance. A tail wind of ten knots also increases the landing distance by about 21 percent.
Performance charts are found in the AFM/POH, as provided by the manufacturer. They allow a pilot to predict the takeoff, climb, cruise, and landing performance of an aircraft. Data from the charts will not be accurate if the aircraft is not in good working order or when operating under adverse conditions.
Charts are not standardized and may appear in a variety of formats. Pilots should be familiar with the conventions of performance charts in the AFM/POH of their airplanes.
See the Pilot's Handbook of Aeronautical Knowledge for examples of various performance charts.
Commercial Pilot & Flight Instructor Test Questions
What effect does high density altitude, as compared to low density altitude, have on propeller efficiency? Efficiency is reduced because the propeller exerts less force at high density altitudes than at low density altitudes.
As density altitude increases, which will occur if a constant indicated airspeed is maintained in a no-wind condition? True airspeed increases; groundspeed increases.
— An increase in density altitude will indicate that the air has become less dense.
Which statement is true regarding takeoff performance with high density altitude conditions? The acceleration rate is slower because the engine and propeller efficiency is reduced.
If atmospheric pressure and temperature remain the same, how would an increase in humidity affect takeoff performance? Longer takeoff distance; the air is less dense.
— Water vapor is less dense than dry air.
What effect does an uphill runway slope have upon takeoff performance? Increases takeoff distance.
In a propeller-driven aircraft, maximum range occurs at maximum lift/drag ratio.
— "Maximum endurance" occurs at minimum power required.
What can a pilot expect when landing at an airport in the mountains? Higher true airspeed and longer landing distance.
What can a pilot expect when landing at an airport located at a much higher elevation? Higher true airspeed and longer landing distance.