Performance and Limitations

Performance Charts

Information in the AFM/POH is not standardized among manufacturers. Some provide the data in tabular form, while others use graphs.

Performance data is usually based on:

• Standard atmospheric conditions (59°F or 15°C, and 29.92" Hg).
• Pressure altitude or density altitude.

Some charts require interpolation for specific flight conditions. Interpolating means finding an intermediate value by calculating it from surrounding known values.

Density Altitude

Aircraft performance is based on density altitude. High density altitude refers to thin air, while low density altitude refers to dense air. Regardless of the actual altitude of the aircraft, it performs as though it were operating at an altitude equal to the existing density altitude.

As density altitude increases:

• Power Decreases: The engine takes in less air.
• Thrust Decreases: A propeller is less efficient in thin air.
• Lift Decreases: The thin air exerts less force on the airfoils.

Factors that Increase Density Altitude

• Low Atmospheric Pressure: At a constant temperature, density decreases directly with pressure.
• High Temperature: Increasing the temperature of a substance decreases its density.
• High Humidity: Water vapor is lighter than air; consequently, air becomes less dense as its water content increases.

Calculating Density Altitude

Density altitude is defined as "pressure altitude corrected for nonstandard temperature variations." Pressure altitude can be read off the altimeter when set to 29.92" Hg.

Density altitude can be found by:

• Using a flight computer.
• Referring to a table and chart.

Correcting for Humidity

Humidity is usually not considered an important factor in aircraft performance, but it is a contributing factor. Its effect can be determined using an online calculator.

Link: https://weather.gov/epz/wxcalc_densityaltitude

Example Calculation
Station Pressure: 22.22" Hg at 8,000'
Temperature: 80°F, Dew Point: 75°F
Density Altitude = 11,564'
With no humidity, the density altitude would be almost 500' lower.

When the temperature is greater than 5°C, a rule of thumb can be used: double the dew point in degrees Celsius and add a zero. Add the result to the density altitude.

Example Calculation
24°C + 24°C = 480' Correction

High-Density Altitude Considerations for Takeoffs

• Ensure the accuracy of weight and balance, takeoff distance, accelerate/stop distance, and climb rate calculations.
• Add a significant safety margin (15% to 50%) to all performance calculations.
• Lean the mixture, if equipped, for maximum horsepower.
• Anticipate a lower-than-normal pitch attitude during the liftoff and climb because of reduced thrust.

• Be aware that the airplane may "settle" after liftoff.
• Know the location of high terrain and obstacles in the vicinity of the airport.

Performance on the Runway

Runway Surface

Typically, performance chart information assumes paved, level, smooth, and dry runway surfaces. Any surface that is not hard and smooth increases the ground roll during takeoff. Runway surfaces for specific airports are noted in the Chart Supplements.

For small airplanes, the factors given below are often quoted in the flight manual as an alternative to data derived from testing or calculation.

Runway Gradient

The gradient (slope) of a runway is the amount of change in runway height over the length. It is expressed as a percentage. A positive gradient indicates the runway height increases, and a negative gradient indicates the runway decreases in height.

Runway gradient information is contained in the Chart Supplements. Depending upon the airplane's manufacturer, runway slope may be accounted for in the AFM/POH performance data.

An upsloping runway impedes acceleration and results in a longer ground run during takeoff. However, landing on an upsloping runway typically reduces the landing roll. A downsloping runway aids in acceleration on takeoff, resulting in shorter takeoff distances. However, landing on a downsloping runway increases landing distances.

Rules of thumb:

• An upslope increases takeoff distance by approximately 7% per degree.
• A downslope reduces takeoff distance by approximately 5% per degree.
• A downslope increases landing distance by approximately 10% per degree.

Safety Margins

The FAA recommends adding a safety margin of at least 15% to the planned takeoff and landing distances. Some pilots add 50% to their takeoff and landing calculations. The resulting distance should be within the runway length available and acceptable for obstacle clearance.

Takeoff Performance

The most critical conditions of takeoff performance are combinations of:

• High gross weight
• High-density altitude
• Contaminated runways
• Tailwinds
• Uphill slopes
• Short runways

Rules of thumb:

• Abort the takeoff if no more than 70% of the takeoff speed is reached by 50% of the runway length (the "50/70" rule).
• Add 50% to the planned takeoff distance over a 50-foot obstacle as a safety margin (the "50/50" rule).

Weight

The effect of gross weight on takeoff distance is significant and proper consideration of this item must be made in predicting the aircraft's takeoff distance.

An increase in gross weight:

• Requires a higher liftoff speed.
• Decreases acceleration.
• Increases the retarding force (drag and ground friction).

If the gross weight increases, more speed is required to get the aircraft airborne.

A 10% increase in takeoff gross weight causes:

• An estimated 5% increase in takeoff velocity.
• At least a 9% decrease in acceleration rate.
• At least a 21% increase in takeoff distance (high thrust-to-weight ratio aircraft).
• At least a 25% increase in takeoff distance (low thrust-to-weight ratio aircraft).

Wind

Rules of thumb:

• A headwind that is 10% of the takeoff airspeed reduces the takeoff distance by approximately 19%.
• A headwind that is 50% of the takeoff airspeed reduces the takeoff distance by approximately 75%.
• A tailwind that is 10% of the takeoff airspeed increases the takeoff distance by approximately 21%.

Density Altitude

An increase in density altitude:

• Requires a greater takeoff speed (true airspeed is higher than it would be at sea level).
• Decreases acceleration due to decreased thrust.

Planning for Intersection Departures

Pilots should assess the suitability of intersection departures during their preflight planning. Pilots may ask ATC for the distance between the intersection and the runway end. However, the distance may not be the same as any published declared distances.

Climb Performance

An airplane can climb from one or a combination of two factors:

• The excess power above that required for level flight. For example, an aircraft equipped with an engine capable of 200 horsepower, but using 130 horsepower to sustain level flight has 70 excess horsepower available for climbing.
• KE can be traded-off for PE by reducing airspeed.

Factors that determine climb performance during a steady climb:

• Airspeed: Too much or too little decreases climb performance.
• Drag: Configuration of gear, flaps, cowl flaps, and propellers must be made with consideration for the least possible drag.
• Power and Thrust: The rate of climb depends on excess power, while the angle of climb is a function of excess thrust.
• Weight: Extra weight in the aircraft negatively affects performance.

Best Angle of Climb

The maximum angle of climb (AOC), obtained at V_X, provides the greatest altitude gain over a certain distance. V_X is maintained when it is necessary for an airplane to clear obstacles after takeoff.

For a given weight of an aircraft, the angle of climb depends on the difference between thrust and drag, or the excess thrust. The maximum angle of climb occurs where there is the greatest difference between the thrust available and the thrust required.

Maximum excess thrust occurs:

• For a jet-powered airplane, at approximately the maximum lift/drag ratio (L/D_MAX).
• For a propeller-powered airplane, at an airspeed just above stall speed and below L/D_MAX.

Best Rate of Climb

The maximum rate of climb (ROC), obtained at V_Y, provides the greatest altitude gain over time. V_Y is maintained when an airplane needs to reach the cruising altitude in the shortest time.

For a given weight of an aircraft, the climb rate depends on the difference between the power available and the power required, or the excess power. The maximum climb rate occurs where there is the greatest difference between the power available and the power required.

Maximum excess power occurs:

• For a jet-powered airplane, at an airspeed above L/D_MAX.
• For a propeller-powered airplane, at an airspeed close to L/D_MAX.

Effect of Weight

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.

An increase in an aircraft's weight produces a twofold effect on climb performance:

• Increased Drag and Power Required: Reserve power available is reduced, which in turn, affects both the climb angle and the climb rate.
• Reduced Rate of Climb: Less reserve thrust is available for climbing due to the increase in drag.

Effect of Altitude

As altitude increases, air density decreases, resulting in reduced available power. Airplanes with fixed-pitch propellers experience a reduction in RPM. Airplanes that are equipped with controllable propellers show a decrease in manifold pressure.

Speeds for the maximum rate of climb (V_Y) and maximum angle of climb (V_x) vary with altitude. As altitude increases, V_Y decreases and V_x increases until they converge at the aircraft's absolute ceiling.

At the absolute ceiling, there is no excess of power, and only one speed allows steady, level flight. Consequently, the aircraft produces a zero rate of climb. The service ceiling is the altitude at which the aircraft cannot climb at a rate greater than 100 FPM.

Cruise Performance

In flying operations, the problem of efficient range operation of an aircraft appears in two general forms:

• To extract the maximum flying distance from a given fuel load; or
• To fly a specified distance with a minimum expenditure of fuel.

Maximum Range

Maximum range (distance) occurs where the ratio of speed to power/thrust required is greatest. The maximum range speed is dependent on the type of powerplant.

The maximum range speed occurs:

• For a jet-powered airplane, above L/D_MAX (near the typical cruise speed).
• For a propeller-driven airplane, at L/D_MAX (minimum drag condition).

A variation in weight alters the values of airspeed and power required to obtain the L/D_MAX. Since fuel is consumed during cruise, the aircraft's gross weight varies, and optimum airspeed, altitude, and power setting can also vary.

The following formula determines the specific range for any given flight condition. It is a useful calculation for comparing the efficiency and range of various aircraft.

Specific Range = NM per Hour ÷ Pounds of Fuel per Hour

Long-range cruise operations are normally conducted at the flight condition that provides 99% of the absolute maximum specific range. The advantage of such an operation is that 1% of the range is traded for 3 to 5% higher cruise speed.

Maximum Endurance

Maximum endurance (flying time) is obtained in a flight condition that requires the minimum amount of fuel flow to maintain steady, level flight.

The maximum endurance speed occurs:

• For a jet-powered airplane, at L/D_MAX (minimum drag and thrust condition).
• For a propeller-driven airplane, at approximately 75% of L/D_MAX (minimum power condition).

The following formula determines the specific endurance for any given flight condition.

Specific Endurance = Flight Hours per Hour ÷ Pounds of Fuel per Hour

Cruise Control

Cruise control of an aircraft implies that the aircraft is operated to maintain the recommended long-range cruise condition throughout the flight. As fuel is consumed, the aircraft's gross weight decreases. The optimum airspeed and power setting decrease, or the optimum altitude increases.

Effects of Wind

Different theories exist on achieving maximum range when a headwind or tailwind is present. Many say that speeding up in a headwind or slowing down in a tailwind helps achieve the maximum range. While this theory may be true in many cases, there are variables in every situation.

Effects of Altitude

A flight conducted at a high altitude has a greater true airspeed (TAS) for the same indicated airspeed (IAS). Drag is the same, but the higher TAS causes a proportionately greater power required.

Range: An aircraft equipped with a reciprocating engine experiences very little, if any, variation of specific range up to its absolute altitude (not considering wind).

Endurance: Since the power required increases with altitude, the maximum endurance of a propeller-driven aircraft is achieved at sea level. If the airplane were over a flat surface, maintaining ground effect could reduce drag and extend the endurance.

Landing Performance

The most critical conditions of landing performance are combinations of:

• High gross weight
• High-density altitude
• Contaminated runways
• Tailwinds
• Downhill slopes
• Less than maximum landing flaps

• Short runways

Rules of thumb:

• Increase the landing distance by 50% for a wet runway.
• Increase the approach speed by 20% if ice is on the wings.
• For every knot above the recommended approach airspeed at the runway threshold, the touchdown point is 100' further down the runway.

Minimum Landing Distances Versus Ordinary Landings

A distinction should be made between the procedures for minimum landing distance and an ordinary landing roll with considerable excess runway available. Minimum landing distance is obtained by creating a continuous peak deceleration of the aircraft (maximum braking). On the other hand, an ordinary landing roll with considerable excess runway may allow extensive use of aerodynamic drag to minimize wear and tear on the tires and brakes.

Height Above Touchdown

Landing distances furnished in the AFM/POH are based on the landing gear being 50' above the runway threshold. For every 10' above the standard 50' threshold crossing height, the landing distance increases by approximately 200'.

Weight

The minimum landing distance varies in direct proportion to the gross weight. An increase in gross weight requires a faster approach speed and requires more effort to decelerate to a stop after landing.

A 10% increase in gross weight causes:

• An estimated 5% increase in landing velocity.
• An estimated 10% increase in landing distance.

Density Altitude

An increase in density altitude increases the landing speed. The aircraft at altitude lands at the same indicated airspeed (IAS) as at sea level, but the true airspeed (TAS) is greater because of the reduced density.

Because a given IAS corresponds to a higher TAS at higher density altitudes, pilots are sometimes "tricked" by visual cues and fly slower than they should.

The approximate increase in landing distance with altitude is approximately 3.5% for each 1,000' of altitude. At 5,000', the required landing distance is 16% greater than at sea level.

Excessive Airspeed and Wind

The speed (acceleration and deceleration) experienced by any object varies directly with the imbalance of force and inversely with the object's mass.

Rules of thumb:

• An increase in the approach speed by 10% increases the landing distance by 20%.
• For every 10 knots of tailwind, increase the landing distance by at least 21%.

Excessive speed upon touchdown places a greater load on the brakes because of the additional kinetic energy. Also, excessive speed increases lift in the normal ground attitude after landing, which reduces braking effectiveness.

Aircraft Weight

Definitions

Standard Empty Weight (SEW): The weight of an aircraft, including unusable fuel, full operating fluids, and full oil.

Basic Empty Weight (BEW): The standard empty weight plus optional equipment.

BEW = SEW + Optional Equipment

Basic Operating Weight (BOW): The basic empty weight plus the weight of the items considered standard by the operator, such as the flight crew, spare parts, and emergency equipment.

BOW = BEW + Standard Items

Payload: The weight of all occupants, cargo, and baggage ("the things that we are paid to fly").

Useful Load: The maximum weight of the occupants, bags, usable fuel, and drainable oil.

Useful Load = Maximum Takeoff or Ramp Weight - BEW

Unusable Fuel: The fuel remaining in the airplane's fuel system after a run-out test was completed during certification.

Usable Fuel: The fuel available for flight planning.

Zero Fuel Weight (ZFW): The weight of an aircraft without fuel.

ZFW = BEW + Payload

Maximum Zero Fuel Weight (MZFW): The maximum weight of the aircraft and everything that is carried exclusive of usable fuel. Any weight added to the aircraft above this weight must be fuel. This weight is established to prevent structural damage.

The MZFW determines the maximum available payload (occupants, cargo, and baggage):

Maximum Payload = MZFW - BEW

Maximum Ramp Weight: The maximum weight approved for ground maneuvers.

Maximum Takeoff Weight: The maximum weight approved for the start of the takeoff roll.

Maximum Landing Weight: The maximum weight approved for the landing touchdown.

Effect of Weight on Aircraft Performance

An overloaded aircraft may not be able to leave the ground, or if it does become airborne, it may exhibit unexpected and unusually poor flight characteristics.

Performance deficiencies of an overloaded aircraft include:

• Faster takeoff speed and a longer takeoff roll
• Reduced rate and angle of climb
• Lower maximum altitude (service ceiling)
• Shorter range
• Reduced cruising speed
• Reduced maneuverability

• Faster stalling speed
• Faster approach speed and longer landing roll

Effect of Weight on Aircraft Structure

Excessive weight can result in structural damage or a complete failure of the aircraft's structure. The effects of overload are magnified by load factors imposed by flight maneuvers and turbulence.

Structural failures that result from overloading may be dramatic and catastrophic, but more often, they affect structural components progressively. Habitual overloading tends to cause cumulative stress and damage that may not be detected during preflight inspections and result in structural failure later during completely normal operations.

Effect of Weight on Stability and Controllability

Although weight distribution is more of a factor, an increase in the aircraft's gross weight may adversely impact stability, regardless of the CG location.

Aircraft Balance

Definitions

Arm: A horizontal distance, usually measured in inches, from the reference datum to the CG or a load in the airplane.

Reference Datum: An imaginary vertical plane from which all horizontal distances (arms) are measured.

Center of Gravity (CG): The point at which an airplane would balance if it were possible to suspend it from that point. The CG is found by dividing the total moment by the total weight. The CG location is typically expressed in inches aft of the datum for small airplanes.

Center of Gravity Limits: The extreme forward and aft CG locations within which the airplane must be operated.

Moment: A force that causes or tries to cause an object to rotate. It is the product of the weight of an item multiplied by its arm.

Moment Index: The moment divided by a reduction number such as 100 or 1,000 to make the moment value smaller.

Station: A location along the airplane fuselage, usually given in terms of distance from the reference datum. For example, an item located at station +50 would have an arm of 50 inches.

Principles of Weight and Balance

Three items are used in weight and balance calculations: moment, weight, and arm.

Moment = Weight × Arm

A simple way to explain the weight and balance calculations is with a seesaw. For the board to balance, the weights must be distributed so that the leverages (moments) are the same on each side of the fulcrum.

Applying Principles of Weight and Balance to an Aircraft

The same principles of weight and balance used for a seesaw can be applied to an aircraft. Instead of balancing the weight at a fulcrum, an aircraft must be loaded so its CG falls within an acceptable range (CG limits).

Considerations in loading an airplane:

• CG Location: The weight must be loaded within the CG limits (forward and aft balance).
• Total Weight: The maximum allowable weight of the airplane must not be exceeded.

Aircraft Weight and Center of Gravity Data

The aircraft manufacturer determines CG and weight limits during the certification process. The CG limits are published in the AFM/POH and the Type Certificate Data Sheet (TCDS). These values apply to all airplanes of the same model unless an airplane is later modified, for example, by a Supplemental Type Certificate (STC).

Each airplane has its empty weight and empty-weight CG location determined after being fully built. The data is recorded in the weight and balance record. The record must be kept on the airplane while it is in flight.

Each airplane also has an equipment list that contains an inventory of the equipment installed by the manufacturer or operator. The equipment list is current at the time the airplane was certified. After that, it must be maintained by the owner.

Updating Weight and Balance Data

The weight and balance record and equipment list for privately-owned and operated aircraft remain valid unless:

• Any item on the equipment list is removed.
• A new piece of equipment is permanently installed.
• The aircraft undergoes an alteration that affects its weight.

When one of these conditions is met, a mechanic must update the weight and balance record and equipment list, as applicable.

Forward Versus Rearward Center of Gravity

The primary concern in balancing an aircraft is the fore and aft location of the CG along the longitudinal axis. Exceeding the forward or aft CG limit can seriously impair the controllability and performance of an aircraft.

Balance Around the Lateral (Roll) Axis

AFMs/POHs do not typically provide information concerning weight distribution along the lateral axis (left and right), although some airplanes may have limitations concerning fuel imbalances between the left and right wing tanks. Pilots should, however, evenly distribute weight between the left and right sides of the aircraft. An asymmetrical distribution can create a tendency for the aircraft to roll towards the heavier side.

Weight and Balance Calculations

Computational Method: In the computational method, a weight/arm/moment calculation determines where the CG is.

General steps of the computational method:

1. List the weight of the empty aircraft, occupants, fuel, and baggage.
2. Calculate the moment for each item listed.
3. Find the total weight and total moment.
4. Divide the total moment by the total weight to determine the CG.

Graph Method: Some manufacturers provide graphs to determine the CG. The graphs are used to determine the moments. Then the CG is computed in the same manner as the computational method.

Center of Gravity Formula

To find the location of the CG in inches aft of the datum, use the following formula.

CG = Total Moment ÷ Total Weight

Weight Shift Formula

Pilots must be able to solve problems involving the shift, addition, or removal of weight.

Scenario One: A Passenger or Cargo is Moved

A passenger or cargo is moved resulting in an unknown CG location. To determine the CG change, use the following formula. The Greek letter delta (Δ) represents a change in values.

Δ CG = (Weight Shifted × Distance Shifted) ÷ Total Weight

The final step is to determine the new CG location. Add if the weight is moved aft. Subtract if it is moved forward.

New CG = Old CG ± ∆ CG

Scenario Two: The CG is Out of Range

A pilot loads an aircraft and discovers the CG limit has been exceeded. The best solution is to shift baggage, passengers, or both. The amount of weight to be shifted can be determined with the following formula.

Weight to Shift = (Total Weight × ∆ CG Required) ÷ Distance Weight is Shifted

Weight Added/Subtracted Formula

The following formula can be used if passengers or cargo are added or removed from the aircraft after completing the weight and balance computations. It can also determine the new CG after fuel is burned.

Weight Lost or Gained ÷ New Total Weight = ∆ CG ÷ (|Weight Arm - Old CG|)

The unknown value is the CG change (∆ CG), which can be determined by an arrangement of the equation. The CG change could be positive or negative depending on whether weight is added or subtracted and whether the change is ahead of or behind the current CG.

Δ CG = ( Weight Lost or Gained × (|Weight Arm - Old CG|) ) ÷ New Total Weight

The final step is to determine the new CG location. Add if the CG is moved aft. Subtract if it is moved forward.

New CG = Old CG ± ∆ CG