Thrust
Velocity (TAS)
Thrust
Velocity (TAS)
(Full PCL)
(Full Throttle)
L/D MAX L/D MAX
TE
TE
TA TA
TR
TR
LEGEND
TE thrust
excess
TA thrust
available
TR thrust
required
AOC angle of
climb
TAS true
airspeed
L/D MAX lift to drag
ratio
maximum
PCL power
control lever
Max AOC (jet)
Max AOC (prop)
Figure 11-8. Comparison of maximum AOC between jet and propeller airplanes.
Altitude
Distance
Max AOC
Max ROC
Figure 11-7. Maximum angle of climb (AOC) versus maximum rate
of climb (ROC).
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 V Y, 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.
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.
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
Power
Velocity (TAS)
Power
Velocity (TAS)
(Full PCL)(Full Throttle)
L/D MAX L/D MAX
PE
PA PR
PA
PE
LEGEND
PE power
excess
PA power
available
PR power
required
ROC rate of
climb
TAS true
airspeed
L/D MAX lift to drag
ratio
maximum
PCL power
control lever
PR
Max ROC (jet) Max ROC (prop)
Figure 11-9. Comparison of maximum ROC between jet and propeller airplanes.
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]
Climb Performance Factors
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 11-10]
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
Indicated airspeed (knots)
Standard altitude (feet)
Service ceiling
Absolute ceiling
Best angle
of climb (Vx)
Best rate
of climb (Vy)
24,000
22,000
20,000
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
Sea level
70 80 90 100 110 120
Figure 11-10. Absolute and service ceiling.
Fuel flow/power required (HP)
Speed
Reference line
At altitude
A
B Maximum range at L/DMAX
Maximum endurance at
minimum power required Applicable for a particular
Weight
Altitude
Configuration
Figure 11-11. Airspeed for maximum endurance.
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.
specific endurance = flight hours
pounds of fuel
or
specific endurance = flight hours/hour
pounds of fuel/hour
or
specific endurance = 1
fuel flow
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 11-11 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.
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.
Range Performance
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:
1. To extract the maximum flying distance from a given
fuel load
2. To fly a specified distance with a minimum
expenditure of fuel
Power required
Speed
L/DMAX
Constant altitude
Higher weight
Lower weight
Basic weight
Figure 11-12. Effect of weight.
specific range = NM
pounds of fuel
or
specific range = NM/hour
pounds of fuel/hour
or
specific range = knots
fuel flow
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:
1. Aircraft gross weight
2. Altitude
3. The external aerodynamic configuration of the aircraft.
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 11-11]
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/D MAX. [Figure 11-12] 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.
Power required
Speed
L/DMAX
Constant weight
Sea level
At altitude
Figure 11-13. Effect of altitude on 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 11-13. 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.
Region of Reversed Command
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 11-14 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
Power setting
Speed
Best endurance speed
Power requiredRegion of
reversed
command
Maximum power available
Excess power
Figure 11-14. Power required curve.
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.
Takeoff and Landing Performance
The majority of pilot-caused aircraft accidents occur during
the takeoff and landing phase of flight. Because of this fact,
the pilot must be familiar with all the variables that influence
the takeoff and landing performance of an aircraft and must
strive for exacting, professional procedures of operation
during these phases of flight.
Takeoff and landing performance is a condition of
accelerated and decelerated motion. For instance, during
takeoff an aircraft starts at zero speed and accelerates to
the takeoff speed to become airborne. During landing, the
aircraft touches down at the landing speed and decelerates
to zero speed. The important factors of takeoff or landing
performance are:
• The takeoff or landing speed is generally a function
of the stall speed or minimum flying speed.
• The rate of acceleration/deceleration during the
takeoff or landing roll. The speed (acceleration and
deceleration) experienced by any object varies directly
with the imbalance of force and inversely with the
mass of the object. An airplane on the runway moving
at 75 knots has four times the energy it has traveling
at 37 knots. Thus, an airplane requires four times as
much distance to stop as required at half the speed.
• The takeoff or landing roll distance is a function of
both acceleration/deceleration and speed.
Runway Surface and Gradient
Runway conditions affect takeoff and landing performance.
Typically, performance chart information assumes paved,
level, smooth, and dry runway surfaces. Since no two
runways are alike, the runway surface differs from one
runway to another, as does the runway gradient or slope.
[Figure 11-15]
Runway surfaces vary widely from one airport to another.
The runway surface encountered may be concrete, asphalt,
gravel, dirt, or grass. The runway surface for a specific
airport is noted in the Chart Supplement U.S. (formerly
Airport/Facility Directory). Any surface that is not hard
and smooth increases the ground roll during takeoff. This
is due to the inability of the tires to roll smoothly along the
runway. Tires can sink into soft, grassy, or muddy runways.
Potholes or other ruts in the pavement can be the cause of
poor tire movement along the runway. Obstructions such
as mud, snow, or standing water reduce the airplane’s
acceleration down the runway. Although muddy and wet
surface conditions can reduce friction between the runway
and the tires, they can also act as obstructions and reduce
the landing distance. [Figure 11-16] Braking effectiveness
is another consideration when dealing with various runway
types. The condition of the surface affects the braking ability
of the aircraft.
The amount of power that is applied to the brakes without
skidding the tires is referred to as braking effectiveness.
Ensure that runways are adequate in length for takeoff
acceleration and landing deceleration when less than ideal
surface conditions are being reported.