The majority of pilot caused airplane accidents occur during the takeoff and landing phase of flight. Because of this fact, the Naval Aviator must be familiar with all the many variables which influence the takeoff and landing performance of an airplane and must strive for exacting, professional techniques of operation during these phases of flight.
Takeoff and landing performance is a condition of accelerated motion. For instance, during takeoff the airplane starts at zero velocity and accelerates to the takeoff velocity to become airborne. During landing, the airplane touches down at the landing speed and decelerates (or accelerates negatively) to the zero velocity of the stop. In fact, the landing performance could be considered as a takeoff in reverse for purposes of study. In either case, takeoff or landing, the airplane is accelerated between zero velocity and the takeoff or landing velocity. The important factors of takeoff or landing performance are:
(1) The takeoff" or landing velocity which
will generally be a function of the stall
speed or minimum flying speed, e. g., 15 percent above the stall speed.
(2) The acceleration during the takeoff or landing roll. The acceleration experienced by any object varies directly with the unbalance of force and inversely as the mass of the object.
(3) The takeoff or landing roll distance is a function of both the acceleration and velocity.
In the actual case, the takeoff and landing distance is related to velocity and acceleration in a very complex fashion. The main source of the complexity is that the forces acting on the airplane during the takeoff or landing roll are ’difficult to define with simple relationships. Since the acceleration is a function of these forces, the acceleration is difficult to define in a simple fashion and it is a principal variable affecting distance. However, some simplification can be made to study the basic relationship of acceleration, velocity, and distance While the acceleration is not necessarily constant or uniform throughout the takeoff or landing roll, the assumption of uniformly accelerated motion will facilitate study of the principal variables. affecting takeoff and landing distance.
From basic physics, the relationship of velocity, acceleration, and distance for uniformly accelerated motion is defined by the following equation: where
S= acceleration distance, ft.
V= final velocity, ft. per sec., after accelerating uniformly from zero velocity a~ acceleration, ft. per sec.2 This equation could relate the takeoff distance in terms of the takeoff velocity and acceleration when the airplane is accelerated uniformly from zero velocity to the final takeoff velocity. Also, this expression could relate the landing distance in terms of the landing velocity and deceleration when the airplane is accelerated (negatively) from the landing velocity to a complete stop. It is important to note that
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TAKEOFF OR LANDING DISTANCE, FT.
|
|
Figure 2.31. Relationship of Velocity, Acceleration, and Distance for Uniformly Accelerated Motion
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the distance varies directly as the square of the velocity and inversely as the acceleration.
As an example of this relationship, assume that during takeoff an airplane is accelerated uniformly from zero velocity to a takeoff velocity of 150 knots (253 5 ft. per sec.) with an acceleration of 6.434 ft. per sec.1 (or, 0.2g, since g = 32.17 ft. per sec.1). The takeoff distance would be:
„ (253-5)2 (2X6.434)
= 5,000 ft.
If the acceleration during takeoff were reduced 10 percent, the takeoff distance would increase
11.1 percent; if the takeoff velocity were increased 10 percent, the takeoff distance would increase 21 percent. These relationships point to the fact that proper accounting must be made of altitude, temperature, gross weight, wind, etc. because any item affecting acceleration or takeoff velocity will have a definite effect on takeoff distance.
If an airplane were to land at a velocity of 150 knots and be decelerated uniformly to a stop with the same acceleration of 0.2g, the landing stop distance would be 5,000 ft. However, the case is not necessarily that an aircraft may have identical takeoff and landing performance but the principle illustrated is that distance is a function of velocity and acceleration. As before, a 10 percent lower acceleration increases stop distance 11.1 percent, and a 10 percent higher landing speed increases landing distance 21 percent.
The general relationship of velocity, acceleration, and distance for uniformly accelerated motion is illustrated by figure 2.31. In this illustration., acceleration distance is shown as a function of velocity for various values of acceleration.
TAKEOFF PERFORMANCE. The minimum takeoff distance is of primary interest in the operation of any aircraft because it defines the runway requirements. The minimum takeoff distance is obtained by takeoff at some minimum safe velocity which allows sufficient margin above stall and provides satisfactory control and initial rate of climb. Generally, the takeoff speed is some fixed percentage of the stall speed or minimum control speed for the airplane in the takeoff configuration. As such, the takeoff will be accomplished at some particular value of lift coefficient and angle of attack. Depending on the airplane characteristics, the takeoff speed will be anywhere from 1.05 to 1.25 times the stall speed or minimum control speed. If the takeoff speed is specified as 1.10 times the stall speed, the takeoff lift coefficient is 82.6 percent of CLmax and the angle of attack and lift coefficient for takeoff are fixed values independent of weight, altitude, wind, etc. Hence, an angle of attack indicator can be a valuable aid during takeoff.
To obtain minimum takeoff distance at the specified takeoff velocity, the forces which act on the aircraft must provide the maximum acceleration during the takeoff roll. The various forces acting on the aircraft may or may not be at the control of the pilot and various techniques may be necessary in certain airplanes to maintain takeoff acceleration at the highest value.
Figure 2.32 illustrates the various forces which act on the aircraft during takeoff roll. The powerplant thrust is the principal force to provide the acceleration and, for minimum takeoff distance, the output thrust should be at a maximum. Lift and drag are produced as soon as the airplane has speed and the values of lift and drag depend on the angle of attack and dyhamic. pressure. Rolling friction results when there is a norinal force on the wheels and the friction force is the product of the normal force and the coefficient of rolling friction. The normal force pressing the wheels against the runway surface is the net of weight and lift while the rolling friction coefficient is a function of the tire type and runway surface texture.
The acceleration of the airplane at any instant during takeoff roll is a function of the net accelerating force and the airplane mass. From Newton’s second law of motion:
a=Fn/M
or
a=g(Fn/W~)
where
a = acceleration, ft, per se<
F«=net accelerating force,
W= weight, lbs. g=gravitational accelerat = 32,17 ft. per sec.2 iVf = mass, slugs = Wjg
The net accelerating force on the airplane, F„, is the net of thrust, T, drag, D, and rolling friction, F. Thus, the acceleration at any instant during takeoff roll is:
Figure 2.32 illustrates the typical variation of the various forces acting on the aircraft throughout the takeoff roll. If it is assumed that the aircraft is at essentially constant angle of attack during takeoff roll, CL and CD are constant and the forces of lift and drag vary as the square of the speed. For the case of uniformly accelerated motion, distance along the takeoff roll is proportional also to the square of the velocity hence velocity squared and distance can be used almost synon – omously. Thus, lift and drag will vary linearly with dynamic pressure (q) or V2 from the point of beginning takeoff roll. As the rolling friction coefficient is essentially unaffected by velocity, the rolling friction will vary as the normal force on the wheels. At zero velocity, the normal force on the wheels is equal to the airplane weight but, at takeoff velocity, the lift is equal to the weight and the normal force is zero. Hence, rolling friction decreases linearly with q or V2 from the beginning of takeoff roll and reaches zero at the point of takeoff.
The total retarding force on the aircraft is the sum of drag and rolling friction (D+F) and, for the majority of configurations, this sum is nearly constant or changes only slightly during the takeoff roll. The net accelerating force is then the difference between the power – plant thrust and the total retarding force,
Fn = T—D—F
The variation of the net accelerating force throughout the takeoff roll is shown in figure 2.32. The typical propeller airplane demonstrates a net accelerating force which decreases with velocity and the resulting acceleration is initially high but decreases throughout the takeoff roll. The typical jet airplane demonstrates a net accelerating force which is essentially constant throughout the takeoff roll. As a result, the takeoff performance of the typical turbojet airplane will compare closely with the case for uniformly accelerated motion.
The pilot technique required to achieve peak acceleration throughout takeoff roll can vary considerably between airplane configurations. In some instances, maximum acceleration will be obtained by allowing the airplane to remain in the three-point attitude throughout the roll until the airplane simply reaches lift-equal-to – weight and flies off the ground. Other airplanes may require the three-point attitude until the takeoff speed is reached then rotation to the takeoff angle of attack to become airborne. Still other configurations may require partial or complete rotation to the takeoff angle of attack prior to reaching the takeoff speed. In this case, the procedure may be necessary to provide a smaller retarding force (D-f F) to achieve peak acceleration. Whenever any form of pitch rotation is necessary the pilot must provide the proper angle of attack since an excessive angle of attack will cause excessive drag and hinder (or possibly preclude) a successful takeoff. Also, insufficient rotation may provide added rolling resistance or require that the airplane accelerate to some excessive speed prior to becoming airborne.
Revised January 1965
In this sense, an angle of attack indicator is especially useful for night or instrument takeoff conditions as well as the ordinary day VFR takeoff conditions. Acceleration errors of the attitude gyro usually preclude accurate pitch rotation under these conditions.
FACTORS AFFECTING TAKEOFF PERFORMANCE. In addition to the important factors of proper technique, many other variables affect the takeoff performance of an airplane. Any item which alters the takeoff velocity or acceleration during takeoff roll will affect the takeoff distance. In order to evaluate the effect of the many variables, the principal relationships of uniformly accelerated motion will be assumed and consideration will be given to those effects due to any nonuniformity of acceleration during the process of takeoff. Generally, in the case of uniformly accelerated motion, distance varies directly with the square of the takeoff velocity and inversely as the takeoff acceleration.
where
S = distance.
V= velocity
a= acceleration
<‘ condition (1) applies to some known takeoff distance, Ті, which was common to some original takeoff velocity, Vu and acceleration, ax.
condition (2) applies to some new takeoff distance, S2, which is the result of some different value of takeoff velocity, V2, or acceleration, a2.
With – this basic relationship, the effect of the many variables on takeoff distance can be approximated.
The effect of gross weight on takeoff distance is large and proper consideration of this item must be made in predicting takeoff distance. Increased gross weight can be considered to produce a threefold effect on takeoff performance: (1) increased takeoff velocity, (2) greater
mass to accelerate, and (3) increased retarding force (P + F). If the gross weight increases, a greater speed is necessary to produce the greater lift to get the airplane airborne at the takeoff lift coefficient. The relationship of takeoff speed and gross weight would be as follows:
тгШ (EAS°’CAV
where •
Vi — takeoff velocity corresponding to some original weight, Wx V2 = takeoff velocity corresponding to some different weight, W2
Thus, a given airplane in the takeoff configuration at a given gross weight will have a specific takeoff speed (EAS or CAS") which is invariant with altitude, temperature, wind, etc. because a certain value of q is necessary to provide lift equal to weight at the takeoff Cb. As an example of the effect of a change in gross weight a 21 percent increase in takeoff weight will require a 10 percent increase in takeoff speed to support the greater weight.
A change in gross weight will change the net accelerating force, Fn> and change the mass, M, which is being accelerated. If the airplane has a relatively high thrust-to-weight ratio, the change in the net accelerating force is slight and the principal effect on acceleration is due to the change in mass.
To evaluate the effect of gross weight on takeoff distance, the following relationship are used:
the effect of weight on takeoff velocity is
(VA2-Wi
01 ~W>
if the change in net accelerating force is neglected, the effect of weight on acceleration is
£t 2 Й2 Ц71
7TWX or71=W2
the effect of these items on takeoff distance is
£>/»!,У
Si wj
(at least this effect because weight will alter the net accelerating force)
This result approximates the effect of gross weight on takeoff distance for airplanes with relatively high thrust-to-weight ratios. In effect, the takeoff distance will vary at least as the square of the gross weight. For example, a 10 percent increase in takeoff gross weight would cause:
a 5 percent increase in takeoff velocity at least a 9 percent decrease in acceleration at least a 21 percent increase in takeoff distance
For the airplane with a high thrust-to-weight ratio, the increase in takeoff distance would be approximately 21 to 22 percent but, for the airplane with a relatively low thrust-to – weight ratio, the increase in takeoff distance would be approximately 25 to 30 percent. Such a powerful effect requires proper consideration of gross weight in predicting takeoff distance.
The effect of wind on takeoff distance is large and proper consideration also must be provided when predicting takeoff distance. The effect of a headwind is to allow the airplane to reach the takeoff velocity at a lower ground velocity while the effect of a tailwind is to require the airplane to achieve a greater ground velocity to attain the takeoff velocity. The effect of the wind on acceleration is relatively small and, for the most part, can be neglected. To evaluate the effect of wind on takeoff distance, the following relationships are used:
the effect of a headwind is to reduce the takeoff ground velocity by the amount of the headwind velocity, V„
Vt=Vi-rv
the effect of wind on acceleration is negligible,
<>i,
a%=ai or—= 1 at
the effect of these items on takeoff distance is
ГУ,-у IP
Л L Ух J
or
where
zero wind takeoff distance St— takeoff distance into the headwind
Vm—headwind velocity Vi~ takeoff ground velocity with zero wind, or, simply, the takeoff airspeed
As a result of this relationship, a headwind which is 1G percent of the takeoff airspeed will reduce the takeoff distance 19 percent. However, a tailwind (or negative headwind) which is 10 percent of the takeoff airspeed will increase the takeoff distance 21 percent. In the case where the headwind velocity is 50 percent of the takeoff speed, the takeoff distance would be approximately 25 percent of the zero wind takeoff distance (75 percent reduction).
The effect of wind on landing distance is identical to the effect on takeoff distance. Figure 2.33 illustrates the general effect of wind by the percent change in takeoff or landing distance as a function of the ratio of wind velocity to takeoff or landing speed.
NAVWEPS 00—80T—80 AIRPLANE PERFORMANCE
і
The effect of runway slope on takeoff distance is due to the component of weight along the inclined path of the airplane. A runway slope of 1 percent would provide a force component along the path of the airplane which is 1 percent of the gross weight. Of course, an upslope would contribute a retarding force component while a downslope would contribute an accelerating force component. For the case of the upslope, the retarding force component adds to drag and rolling friction to reduce the net accelerating force. Ordinarily, a 1 percent runway slope can cause a 2 to 4 percent change in takeoff distance depending on the airplane characteristics. The airplane with the high thrust-to-weight ratio is least affected while the airplane with the low thrust – to-weight ratio is most affected because the slope force component causes a relatively greater change in the net accelerating force.
The effect of runway slope must be considered when predicting the takeoff distance but the effect is usually minor for the ordinary runway slopes and airplanes with moderate thrust-to-weight ratios. In fact, runway slope considerations are of great significance only when the runway slope is large and the airplane has an intrinsic low acceleration, i. e., low thrust-to-weight ratio. In the ordinary case, the selection of the takeoff runway will favor the direction with an upslope and headwind rather than the direction with a downslope and tailwind.
The effect of proper takeoff velocity is important when runway lengths and takeoff distances are critical. The takeoff speeds specified in the flight handbook are generally the minimum safe speeds at which the airplane can become airborne. Any attempt to take off below the recommended speed may mean that the aircraft may stall, be difficult to control, or have very low initial rate of climb. In some cases, an excessive angle of attack may not allow the airplane to climb out of ground effect. On the other hand, an excessive airspeed at takeoff may improve the initial rate of climb and “feel” of the airplane but will produce an undesirable increase in takeoff distance. Assuming chat the acceleration is essentially unaffected, the takeoff distance varies as the square of the takeoff velocity,
i?=/T? Y Ti vj
Thus, 10 percent excess airspeed would increase the takeoff distance 21 percent. In most critical takeoff conditions, such an increase in takeoff distance would be prohibitive and the pilot must adhere to the recommended takeoff speeds.
The effect of pressure altitude and ambient temperature is to define primarily the density altitude and its effect on takeoff performance. While subsequent corrections are appropriate for the effect of temperature on certain items of powerplant performance, density altitude defines certain effects on takeoff performance. An increase in density altitude can produce a two-fold effect on takeoff performance: (1) increased takeoff velocity and (2) decreased thrust and reduced net accelerating force. If a given weight and configuration of airplane is taken to altitude above standard sea level, the airplane will still require the same dynamic pressure to become airborne at the takeoff lift coefficient. Thus, the airplane at altitude will take off at the same equivalent airspeed (EAS) as at sea level, but because of the reduced density, the true airspeed (TAS) will be greater. From basic aerodynamics, the relationship between true airspeed and equivalent airspeed is as follows:
TAS 1 EAS~ffJ
where
ТЛТ=тіе airspeed EAS=equivalent airspeed n = altitude density ratio
The effect of density altitude on powerplant thrust depends much on the type of power – plant. An increase in altitude above standard sea level will bring an immediate decrease in power output for the unsupercharged or ground boosted reciprocating engine or the turbojet and turboprop engines. However, an increase in altitude above standard sea level will not cause a decrease in power output for the supercharged reciprocating engine until the altitude exceeds the critical altitude. For those power – plants which experience a decay in thrust with an increase in altitude, the effect on the net accelerating force and acceleration can be approximated by assuming a direct variation with density. Actually, this assumed variation would closely approximate the effect oft airplanes with high thrust-to-weight ratios. This relationship would be as follows:
£2 _ Fti’i _ _p _
ai Ffh po
where
au F«j = acceleration and net accelerating force corresponding to sea level a2, Fn2 = acceleration and net accelerating force corresponding to altitude cr= altitude density ratio
In order to evaluate the effect of these items on takeoff distance, the following relationships are used:
if an increase in altitude does not alter acceleration, the principal effect would be due to the greater TAS
where
Si=standard sea level takeoff distance T2= takeoff distance at altitude <r=altitude density ratio
if an increase in altitude reduces acceleration in addition to the increase Іп TAS, the combined effects would be approximated for the case of the airplane with high intrinsic acceleration by the following:
where
ii = standard sea level takeoff distance Т2=takeoff distance at altitude <r=altitude density ratio
As a result of these relationships, it should, be appreciated that density altitude will affect takeoff performance in a fashion depending much on the powerplant type. The effect of density altitude on takeoff distance can be appreciated by the following comparison:
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TABLE S-1. Approximate Effect of Altitude on Takeoff Dlstaate
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Density ikitude
|
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<r
|
|
Percent inc off (list stand»
Super
charged
recipro
cating
airplane
below
critical
altitude
|
tease it ante frt d sea le
Tur
bojet
Sth
|
СЙІСС-
>m
vel
Tur
bojet
low
СГ/И0
|
|
Sea level…………
|
1.000
|
1.000
|
1.000
|
0
|
0
|
0
|
|
1,000 ft………….
|
.9711
|
1.0298
|
1.0605
|
2.9B
|
6.05
|
9.8
|
|
2,000 ft………….
|
.9428
|
1.0605
|
1.125
|
6.05
|
12.5
|
19.9
|
|
3,000 ft………….
|
.9151
|
1.0928
|
1.195
|
9-28
|
19.5
|
3Q.1
|
|
4,000 ft………….
|
.8881
|
1.126
|
1.264
|
12.6
|
26.4
|
40.6
|
|
5,000 ft………….
|
.8617
|
1.1605
|
1.347
|
16.05
|
34.7
|
52.3
|
|
6,000 ft………….
|
.8359
|
1.1965
|
1.432
|
19.65
|
43.2
|
65.8
|
|
From the previous table, some approximate rules of thumb may be derived to illustrated the differences between the various airplane types. A 1,000-ft. increase in density altitude
will cause these approximate increases in takeoff distance:
ЪУ2 percent for the supercharged reciprocating airplane when below critical altitude
7 percent for the turbojet with high thrust – to-weight ratio
10 percent for the turbojet with low thrust-to-weight ratio
These approximate relationships show the turbojet airplane to be much more sensitive to density altitude than the reciprocating powered airplane. This is an important fact which must be appreciated by pilots in transition from propeller type to jet type airplanes. Proper accounting of pressure altitude (field elevation is a poor substitute) and temperature is mandatory for accurate prediction of takeoff roll distance.
The most critical conditions of takeoff performance are the result of some combination of high gross weight, altitude, temperature and unfavorable wind. In all cases, it behooves the pilot to make an accurate prediction of takeoff distance from the performance data of the Flight Handbook, regardless of the runway available, and to strive for a polished, professional takeoff technique.
In the prediction of takeoff distance from the handbook data, the following primary considerations must be given:
Reciprocating powered airplane
(1) Pressure altitude and temperature— to define the effect of density altitude on distance.
(2) Gross weight—a large effect on distance.
0) Specific humidity—to correct takeoff distance for the power loss associated with water vapor.
(4) Wind—a large effect due to the wind or wind component along the runway.
Turbine powered airplane
(1) Pressure altitude and temperature— to define the effect of density altitude.
(2) Gross weight.
(3) Temperature—an additional correction for nonstandard temperatures to account for the thrust loss associated with high compressor inlet air temperature. For this correction the ambient temperature at the runway conditions is appropriate rather than the ambient temperature at some distant location.
(4) Wind.
In addition, corrections are necessary to account for runway slope, engine power deficiencies, etc.
LANDING PERFORMANCE. In many Cases, the landing distance of an airplane will define the runway requirements for flying operations. This is particularly the case of high speed jet airplanes at low altitudes where landing distance is the problem rather than takeoff performance. The minimum landing distance is obtained by landing at some minimum safe velocity which allows sufficient margin above stall and provides satisfactory, control and capability for waveoff Generally, the landing speed is some fixed percentage of the stall speed or minimum control speed for the airplane in the landing configuration. As such, the landing will be accomplished at some particular value of lift coefficient and angle of attack. The exact value of Cl and * for landing will depend on the airplane characteristics but, once defined, the values are independent of weight, altitude, wind, etc. Thus, an angle of attack indicator can be a valuable aid during approach and landing.
To obtain minimum landing distance at the specified landing velocity, the forces which act on the airplane must provide maximum deceleration (or negative acceleration} during the landing roll. The various forces acting, on the airplane during the landing roll may require various techniques to maintain landing deceleration at the peak value.
Figure 2.34 illustrates the forces acting on the aircraft during landing roll. The power – plant thrust should be a minimum positive value, or, if reverse thrust is available, a maximum negative value for minimum landing distance. Lift and drag are produced as long as the airplane has speed and the values of lift and drag depend on dynamic pressure and angle of attack. Braking friction results when there is a normal force on the braking wheel surfaces and the friction force is the product of the normal force and the coefficient of braking friction. The normal force on the braking surfaces is some part of the net of weight and lift, i. e., some other part of this net may be distributed to wheels which have no brakes. The maximum coefficient of braking friction is primarily a function of the runway surface condition (dry, wet, icy, etc.) and rather independent of the type of tire for ordinary conditions (dry, hard surface runway). However, the operating coefficient of braking friction is controlled by the pilot by the use of brakes.
The acceleration of the airplane during the landing roll is negative (deceleration) and will be considered to be in that sense. At any instant during the landing roll the acceleration is a function of the net retarding force and the airplane mass. From Newton’s second law of motion:
a= FrjM or
a = g (FrJW)
where
a = acceleration, ft. per sec.2 (negative) Fr= net retarding force, lbs. g= gravitational acceleration, ft. per sec.2 W= weight, lbs.
Af = mass, slugs
-Wig
The net retarding force on the airplane, Fr, is the net of drag, D, braking friction, F, and thrust, T. Thus, the acceleration (negative) at any instant during the landing roll is:
a=£(D+F-T)
w
Figure 2.34 illustrates the typical variation of the various forces acting on the aircraft throughout the landing roll. If it is assumed that the aircraft is at essentially constant angle of attack from the point of touchdown, CL and CD are constant and the forces of lift and drag vary as the square of the velocity. Thus, lift and drag will decrease linearly with ^ or Vі from the point of touchdown. If the braking coefficient is maintained at the maximum value, this maximum value of coefficient of friction is essentially constant with speed and the braking friction force will vary as the normal force on the braking surfaces. As the airplane nears a complete stop, the velocity and lift approach zero and the normal force on the wheels approaches the weight of the airplane. At this point, the braking friction force is at a maximum. Immediately after touchdown, the lift: is quite large and the normal force on the wheels is small. As a result, the braking friction force is small. A common error at this point is to apply excessive brake pressure without sufficient normal force on the wheels. This may develop a skid with a locked wheel and cause the tire to blow out so suddenly that judicious use of the brakes is necessary.
The coefficient of braking friction can reach peak values of 0.8 but ordinarily values near
0. 5 are typical for the dry hard surface runway. Of course, a slick, icy runway can reduce the maximum braking friction coefficient to values as low as 0.2 or 0.1.’ If the entire weight of the airplane were the normal force on the braking surfaces, a coefficient of braking friction of
0. 5 would produce a deceleration of jig, 16.1 ft. per sec.2 Most airplanes in ground effect rarely produce lift-drag ratios lower than 3 or 4. If the lift of the airplane were equal to the weight, an L/D — 4 would produce a deceleration of %g, 8 ft. per sec.2 By this comparison it should be apparent that friction braking offers the possibility of greater deceleration than airplane aerodynamic braking. To this end, the majority of airplanes operating from
dry hard surface runways will require particular techniques to obtain minimum landing distance. Generally, the technique involves lowering the nose wheel to the runway and retracting the flaps to increase the normal force on the braking surfaces. While the airplane drag is reduced, the greater normal force can provide greater braking friction force to compensate for the reduced drag and the net retarding force is increased.
The technique necessary for minimum landing distance can be altered to some extent in certain situations. For example, low aspect ratio airplanes with high longitudinal control power can create very high drag at the high speeds immediate to landing touchdown. If the landing gear configuration or flap or incidence setting precludes a large reduction of CLf the normal force on the braking surfaces and braking friction force capability are relatively small. Thus, in the initial high speed part of the landing roll, maximum deceleration would be obtained by creating the greatest possible aerodynamic drag. By the time the aircraft has slowed to 70 or 80 percent of the touchdown speed, aerodynamic drag decays but braking action will then be effective. Some form of this technique may be necessary to achieve minimum distance for some configurations when the coefficient of braking friction is low (wet, icy runway) and the braking friction force capability is reduced relative to airplane aerodynamic drag.
A distinction should be made between the techniques for minimum landing distance and an ordinary landing roll with considerable excess runway available. Minimum landing distance will be obtained from the landing speed by creating a continuous peak deceleration of the airplane. This condition usually requires extensive use of the brakes for maximum deceleration. 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. If aerodynamic drag is
sufficient to cause deceleration of the airplane it can be used in deference to the brakes in the early stages of the landing roll, i. e., brakes and tires suffer from continuous, hard use but airplane aerodynamic drag is free and does not | wear out with use. The use of aerodynamic drag is applicable only for deceleration to 60 or 70 percent of the touchdown speed. At speeds less than 60 to 70 percent of the touchdown speed, aerodynamic drag is so slight as to be of little use and braking must be utilized to produce continued deceleration of the airplane.
Powerplant thrust is not illustrated on figure 2.34 for there are so many possible variations. Since the objective during the landing roll is to decelerate, the powerplant thrust should be the smallest possible positive value or largest possible negative value. In the case of the turbojet aircraft, the idle thrust of the engine is nearly constant with speed throughout the landing roll. The idle thrust is of significant magnitude on cold days | because of the low compressor inlet air temperature and low density altitude. Unfortunately, such atmospheric conditions usually have the corollary of poor braking action because of ice or water on the runway. The thrust from a windmilling propeller with the engine at idle can produce large negative thrust early in the landing roll but the negative force decreases with speed. The large negative thrust at high speed is valuable in adding to drag and braking friction to increase the net retarding force.
Various devices can be utilized to provide greater deceleration of the airplane or to minimize the wear and tear on tires and brakes. The drag parachute can provide a large retarding force at high ^ and greatly increase the deceleration during the initial phase of landing roll. It should be noted that the contribution of the drag chute is important only during the high speed portion of the landing roll. For maximum effectiveness, the drag chute must be deployed immediately after the airplane is in contact with the runway. Reverse thrust of
propellers is obtained by rotating the blade angle well below the low pitch stop and applying engine power. The action is to extract a large amount of momentum from the airstream and thereby create negative thrust. The magnitude of the reverse thrust from propellers is very large, especially in the case of the turboprop where a very large shaft power can be fed into the propeller. In the case of reverse propeller thrust, maximum effectiveness is achieved by use immediately after the airplane is in contact with the runway. The reverse thrust capability is greatest at the high speed and, obviously, any delay in producing deceleration allows runway to pass by at a rapid rate. Reverse thrust of turbojet engines will usually employ some form of vanes, buckets, or clamshells in the exhaust to turn or direct the exhaust gases forward. Whenever the exit velocity is less than the inlet velocity for negative), a negative momentum change occurs and negative thrust is produced. The reverse jet thrust is valuable and effective but it should not be compared with the reverse thrust capability of a comparable propeller powerplant which has the high intrinsic thrust at low velocities. As with the propeller reverse thrust, jet reverse thrust must be applied immediately after ground contact for maximum effectiveness in reducing landing distance.
FACTORS AFFECTING LANDING PERFORMANCE, In addition to the important factors of proper technique, many other variables affect the landing performance of an airplane. Any item which alters the landing velocity or deceleration during landing roll will affect the landing distance. As with takeoff performance, the relationships of uniformly accelerated motion will be assumed applicable for studying the principal effects on landing distance. The case of uniformly accelerated motion defines landing distance as varying directly as the square of the landing velocity and inversely as the acceleration during landing roll.
where
= landing distance resulting from certain values of landing velocity, V, and acceleration, a
Tj = landing distance resulting from some different values of landing velocity, V2, or acceleration, a2
With this relationship, the effect of the many variables on landing distance can be approximated.
The effect of gross weight on landing distance is one of the principal items determining the landing distance of an airplane One effect of an increased gross weight is that the airplane will require a greater speed to support the airplane at the landing angle of attack and lift coefficient. The relationship of landing speed and gross weight would be as follows:
vr^W, or CAS)
where
Fi = landing velocity corresponding to some original weight,
V2 = landing velocity corresponding to some different weight, W2 Thus, a given airplane in the landing configuration at a given gross weight will have a specific landing speed (EAS or CAS) which is invariant with altitude, temperature, wind, etc., because a certain value of q is necessary to provide lift equal to weight at the landing CL. As an example of the effect of a change in gross weight, a 21 percent increase in landing weight will require a 10 percent increase in landing speed to support the greater weight.
When minimum landing distances are considered, braking friction forces predominate during the landing roll and, for the majority of airplane configurations, braking friction is the main source of deceleration. In this case, an increase in gross weight provides a greater
normal force and increased braking friction force to cope with the increased mass. Also, the higher landing speed at the same CL and CD produce an average drag which increased in the same proportion as the increased weight. Thus, increased gross weight causes like increases in the sum of drag plus braking friction and the acceleration is essentially unaffected.
To evaluate the effect of gross weight on landing distance, the following relationships are used;
the effect of weight on landing velocity is
Уг fWi Vi W1
if the net retarding force increases in the same proportion as the weight, the acceleration is unaffected.
the effect of these items on landing distance is,
or
S2 _Wi
In effect, the minimum landing distance will vary directly as the gross weight. For example, a 10 percent increase in gross weight at landing would cause:
a 5 percent increase in landing velocity a 10 percent increase in landing distance A contingency of the previous analysis is the relationship between weight and braking friction force. The maximum coefficient of braking friction is relatively independent of the usual range of normal forces and rolling speeds, e. g., a 10 percent increase in normal force would create a like 10 percent increase in braking friction force. Consider the case of two airplanes of the same type and c. g. position but of different gross weights. If these two airplanes are rolling along the runway at some speed at which aerodynamic forces are negligible, the use of the maximum coefficient of
braking friction will bring both airplanes to a stop in the same distance. The heavier airplane will have the greater mass to decelerate but the greater normal force will provide a greater retarding friction force. As a result, both airplanes would have identical acceleration and identical stop distances from a given velocity. However, the heavier airplane would have a greater kinetic energy to be dissipated by the brakes and the principal difference between the two airplanes as they reach a stop would be that the heavier airplane would have the hotter brakes. Therefore, one of the factors of braking performance is the ability of the brakes to dissipate energy without developing excessive temperatures and losing effectiveness.
To appreciate the effectiveness of modern brakes, a 30,000-lb. aircraft landing at 175 knots has a kinetic energy of 41 million ft.-lbs. at the instant of touchdown. In a minimum distance landing, the brakes must dissipate most of this kinetic energy and each brake must absorb an input power of approximately 1,200 h. p. for 25 sccohds. Such requirements for brakes are extreme but the example serves to illustrate the problems of brakes for high performance airplanes.
While a 10 percent increase in landing weight causes:
a 5 percent higher landing speed
a 10 percent greater landing distance, it also produces a 21 percent increase in the kinetic energy of the airplane to be dissipated during the landing roll. Hence, high landing weights may approach the energy dissipating capability of the brakes.
The effect of wind on landing distance is large and deserves proper consideration when predicting landing distance. Since the airplane will land at a particular airspeed independent of the wind, the principal effect of wind on landing distance is due to the change in the ground velocity at which the airplane touches down. The effect of wind on acceleration during the landing distance is identical to the
effect on takeoff distance and is approximated by the following relationship:
where
Ti=Zero wind landing distance ^2= landing distance into a headwind Fw = headwind velocity Vi= landing ground velocity with zero wind or, simply, the landing airspeed
As a result of this relationship, a headwind which is 10 percent of the landing airspeed will reduce the landing distance 19 percent but a tailwind (or negative headwind) which is 10 percent of the landing speed will increase the landing distance 21 percent. Figure 2.33 illustrates this general effect.
The effect of runway slope on landing distance is due to the component of weight along the inclined path of the airplane. The relationship is identical to the case of takeoff performance but the magnitude of the effect is not as great. While account must be made for the effect, the ordinary values of runway slope do not contribute a large effect on landing distance. For this reason, the selection of the landing runway will ordinarily favor the direction with a downslope and headwind rather than an upslope and tailwind.
The effect of pressure altitude and ambient temperature is to define density altitude and its effect on landing performance. An increase in density altitude will increase the landing velocity but will not alter the net retarding force. If a given weight and configuration of airplane is taken to altitude above standard sea level, the airplane will still require the same q to provide lift equal to weight at the landing Ct. Thus, the airplane at altitude will land at the same equivalent airspeed (EAS) as at sea level but, because of the reduced density, the true airspeed (TAS) will be greater. The relationship between true airspeed and equivalent airspeed is as follows:
TAS= 1 EAS – fa
where
TAS = true airspeed EAS= equivalent airspeed <r=altitude density ratio
Since the airplane lands at altitude with the same weight and dynamic pressure, the drag and braking friction throughout the landing roll have the same values as at sea level. As long as the condition is within the capability of the brakes, the net retarding force is unchanged and the acceleration is the same as with the landing at sea level.
To evaluate the effect of density altitude on landing distance, the following relationships are used:
since an increase in altitude does not alter acceleration, the effect would be due to the greater TAS
where
Ті = standard sea level landing distance
T2 = landing distance at altitude <r=altitude density ratio
From this relationship, the minimum landing distance at 5,000 ft. (<r=0.8617) would be 16 percent greater than the minimum landing distance at sea level. The approximate increase in landing distance with altitude is approximately 3K percent for each 1,000 ft. of altitude. Proper accounting of density altitude is necessary to accurately predict landing distance.
The effect of proper landing velocity is important when runway lengths and landing distances are critical. The landing speeds specified in the flight handbook are generally the minimum safe speeds at which the airplane can be landed. Any attempt to land at below the specified speed may mean that the airplane may stall, be difficult to control, or develop high rates of descent. On the other hand, an excessive speed at landing may improve the controllability (especially in crosswinds) but will cause an undesirable increase in landing distance. The principal effect of excess landing speed is described by:
Si
Thus, a 10 percent excess landing speed would cause a 21 percent increase in landing distance. The excess speed places a greater working load on the brakes because of the additional kinetic energy to be dissipated. Also, the additional speed causes increased drag and lift in the normal ground attitude and the increased lift will reduce the normal force on the braking surfaces. The acceleration during this range of speed immediately after touchdown may suffer and it will be more likely that a tire can be blown out from braking at this point. As a result, 10 percent excess landing speed will cause at least 21 percent greater landing distance.
The most critical conditions of landing performance are the result of some combination of high gross weight, density altitude, and unfavorable wind. These conditions produce the greatest landing distance and provide critical levels of energy dissipation required of the brakes. In all cases, it is necessary to make an accurate prediction of minimum landing distance to compare with the available runway. A polished, professional lajiding technique is necessary because the landing phase of flight accounts for more pilot caused aircraft accidents than any other single phase of flight.
In the prediction of minimum landing distance from the handbook data, the following considerations must be given:
(1) Pressure altitude and temperature—to define the effect of density altitude.
(2) Gross weight—which define the CAS or EAS for landing.
СЗ) Wind—a large effect due to wind or wind component along the runway.
(4) Runway slope—a relatively small correction for ordinary values of runway slope. IMPORTANCE OF HANDBOOK PERFORMANCE DATA. The performance section or supplement of the flight handbook contains all the operating data for the airplane. For example, all data specific to takeoff, climb, range, endurance, descent and landing are included in this section. The ordinary use of these data in flying operations is mandatory and great knowledge and familiarity of the airplane can be gained through study of this material. A complete familiarity of an airplane’s characteristics can be obtained only through extensive analysis and study of the handbook data.
