Chapter: 10. Takeoff and Landing

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Chapter: 10. Takeoff and Landing


10.01 Introduction

Takeoff and Landing performance is more difficult to predict accurately than in-flight performance. There are many reasons for this, including the very dynamic nature of these phases, a high sensitivity to piloting technique, the large number of unknowns related to retardation devices, and uncertainties in aerodynamics for the low-speed ('dirty') configuration (see Chapter#05section16 ). Within these natural constraints, Piano provides good analytical estimates using step-by-step integration procedures and based on standard FAR-25/JAR-25 rules.

Sample Takeoff/Landing Report

 TAKEOFF PERFORMANCE {162040.lb., elevation 0.feet, ISA+15.deg.C.} 
 ___________________

 JAR25 Takeoff Field Length     7633. feet 

 115% Factored All-Eng.Dist.    7317. feet
 Balanced Field Length          7633. feet

 2nd Segment Climb Gradient     3.73 %

 Takeoff CLmax            2.40  {trapezoidal ref.area}
 Takeoff Vstall           129.  keas
 Takeoff Vfail            147.  keas
 Takeoff V2               154.  keas
 L/D at 2nd segment      12.36  {incl.windmill & asymm.}

 Takeoff Wing Loading     134.  p.s.f.{trap.W/S}
 Takeoff Thrust/Weight   0.290  available static 


 LANDING PERFORMANCE {142198.lb., elevation 0.feet, ISA+0.deg.C.}
 ___________________

 JAR25 Landing Field Length     4887. feet

 Landing Distance (LFL*0.6)     2932. feet
 Landing Ground Roll            1633. feet

 Landing  CLmax           3.31  {trapezoidal ref.area}
 Landing  Vstall          102.  keas
 Approach Speed           133.  keas
 Approach L/D             5.88  {gear down} 

Takeoff and Landing Field Lengths (TOFL, LFL) are calculated via the 'Field Lengths' item under the 'Report' menu (keyboard equivalent Command-I). They are based on the current MTOW and MLW respectively (according to mto-mass and max-landing-mass-ratio ). If you hold down the Shift key when you select 'Field Lengths', you can specify any other mass.

You can set the takeoff conditions in terms of airfield elevation and temperature deviation (delta-ISA) via the 'Takeoff Cond...' item ('Report' menu). There are two separate settings for the takeoff, one for the standard design case and another for the off-design cases used by 'Mission @Mass...' and 'Mission @Range...'. Landing performance is usually evaluated at Sea Level ISA conditions, but that setting can be changed too.


10.02 Thrust and Aerodynamics

The fundamental prerequisites include knowledge of the takeoff thrust characteristics (see Chapter#07section04 , Chapter#07section13 ) and reliable CLmax and L/D values (see Chapter#05section17 , Chapter#05section18 ).

Thrust is determined by the reference-thrust-per-engine and by the data contained in the 'max takeoff' and 'description' files of the current engine. These define the decay of thrust with speed and the 'flat rating' behaviour. You can adjust the takeoff thrust without affecting other characteristics via the parameter user-factor-on-takeoff-rating . Subject to certification rules, it may be permissible to use automatic systems that over-boost the remaining engines after an engine failure. Use thrust-factor-at-2nd-segment for such cases only.

The most relevant aerodynamic characteristics are the CLmax and the L/D ratio at the takeoff safety speed V2. Their current values are shown in the 'Field Lengths' reports. You can adjust them via user-factor-on-takeoff-clmax and user-factor-on-takeoff-l/d . The L/D ratio at V2 is quoted with one engine inoperative and includes asymmetric and windmilling drag contributions (see Chapter#05section19 ). It excludes the drag of the undercarriage, which is retracted in the second-segment condition.


10.03 TOFL and BFL definitions

Takeoff is calculated from standstill to a height given by takeoff-screen-height , which is normally 35 feet.

The Takeoff Field Length (TOFL) is by definition the greater of the Balanced Field Length (BFL) and 115% of the all-engines-operative takeoff distance.

The BFL is determined by the condition that the distance to continue a takeoff following failure of an engine at some critical speed (Vfail) be equal to the distance required to abort it. It represents the 'worst case' scenario, since failure at a lower speed requires less distance to abort, whilst failure at a higher speed requires less distance to continue the takeoff. Use the 'B.F.L. Sketch' item (under the 'Study' menu) to see a graphic illustration of the BFL calculations.

Source codes: Basic functions are find-takeoff-field-length , find-balanced-field-length , find-factored-all-eng-takeoff-distance .


10.04 Second Segment Gradient

The critical 'second segment' condition is defined at the takeoff-screen-height , with the high-lift devices still at takeoff position, undercarriage retracted, outside of ground effect, and with one (critical) engine inoperative. At this point, the speed will be no less than V2, the takeoff safety speed. V2 is the product of Vstall and the v2-speed-ratio , which equals 1.2 by default. The stall speed Vstall is derived directly from the CLmax for 1g steady-state flight (strictly speaking, for a nominal deceleration of 1kt/sec during flight tests).

Calculations are conducted at the flap deflection given by takeoff-flap-deg , which defaults to 15 degrees. According to FAR-25 however, the second-segment climb gradient with one engine inoperative must not be less than 2.4% for twin-engined aircraft, or 2.7% for three-engined, or 3% for four-engined aircraft. If the calculated gradient falls below this limit, an iterative procedure is used that reduces the flap setting until the minimum gradient is met. The chosen setting is then shown in the field report, together with a suitable warning. (The value of takeoff-flap-deg is not affected). If the minimum requirement cannot be met even with the flaps up, takeoff is deemed to be impossible. Your last option may then be to increase the value of v2-speed-ratio , a situation known as 'over-speeding', which could improve the gradient at the expense of distance.

The automatic procedure for reducing flap to satisfy the minimum gradient assumes that the flap setting is infinitely variable (a so-called 'dial a flap' system).

Source codes: See find-2nd-segment-gradient and find-iterated-2nd-segment-gradient .


10.05 Flap Effects on Takeoff

A value of 15 degrees for takeoff-flap-deg is sufficiently representative for sizing purposes. Any definitive choice will be subject to operational details and precise flap characteristics. There is a trade-off between takeoff distance and climb gradient as a function of flap deflection. You can examine this via the 'Flap Effects...' item ('Study' menu). The picture ignores possible operational limitations such as the minimum control speed (Vmc), which depends on the control systems and is not easily quantified. Usable settings of takeoff-flap-deg are therefore unlikely to exceed 15 to 20 degrees in practice. Normally, the picture is based on the mto-mass , but you can specify another mass if you hold down the Shift key whilst selecting the 'Flap Effects...' item.

You can use the 'T.O.F.L. vs Range' item to study variations in takeoff distance with range (weight). This also uses the current setting for takeoff-flap-deg unless reduced by gradient considerations, as discussed previously.


10.06 Ground Run and Airborne Path

The ground run from standstill to a particular speed is found by integration from the calculated acceleration performance. During this period there is only minimal lift, and initially little drag, corresponding to a level attitude. Rolling resistance is calculated from the value of the rolling-friction coefficient, which defaults to 0.02. The airborne flight path is characterised by a circular-arc transition to the calculated climb gradient, followed (if necessary) by a constant-gradient segment until the screen height is reached.

Variations in speed and drag during the intervening rotation phase and at the start of the transition are complex and very dependent on piloting technique. Piano makes the normal simplifying assumption that the transition phase will be flown at a constant speed. This is set to V2 in engine-out cases (see v2-speed-ratio ), and to an intermediate value between V2 and V3 (the all-engines operative speed at the screen height) during normal takeoffs. For typical flying techniques, V3 exceeds V2 by roughly 10 kts and is set by the parameter v3-v2-speed-increment . The radius of the circular-arc segment of the flight path is calculated from the incremental load factor that a pilot would apply (delta-g), which is assumed to be 0.4g normally or 0.2g with one engine inoperative.

At light takeoff weights, V2 may be restricted by the requirement that (V2min >= 1.1 Vmc), where Vmc is the minimum control speed. The determination of Vmc depends on the value of fin-cl-limit-at-vmc , which represents the effectiveness of the fin and rudder in balancing engine-out asymmetry.

Source codes: Acceleration data are compiled by find-takeoff-accel-lists according to ground-accel-at and integrated by trapezoidal-rule . Airborne paths etc are set in prepare-bfl and prepare-all-eng-takeoff .


10.07 Accelerate-Go and Accelerate-Stop

The Balanced Field Length is determined by the intersection of the accelerate-go and accelerate-stop curves. When an engine fails at the critical failure speed Vfail, the pilot reacts in a time given by engine-failure-reaction-time . In the case of accel-stop, some distance is covered thus (assuming a roughly constant speed), following which the remaining engines are throttled back, spoilers deployed, and braking commences. Deceleration is then calculated at a representative value of the braking-friction coefficient, reflecting the technology level of the braking systems. Normally, it is not permissible to use reverse thrust on the remaining engines unless the resulting asymmetry can be controlled. This may be changed via reverse-thrust-used-for-abort . In the case of accel-go, the takeoff simply continues to the screen height without any changes to the aircraft configuration. The BFL is found by iteration through a search for the critical speed Vfail. On rare occasions, it may not be possible to balance the two cases, in which case the greater of the accel-stop and accel-go distances is used.

Source codes: Iterations are carried out by find-balanced-field-length and the regula-falsi procedure using bfl-dist-to-abort-from , bfl-dist-to-continue-from and bfl-dist-to-get-to .


10.08 Rotation Check

An approximate rotation angle is calculated internally to check that the required pitch attitude does not cause a tailstrike. If this appears likely, Piano will issue a warning. You can choose to either ignore the situation or ask Piano to reduce the rotation angle as necessary (resulting in a loss of usable CL), according to the setting of the parameter takeoff-rotation-check . Although the static geometry can be estimated from the undercarriage length (see Chapter#03section11 ) and rear fuselage shape, the rotation phase is in reality highly dynamic (the tail may still be moving down whilst the c.g. of the aircraft is going up) and the calculations are based on a statistical approach.

Source codes: See find-rotation-limits .


10.09 Landing Field Length

Landing performance is calculated from a screen height given by landing-screen-height (normally 50 feet) to a fullstop. The Landing Field Length (LFL) is defined by FAR-25 as the total distance divided by 0.6 (rather confusingly). Flap deflection corresponds to the value of landing-flap-deg , the maximum setting. It defaults to 50 degrees and is also used in estimating flap mass. Aerodynamic characteristics in the final approach configuration (CLmax and L/D ratio) are shown in the 'Field Lengths' reports and can be adjusted via user-factor-on-landing-clmax and user-factor-on-landing-l/d . The corresponding drag includes the undercarriage contribution, according to the value of delta-cd-due-to-u/c .

Source codes: See find-factored-landing-field-length .


10.10 Landing Approach

The airborne segment of the landing starts at the landing-screen-height and at Vapp, the final approach speed. Vapp is given by the product of the approach-speed-ratio (which defaults to 1.3) and Vstall, the calculated stall speed in the landing configuration. The airborne path consists mostly of a gradual decelerating flare and float period that is extremely sensitive to piloting technique. Typically, the aircraft will be 'held off' until speed has reduced to about 1.15 times Vstall (you can change this through the parameter touchdown-speed-ratio ). It is then possible to calculate the distance covered directly from energy considerations for a given L/D ratio. This approach corresponds to the 'standard' setting of the parameter approach-method . Other options for approach-method correspond to constant-angle approaches of between 3 and 6 degrees, which would result in rather 'hard' STOL-type landings. In such cases the touchdown speed will vary and is found from energy considerations.

Source codes: See lfl-airborne-distance , find-touchdown-speed-tas .


10.11 Landing Ground Roll

The landing ground roll from touchdown to a fullstop is calculated by integration, in a similar fashion to the accelerate-stop analysis during takeoff. After touchdown, a time equal to landing-free-roll-time (default 2 sec) is assumed to elapse before the pilot applies the brakes and deploys the spoilers. During this 'free roll' time a constant speed is used (conservatively).

The effectiveness of the braking system is dictated by the braking-friction coefficient. Spoilers reduce residual lift to essentially zero and contribute some drag. If there are no spoilers, the parameter spoiler-exp-span-fraction should be set to zero. Reverse thrust is not used for certification purposes unless otherwise specified by the parameter reverse-thrust-used-for-landing . If this is 'false', only any residual idle thrust is used during the ground roll. Otherwise, reverse thrust is calculated as the product of the normal engine thrust and the reverse-thrust-fraction , which defaults to 0.3.

Reality Check: Any analysis of landing performance is necessarily fraught with uncertainties regarding the performance of retardation systems (anti-skid, torque and energy limits etc.) and must make multiple assumptions concerning flying techniques and criteria. This reality is reflected in the size of the LFL factor (1/0.6). It is common for manufacturers to restrict themselves to merely quoting the approach speed Vapp as a more meaningful measure of performance. Fortunately, landings are rarely critical in comparison with takeoffs, because of the reduced mass and speed and the magnitude of braking forces compared to engine thrust.

Source codes: See lfl-ground-roll , ground-accel-at , and trapezoidal-rule .


10.12 WAT Limits and Fields Required

Operational restrictions on takeoff Weight / Altitude / Temperature (the so-called 'WAT limits') can be examined via the 'W.A.T. Limits...' item under the 'Study' menu. This shows a matrix of all the limiting conditions that will satisfy the minimum second-segment climb gradient requirement at a given flap setting. When these limits are exceeded, the aircraft is not allowed to take off irrespective of the runway length that is available.

The 'Required TOFL...' and 'Required LFL...' items ('Study' menu) will generate comprehensive plots and tabulations of the required Takeoff Field Length and Landing Field Length for any airfield pressure altitude and Delta-ISA combination. These calculations are done at a given flap setting, except the flap may be reduced automatically to satisfy the minimum gradient requirements, when so indicated on the graphs.


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