12.1 Transport Category Takeoff Performance & V-Speeds

Transport Category Takeoff Performance & V-Speeds

Core Airline Transport Principle: Takeoff in a multi-engine transport category turbojet is engineered around deterministic failure containment under 14 CFR Part 25. Every takeoff calculation guarantees that if a critical engine catastrophically fails at or after the Engine Failure Speed ($V_{EF}$), the flight crew can either bring the aircraft to a complete stop within the Accelerate-Stop Distance Available (ASDA) or safely rotate, become airborne, and clear all runway obstacles to 35 feet at Takeoff Safety Speed ($V_2$) within the Takeoff Distance Available (TODA).

---

1. Transport Category V-Speed Definitions & Certification Constraints

Transport category aircraft certified under 14 CFR Part 25 operate within an exact aerodynamic and regulatory speed envelope. Each V-speed serves a distinct safety function and is bounded by strict mathematical inequalities.

+-----------------------------------------------------------------------------+
|                   TAKEOFF V-SPEED HIERARCHY & PROGRESSION                   |
|                                                                             |
|   Brake            VEF          V1           VR         VLOF           V2   |
|  Release          Engine      Decision    Rotation    Liftoff       Takeoff |
|     |            Failure       Speed        Speed      Speed        Safety  |
|     |               |            |            |          |             |    |
|     v               v            v            v          v             v    |
|  (0 kt) ---------[VMCG]=======[======]=====[======]====[VMU]========[35 ft] |
|                     |            |            |          |                  |
|                     +-- >= 1.0s -+            |          +-- >= 1.10 VMU (AEO)
|                         Margin                +-- >= 1.05 VMCA      >= 1.05 VMU (OEI)
|                                                                             |
|   ABSOLUTE HIERARCHY:  V_MCG <= V_EF < V_1 <= V_R <= V_LOF <= V_2           |
+-----------------------------------------------------------------------------+

The Takeoff V-Speed Spectrum

• $V_{EF}$ (Engine Failure Speed): The calibrated airspeed at which the critical engine is assumed to fail catastrophically during takeoff certification. It is the instant of physical thrust loss.
• $V_1$ (Takeoff Decision Speed): Under 14 CFR 25.107, $V_1$ is the maximum speed in the takeoff at which the pilot must take the first action (e.g., applying brakes, reducing thrust, deploying speedbrakes) to stop the airplane within the accelerate-stop distance. It is also the minimum speed following critical engine failure at $V_{EF}$ at which the pilot can continue the takeoff and achieve the required height above the takeoff surface within the takeoff distance.
  • Time Margin: $V_1$ must exceed $V_{EF}$ by the time required for the pilot to recognize the engine failure and initiate braking (certified as at least 1.0 second of reaction time).
  • Operational Rule: Prior to $V_1$, the takeoff MUST be rejected for any engine failure, fire warning, predictive windshear alert, or unsafe condition. At and after $V_1$, the takeoff MUST continue; rejecting after $V_1$ virtually guarantees runway excursion.
• $V_R$ (Rotation Speed): The speed at which the pilot initiates pitch rotation at a certified rate (typically $2.5^\circ$ to $3.0^\circ$ per second) toward the target takeoff pitch attitude ($12^\circ$ to $18^\circ$).
  • Constraint: $V_R$ cannot be less than $V_1$, and it must be at least $1.05 \times V_{MCA}$.
  • Margin: $V_R$ must ensure the aircraft accelerates to $V_2$ before reaching 35 feet above the runway.
• $V_{MU}$ (Minimum Unstick Speed): The minimum calibrated airspeed at which the airplane can be made to safely lift off the ground and continue the takeoff without encountering hazardous aerodynamic buffet, pitch-up, or ground-strike geometry.
• $V_{LOF}$ (Lift-Off Speed): The actual airspeed at which the aircraft tires leave the runway surface.
  • All-Engines-Operating (AEO) Margin: $V_{LOF} \ge 1.10 \times V_{MU}$ (or $1.08 \times V_{MU}$ for certain thrust-to-weight configurations).
  • One-Engine-Inoperative (OEI) Margin: $V_{LOF} \ge 1.05 \times V_{MU}$.
• $V_2$ (Takeoff Safety Speed): The target climb speed that must be attained by the 35-foot screen height (or 15-foot screen height on wet/contaminated runways) with one engine inoperative, and maintained throughout the 2nd Climb Segment.
  • Stall Margin: $V_2 \ge 1.13 \times V_{SR}$ (Reference Stall Speed) under modern Part 25 certification (or $1.20 \times V_S$ under older rules).
  • Directional Margin: $V_2 \ge 1.10 \times V_{MCA}$.

+-----------------------------------------------------------------------------+
|              SUMMARY OF 14 CFR PART 25 V-SPEED CERTIFICATION LIMITS         |
|                                                                             |
|   V-Speed   Regulatory Constraint                     Physical Basis        |
|   -------   ---------------------------------------   --------------------- |
|   V_1       V_MCG <= V_EF < V_1 <= V_R                Ground controllability|
|   V_R       V_R >= V_1  AND  V_R >= 1.05 * V_MCA      Air controllability   |
|   V_LOF     V_LOF >= 1.10 * V_MU (AEO)                Tail strike / buffet  |
|             V_LOF >= 1.05 * V_MU (OEI)                Stall margin at lift  |
|   V_2       V_2 >= 1.13 * V_SR  (or 1.20 * V_S)       2nd segment climb     |
|             V_2 >= 1.10 * V_MCA                       OEI roll/yaw control  |
+-----------------------------------------------------------------------------+

---

2. The Balanced Field Length (BFL) Concept

In airline performance calculations, runway requirements are categorized into two fundamental distances:

1. Accelerate-Stop Distance Required (ASDR): The distance required to accelerate from brake release to $V_{EF}$, recognize the failure at $V_1$, initiate maximum braking, deploy ground spoilers/speedbrakes, and bring the aircraft to a full stop on the remaining runway/stopway.
2. Accelerate-Go Distance Required (AGDR): The distance required to accelerate from brake release to $V_{EF}$, suffer an engine failure, continue accelerating on remaining engine(s) through $V_1$ to $V_R$, rotate, lift off, and achieve 35 feet AGL at $V_2$ over the runway/clearway.

+-----------------------------------------------------------------------------+
|                        BALANCED FIELD LENGTH DYNAMICS                       |
|                                                                             |
|   Distance                                                                  |
|     ^                                                                       |
|     |  \ (AGDR - Accelerate-Go)                     / (ASDR - Accelerate-   |
|     |   \                                          /         Stop)          |
|     |    \                                        /                         |
|     |     \                                      /                          |
|     |      \                                    /                           |
|     |       \                                  /                            |
|     |        \        BALANCED FIELD          /                             |
|     |         \         POINT (BFL)          /                              |
|     |          \             v              /                               |
|     |           \___________( X )__________/                                |
|     |                       | |                                             |
|     +-----------------------+-+-------------------------------------------> |
|    0                       V1_opt                                        V1 |
|                                                                             |
|   * Lower V1: Shorter Stop Distance, but LONGER Accelerate-Go Distance.     |
|   * Higher V1: Shorter Accelerate-Go Distance, but LONGER Stop Distance.    |
|   * Balanced V1: Point where ASDR EQUALS AGDR (Minimum total runway).       |
+-----------------------------------------------------------------------------+

Mathematical Dynamics of $V_1$ Variation

• If $V_1$ is decreased: The stopping distance decreases because the reject begins at a lower kinetic energy ($KE = \frac{1}{2} m V^2$). However, the accelerate-go distance increases dramatically because the remaining engine must accelerate the aircraft over a larger speed range ($V_1$ to $V_R$) with degraded single-engine thrust.
• If $V_1$ is increased: The accelerate-go distance decreases because the aircraft was accelerated to a higher speed with all engines operating. However, the accelerate-stop distance increases because the brakes must absorb significantly higher kinetic energy to stop the heavier, faster aircraft.
• Balanced Field Length: The precise operational condition where $\text{ASDR} = \text{AGDR}$. This unique $V_1$ (termed the Balanced $V_1$) minimizes the required runway length for a given gross weight, or conversely, maximizes the allowable takeoff weight for a fixed runway length.

---

3. Declared Distances, Clearways, and Stopways (14 CFR 25.113)

Airport runways utilize internationally standardized declared distances defined by the FAA (AC 150/5300-13) and ICAO Annex 14.

+-----------------------------------------------------------------------------+
|                  DECLARED RUNWAY DISTANCES & INFRASTRUCTURE                 |
|                                                                             |
|   [=========== PAVED RUNWAY SURFACE ===========][ STOPWAY ][   CLEARWAY   ] |
|   |<---------------- TORA -------------------->|          |                |
|   |<---------------- ASDA -------------------------------->|                |
|   |<---------------- TODA ------------------------------------------------->|
|   |<---------------- LDA --------------------->|                            |
|                                                                             |
|   * TORA = Takeoff Run Available (Full-strength paved surface).             |
|   * ASDA = Accelerate-Stop Distance Available (TORA + Stopway).             |
|   * TODA = Takeoff Distance Available (TORA + Clearway, max 1.5 * TORA).    |
|   * LDA  = Landing Distance Available (Usable paved landing distance).      |
+-----------------------------------------------------------------------------+

Regulatory Distances Defined

• TORA (Takeoff Run Available): The length of runway declared available and suitable for the ground run of an airplane taking off.
• ASDA (Accelerate-Stop Distance Available): $\text{TORA} + \text{Stopway}$. The runway plus any certified stopway available for decelerating an abandoned takeoff.
• TODA (Takeoff Distance Available): $\text{TORA} + \text{Clearway}$. The length of the takeoff run available plus the length of the clearway, if available.
  • Limitation (14 CFR 25.113): The clearway credit cannot exceed 50% of TORA (i.e., $\text{TODA} \le 1.50 \times \text{TORA}$) to ensure sufficient wheel-to-ground acceleration before liftoff.
• LDA (Landing Distance Available): The length of runway declared available and suitable for the ground run of an airplane landing.

Stopway vs. Clearway Technical Standards

---

4. Reduced Thrust Takeoffs: Assumed Temperature (ATM/FLEX) vs. Fixed Derates

Operating turbine engines at maximum rated takeoff thrust during every departure causes severe thermal fatigue, accelerated turbine blade creep, and premature high-pressure turbine deterioration. Under 14 CFR 25 and FAA Advisory Circular AC 25-13, airlines utilize two primary methods of thrust reduction to prolong engine life and reduce operating costs.

+-----------------------------------------------------------------------------+
|              ASSUMED TEMPERATURE (ATM) VS. FIXED DERATE (DERATE)            |
|                                                                             |
|   Parameter           Assumed Temperature (ATM / FLEX) Fixed Derate (TO-1)   |
|   -----------------   -------------------------------- ------------------- |
|   Thrust Calculation  Fictitious high ambient temp     Electronically lower |
|                       entered into FMS (Flat-rate)     permanent rating     |
|   Maximum Reduction   25% reduction below rated thrust 10% to 20% steps     |
|   V-Speeds Basis      Calculated for ACTUAL weight at  Calculated for LOWER |
|                       rated thrust limits              rated VMCG / VMCA    |
|   Throttles to Wall   PERMITTED: Full rated thrust     PROHIBITED: May loss |
|   in Emergency?       is aerodynamically controllable  directional control  |
|   Contaminated Runway STRICTLY PROHIBITED              PERMITTED (Subject to|
|   Operations?         (Wet allowed if data published)  AFM contaminated)    |
|   Inoperative Antiskid STRICTLY PROHIBITED             Follow AFM/OpSpecs   |
|   Other Restrictions   Follow AFM and operator procedures Follow AFM/OpSpecs |
+-----------------------------------------------------------------------------+

Assumed Temperature Method (ATM / FLEX)

• Operating Principle: Turbofan engines are flat-rated (produce constant maximum thrust up to a "corner point" temperature, typically $+30^\circ\text{C}$ or $+86^\circ\text{F}$, above which thrust drops as air density decreases). By entering an artificially high "assumed temperature" (e.g., $+48^\circ\text{C}$) into the Flight Management System (FMS), the Full Authority Digital Engine Control (FADEC) commands a reduced thrust level matching the performance required for the actual takeoff weight on that runway.
• Regulatory Limits:
  1. Maximum 25% Reduction: AC 25-13 caps the maximum allowable thrust reduction at 25% below the full certified takeoff thrust rating.
  2. Controllability: Minimum control speeds ($V_{MCG}$ and $V_{MCA}$) remain referenced to the full certified thrust rating. Therefore, if an emergency arises (such as severe windshear), the pilot may immediately advance thrust levers to the forward mechanical stops (full rated takeoff thrust) without risking loss of directional control.

[!CAUTION] Strict Operational Prohibitions for Assumed Temperature (ATM/FLEX): Under FAA AC 25-13, reduced takeoff thrust may not be used:

1. On a runway contaminated by standing water, snow, slush, or ice. A wet runway is usable only when approved wet-runway performance accountability is provided.
2. With the antiskid system inoperative.

+> AC 25-13 does not impose a blanket reduced-thrust ban for an inoperative thrust reverser or every windshear report. Aircraft limitations, the AFM, MEL procedures, and the certificate holder's approved policies may impose additional restrictions and must be followed.

Fixed Derate (De-Rated Thrust)

• Operating Principle: A Fixed Derate (e.g., Derate 1 = $-10%$, Derate 2 = $-20%$) establishes a new, legally distinct, permanently lower engine thrust rating for the takeoff.
• $V_{MCG}$ Advantage: Because the certified maximum thrust for that rating is lower, the asymmetric yawing moment during an engine failure is significantly smaller. Consequently, certified $V_{MCG}$ and $V_{MCA}$ are lower, allowing takeoff at lower minimum weights and speeds on short or slippery runways.
• Operational Hazard: Advancing the thrust levers beyond the fixed derate limit during an engine failure at low speed (below rated $V_{MCG}$) may generate an uncontainable yawing moment, leading to catastrophic runway excursion or loss of control.