15.2 Climb Gradients, Obstacle Clearance & Runway Limitations

15.2 Climb Gradients, Obstacle Clearance & Runway Limitations

Once a transport category aircraft lifts off the runway and crosses the 35-foot screen height following an engine failure at $V_1$, the takeoff profile transitions from a ground-run acceleration problem into a vertical climb performance problem. Under Title 14 CFR Part 25 (§ 25.115 and § 25.121) and 14 CFR § 121.189, the flight must comply with rigid climb gradient standards and obstacle clearance requirements across four distinctly defined climb segments.

For the aircraft dispatcher, these climb limits dictate the Climb-Limited Maximum Takeoff Weight (WAT Limit: Weight, Altitude, Temperature). If atmospheric temperatures are high or the airport elevation is significant, air density drops, degrading both aerodynamic lift and turbofan thrust. The dispatcher must restrict aircraft gross weight to guarantee that the aircraft achieves these certified climb gradients even on the hottest days.

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The Four One-Engine-Inoperative Takeoff Climb Segments

14 CFR § 25.121 divides the takeoff flight path into four chronological segments, extending from the 35-foot screen height up to a minimum clean configuration altitude of at least 1,500 feet Above Ground Level (AGL).

                                                [ Fourth / Final Segment ]
                                              Clean, MCT, Climb to >= 1,500 ft AGL
                                              Gradients: 1.2% / 1.5% / 1.7%
                                           /
            [ Third Segment ]             /
         Level Acceleration, Flap Retract
         From V2 to Vfs at Accel Alt (>= 400 ft)
       ----------------------------------
      /
     /  [ Second Segment ] (MOST CRITICAL)
    /   Gear UP, Flaps Takeoff, Speed V2, Max Takeoff Thrust
   /    Gradients: 2.4% (2-eng) / 2.7% (3-eng) / 3.0% (4-eng)
  /
 /
/ [ First Segment ] 35 ft to Gear Retraction, Gear DOWN, Flaps Takeoff, Speed V2
  Gradients: > 0% (2-eng) / 0.3% (3-eng) / 0.5% (4-eng)

1. First Segment (Gear Retraction Phase)

• Initiation Point: The 35-foot screen height above the takeoff surface at the end of the takeoff distance.
• Termination Point: The point at which the landing gear is fully retracted and the gear doors are closed.
• Aircraft Configuration:
  • Landing gear: Extended (Down), transitioning to retracted.
  • Wing flaps: In certified Takeoff position.
  • Operating engine(s): Operating at Maximum Takeoff Thrust.
  • Inoperative engine: Critical engine windmilling or feathered.
  • Airspeed: Maintained at $V_2$ (or between $V_{lof}$ and $V_2$).
• Mandatory Gross Climb Gradients (14 CFR § 25.121(a)):
  • Two-engine aircraft: Must produce a climb gradient measurably greater than zero ($> 0.0%$) (positive climb).
  • Three-engine aircraft: Minimum climb gradient of $0.3%$.
  • Four-engine aircraft: Minimum climb gradient of $0.5%$.

2. Second Segment (The Most Critical Climb Segment)

• Initiation Point: Landing gear fully retracted and locked.
• Termination Point: The acceleration altitude, which must be at least 400 feet AGL (airline procedures typically designate between 800 and 1,500 feet AGL).
• Aircraft Configuration:
  • Landing gear: Retracted (Up).
  • Wing flaps: In certified Takeoff position.
  • Operating engine(s): Operating at Maximum Takeoff Thrust (subject to the 5-minute or 10-minute certification limit).
  • Inoperative engine: Critical engine stopped, windmilling, or feathered.
  • Airspeed: Maintained strictly at $V_2$.
• Mandatory Gross Climb Gradients (14 CFR § 25.121(b)):
  • Two-engine aircraft: Minimum climb gradient of $2.4%$.
  • Three-engine aircraft: Minimum climb gradient of $2.7%$.
  • Four-engine aircraft: Minimum climb gradient of $3.0%$.

Operational Significance: The Second Segment is universally recognized as the most restrictive climb gradient in transport category operations. Because the aircraft is still in high-drag takeoff flap configuration and climbing on one engine, the thrust required to achieve a 2.4% gradient often forces significant reductions in takeoff weight on hot days or at high airport elevations. This is the classic Second-Segment WAT Limit.

3. Third Segment (Level Acceleration & Flap Retraction Phase)

• Initiation Point: Reaching the acceleration altitude (minimum 400 feet AGL).
• Termination Point: Flaps and slats fully retracted, aircraft in clean configuration, and airspeed accelerated to final segment climb speed ($V_{fs}$ / clean minimum maneuver speed).
• Aircraft Configuration:
  • Landing gear: Retracted (Up).
  • Wing flaps: Retracting in scheduled steps to clean position.
  • Flight Profile: The aircraft levels off (or maintains a nominal climb) to accelerate.
  • Operating engine(s): Maximum Takeoff Thrust, transitioning to Maximum Continuous Thrust (MCT) at the end of the segment.
  • Airspeed: Accelerating from $V_2$ to $V_{fs}$.
• Climb Requirement (14 CFR § 25.121(c)):
  • The aircraft must be capable of accelerating to $V_{fs}$ while maintaining an equivalent net positive climb margin, or climb at specified minimum gradients while retracting flaps.

4. Fourth / Final Segment (En Route Clean Climb Phase)

• Initiation Point: Flaps fully retracted into clean configuration.
• Termination Point: Reaching at least 1,500 feet AGL (or the designated en route obstacle clearance altitude / MEA).
• Aircraft Configuration:
  • Landing gear: Retracted (Up).
  • Wing flaps: Clean (Fully Retracted).
  • Operating engine(s): Set to Maximum Continuous Thrust (MCT) (no time limit).
  • Airspeed: Maintained at $V_{fs}$ (Final Takeoff Segment Speed / Clean Best Rate of Climb Speed).
• Mandatory Gross Climb Gradients (14 CFR § 25.121(d)):
  • Two-engine aircraft: Minimum climb gradient of $1.2%$.
  • Three-engine aircraft: Minimum climb gradient of $1.5%$.
  • Four-engine aircraft: Minimum climb gradient of $1.7%$.

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Master Summary: Takeoff Climb Segments

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Gross vs. Net Takeoff Flight Path (14 CFR § 121.189)

A fundamental concept tested heavily on the FAA ADX exam is the legal and physical distinction between the Gross Takeoff Flight Path and the Net Takeoff Flight Path.

The Conceptual Difference

• Gross Takeoff Flight Path: The actual climb profile demonstrated by manufacturer test pilots under pristine certification conditions. It represents the exact aerodynamic performance that an airframe produces with an inoperative engine.
• Net Takeoff Flight Path: The operational climb profile that airline dispatchers are legally required to use when calculating obstacle clearance under 14 CFR § 121.189. The net flight path is derived by mathematically reducing the gross climb gradient by a statutory safety margin.

Mandatory Regulatory Gradient Deductions

Under 14 CFR § 121.189(d), the gross climb gradient in each segment must be penalized by:

• $0.8%$ for two-engine aircraft;
• $0.9%$ for three-engine aircraft;
• $1.0%$ for four-engine aircraft.

$\text{Net Gradient (\%)} = \text{Gross Gradient (\%)} - \text{Regulatory Decrement}$

Altitude ^
         |                 / Gross Flight Path (Demonstrated Test Pilot Performance)
         |                / 
         |               /  <--- 0.8% Gradient Reduction (Twin-Engine Margin)
         |              / 
         |             /  Net Flight Path (Dispatched Operational Path)
         |            /
         |           /  | 
         |          /   | >= 35 ft Vertical Clearance over Obstacle
         |         /    v
         |        /   [ OBSTACLE ]
         +--------------------------------------------------------> Distance

Mathematical Gradient Calculations

In aeronautical engineering, climb gradient is expressed as the ratio of vertical height gained ($\Delta h$) to horizontal distance traveled ($\Delta d$), expressed as a percentage:

$\text{Gradient (\%)} = \left( \frac{\Delta h}{\Delta d} \right) \times 100$

To convert between rate of climb in feet per minute (fpm) and climb gradient in percent at a given groundspeed (knots):

$\text{Rate of Climb (fpm)} = \text{Groundspeed (kts)} \times \text{Gradient (\%)} \times 1.0127$ $\text{Gradient (\%)} \approx \frac{\text{Rate of Climb (fpm)}}{\text{Groundspeed (kts)}}$

Worked Example: A twin-engine Boeing 737 is climbing in the second segment at a groundspeed of 150 knots. The aircraft's gross climb performance produces a rate of climb of 600 fpm.

• Gross Gradient: $(600 / 150) = 4.0%$.
• Net Gradient: $4.0% - 0.8% = \mathbf{3.2%}$.
• Net Rate of Climb for Obstacle Planning: $150 \times 3.2 = \mathbf{480\text{ fpm}}$.

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Obstacle Clearance Requirements (14 CFR § 121.189)

Under 14 CFR § 121.189, no person operating a turbine-powered transport category airplane may take off at a weight exceeding that at which the net takeoff flight path clears all obstacles along the departure corridor.

Vertical and Horizontal Clearance Standards

1. Vertical Obstacle Clearance: The net takeoff flight path must clear every obstacle in the departure path by a vertical margin of at least 35 feet.
2. Horizontal Corridor Boundaries:
   • The departure corridor begins at the departure end of the runway (DER) with a width of 300 feet (150 feet on either side of the runway centerline).
   • The corridor splays outward at an angle of $12.5%$ (a $1:8$ splay ratio) as distance from the runway increases.
   • Within the airport boundaries: The required lateral obstacle clearance is 200 feet.
   • Beyond the airport boundaries: The required lateral obstacle clearance expands to 300 feet.

Turning Departures One-Engine-Inoperative

If the departure procedure mandates a turn to avoid terrain or air traffic restrictions:

• 14 CFR Part 25 prohibits assuming bank angles greater than 15 degrees prior to reaching 400 feet AGL.
• When an aircraft banks, the total lift vector tilts. To maintain altitude or climb, the wing must operate at a higher angle of attack, generating higher induced drag. This induced drag penalty reduces the climb gradient.
• Flight management systems and dispatch performance software automatically reduce net climb gradients during turns (typically a gradient reduction of $0.5%$ to $1.0%$ for a 15-degree bank).

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Runway Surface Conditions & Contaminants

Takeoff performance calculations change dramatically when the runway surface deviates from clean, dry concrete.

Wet Runway Takeoff Limitations (§ 121.189(e))

Under 14 CFR § 121.189(e), no transport category airplane may take off on a wet runway unless:

• The takeoff distance does not exceed the available takeoff runway length multiplied by certified wet performance data; or
• The required runway length is increased by $115%$ ($1.15 \times \text{Dry Runway Distance}$) unless specific wet runway data is approved in the AFM.

Contaminated Runway Physics (AC 25-31 & AC 91-79B)

A runway is classified as contaminated whenever more than $25%$ of the runway surface area within the required length and width is covered by:

• Surface water, slush, or wet snow deeper than $3\text{ mm}$ ($0.125\text{ inches}$);
• Compacted snow;
• Ice (including wet ice).

When accelerating through slush or standing water, the aircraft experiences two severe retarding aerodynamic forces:

1. Displacement Drag ($D_d$): The fluid resistance generated as tires push aside standing fluid.
2. Impingement Drag ($D_i$): The immense spray force of high-pressure water and slush thrown upward by the nose and main tires against the aircraft flaps, landing gear doors, and lower fuselage.

These combined retardant forces drastically degrade acceleration, prolong ground roll, and impair stopping capability.

Reduced Thrust Takeoff Prohibitions (AC 25-13 / FLEX / Assumed Temperature)

Airlines frequently use Reduced Thrust (Assumed Temperature Method - ATM or FLEX) to reduce turbine temperatures, extend engine life, and lower maintenance costs. The dispatcher inputs a fictitious high temperature into the FMS, commanding the FADEC to deliver derated thrust (up to a maximum allowable reduction of $25%$ below rated takeoff thrust).

Under FAA regulations and airline operations specifications, reduced thrust takeoffs are strictly prohibited under any of the following conditions:

1. When the runway is contaminated by standing water, slush, snow, or ice;
2. When the runway is declared slippery when wet;
3. When antiskid or thrust reversers are inoperative (per MEL);
4. When windshear advisories or warnings are in effect;
5. When an engine-out departure procedure requires full rated thrust to meet obstacle clearance.