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Bank Angle Impact on Climb Gradient

Departure Obstacle Analysis

If your AFM-derived climb gradient just barely beats the obstacle or SID requirement you might need to consider the impact of a turn on that performance. If, for example, the procedure requires a 25° bank turn at the most critical point, will that bank angle subtract from your climb performance? Obviously yes, but by how much?


 

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Figure: Theoretical (but wrong) view of the impact of a 15° bank turn on climb gradient, from Eddie's notes.

Regulatory Assumptions

14 CFR 91 is silent on this subject. 14 CFR 25 only mentions bank angles in conjunction with minimum control speeds, in which case the magic number is 5°. The notes in 14 CFR 121 and 135 are identical, the maximum bank to be considered is 15°.

[14 CFR 121, §121.189] Large transport category airplanes: Turbine engine powered: Takeoff limitations.

(f) For the purposes of this section, it is assumed that the airplane is not banked before reaching a height of 50 feet, as shown by the takeoff path or net takeoff flight path data (as appropriate) in the Airplane Flight Manual, and thereafter that the maximum bank is not more than 15 degrees.

[14 CFR 135, §135.379] Large transport category airplanes: Turbine engine powered: Takeoff limitations.

(f) For the purposes of this section, it is assumed that the airplane is not banked before reaching a height of 50 feet, as shown by the takeoff path or net takeoff flight path data (as appropriate) in the Airplane Flight Manual, and thereafter that the maximum bank is not more than 15 degrees.

[14 CFR 135, §135.398] Commuter category airplanes performance operating limitations.

(e) For the purposes of this section, it is assumed that the airplane is not banked before reaching a height of 50 feet, as shown by the takeoff path or net takeoff flight path data (as appropriate) in the Airplane Flight Manual, and thereafter that the maximum bank is not more than 15 degrees.

Climb Gradient Decrement (15° Bank or Less)

[AC 120-91, ¶14.b.]

(1) The AFM generally provides a climb gradient decrement for a 15 degree bank. For bank angles less than 15 degrees, a proportionate amount of the 15 degree value may be applied, unless the manufacturer or AFM has provided other data. Bank angles over 15 degrees require additional gradient decrements.

For example, the Bombardier Global Express:

[BD-700 Airplane Flight Manual, Chapter 7, Supplement 24, ¶6.A.] Take-Off Performance For Airport Elevations Sea Level to 10,000 Feet

(6)The gradient loss in a steady turn is tabulated below for a 15° bank turn.

SLAT/FLAP GRADIENT LOSS (%)
IN/0° 0.30
OUT/0° 0.45

For bank angle less than 15°, the gradient loss may be considered proportional to the bank angle.

No Published Gradient Loss

Not all manufacturers provide a gradient loss table but for those that do the worst case seems to be about a half a percent for a 15% bank turn. The DA 2000, for example, shows no more than 0.46% in four different flap and slat configurations. The CL-604 has a maximum of 0.38% for the worst condition. Note these are gradient losses, you subtract them from the AFM value. If, for example, your published gradient is 10.0% and the gradient loss is 0.5%, your resulting gradient is 9.5%.

Aircraft that do not have published gradient loss figures are in a bit of a quandary. Here are two possible solutions:

  • If you reason the climb gradient is reduced by the same factor the vertical component of lift is reduced, as shown in the diagram on the top of this page, you could say the climb gradient is equal to the cosine of 15°, which comes to 0.966. That would be a gradient loss of 3.4%, much higher than the published numbers for most aircraft. This is because this method ignores the contribution to the vertical component made by the engines.
  • If you reason your airplane should have a similar loss as shown by the three example aircraft, (the BD-700, DA-2000, and CL-604), you could reason that your climb gradient loss will be no more than 0.5%.

Between 0.5% and 3.4%, not much help to be sure. I suppose the conservative approach would be to reduce your climb gradient by 3.4%.

Climb Gradient Decrement (Greater than 15° Bank)

[AC 120-91, ¶14.b.]

(2) If bank angles of more than 15 degrees are used, V2 speeds may have to be increased to provide an equivalent level of stall margin protection and adequate controllability (i.e., VMCA (minimum control speed, air)). Unless otherwise specified in the AFM or other performance or operations manuals from the manufacturer, acceptable adjustments to ensure adequate stall margins and gradient decrements are provided by the following table:

Bank Angle Speed 'G' Load Gradient Loss
15° V2 1.035 AFM 15° Gradient Loss
20° V2 + XX/2 1.064 Double 15° Gradient Loss
25° V2 + XX 1.103 Triple 15° Gradient Loss

Where 'XX' = the all-engines-operating operating speed increment (usually 10 or 15 knots)

NOTE: On some airplanes, the AFM standard V-speeds may already provide sufficient stall margin protection without additional adjustments.

(3) Bank angles over 25 degrees may be appropriate in certain circumstances but require specific evaluation and FAA certificate-holding district office (CHDO) approval.

(4) Accountability for speed increase for bank angle protection may be accomplished by increasing V-speeds by the required increment shown above or by accelerating to the increment above V2 after liftoff. The following are examples of acceptable methods:

(a) If available, AFM data for "improved climb" or "overspeed" performance may be used to determine weight decrements for the desired increase to V1, VR, and V2.

(b) Calculate a weight decrement from the weight/V-speed relationship in the AFM for the desired increase in V1, VR, and V2.

(c) Account for the acceleration above V2 by trading the climb gradient for speed increase. Integrate this climb gradient loss over the distance required to accelerate to determine an equivalent height increment to be added to all subsequent obstacles.

(5) Gradient loss in turns may be accounted for by increasing the obstacle height by the gradient loss multiplied by the flight path distance in the turn. This will result in an equivalent obstacle height that can be analyzed as a "straight-out" obstacle in the operator's airport analysis programs.

(6) For bank angles greater than 15 degrees, the 35-foot obstacle clearance relative to the net takeoff flight path should be determined from the lowest part of the banked airplane.

References

14 CFR 25, Title 14: Aeronautics and Space, Airworthiness Standards: Transport Category Airplanes, Federal Aviation Administration, Department of Transportation

14 CFR 91, Title 14: Aeronautics and Space, General Operating and Flight Rules, Federal Aviation Administration, Department of Transportation

14 CFR 121, Title 14: Aeronautics and Space, Operating Requirements: Domestic, Flag, and Supplemental Operations, Federal Aviation Administration, Department of Transportation

14 CFR 135, Title 14: Aeronautics and Space, Operating Requirements: Commuter and On Demand Operations and Rules Governing Persons on Board Such Aircraft, Federal Aviation Administration, Department of Transportation

Advisory Circular 120-91, Airport Obstacle Analysis, 5/5/06, U.S. Department of Transportation

Bombardier BD-700-1A10 Airplane Flight Manual, Rev 80, Jun 03/2014.

Revision: 20141214
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