Climb and Descent
Performance
Dr. C.P. Lawson
C.P. Lawson@cranfield.ac.uk
01 November 2017
www.cranfield.ac.uk
Climb and Descent Performance
Overview
• Introduction
• Descent Performance in Aircraft
Operations
• En-route Descent
• Terminal Area Descent
• Final Approach
• Emergency Descent
• Climb and Descent Performance
Analysis
• Generalised Climb and Descent
Performance
• Jet-Engined Aircraft
• Propeller Driven Aircraft
• Mixed Power-plants
• The Effects of Wind on Climb and
Descent Performance
• Climb Performance in Aircraft
Operations
• Climb Gradient
• Climb Rate
• Minimum Fuel Climb
• Noise Limitations
• High Performance Climb
• Conclusions
2
Climb and Descent Performance
Introduction
• Aims of Lecture
• Introduce Performance Analysis for Modest Thrust-to-Weight Ratio
Aircraft
• Introduce Energy Method for Analysis of High Thrust-to-Weight Ratio
Aircraft
• Consider the Application of Climb and Descent Performance
3
Climb and Descent Performance
Introduction
• If Aircraft Thrust is Greater than Drag
• Excess Thrust
• Aircraft can Climb
• Issues for Climb Application
• Sufficient Rates for Safety
• Economics
• If Aircraft Thrust is Less than Drag
• Aircraft can Descend
• Issues for Descent Application
• Safety Re-pressurisation
• Systems Power
• Rates Depend on Magnitude of
Difference between Thrust and Drag
• A Change in Potential Energy is
Implicit
• High Rates Imply a Change in
Kinetic Energy also
4
Climb and Descent Performance
Introduction
• Climb is Usually Performed at Constant EAS or Constant M
• Constant EAS => TAS and M Increase as Density Falls
• Constant M => EAS Falls and TAS Falls in Troposphere as Temperature and
Mach Number Decreases
5
Climb and Descent Performance
Introduction
• Climb is Usually Performed at Constant EAS or Constant M
• Following Constant EAS - Mcrit May Eventually be Reached
• Following Constant M – Stalling Speed May be Reached
6
Climb and Descent Performance
Introduction
• In Practice a Climb at
Constant EAS Projected to
Reach Mcrit
• Start at Constant EAS
• Constant AoA
• Continue at Constant M
• Not Optimum
Aerodynamic Efficiency
7
Climb and Descent Performance
Introduction
• Philosophy of Climb and Descent Analysis
• Modest Thrust-to-Weight Ratio
• Low Rate of Climb
• Low Rate of Reduction in Density
• Low Rate of Increase of TAS (Acceleration)
• Consider Only Change in Potential Energy
• Quasi-Steady State
• High Thrust-to-Weight Ratio
• Not Steady State
• Consider Change in Potential and8Kinetic Energy
Climb and Descent Performance
Climb and Descent Performance Analysis
• Steady State Climb and Descent
• Suitable for Most Subsonic Aircraft
• Transport Aircraft T/W 0.3 at Takeoff
• Rate of Climb or Descent is the
Vertical Velocity dH/dt
• Gradient as a Percentage
• grad% = 100.tang2
• Climb or Descent Gradient
•
• H is Geopotential Height (Height
Above Datum)
• Jet-Engined and Propeller Driven
Aircraft are Considered Separately
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Climb and Descent Performance
Aircraft with Jet Engines – Quasi-Steady Climb
• Equations of Motion for Straight,
Wings Level Climb
•
• For Low T/W Ratio Neglect
Acceleration Term
•
• Excess Thrust over Weight give
Climb Gradient
• [FN – D] / W = sing2
• Minimum Drag (Speed) Gives Best
Gradient of Climb
10
Climb and Descent Performance
Aircraft with Jet Engines – Quasi-Steady Climb
• Best Rate of Climb
• [FN – D].V / W = dH / dt
• Maximised at Minimum D.V
• No Simple Solution for Best
Rate of Climb
• Occurs Greater then
Minimum Drag Speed
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Climb and Descent Performance
Climb Performance in Aircraft Operations
• Climb Performance Optimised for
• Maximum Gradient or
• Maximum Rate
• Depending Upon Requirement
• Minimum Climb Gradient
• 2% Under All Conditions
• Engine Out
• Design Case?
• Best Climb Gradient
• Obstacle Avoidance
• Take-off
• Initial Climb
• Airfield Departure Path
• 2% for 15 km
• Speed for Best Climb Gradient
• Minimum Drag Speed (Jet)
• Sub Min Drag Speed (Prop)
• Limited by Stall or Lateral
Control – Must Fly Faster
12
Climb and Descent Performance
Descent Performance in Aircraft Operations
• Below Minimum Drag Speed
• Instability of Flight Path
• Elevator and Throttle Required
• Backside of Drag Curve
• Above Minimum Drag Speed
• Elevator Control Only
• Pitch Down to Increase Gradient
• Pitch Up to Reduce Gradient
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Climb and Descent Performance
Descent Performance in Aircraft Operations
• Practical Considerations
• Steep Nose Down Uncomfortable
• Rate of Change of Cabin Pressure
• Max 300 ft/min
• Emergencies Excepted
• Minimum Engine Thrust Limited by Systems Power
• Jet’s Drag Increased
• Flaps
• Spoilers
• Airbrakes
• Landing Gear
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Climb and Descent Performance
Descent Performance in Aircraft Operations
• Descent Phases
• En-route Descent
• Terminal Area Descent
• Final Approach
• En-route Descent
• High Airspeed
• Thrust Limited for Systems Power Provision
• Scheduled Mach or Airspeed to Avoid Mcrit or Stall
• Rate Limited by Change of Cabin Pressure Below 8,000ft
15
Climb and Descent Performance
Descent Performance in Aircraft Operations
• Terminal Area Descent
• Air Traffic Control Restrictions
• Airspeed Dictated to Maintain
Safe Separation
• Performance Optimised by
Configuration Changes
• Maximum Endurance Speed
Desirable
• Priority to Manoeuvre
Performance
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Climb and Descent Performance
Descent Performance in Aircraft Operations
• Final Approach
• Gradient Control Prioritised
• Steep Enough to Avoid Obstacles
• Shallow Enough to Avoid
Excessive Flare at Touchdown
• Large Transport 5% (3o)
• Lowest Airspeed Safely Above
Stall Speed and Minimum Drag
Speed
• High Drag Configuration Reduces
Minimum Drag Speed
• Relatively High Thrust
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Climb and Descent Performance
Descent Performance in Aircraft Operations
• Emergency Descent
• Descend Below 10,000 ft
• High Airspeed, Clean
Configuration, Minimum Thrust
• Limited by Mach Number
• Low Airspeed, High Drag Devices
Deployed, Pitch Nose-Down,
Structurally Limited Airspeed
• Aircraft Specific Implementation
18
Climb and Descent Performance
The Effects of Wind on Climb and Descent Performance
• So far Still Air Assumed
• Moving Air Mass
• Actual Performance Unaffected
• Perceived (Ground Observer) Performance Affected
• Ability to Clear Ground Obstacles Affected
• Wind Velocity
• Relative Velocity Between Air Mass and Ground
• Terrain Following
• Horizontal over Level Terrain
• Horizontal at Altitude
19
Climb and Descent Performance
The Effects of Wind on Climb and Descent Performance
• Tailwind
• TAS Reduced
• Perceived Gradient Reduced
• Inferior Ability to Clear Obstacles
•
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Headwind
• TAS Increased
• Perceived Gradient Increased
• Superior Ability to Clear
Obstacles
Climb and Descent Performance
The Effects of Wind on Climb and Descent Performance
• Wind Close to the Ground
• Boundary Layer Effects
• Significant dV/dH
• Tailwind 150%
• Headwind 50%
• Wind-Shear
• Close to Ground
• Severe Meteorology
• May be Beyond Performance of Aircraft
• Sensors for Early Response
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Climb and Descent Performance
High Performance Climb
• High Performance Strike Aircraft
• 50,000 ft/min Climb Rate
• Consider Constant EAS Climb 40,000 ft/min
• Relative Density falls to 0.25
• TAS Doubles
• Kinetic Energy Change Significant
• Specific Total Energy (Energy Height)
• Et = mgH + mV2/2
• Es = H + V2/2g = Et / mg
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Climb and Descent Performance
Conclusions
• Climb is Important in Aircraft Design
and Operation
• Climb Gradient - Single Engine
Failure
• Fuel Burn – Second Only to Cruise
• Descent
• Low Fuel Burn
• Many Options for Optimised Enroute Descent
• Rate and Gradient
• Configuration and Airspeed
• Time Saved
• Limiting Factors
• Theoretically Optimised Climb and
Descent Considered
• Practical Considerations
• Safety Margins
• Stall Speed
• Minimum Control Speed
• Rate of Change of Cabin
Pressure
• Systems Power Requirements
• Other Constraints
• Pitch Attitude
• Critical Mach Number
• May Strongly Influence Aircraft Design
and Engine Sizing
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Climb question
• a) V = 82.6 m/s (@1,500ft), dH/dt = 13.54 m/s, g2 = 9.44o
t = 33.8 s, d = 2789 m, m = 54,902 kg
• b) Calc conditions at 1,500ft and 5,000ft and take average: dH/dt
= 14.7 m/s, using energy method
Es = 1945.5 m, t = 132.2 s, d = 15716 m, m = 54678 kg
• c) g2 = 6.09o , dH/dt = 17.8 m/s, t = 171.5 s, d = 28735 m, m = 54,440 kg
• d) g2 = 3.79o , dH/dt = 13.0 m/s, t = 233.8 s, d = 46119 m , m = 54,199 kg
• e) g2 = 2.18o , dH/dt = 8.1 m/s, t = 377.8 s, d = 80127 m , m = 53,981 kg
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