1. Lecture 5: Climb PERFORMANCE
AIRCRAFT WEIGHT & PERFORMANCE

2. Introduction
One of the most important aspects of aircraft performance is the ability to climb.
CLIMB starts after take off and it ends when aircraft levels off at the cruising level.
Climb
Cruise / En-route
Descend
Approach & Landing
Take-off
The climb phase of a flight starts after take off, when the aircraft reaches a certain height above the ground, and it ends when aircraft levels off at the cruising level.
For the first portion of the climb it is more convenient to consider the climb gradient rather then the rate of climb. Climb gradient is the ratio of height gained to distance traveled, and it is expressed in percentage. All instrument departure procedures have the minimum climb gradient specified in the charts. This climb gradient is required to over fly the obstacles in the departure area at a safe altitude defined as minimum obstacle clearance.
When the obstacles are over flown it is more convenient to consider the rate of climb, since the aircraft would normally require to climb at the maximum rate of climb so as to reach the required altitude in the least possible time. Rate of climb is the vertical component of the aircraft’s velocity.

3. Phases of flight

4. Introduction
An aircraft can climb only if it can produce excess thrust (thrust minus drag).
This excess thrust is needed to overcome drag.
For example, if an aircraft is producing 1,000 pounds of thrust and has 700 pounds of drag, it would have 300 pounds of excess thrust available.
An aircraft can climb only if it can produce excess thrust. This excess is the pounds of thrust force being produced beyond that needed to overcome drag. For example, if an aircraft is producing 1,000 pounds of thrust and has 700 pounds of drag, it would have 300 pounds of excess thrust available. In a climb, a component of weight acts rearward along the flight path. The steeper the climb angle, the greater this component. In a steady-state climb, meaning the climb angle is constant and the airspeed is not changing, the forward-acting thrust must equal the rearward-acting forces of drag plus the weight component. The greater the excess thrust, the steeper the possible climb.. To maximize excess thrust, a jet-powered aircraft will climb at a speed where drag is minimum. This is called the best angle of climb speed, abbreviated Vx.

5. Climb Gradient/Angle of climb
For the first portion of the climb it is more important to consider the climb gradient or angle of climb.
Why ??
Climb gradient or angle of climb is important to ensure aircraft overfly the obstacles in the departure area at a safe altitude.
It is defined as minimum obstacle clearance

6. Climb Gradient
The climb gradient by definition is the ratio of height gained to the horizontal distance traveled by aircraft.
Basically, climb gradient depends on the difference between the thrust and drag (the excess thrust) and the mass of the aircraft.
Factors that affect these forces will have affect on the climb gradient.
Climb gradient = (THRUST - DRAG) / WEIGHT
EXCESS THRUST

7. Angle of climb
The angle of climb is the angle between height gained to the horizontal distance traveled by aircraft during climb.

8. Climb Gradient/Angle of Climb
The climb gradient by definition is the ratio of height gained to distance traveled. If the angle of climb  is known then the climb gradient is equal to tan (). For small angles
tan () = sin (). Now taking into the consideration the formulas from the drawing above:
Climb gradient = tan () = sin () = (Thrust – Drag) / Weight
This shows that the climb gradient depends on the difference between the thrust and drag (the excess thrust) and the mass of the aircraft. Factors that affect these forces will have affect on the climb gradient.
Climb gradient = tan(a) = sin(a) = (THRUST - DRAG) / WEIGHT

9. Rate of Climb (ROC).
When the obstacles are over flown it is the important to consider the rate of climb.
Rate of climb is the vertical component of the speed, , expressed in feet per minute. It depends on the airspeed (V) and the angle of climb or climb gradient.
Rate of climb = V x sin () = V x Climb gradient = V x (Thrust – Drag) / Weight
Best rate of climb is important to ensure aircraft reach required altitude in the minimum time.

10. Three types of climb
There are three types of climbs – a normal climb, best angle of climb and best rate of climb.
A normal climb is a slow, but comfortable (for the passengers!), climb with a low rate of climb and high speed.
The best angle climb is the slowest climb, but at a high angle. This is used to clear obstacles at the end of the runway.
The best rate climb is a tradeoff between the two – giving best rate of climb and a moderate amount of airspeed.

11. NORMAL CLIMB
Normal climb is performed at an airspeed recommended by the airplane manufacturer.
Normal climb speed is generally somewhat higher than the airplane’s best rate of climb.
The additional airspeed provides better engine cooling, easier control, and better visibility over the nose. Normal climb is sometimes referred to as “cruise climb.”
Complex or high performance airplanes may have a specified cruise climb in addition to normal climb.

12. Two Airspeed during climb
There are two airspeeds relating to climb performance which are, Vx and Vy.
Vx is the indicated airspeed for best angle of climb.
Vy is the indicated airspeed for best rate of climb.
Best Angle of Climb Speed (Vx)
Gain maximum altitude in shortest distance
Best Rate of Climb Speed (VY )
Gain maximum altitude in shortest time
Best angle-of climb airspeed (Vx) is considerably lower than best rate of climb (VY ).
Vx is slower than Vy.

13. Best Angle of Climb Speed (Vx)
Best angle of climb airspeed for an airplane is the speed at which the maximum excess thrust is available over that required for level flight.
The best angle of climb will result in a steeper climb path, although the airplane will take longer to reach the same altitude than it would at best rate of climb.
The best angle of climb, therefore, is used in clearing obstacles after takeoff.
Excess thrust is the difference between the total drag of the aircraft, and the thrust output of the powerplant. For a jet aircraft, this speed is very close to the speed at which the total minimum drag occurs
Best angle of climb (VX) is performed at an airspeed that will enable aircraft achieve best altitude in a specific distance
It should be noted that, as altitude increases, the speed for best angle of climb increases, and the speed for best rate of climb decreases.
The point at which these two speeds meet is the absolute ceiling of the airplane.

14. Best Rate of Climb Speed (VY )
Best rate of climb (VY) is performed at an airspeed where the most excess power is available over that required for level flight.
This condition of climb will produce the most gain in altitude in the least amount of time (maximum rate of climb in feet per minute).
Rate of climb = V x (THRUST - DRAG) / WEIGHT
To calculate an aircraft's climb rate in feet per minute, multiply the constant 33,000 by the excess thrust horsepower divided by weight.
The rate of climb (ROC) can be found by the simple formula:
Another way to measure a climb is by the rate (feet per minute) rather than the angle of ascent. The ability of an aircraft to climb in terms of rate is a function of excess power. You may recall from physics that power is defined as the rate at which work is done. Work, you will recall, is a force applied through a distance. To lift a 600,000-pound jet to an altitude of 10,000 feet takes six billion foot pounds of work (600,000 pounds x 10,000 feet). To complete this climb in 10 minutes (or 600 seconds) would require 10,000,000 foot pounds per second of power (6,000,000,000 foot pounds/600 seconds). Thanks to British physicist James Watt, who determined that a horse is capable of producing roughly 550 foot pounds of power per second, we can express this figure in terms of horsepower. In our example, the amount of power required would be a little more than 18,000 horsepower.
The best rate of climb made at full allowable power is a maximum climb. It must be fully understood that attempts to obtain more climb performance than the airplane is capable of by increasing pitch attitude will result in a decrease in the rate of altitude gain

15. Best V x or Best VY For a given aircraft mass
The maximum climb gradient will occur when the excess thrust is greatest.
Maximum rate of climb will occur when the product of the speed and the excess thrust is greatest.
For each climb the pilot must determine whether it is more important to climb at the steepest angle (best Vx) to clear obstacles, or at the fastest rate (best Vy).

16. Example
F-16 fighter aircraft, for example, according to the Lockheed Martin Corporation, climbs at 50,000 feet per minute at sea level.
An F-15 Eagle climbing and releasing flares.

17. Example
The greater the excess thrust, the steeper(almost perpendicular) the possible climb.
To perform this vertical climb, the amount of thrust created must equal the drag the aircraft is experiencing plus the entire weight of the aircraft.
If a jet aircraft has more thrust available than the sum of weight and drag, not only could it climb straight up, it could also accelerate its airspeed while climbing

18. Speed and Acceleration Retraction of flap and landing gear
Factors Affecting the Climb performance (Climb Angle and Rate of Climb)
Speed and Acceleration
Aircraft
Mass
Temperature
& Air Density
Wind
Retraction of flap and landing gear
Cabin Pressurization

19. SPEED AND ACCELERATION
When the aircraft is accelerating during climb some portion of the excess thrust is required for the acceleration, so there will be less excess thrust and therefore reduce the angle of climb.
For a given aircraft mass the maximum rate of climb will occur when the product of the speed and the excess thrust is greatest. As both thrust and drag vary with speed, there will be a particular speed at which this occurs that is different from the best angle of climb speed. If the speed is increased above that for the best angle of climb although the climb angle will decrease, the rate of climb will initially increase.
If the aircraft is required to fly at different speed, the rate of climb will be reduced.

20. AIRCRAFT MASS
Increased mass gives higher drag which reduces the excess thrust (the difference between the thrust and drag), and therefore reduces the climb angle for a given thrust & reduces the rate of climb.

21. TEMPERATURE
The higher the air temperature, less thrust can be produced by the engines.
Because of that the difference between the thrust and the drag during climb is smaller. Therefore the climb gradient & the rate of climb will be reduced.

22. AIR DENSITY
Density Altitude (increasing altitude thus decreasing density) will reduce thrust and therefore reduce the climb angle & the rate of climb.
Density altitude significantly affects the climb performance of an aircraft. High density altitude, the performance altitude at which the machine is operating, reduces climb performance. Humidity, which can be factored into density altitude, also reduces performance primarily through adversely affecting engine performance. High humidity results in reduced power output and thus reduced ETHP. A humid day with high density altitude may seriously decrease our ability to climb.

23. WIND HAS NO AFFECT ON THE RATE OF CLIMB
In wind conditions, headwind or tailwind will have affect on the aircraft’s ground speed.
So, a headwind will reduce the ground speed and therefore reduce the horizontal distance that an aircraft travels in comparison to the no wind conditions.
Therefore a headwind gives increased climb angle, while a tailwind affects in opposite direction and gives reduced climb angle. Crosswind component has no effect on the climb gradient.
WIND HAS NO AFFECT ON THE RATE OF CLIMB
Wind
The rate of climb is independent from the wind speed, because it is always considered in reference to the air not the ground

24. Retraction of flap and landing gear
When the flap and landing gears are retracted, the drag is reduced, resulting in an increase in excess thrust, therefore the rate of climb is increased.

25. Cabin pressurization
The rate of change of the cabin pressure has to be proportional to the rate of change of the atmospheric pressure (rate of climb).
Modern aircraft operate at high altitudes and can achieve high rates of climb.
In order to take advantage of these properties the interior of an aircraft flying at high altitude is pressurized to allow passengers and crew to function normally without any need for additional oxygen.
Cabin pressurization systems are designed to produce conditions equivalent to those at approximately 8000 feet.

26. Cabin pressurization
When the aircraft is climbing, the change of cabin pressure is proportional to the change of the ambient pressure, in order to control the structural stress on the fuselage from the inside.
This is performed automatically by sophisticated control system.
However, if the cabin pressure is manually controlled or in case of system degradation, care should be taken to ensure that the climb rates are safe and ensure that the structural stress is not exceeding the maximum limit.

27. Cabin pressurization The maximum rate of climb is therefore limited.
When exceeded the aircraft structure is overstressed from inside and structural failure (explosion) is possible.
Passengers comfort is also a factor.
Usually the best comfort is achieved at rates of climb of 1500 feet per minute.

28. Summary There are three climbing flight conditions:
Steepest climb (best angle of climb)-to clear obstacle after take-off
Fastest climb (best rate of climb)-to reach cruise altitude with minimum time.
Economical climb (less fuel consumption)
The airspeed for economical climb is lower than that for fastest climb but is much closer to the fastest climb airspeed than to the steepest climb airspeed.

29. Summary Factors affecting climb performance
Greater mass reduced climb angle and rate of climb.
Higher temperature, lower air density also reduced climb angle and rate of climb.
Headwind condition, greater climb angle. Tailwind reduce climb angle. Wind no effect on rate of climb.
Quick retraction of flaps and landing gear, greater climb angle and greater speed.

30. Question Bank
An aircraft will be taking-off from a sea-level airfield, and climbing to a cruising level of FL75 (i.e. 7500ft pressure altitude). Using Fuel Time Distance Climb table & assume condition during no wind, calculate:
How long will the climb take (time)?
How much fuel used?
How far the climb distance?
2. Based on question 1, calculate the climb distance traveled if there is 15knot tailwind.