3. ENGINE RATINGS
Engines are certified to deliver standard thrusts depending upon
atmospheric conditions:
Maximum Takeoff Thrust: This is the maximum thrust that the engine
can deliver for 5 minutes at standard sea level atmosphere.
MCT - Maximum Continuous Thrust: This is the maximum thrust that
the engine can deliver with no time limit.
MCL - Maximum Climb Thrust: This is the maximum thrust certified for
en-route climb; sometimes it is the same as MCT. (not certified)
MCR - Maximum Cruise Thrust: This is the thrust allowable for
unlimited flight duration at the design altitude. (not certified)
5. CLIMB ANALYSIS
From the previous graph it can be deduced that:
sin φ = (T – D) / W
In addition, the rate of climb (R/C) is the vertical component of the True
Airspeed of the aircraft, so it is affected by the climb angle:
R/C = TAS · sin φ
φ
R/C
TAS
6. CLIMB ANALYSIS
Combining the two previous formulas we obtain:
Therefore, the rate of climb will increase then with: a higher TAS, a
higher excess of thrust and with a lower weight.
W
D-T
·TASR/C =
10. CLIMB ANALYSIS
In general terms, it can be concluded that:
Vy is always greater than Vx.
As the altitude increases, Vx increases and Vy decreases (IAS).
A higher flap setting will decrease both speeds.
Vx (piston) is close to Vs, while Vx (jet) is close to the L/DMAX
speed. Therefore, Vx is greater in jet aircraft than in piston-
powered aircraft.
Vy (jet) is also greater than Vy (piston).
12. CLIMB SPEEDS
CLIMB AT MAXIMUM ANGLE SPEED
Climbing at maximum angle speed (Vx) enables a given altitude to be
reached over the SHORTEST DISTANCE.
CLIMB AT MAXIMUM R/C SPEED
Climbing at maximum R/C speed (Vy) enables a given altitude to be
reached within the SHORTEST TIME.
13. CLIMB SPEEDS
CLIMB AT CONSTANT IAS
Climbing at a constant IAS would simplify the operation, but it have
some disadvantages. As the aircraft climbs TAS increases, drag
increases (due to compressibility effects) and therefore R/C decreases.
This results in a long and inefficient climb.
% Climb
capability FL330
IAS
FL290
FL250
FL200
100
90
80
70
60
50
14. CLIMB SPEEDS
CLIMB AT CONSTANT IAS/MACH
Since it is impractical to climb at decreasing IAS speeds, the constant
IAS/M climb is usually performed, simplifying the operation:
The climb is performed at a constant IAS until a certain MACH is
reached. Then the climb is continued keeping this MACH number.
For instance, a climb profile for an A320 is:
250kt / 300kt / M.78
Below FL100
(due to ATC) Above FL100
until reaching
M.78
(crossover
altitude)
Until the end
of climb
15. CLIMB SPEEDS
In the first part of the climb (constant IAS), TAS is increased as the
aircraft climbs.
In the second part of the climb (constant MACH), TAS is decreased as
the aircraft climbs.
TAS
Theoretical R/C
TROPOPAUSE
25%
9%
30%
R/C
PA PA
Real R/C
16. CLIMB SPEEDS
OPTIMUM CLIMB SPEED
The optimum climb speed is the result of taking into account all the
factors that affect climb in terms of efficiency and operative costs.
It is usually higher than the best R/C speed (Vy).
Factors that affect this speed:
Weight: Optimum climb speed increases with more weight.
Wind: It barely affects optimum climb speed (+5 kt / 100 kt HW).
Fuel price: If it increases the optimum climb speed will decrease.
Maintenance and crew costs: If they increase the optimum climb speed
will also increase.
OAT and final cruise level do not affect the optimum climb speed.
17. SOME FACTORS AFFECTING CLIMB
Climb gradient ↓
PRESSURE ALTITUDE ↑
Rate of climb ↓
Climb gradient ↓
TEMPERATURE ↑
Rate of climb ↓
Climb gradient ↓
WEIGHT ↑
Rate of climb ↓
18. OPERATIVE CEILINGS
ABSOLUTE OR AERODYNAMIC CEILING
The aircraft cannot climb beyond the aerodynamic ceiling, which is
determined by the aerodynamic properties of the aircraft. This
situation of R/C = 0 fpm (impractical) could only be established at one
speed (Vx equals Vy at this point).
In this case, the aircraft reaches a situation in which a higher speed
would produce a high-speed stall, and a lower speed would produce a
low-speed stall. This situation is known as “coffin corner”.
PROPULSION CEILING
Is that altitude that the available thrust provided by the engines
permits to reach. It is usually lower than the aerodynamic ceiling.
19. OPERATIVE CEILINGS
SERVICE CEILING
Since reaching the absolute ceiling is impossible in practice, the
service ceiling is considered. At this altitude the aircraft has a
maximum rate of climb of 100 fpm.
DESIGN CEILING
It is the maximum altitude that the aircraft can reach taking into
account the structural limits (maximum differential pressure, etc).
20. OPERATIVE CEILINGS
OTHER CEILINGS
Other ceilings have been established as a reference. To sum up, we
have four ceilings based upon the maximum rate of climb:
Absolute ceiling: R/CMAX = 0 fpm
Service ceiling: R/CMAX = 100 fpm
Cruise ceiling: R/CMAX = 300 fpm
Combat ceiling: R/CMAX = 500 fpm
21. STEP CLIMB
The optimum cruise altitude is increased as the aircraft loses weight
(due to fuel consumption). Since it is impractical to perform a
continuous and slow climb during the cruise phase, a solution known
as step climb has been established.
Step climb is only used in long haul flights, and consists of climbing
from time to time at a higher level in order to keep the aircraft close to
the optimum altitude.
Optimum altitude
