Calculating Maximum Takeoff Thrust
Regulation requires that a transport category airplane's takeoff weight must be such that if, at any time during the takeoff run, the critical engine fails, the airplane can either be stopped on the runway and stopway remaining, or that it can safely continue the takeoff. This is called runway limited takeoff weight. The critical engine is the engine whose failure would most adversely affect the performance or handling qualities of the aircraft. This means that a maximum takeoff weight must be computed for each takeoff. Factors which determine the maximum takeoff weight for an airplane include runway length, wind, flap position, runway braking action, pressure altitude and temperature.
In addition to the runway limited takeoff weight, each takeoff requires a computation of a climb limited takeoff weight that will guarantee acceptable climb performance after takeoff with an engine inoperative. The climb limited takeoff weight is determined by flap position, pressure altitude and temperature.
When the runway limited and climb limited takeoff weights are determined, they are compared to the maximum structural takeoff weight. The lowest of the three weights is the limit that must be observed for that takeoff. If the airplane's actual weight is at or below the lowest of the three limits, adequate takeoff performance is assured. If the actual weight is above any of the limits, a takeoff cannot be made until the weight is reduced or one or more limiting factors (runway, flap setting, etc.) is changed to raise the limiting weight.
After the maximum takeoff weight is computed and it is determined that the airplane's actual weight is within limits, then V1, VR and V2 are computed. These takeoff speed limits are contained in performance charts and tables of the airplane flight manual, and are observed on the captain's airspeed indicator. By definition, they are indicated airspeeds.
V1 (Takeoff Decision Speed) is the speed during the takeoff at which the airplane can experience a failure of the critical engine and the pilot can abort the takeoff and come to a full, safe stop on the runway and stopway remaining, or the pilot can, at his/her option, continue the takeoff safely. If an engine fails at a speed less than V1, the pilot must abort; if the failure occurs at a speed above V1 he/she must continue the takeoff.
VR (Rotation Speed) is the IAS that the aircraft is rotated to its takeoff attitude with or without an engine failure. VR is at or just above V1.
V2 (Takeoff Safety Speed) ensures that the airplane can maintain an acceptable climb gradient with the critical engine inoperative.
VF—design flap speed
VFE—maximum flap extended speed
VMO—maximum operating limit speed
VLO—maximum landing gear operating speed
VS0—stalling speed or minimum steady flight speed in the landing configuration
V1 is computed using the actual airplane gross weight, flap setting, pressure altitude and temperature. Raising the pressure altitude, temperature or gross weight will all increase the computed V1 speed.
While the headwind or tailwind component does affect the runway limited takeoff weight, it usually has no direct effect on the computed V1 speed. The performance tables for a few airplanes include a small correction to V1 with very strong winds. A headwind will increase V1 and a tailwind will decrease it. The wind does change the groundspeed at which V1 is reached, but this influence is accounted for in the runway limited takeoff weight calculations.
If there is slush on the runway or if the antiskid system is inoperative, the stopping performance of the airplane is degraded. This requires that an aborted takeoff start at a lower speed and with more runway and stopway remaining. This means that both the runway limited takeoff weight and the V1 used for takeoff will be lower than normal.
The table in FAA Figure 2 allows the flight crew to quickly determine the V1, VR and V2 speeds under a wide range of operating conditions.
Consider the following problem:
What are the V1, VR and V2 speeds under the following conditions?
Gross weight.............................310,000 pounds
Pressure altitude.......................428 feet
OAT..........................................+96°F
Flaps.........................................15°
Headwind..................................15 knots
Airport.......................................SEA Runway 16
1. Enter the table at the upper left-hand corner and find the altitude range (0 to 1) that includes the altitude of 428 feet.
2. From that altitude range, follow the row across to the column with the temperature range (95 to 105) that includes the temperature of +96°F.
3. Go to the lower section of the table and find the 15° flap section and the weights of 300,000 and 320,000 pounds. Since 310,000 pounds is not listed, we must interpolate. Follow the two rows over until they intersect the column that contains our altitude and temperature. Interpolating between the V speeds for the weights of 300 and 320 we get:
V1 = 141, VR = 157 and V2 = 166
4. Refer to the notes below the table for corrections to the basic V1 speed. In this case, we add 1 knot for the 15-knot headwind and subtract 3 knots for runway 16 at SEA. The total correction to V1 is -2 knots. There are no corrections to the VR and V2 speeds. The final speeds are:
V1 = 139, VR = 157 and V2 = 166
Most jet aircraft set thrust by use of EPR (Engine Pressure Ratio). The actual EPR value used for takeoff power varies with altitude, temperature and engine bleed air configuration. The table in FAA Figure 16 allows you to determine the takeoff EPR for a four-engine airplane at various altitudes, temperatures and bleed air configurations for turbocompressors.
Example:
Calculate the maximum takeoff EPR under the following conditions.
Pressure altitude.......................2,000 feet
OAT..........................................+59°F
Turbocompressors....................Nos. 2 and 3 ON, No. 4 OFF
Engine A/I..................................ON
1. Determine the maximum EPR for +59°F. The table gives a value of 1.83 for T/C ON and 1.85 for T/C OFF.
2. Determine the maximum EPR for an altitude of 2,000 feet. The values are 1.93 (T/C ON) and 1.96 (T/C OFF).
3. Using the lower of the two values, determine the maximum EPR for each engine based on its air bleed configuration. Engines 2 and 3: 1.83 and Engine 4: 1.85. Engine 1 does not have a turbo-compressor so use the T/C OFF value of 1.85. The note at the lower left corner of the table states that the EPRs are valid with Engine A/I (Anti-Ice) either on or off.
If an EPR gauge becomes inoperative, the N1 indication may be used in its place. Determine the maximum takeoff power settings under the following conditions:
Pressure altitude.......................Sea level
OAT..........................................+15°C
A/C bleed..................................No. 1 and 2 OFF, No. 3 ON
Engine A/I..................................OFF
No. 2.........................................Engine EPR gauge inoperative
1. From FAA Figure 15, determine the basic sea level EPR settings for Engines 1 and 3 at 15°C. The uncorrected table value is 2.10.
2. Correct the EPR settings as necessary for non-standard air bleed configurations. The notes in the upper right-hand corner of the table indicate that the standard condition for takeoff is Engines 1 and 3 airbleed on and Engine 2 airbleed off. The corrections table in the lower left-hand corner indicates that .04 should be added to the Engine 1 EPR because the air conditioning (A/C) is OFF on that engine. The takeoff EPR for Engine 1 is 2.14 and for Engine 3, it is 2.10.
3. From FAA Figure 14, determine the Engine 2 uncorrected N1. At sea level and +15°C the table value is 96.9%.
4. Correct (if necessary) for the airbleed configuration. The note in the lower left-hand corner says to add 1.3% if 1 and 3 bleeds are off. This correction does not apply. The Engine 2 N1 is 96.9%.
Often, the takeoff weight of an airplane is such that full power is not required to meet the performance requirements. When this is the case, a reduced power takeoff is made to prolong engine life. On some aircraft, the reduced power setting is referred as Normal Takeoff Thrust.
Normal Takeoff Thrust is usually calculated by using the Assumed Temperature Method. In this procedure, the maximum temperature for which the aircraft's weight would be legal is determined and then an "assumed" temperature is used to calculate the new EPR.
Determine the normal takeoff EPR for the following conditions:
Pressure altitude.......................2,000 feet
OAT...........................................+47°F
Assumed temperature..............+95°F
Cabin compressors 2................OFF
Rain removal.............................OFF
1. Using FAA Figure 17, determine the maximum takeoff thrust setting from the lower table. Using the OAT of +47°F and the altitude of 2,000 feet, the maximum thrust is 1.90.
2. Enter the upper table with the maximum takeoff thrust and the assumed temperature to determine the normal EPR. Using a MAX EPR of 1.90 and an assumed temperature of 95°F, the uncorrected, normal EPR is 1.80.
3. Apply adjustment as necessary. The adjustments are listed below the upper table. In this case, add .01 to the normal EPR for cabin compressors OFF. The normal takeoff EPR is 1.81.
Prior to each landing, a go-around EPR must be calculated in case a missed approach becomes necessary. This is done in the same manner as the takeoff EPR settings.
Determine the go-around EPR under the following conditions:
Pressure altitude.............................3,000 feet
TAT (Total Air Temperature)...........0°C
A/C bleeds......................................Normal
Anti-ice............................................Eng. and wing ON; 2 bleeds
1. From FAA Figure 13, determine the uncorrected EPR values for the given altitude and temperature. With a TAT of 0°C and a pressure altitude of 3,000 feet, the EPR for Engines 1 and 3 is 2.20 and the EPR for Engine 2 is 2.22.
2. Apply corrections to the table values as required. The notes in the upper right-hand corner of the table indicate that the normal bleed configuration is Engine 1 and 3 A/C ON and Engine 2 NO BLEED. In this case, no correction needs to be made for A/C bleeds. With the engine and wing anti-ice on (2 bleeds) the corrections are -.09 for Engines 1 and 3 and -.03 for Engine 2. The go-around EPR values are 2.11 for Engines 1 and 3 and 2.19 for Engine 2.
Specific Range is the term used to describe how efficiently fuel is consumed. It is really a variation of the miles-per-gallon used for automobiles. Specific Range for a turbojet aircraft is computed by dividing the true airspeed (in knots) by the total fuel flow (in pounds per hour). The formula is:
Specific Range = Knots / Pounds per Hour
or, Specific Range is the ratio of nautical miles per hour to fuel flow in pounds per hour.
Specific Range for jet aircraft is usually expressed in Nautical Air Miles (NAM) per 1,000 pounds of fuel burned. The aircraft's True Airspeed (TAS) and its fuel flow in pounds per hour are the only two numbers required to determine NAM/1,000. The formula is:
NAM/1,000 = TAS × 1,000 ÷ Fuel flow
Example:
An airplane has been cruising for 2 hours 15 minutes at a speed of Mach .82. Total fuel burn in that time has been 27,250 pounds. If Mach 1.0 is 595 knots, what has been the nautical air miles per 1,000 pounds of fuel?
1. Determine the true airspeed.
TAS = .82 × 595 = 487.9 knots
2. Determine the average fuel flow in pounds per hour.
Fuel flow = 27,250 ÷ 2.25 = 12,111.1 lbs/hr
3. Determine the NAM/1,000.
NAM/1,000 = 487.9 × 1,000 ÷ 12,111.1 = 40.28 NAM/1,000 lbs
The fuel flow in pounds per hour and the total fuel burn can be computed from the NAM/1,000. The flow in pounds per hour is calculated using the formula:
Fuel Flow = TAS × 1,000 ÷ NAM
The total fuel burn is calculated by multiplying the fuel flow times the hours flown.
Example:
Given the following, what is the total fuel burn?
NAM/1,000................................55.4
TAS...........................................200 knots
Wind component.......................10 knots headwind
Cruise time................................4.0 hours
1. Determine the fuel flow in pounds per hour.
Fuel flow = 200 × 1,000 ÷ 55.4 = 3,610.1 lbs/hr
2. Determine the total fuel burn by multiplying the cruise time by the fuel flow. Ignore the wind component as it is irrelevant here.
Fuel burn = 3,610.1 × 4.0 = 14,440.4 lbs
Occasionally it is necessary to dump fuel before landing. Anytime fuel has to be dumped, remember that the aircraft is also burning fuel, so the weight reduction is the fuel dumped plus the fuel burned during the dump. Determine the amount of fuel remaining after dumping under the following conditions:
Aircraft weight at start of dump .......................113,000 pounds
Zero fuel weight...............................................77,000 pounds
Dump rate........................................................1,350 pounds/minute
Fuel flow .........................................................1,200 pounds per hour per engine
Number of operating engines..........................4
Dump time.......................................................22 minutes
1. Determine the total fuel flow in pounds per minute during the dump. The formula is:
Fuel flow (lbs/min) = Fuel flow (lbs/hr) × No. of engines ÷ 60
Fuel flow (lbs/min) = 1,200 × 4 ÷ 60 = 80 lbs/min
2. Determine the total dump and burn rate (pounds per minute).
Dump and burn rate = 1,350 + 80 = 1,430 lbs/min
3. Determine the total fuel dumped and burned.
1,430 × 22 = 31,460 lbs
4. Determine the amount of fuel before the start of dump by using the formula:
Fuel load = aircraft weight - zero fuel weight
Fuel load = 113,000 - 77,000 = 36,000 lbs
5. Determine the fuel remaining.
36,0000 - 31,460 = 4,540 lbs
The most common reason that fuel has to be dumped is that an emergency has occurred right after takeoff and the aircraft has to return to the departure airport for landing. In such a circumstance, the flight engineer must figure out how long he/she must dump fuel for the aircraft to be able to land at or below its maximum landing weight.
Consider the following problem:
One of four engines has been shut down. How many minutes of dump time will be required to reach maximum landing weight at touchdown?
Cruise weight .............................................270,000 lbs
Maximum landing weight ...........................207,000 lbs
Average fuel flow........................................3,750 lbs/hr/engine
Time from start of dump to landing.............21 minutes
Fuel dump rate ..........................................3,660 lbs/minute
1. Determine the weight of fuel that must be dumped and burned.
Fuel to dump and burn = Cruise weight - Landing weight
Fuel = 270,000 - 207,000 = 63,000 lbs
2. Determine how much of that amount will be burned before landing. Remember, only three engines are operating.
Burn rate (lbs/min) = 3,750 × 3 ÷ 60 =187.5 lbs/min
Total burned = 187.5 × 21 = 3,937.5 lbs
3. Determine how much fuel must be dumped.
63,000 - 3,937.5 = 59,062.5 lbs to dump
4. Determine the dump time.
Dump time = Fuel to dump ÷ Dump rate
Dump time = 59,062.5 ÷ 3,660 = 16.1 minutes
The table in FAA Figure 3 allows you to calculate the cabin oxygen duration for various altitudes and numbers of passengers. What is the approximate duration of the oxygen system under the following conditions?
Cabin altitude..................................20,000 feet
Passengers.....................................75
Bottle pressure...............................1,200 PSI
1. From the table, determine the uncorrected bottle duration. At 20,000 feet cabin altitude, the fully charged bottle would supply 75 passengers for 26 minutes.
2. Correct for the fact that there is less than 1,500 PSI pressure in the bottle. The note at the bottom of the table says to reduce the duration by 8% for each 100 PSI less than 1,500. Here, a reduction of 24% is required.
Reduction = .24 × 26 = 6.24 minutes
Oxygen Duration = 26 - 6.24 = 19.76 minutes