Hi guys,

for today I've prepared a somewhat more complicated topic. Of course I'll keep it as short as possible. I want to share with you the way a pilot would compute his takeoff assumed temperature to derate and lengthen the life of his engines in a Boeing 737-300 with B1 engines (20K rated thrust). This method applies to all derate-capable airliners but the charts only apply to the 737-300 20K variant. Furthermore, in real life, pilots usually get this info already computed from a dispatcher office, but it doesn't hurt to know

. The reason for doing this and the up-coming application is because there are no takeoff and landing performance profiles out there for the IXEG B737-300 Classic and I need one.

The method for computing anything related to airliners can be found in a "little" document published by the manufacturer called the Airplane Flight Manual (AFM). Unfortunately I have a very poor resolution copy of the B737-300's AFM that I found on the Internet, but it'll do.

**Assumed Temperature**Maybe I should first write a bit about what an assumed takeoff temperature is for the beginners out there. The plague of any engine is the high temperatures reached inside it. Materials that compose the engine are prone to thermal fatigue that adds up throughout the lifespan of an engine so engines need to be checked and overhauled periodically to lengthen the life of an engine. The temperature reached inside an engine is directly proportional to what is called the N1 rpm of a gas turbine engine (tubojet, turbofan and turboprop). The N1 rpm is the speed of rotation of one of the engines axes (usually they have 2, but there are with 3 and even with 1). So the faster an engine spins, the more fuel it needs to keep the rotation and thus the higher the temperature.

In the same time, a gas turbine engine is governed by a computer that maintains its' stable regimes, a feat that a human will not be able to do - not unless he/she wants to also fly the plane. The computer takes inputs from different sensors and after they go through a black box the adjustments are applied to the engine. The inputs are usually related to pressures in different parts of the engine cycle, fuel flows and temperatures in different parts of the engine cycle again. One of the main inputs that any kind of turbine engine takes in is the outside temperature, the temperature of the air before entering the engine. This, coupled with the pressure at the inlet can give the algorithms a good approximation of the air density entering the engine for combustion purposes.

Usually, at a sea level temperature of 15

^{o} C and a sea level pressure of 1013.25 mbar or 29.92 inHg (ISA atmosphere), any engine should be able to reach its' maximum N1 rpm (100% N1). This means that the maximum engine rating is reached in ISA atmosphere at sea level, which is expected. This also means that if you go to lower temperatures and higher pressures you can reach higher N1 ratings and vice-versa in higher temperatures and lower pressures. Lower is definitely not a problem, though higher N1s are because of mechanical stresses at higher rpms that destroy the compressors' and turbines' blades. In any case, the air temperature is a factor affecting the maximum N1 output (and inside temperatures and material fatigue). The higher the temperature, (the lower the density) the lower the rpm, temperature and fatigue inflicted.

So manufacturers added a feature in their airliners that gives the pilot the possibility to fake the outside temperature and make the engine governor think it's warmer outside and in turn lower the fatigue inflicted on the engine at takeoff. You may think it's a breach of flight safety because now you don't have the maximum power available at your disposal from the engines. But that is solved by putting in safety overrides that can disregard any temperature derate - don't forget that the engine governor knows the actual outside temperature, this is just a gas pedal pull-back, NOT a hard limit.

Another thing you may think about is how can the airplanes takeoff if they don't have all the available thrust at their disposal. Well, runways are usually much longer then what the airplane actually needs for the takeoff run. So you eat up a little more runway but you save up a lot of the engine lifespan. It's a good compromise. And as you will see, the computation is highly related to the length of the runway.

**Description**The procedure involves looking up and matching values in manufacturer published plots in the AFM. The first step is to get the

*corrected runway length*. This is a value that corrects the actual runway length to the known airplane characteristics and to runway weather conditions.

The next step is to get the maximum assumed temperature the pilots can use in the two possible takeoff limits: field limit and takeoff climb limit. The field limit assumed temperature is dependent on the corrected runway length while the takeoff climb limit is dependent only on the takeoff weight and it assures a normal climb gradient after liftoff.

This is the quick rundown of the procedure so let's get to an actual example and see what plots to use and how.

**Example**So let's say we are taking off from an airport that is 2'000 ft above sea level (pressure altitude) and we want to take off from a runway that is 10'000 ft long and has a +1% slope. The aircraft takeoff weight is 50 tonnes (110'230 lbs). The wind has a 6 kts headwind component for the runway heading and the temperature is -15

^{o} C. And we will look for a flaps 1 takeoff (there are lots of plots for every parameter) and a 500 ft clearway from the runway end. Because we are equipped with a 20'000 lbs thrust we will use Appendix 9KS of the AFM for all our calculations.

**I) Get the corrected runway length**This step is composed of 6 sub-steps, so...

*1) get the all engines operating corrected runway length*So we start from 10'000 ft and insert the 500 ft clearway. We then move to the runway slope reference line and insert the +1% slope. Next is the wind component dependency so we move to the reference line for the wind and insert the 6 kts headwind. Next is the anti-ice protection ON or OFF dependency but we have no clouds so no anti-ice. We thus get an all engine operative corrected runway length of 10'400 ft.

*2) get the engine inoperative corrected takeoff distance*We again start from the 10'000 ft runway length and add the 500 ft clearway. We move through the same steps as in the all engine operative (though with different dependencies) and get the corrected engine out takeoff distance of 9'400 ft.

*3) get the corrected accelerate/stop distance*This is a little more complex in concept. It is the maximum distance available to accelerate to a speed lower than V1 and decelerate to 0. The procedure is the same so we get a distance of 9'900 ft.

*4) get the emergency region for takeoff in*This is an aircraft dependent feature. For the 737-300 20K there are 4 regions defined by the airport temperature and pressure altitude. In our case the -15

^{o} C and the 2'000 ft altitude sets us in the B region. The region defines what plots we use for the next step.

*5) get the corrected emergency runway length and the V*_{1} to V_{r} ratio for our regionAs you can see we use the FLAPS 1 and REGION B plot. In this plot we enter with the corrected accelerate/stop distance and the corrected engine out takeoff distance and get 9'700 ft. The ratio between V

_{1} and V

_{r} is .995.

*6) get the corrected runway length*This is simple. The corrected runway length is the smaller number between the corrected emergency runway length and the corrected all engines operative runway length. So the minimum between step 1 and step 5 = 9'700 ft.

**II) Get the field length limit maximum assumed temperature**So we enter the FLAPS 1, A/C OFF plot with the takeoff weight of 50'000 kg. At the intersection with our computed corrected runway length of 9'700 ft we move left and intersect the airport field elevation of 2'000 ft. We then can read the maximum assumed temperature given by the field length limit on the abscissa. In our case we find a temperature of 60

^{o} C.

**III) Get the takeoff climb limit maximum assumed temperature**So we enter the plot with our takeoff weight and intersect the field elevation line of 2'000 ft and read the maximum takeoff climb limit assumed temperature on the ordinate as of being 47

^{o} C.

**IV) Get the maximum assumed temperature for engine derate**The maximum assumed temperature for engine derate is the minimum of the two temperatures found for field length and takeoff climb limits. In our case we can use a maximum assumed temperature of 47

^{o} C.

Of course, we can use a lower temperature to have better performance during the takeoff, but this is the maximum and still safe assumed temperature. Also, after the FMC computes your V

_{r} you should recompute your V

_{1} and modify it by using the ratio given in step

**I.5.**. Otherwise, in case of emergency you will not have the correct takeoff abort speed

.

**Future**Because I hate to have my desk filled with papers and notebooks, I will definitely transform all these plots into an application (for Android most probable in Play Store so stay tunned) just as the guys making TOPCAT do

.

Cheers and hope you liked the read,

Adrian