# Why does the takeoff N1 limit start to decrease below 30°C OAT?

It's easy to understand why the takeoff N1 limit decreases with an increase in the OAT in the chart above; the engines get less dense air at higher temperatures, and less dense air means less engine power capability. But why does the takeoff N1 limit start to decrease with a decrease in the OAT below 30 degrees Celsius? For your information, the chart is an airport analysis chart for Boeing 737.

• Not sure, so not giving an answer. But I expect another parameter becomes the limiting factor at cold temperatures, and the N1 maximum allowed must be reduced to avoid exceeding it. Commented Dec 2, 2019 at 3:16
• I definitely don't find it easy to understand why the N1 limit decreases with an increase in the OAT. Because less dense air means a turn of the fan moves less air, but that also gives it less resistance, so it gives less power, but should be able to spin as fast. Commented Dec 2, 2019 at 19:15
• Since this Q is in hot network questions: What are N1 and N2? for background for the idly curious wondering what this question is actually about. Commented Dec 3, 2019 at 6:25

There are basically 3 limits that the engine faces, temperature (maximum turbine entry temperature or maximum combustor exit temperature or sometimes maximum first stage HPT stator exit temperature), pressure (maximum compressor exit pressure) and stress (maximum stress in the blades and disks as a result of spool speed).

Varying the OAT for a specific engine design will hit one of these limits. When the OAT increases, the amount of fuel you can add to the system reduces as you get over-temperature, when the OAT decreases you could add more fuel, but that will increase spool speed which is also limited. From this figure you see the effects on SOT (turbine Stator Outlet Temperature, which is proportional to Turbine Inlet Temperature, TIT):

But why does the takeoff N1 limit start to decrease with a decrease in the OAT below 30 degrees Celsius?

The limit on the left is the decrease in spool speed, note that the corrected spool speed is constant (N / √(T)) so for a lower temperature, the N also decreases.

It's easy to understand why the takeoff N1 limit decreases with an increase in the OAT in the chart above

Yes it is, this is limited by the turbine inlet temperature (or a maximum exhaust compressor temperature as used in the image above, denoted as T3). The maximum turbine inlet temperature is fixed, the higher the inlet combustor temperature (exit high pressure compressor temperature), the less fuel can be added to heat to the air in the combustor, the less energy is available to expand in the turbines.

The constraining/limiting of the power output (thrust) is called flat rating.

This effect can be simulated with an engine model. If we would vary OAT for a certain power setting, e.g. constant (corrected) spool speed for a large bypass turbofan engine with imposed compressor exit pressure and turbine inlet temperature limit a model would look like:

After the variation of OAT you will yield the blue performance curves for a non-limited engine, and the brown dash-dotted curves for a limited engine:

Note that the compressor outlet pressure is the limiting factor in the graph on the left, but spool speed and compressor pressure are linked. The question is which of the two is reached first, this depends on the input and the design constraints.

• Good Lord! An answer with a simulation! Unreal. Commented Dec 2, 2019 at 18:43
• What software is that? Is it free? Commented Dec 3, 2019 at 10:18
• @ThomasWeller Yes it is free, but it is not appropriate at SE to promote your own software... If you look closely you see the product name and version number in the graph of the bottom image. Google is your friend. Commented Jan 29, 2021 at 10:13
• Thanks, 0scar. IMHO it's ok as long as you disclose the affiliation. And to me it seems to be especially ok in comments after someone asked for it. Comments are transient anyway. For those interested: gspteam.com/products.html It has a free evaluation version. Commented Jan 29, 2021 at 10:21

What you see is called a flat rated engine. It means the maximum thrust from the engine is constant below the flat rated temperature (usually 30°C). Above that temperature, thrust will decrease due to the EGT (exhaust gas temperature) limit. In order to achieve a constant thrust at lower temperatures, the N1 needs to be decreased accordingly.

(CFM56-5A Lufthansa Training Manual, page 4)