# Jet Engine performance in Cold Weather

1. Nov 7, 2013

### ZoraxDoom

Hey guys.

I was studying up jet-engines and their performances with varying ambient temperatures and found myself stuck on something that is probably very trivial.

What I've read online and in my notes is all generally the same - that as temperature falls air density rises and as such more mass is pushed through the engine leading to better performances at the same power.

While the material I've been given to study from agrees with this, it also states that the Speed of Airflow through the engine is proportional to the square root of temperature.

So if we take Thrust as: Mass * (Jet Air Velocity - Aircraft Velocity), we can get:
Thurst = Density of Air * Area of Entry for air at engine inlet * Velocity of Aircraft * (Jet Air Velocity - Aircraft Velocity)
These two mean the same thing.

Now, the step between here and the formula I show next has not been explained, but I believe it goes along these lines - given that mass flow increases as pressure does, but decreases as temperature does, we can say that Mass is proportional to (Pressure/Temperature)

Thus, Thrust can be taken as proportional to (Pressure/Temperature) * (Square root of Temperature) * (Square root of Temperature).

Thus, the temperature term cancels out, and we see that Thrust produced by the engine is actually independent of the Temperature of the ambient air.

So I don't understand this - if the Thrust produced by the Engine is independent of the Temperature of the ambient air, then how does it give better performance at lower temperatures?

2. Nov 7, 2013

3. Nov 7, 2013

### AlephZero

I'm not sure exactly what situation you are talking about in your OP, but for "real" jet engines the thrust produced is limited by the maximum RPM of the compressors and turbines. The stress in the rotating parts increases with the RPM, and the RPM that causes the maximum permissible stress is (almost) independent of ambient temperature.

At the maximum RPM, cold air gives more mass flow, which lets you burn more fuel, and produces higher thrust.

Real life is not quite so simple of course. For example on some engine types on the Boeing 747, you can't actually reach the maximum permitted RPM in "cold" conditions at sea level when the aircraft speed is zero on the runway, because the engine inlets restrict and distort the airflow. You can only reach the maximum RPM and thrust as the aircraft speed increases during the takeoff roll. But that is not a big problem in practice, because you have much more thrust available taking off from sea level at Reykjavik in Iceland, compared with a hot day and a runway 9000 feet above sea level in Nairobi.

4. Nov 14, 2013

### qumf

Zoraxdoom：

“Thus, Thrust can be taken as proportional to (Pressure/Temperature) * (Square root of Temperature) * (Square root of Temperature).”
Personally I think the conclusion is not very proper, because "Speed of Airflow through the engine is proportional to the square root of temperature." should has some premises and some limits, you might ignore the conditions.