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?