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So I'm reading the Gas Turbine Engine Fundamental, and suddenly come across the airflow passes through one axial compressor stage. I wonder why the Resultant Rotor Inlet Velocity is pointing downward, while the Rotor Speed vector is pointing upward. The Resultant Rotor Inlet Velocity is the sum of two vectors Air Inlet Velocity and Rotor Speed. The Resultant Rotor Inlet Velocity is supposed to pointing upward right ??

The same thing happen the rotation direction is downward, why would the Resultant vector pointing upward ?? enter image description here

Can anyone explain for me plz ? Its really confuse me to be honest.


2 Answers 2


The rotor speed vector (green vector in second image) is showing the motion of the rotor in the engine's rest frame. What you are interested in however, is the velocity vector of the air in the rotor rest frame. That means you need transform into the rotating frame by subtracting the rotation vector:

$$ \color{red}{\vec{v}_\text{resultant}} = \color{blue}{\vec{v}_\text{air inlet}} - \color{green}{\vec{v}_\text{rotor}} $$

That way, the resultant vector (red in second image) is the incoming velocity vector for the air from the point of view of the rotor blade.

  • 1
    $\begingroup$ Velocity triangle was also the topic of this previous question. $\endgroup$
    – mins
    Dec 5, 2021 at 18:42
  • $\begingroup$ Thank you so much for your answer I really really appreciate it, I think I'm quite understand my problem. There just one last thing, I wonder why the velocity at the inlet of the rotor has an opposite direction with the velocity vector at the outlet, although they have the same magnitude ? Anyway, thanks for you help ! $\endgroup$ Dec 6, 2021 at 16:49

The confusion is because the hypotenuse resultant vector isn’t really the resultant… at least it’s not the resultant of the two other vectors that are depicted. (Although it IS the resultant airflow across the rotor…)

As Bianfable mentions, the frame of reference shifts in the labeling of the vectors. The creator of the graphic is mixing and matching vector labels in a way that might make the point for some, but is confusing for others who are steeped in proper vector math.

To my point, in the first diagram, two vectors represent the direction and magnitude of airflow, while one represents the direction and magnitude of the rotor. The math doesn’t work when you mix units like this!

So, to make the vector units match just flip the direction of the rotor arrow. Because the direction and magnitude of airflow over the rotor is opposite to its direction of travel.

  • $\begingroup$ Thanks for your answer, I finally understand it. I really appreciate your answer ! $\endgroup$ Dec 6, 2021 at 13:55

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