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Example: Wake Turbulence in the Terminal Airspace

We demonstrate our overall approach through a simulated scenario in which we predict the threat of a following aircraft encountering a leading aircraft’s wake turbulence and show how these predictions evolve in time as flight operations progress.

Wake turbulence is caused by wake vortex produced by aircraft at wingtips due to pressure differences on the wing when generating lift. The weight, wingspan, and speed of the aircraft determines the initial strength and motion of the vortices, while ambient atmosphere such as wind, stability, and turbulence determine the eventual motion and decay rate, as shown below. The induced rolling moment on an aircraft encountering wake turbulence can cause it to lose control by exceeding its roll control. In general, pilots are responsible for maintaining adequate horizontal and vertical separation for wake turbulence avoidance during flight. Separation standards followed by controllers in a radar environment are determined partially for wake turbulence avoidance.


Computed wake turbulence region at time t.

For this example, we consider the terminal airspace of the San Francisco International Airport (SFO). SFO has two sets of intersecting parallel runways. In typical (good weather) operations, aircraft take off from runways 01L and 01R, and land on runways 28L and 28R. During inclement weather, the winds typically come from the S or SE, and as a result, SFO operations shift to utilize runways 19L and 19R for departure and 10L and 10R for arrival. In our specific demonstration scenario, as shown below, a light aircraft A1 (e.g., Piper Aztec) is waiting on 01L for takeoff clearance from the tower controllers. A large aircraft A2 (e.g., Boeing 777) is coming in for a landing on 28L. As the scenario proceeds, the pilot of A2 decides to do a go-around right after touching down because of the difficulties with maintaining directional control due to a strong crosswind (19 knots, coming from the north). As the aircraft accelerates again for the go-around and starts generating lift, a region of wake turbulence is formed behind it. Due to the wind, the vortices will drift onto runways 01L and 01R. Ordinarily, there are no issues with residual wake turbulence in the general area of runway intersection as landing aircraft touch down (and stop generating lift) well before it and departing aircraft rotate (and start generating wake vortices) well after the intersection. In this somewhat rare scenario, a controller may not consider all of the implications of A2’s go-around and clear A1 for departure as soon as A2 is clear of the runway, while the region of wake turbulence is still present (which may be particularly dangerous for the lighter A1 since it may rotate before the intersection of the runways).


Wake turbulence scenario at 100s (Aircraft not drawn to scale).


Wake turbulence scenario at 220s (Aircraft not drawn to scale).

From the controller’s perspective, probability of a wake turbulence event happening in the next 5 minutes can be computed, as shown below. This information can be used to show trouble spots on the controller’s display, which could in turn result in controller not giving takeoff clearance to A1 till the wake turbulence of A2 dissipates.


Probability of A1 being in the wake of A2 within the next 5 minutes as a function of time.

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