Automated Cheating Detection

Here are the equations for detecting cheating in each category, based on the pilot skills and cellphone data used. The equations quantify the expected vs. actual flight characteristics to flag suspicious behavior.

Dead Reckoning Cheating Detection ( $C_{D R}$ )

Dead reckoning cheating is detected when a pilot’s flight path is unnaturally straight, suggesting the use of a GPS. This is measured by analyzing the curvature of the flight path.

Let $P_{i}$ be the $i^{t h}$ point in the GPX track log with coordinates $(x_{i}, y_{i})$ .
The curvature at a point is a measure of how much the path deviates from a straight line. A common way to calculate this is using the circumcircle of three consecutive points. A simpler, effective proxy is to measure the average perpendicular deviation from a straight-line segment.
Let $D_{se g}$ be the declared straight-line path for a leg.
Let $D_{a c t u a l}$ be the actual flown path.

The cheating penalty is based on a Straightness Index ( $S I$ ), where a value close to 1 indicates a perfectly straight line (cheating) and a lower value indicates a hand-flown path.

S I = 1 - Expected Hand-Flown Curvature Actual Path Curvature

The Dead Reckoning Cheating Penalty ( $C_{D R}$ ) is then applied if the Straightness Index exceeds a predefined threshold ( $T_{S I}$ ), which is set by the judges.

C_{D R} = {Disqualification 0 if S I > T^{S I} if S I \leq T^{S I}

For example, a Hand-Flown Curvature would be a value (e.g., 0.005) that represents the expected slight “S-turns” and heading corrections a pilot makes to stay on a compass course. If the pilot’s path is straighter than this, it’s a red flag.

VOR/NDB Cheating Detection ( $C_{V OR}$ )

Cheating in the VOR/NDB category is detected when the pilot’s flight path is too straight for a VOR radial, which requires constant correction. The system compares the pilot’s flown track to the declared VOR radial.

Let $R$ be the declared VOR radial (a theoretical straight line originating from the VOR).
Let $D_{V OR_p a t h}$ be the average distance of the pilot’s track points from the declared VOR radial.
Let $W_{d r i f t}$ be the weighting factor for drift (e.g., $W_{d r i f t} = 0.5$ ).

The VOR Cheating Penalty ( $C_{V OR}$ ) is calculated as:

C_{V OR} = W_{d r i f t} \times D_{V OR_p a t h}

If a pilot uses a GPS to fly a direct course instead of the VOR radial, their track will be a straight line that doesn’t follow the radial’s subtle curves. This would result in a very high $D_{V OR_p a t h}$ value, which triggers a significant penalty or even disqualification.

Advanced Navigation Cheating Detection ( $C_{A D V}$ )

Cheating in the advanced category is less about the flight path and more about the use of undeclared instruments. For instance, a pilot might claim to use a basic GPS but actually have a more sophisticated, coupled autopilot. This is harder to detect from a simple track log, but certain metrics can provide clues.

Speed and Time Discrepancy: The most common form of cheating would be to fly at an un-declared higher speed and then loiter to arrive at the waypoint on time.
Loitering Penalty ( $P_{L o i t er}$ ): The system detects loitering by analyzing flight speed. Let $V_{pl an}$ be the planned speed for a leg. The system checks the actual ground speed ( $V_{a c t u a l}$ ) at frequent intervals. If the pilot’s speed drops significantly below a reasonable threshold (e.g., 50% of $V_{pl an}$ ) for more than a few minutes in a non-holding pattern, a loitering penalty is applied.

P_{L o i t er} = number of minutes loitering \times penalty factor

The Advanced Cheating Penalty ( $C_{A D V}$ ) would be the sum of penalties for all such infractions:

C_{A D V} = \sum P_{L o i t er} + other penalties for specific infractions

In this category, the focus is on penalizing deviations from the pilot’s declared flight plan, as it is assumed that all declared tools are being used. Any deviation is considered a skill deficiency rather than cheating.

Final Cheating Score

The final cheating score for each pilot is calculated based on their category:

Final Cheating Score = C_{D R} or C_{V OR} or C_{A D V}

This score is added to the overall penalty score from the previous response, providing a holistic and unbiased final result.

Automated Cheating Detection

Dead Reckoning Cheating Detection (CDR​)

VOR/NDB Cheating Detection (CVOR​)

Advanced Navigation Cheating Detection (CADV​)

Final Cheating Score

Dead Reckoning Cheating Detection ( $C_{D R}$ )

VOR/NDB Cheating Detection ( $C_{V OR}$ )

Advanced Navigation Cheating Detection ( $C_{A D V}$ )