Regularity Rally Judging

The following is a method of automatically judging a Regularity Rally based on a flight plan submitted, and the cellphone exported flight route data.

Based on the cellphone GPS data provided, the judging system normalizes scoring across different pilot skillsets and categories. The goal is to produce a single, socially unbiased score by weighting each skill appropriately.

Scoring Equations

All scoring equations are designed to generate a “penalty score,” where a lower score is better. The final score is the sum of these penalties, and a normalization function is applied at the end to make scores comparable across different categories and aircraft.

1. Time Management Penalty ( $S_{T}$ )

This penalty measures the pilot’s ability to maintain their planned schedule throughout the flight. It uses a series of incremental checks rather than a single check at the end of each leg.

For each leg of the flight:
- Let $P_{pl an_i}$ be the declared time for leg $i$ .
- Let $T_{a c t u a l_i}$ be the actual time taken for leg $i$ .
- Let $W_{t}$ be the weighting factor for time management (e.g., $W_{t} = 0.5$ ).

The penalty for each leg is calculated as the absolute difference between the actual and planned time, weighted to prevent loitering:

S_{T_i} = W_{t} \times ∣ T_{a c t u a l_i} - T_{pl an_i} ∣

The total time management penalty is the sum of penalties for all legs:

S_{T} = i = 1 \sum n S_{T_i}

2. Route Deviation Penalty ( $S_{R}$ )

This penalty measures how closely the pilot follows their declared flight path. It’s a key metric for detecting cheating in the Dead Reckoning and VOR/NDB categories.

For each leg of the flight:
- Let $D_{t r a c k_i}$ be the average perpendicular distance of the actual flight path from the declared flight path for leg $i$ .
- Let $W_{r}$ be the weighting factor for route deviation (e.g., $W_{r} = 0.3$ ).

The penalty for each leg is the weighted average deviation:

S_{R_i} = W_{r} \times D_{t r a c k_i}

The total route deviation penalty is the sum of penalties for all legs:

S_{R} = i = 1 \sum n S_{R_i}

3. Altitude Management Penalty ( $S_{A}$ )

This penalty measures how well the pilot maintains their declared altitude, which is crucial for safety and navigation.

For each leg of the flight:
- Let $A_{a c t u a l_i}$ be the average actual altitude for leg $i$ .
- Let $A_{pl an_i}$ be the declared altitude for leg $i$ .
- Let $W_{a}$ be the weighting factor for altitude management (e.g., $W_{a} = 0.1$ ).

The penalty for each leg is the weighted absolute difference between the actual and planned altitudes:

S_{A_i} = W_{a} \times ∣ A_{a c t u a l_i} - A_{pl an_i} ∣

The total altitude management penalty is the sum of penalties for all legs:

S_{A} = i = 1 \sum n S_{A_i}

Category-Specific Modifiers and Normalization

The “socially unbiased” aspect comes from applying a normalized scoring approach that accounts for the differing challenges of each category.

1. Dead Reckoning Penalty Modifier ( $M_{D R}$ )

This modifier applies a penalty for a flight path that is too straight, indicating the likely use of a GPS. Gemini.ai’s analysis of the GPX data would calculate the path’s curvature or “straightness index.”

S_{D R} = M_{D R} \times (Straightness Index)

Where $M_{D R}$ is a penalty factor set by judges. A Straightness Index close to 1 indicates a perfectly straight line, while a lower value indicates a more natural, hand-flown path.

2. VOR/NDB Penalty Modifier ( $M_{V OR}$ )

This modifier rewards a pilot who shows excellent skill in maintaining a VOR radial against wind.

S_{V OR} = M_{V OR} \times (Deviation from Radial)

Where $M_{V OR}$ is a penalty factor. The “Deviation from Radial” is a measure of how far the pilot’s track deviates from the declared VOR radial. This penalizes significant drift but rewards the small, consistent corrections that demonstrate skill.

3. Weighting Normalization

To ensure fairness, a Normalization Factor ( $N$ ) is applied to the final score for each pilot. This factor accounts for the aircraft type and category, ensuring a pilot in a Cessna 172 is not unfairly penalized against a pilot in a high-performance aircraft.

N = Pilot Declared Performance Baseline Performance \times Category Difficulty

The Category Difficulty is a number (e.g., Dead Reckoning = 1.0, VOR/NDB = 0.8, Advanced = 0.5) set by judges to reflect the skill required.

Final Normalized Score

The final, normalized score for each pilot is calculated as:

Final Score = N \times (S_{T} + S_{R} + S_{A} + S_{D R} + S_{V OR})

The lowest final score wins. This system provides a clear, quantitative, and unbiased way to judge pilot skill based on quantifiable data, promoting fairness and rewarding airmanship for each category.

Regularity Rally Judging

Scoring Equations

1. Time Management Penalty (ST​)

2. Route Deviation Penalty (SR​)

3. Altitude Management Penalty (SA​)