Assumptions & known limitations
The displayed hold is a numerical intercept solution, not speed multiplied by pellet flight time. These are the public governing assumptions; fitted coefficients, calibration data, and solver implementation remain internal.
Pellet flight — always enabled
Turning realistic clay air effects off does not turn pellet drag off. Each pellet is advanced through standard atmosphere with gravity and speed-dependent sphere drag:
mp dv p /dt = mp g − ½ρ Ap CD (M,Re)|v rel |v rel
The model accounts for pellet size, muzzle velocity, deceleration, time of flight, and vertical drop. Its drag behavior is checked against published shotshell ballistic data.
Realistic air effects ON
The clay follows a three-dimensional, time-stepped rigid-disc flight model. Gravity, aerodynamic drag, and spin-dependent lift act simultaneously:
mc dv c /dt = mc g + ½ρAc |v rel |² [−CD (α)v̂ + CL (α)l̂ ]
α = −sin−1 (n ·v̂ ) and dn /dt = ω ×n
n is the clay face normal, ω its spin, and α the instantaneous angle of attack. The launch attitude is gyroscopically preserved in the default model while the curved velocity path changes α throughout the flight. Clay size, mass, face area, roll, and rabbit edge-on attitude affect the result.
Realistic air effects OFF
The clay becomes an ideal vacuum projectile: no clay drag, lift, or aerodynamic attitude effect. This is useful as a transparent baseline, but it normally carries too much speed late in flight.
r c (t) = r 0 + v 0 t + ½g t²
Pellet drag and pellet drop still remain active, so OFF compares two different clay models against the same ballistic pellet solution.
The intercept and displayed lead
For every possible trigger time, the solver finds the pellet travel time τ and muzzle direction that place pellet and clay at the same point:
r p (tfire +τ) = r c (tfire +τ)
L = |(I − C ) − [(I − C )·ŝ ]ŝ |
The second equation is the sight-plane separation between the intercept point I and current clay position C , perpendicular to the sight line ŝ . Horizontal and vertical hold are reported separately.
Auditory release timing
Where sound triggers the next event, the timeline includes a 0.3 s response delay. Voice activation releases the first target 0.3 s after the detected “Pull” onset. In a report pair, the second target is released 0.3 s after the first shot is fired.
tlaunch = tsound + 0.3 s
This represents the trapper or release system hearing and responding to the sound. It changes target age and position on the shared clock; it does not add an assumed shooter reaction time or gun-movement delay.
Known limitations
Atmosphere: standard sea-level density; no temperature, humidity, altitude, or wind input yet.Clay attitude: the default spinning face keeps its launch orientation rather than being forced to follow the arc. Real targets can precess, wobble, curl, or tip; predicting those motions requires measured launch spin and validated moment dynamics.Pellets: treated as round, individual pellets. Setback deformation, shot-to-shot variation, pattern spread, and shot-string length are not simulated.Shooter: maintained-lead geometry only. Reaction time, gun acceleration, swing-through technique, visual perception, and a stopped gun are outside the calculation.Terrain: trap and shooter ground heights are supported, but intervening slopes are not. Rabbit air drag continues during its ground roll; grass friction is not yet modeled.Confidence: ordinary early- and mid-flight presentations are the strongest use case. Extreme curlers, battue tip-over, long rabbit rolls, damaged targets, and unusual launch attitudes carry more uncertainty.
