The relatively poor SD of my .223 load will become a problem much past 600m. Required sample size to confidently estimate a MPOI becomes too much at 800+.
AB and 4DOF give 0.5mil different solutions for 600m and 20 degrees, that difference should be visible.
Perhaps the real solution will be halfway in the middle
Can you explain what you mean regarding the rifleman's rule? I don't intend to apply the rifleman's rule here, I'm looking to test the solutions from solvers (which to the best of my knowledge do not use the rifleman's rule) against reality.
Of course you’re right not to use the Rifleman’s Rule for solver validation — it was only mentioned as an example of a geometric shortcut whose errors can be hidden by measurement noise; proceed by measuring Sigma with a 600 m/20° test, compare each solver directly to MPOI with identical measured inputs, run sensitivity sweeps to diagnose the 0.5 mil gap, and only attempt 800 m/30° tests if the test shows sample‑size feasibility.
My basic procedure is as follows:
Phase 1 Baseline horizontal tests
• Distances: 300 m and 600 m horizontal.
• Test strings: 15–20 shots per distance to estimate Sigma (MPOI scatter in MRAD).
• Per‑shot records: slant range (equal to horizontal), V0 (chrono), BC used, temperature, pressure, humidity, wind, MPOI vertical (MRAD vs POA), MPOI lateral, prediction_4DOF (MRAD), prediction_AB (MRAD).
• Outputs: mean MPOI, Sigma, solver bias = mean(prediction − MPOI) for each solver.
• Go/no‑go: if Sigma ≤ 1.0 MRAD proceed; if Sigma > 1.0 MRAD improve load/consistency or increase test size.
Phase 2 Moderate‑angle tests to detect ~0.5 MRAD
- Geometry: slant range 600 m at ±20° (both uphill and downhill if feasible).
- Test strings: 15–20 shots per condition to estimate Sigma at angle; then compute required n with the sample‑size guideline below.
- Sample‑size guideline (two‑sample / sample‑vs‑prediction, α=0.05, power=0.8):
- Use Z values 1.96 and 0.84.
- Compute n ≈ 2 * ((1.96 + 0.84) / (Delta / Sigma))^2, where Delta is the difference to detect (e.g., 0.5 MRAD) and Sigma is observed MPOI SD in MRAD.
- Practical guidance: if Sigma ≲ 1.0 MRAD, roughly 15–30 shots per condition may detect 0.5 MRAD; if sigma ≈ 1.0–1.5 MRAD, required n becomes large.
Phase 3 Solver sensitivity sweeps
- For each solver, systematically vary plausible input parameters and record holdover change:
- BC: −10%, 0%, +10%.
- MV: ±10–20 FPS around measured mean.
- Produce sensitivity curves: mil change per unit change of parameter.
- Identify which parameter adjustments produce the observed ~0.5 MRAD offset and assess physical plausibility.
Phase 4 Conditional amplification tests at 800 m / ≥30°
- Run only if Phases 1–3 show Sigma small enough that required n for Delta = 0.5 MRAD is practical.
- Target: 800 m slant at ≥30°; test uphill and downhill as practical.
- Scope: focused strings (e.g., 20–30 shots per condition) rather than broad sweeps.
- Use identical per‑shot logging and solver inputs; compare results to sensitivity predictions.
Analysis, decision rules and reporting
• Per condition compute: mean MPOI, Sigma, 95% CI, bias for each solver, and p‑value for solver vs MPOI (t‑test or bootstrap).
• Diagnostic rules:
• If bias > 0.5 MRAD and statistically significant, mark solver discrepant and propose parameter corrections from sensitivity sweeps.
• If solvers straddle MPOI and MPOI is between them, do not accept midpoint as truth without identifying physical cause.
• If noise dominates (Sigma too large), improve load consistency or increase n; avoid 800 m until Sigma allows feasible n.
• Deliverable: table per condition {slant; angle; mean MPOI; sigma; pred_4DOF mean; pred_AB mean; bias4DOF; biasAB
