Appendix A· 1 min read
Formula Reference Card
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A consolidated formula card. Each entry references the chapter where the formula is introduced and worked through.
| Quantity | Formula | Chapter |
|---|---|---|
| Beer-Lambert absorbance | A = ε × c × l | 2 |
| Bragg's law (XRD) | n λ = 2d sin θ | 2 |
| Rf value (TLC) | spot distance / solvent distance | 2 |
| Bloodstain angle of impact | sin θ = w / l | 3 |
| Foot-stature regression | foot length ≈ 0.15 × stature | 3 |
| Likelihood ratio | LR = P(E|Hp) / P(E|Hd) | 4 |
| Bayesian update (odds) | posterior odds = prior odds × LR | 4 |
| Standard error of mean | SEM = SD / √n | 4 |
| Coefficient of variation | CV = (SD / mean) × 100% | 4 |
| Random match probability | RMP = ∏ per-locus probabilities | 4 |
| Empirical rule | 68 / 95 / 99.7% within 1 / 2 / 3 SD | 4 |
| Photogrammetric height | H = h × d / f | 6 |
| Skid-distance speed | v = √(2gμd) | 8 |
| Yaw-mark speed | v = √(g × r × μ) | 8 |
| Pedestrian throw (Searle) | v = √(2gdμ / (1+μ²)) | 8 |
| Pedestrian throw (Han) | v ≈ 4.06 + 0.89 √d | 8 |
| Conservation of momentum | mAvA + mBvB = (mA+mB)vf | 8 |
| Stopping distance | d = v² / (2a) | 8 |
| Static Stability Factor | SSF = (track / 2) / CG height | 8 |
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