What is this?

blast-physics-js is a free, open-source npm library that provides blast engineering models for the mining industry, implemented in pure JavaScript with zero rendering dependencies.

It is the physics companion to Kirra — extracting the analytical models from Kirra's GPU shader pipeline into a standalone, testable, composable library that any mining engineer or software developer can use.

npm install blast-physics-js

0.3.0 changes published numbers. Several models disagreed with the papers they cite; the corrections are listed under Breaking changes in 0.3.0 below. If you have results computed with 0.2.x, read that section before comparing.

Features

• Zero rendering dependencies — no Three.js, no WebGL, no DOM. Pure computational library.
• Isomorphic — runs identically in browser (ES modules) and Node.js (CommonJS).
• SI units throughout — metres, kilograms, seconds, Pascals, m/s.
• Typed array output — all grid computations return Float32Array / Float64Array for direct GPU upload.
• Model fidelity hierarchy — simple site-law PPV through to full Blair & Minchinton time-domain waveform superposition.
• Per-deck architecture — multi-deck holes, air gaps, COUPLED/DECOUPLED charges, and per-product VOD/density are first-class concepts.

Models

| Domain | Models | Output | |--------|--------|--------| | Vibration | PPV, PPV Per-Deck, Scaled Heelan, Blair Lite, Heelan Original, Blair & Minchinton | mm/s | | Site law | Regression (K50/K90/K95, B, σ), inverse (max allowable charge / distance), receptor evaluation (peak, coherence-window RMS, compliance, dominant hole), Blair 2011 Probability of Exceedance | mm/s, kg, P | | Ripple tank | Coherent forward wave field — P and S fronts from every charge, Ricker / Gaussian / damped / Berlage / measured wavelets | signed mm/s | | Signal | FFT, IDI, impulse-train spectrum, time-window (MIC) histogram, seed-wavelet superposition (linear + Blair non-linear), 3-component forward-array synthesis with Love waves, spectral-division signature deconvolution, detune / constrain | Hz, mm/s | | Damage | Holmberg-Persson, Jointed Rock | mm/s, ratio | | Pressure / energy | Borehole Pressure, Powder Factor, Specific Explosive Energy | MPa, kg/m³, GJ/m³ | | Detonation | Multi-primer front propagation, Em computation | ms, kg^A | | Flyrock | Richards & Moore, Lundborg, McKenzie (SDoB), Roth (Gurney), volumetric SDoB grid, ballistics (range / apex / flight time / drag) | metres, m/s | | Movement | Voxel blast throw: Yang 3DMuck kinematic launch + sphere DEM transport (optional Rapier3D adapter), survey calibration | displacement vectors, swell, muckpile surface | | IO | Kirra .kap archives (holes, charging, primers, surfaces), Instantel / Texcel monitor CSVs | HoleEntry / DeckEntry / surfaces |

Demos

npm run dev

Opens http://localhost:5175 with three pages:

| Page | What it shows | |------|---------------| | index.html | Pre-computed volumetric vibration / damage / pressure point clouds with slice planes | | throw.html | Blast throw / muckpile simulator — loads examples/SWELLFACTOR.kap (531 holes, PREBLAST_VOLUME, SHELL, POSTBLAST_MUCKPILE), voxelises the blast volume, launches blocks with Yang 3DMuck kinematics, runs the sphere DEM, and back-calculates Pe from the surveyed muckpile. Drop any Kirra .kap on it. | | ripple.html | Ripple tank wave field with wave-front rings, IDI stems, impulse-train FFT and a click-to-place monitor with L/T/V forward-array synthesis and PoE readout |

The throw demo defaults are the calibrated "throw_4" settings (1.5 m voxels, Pe 1.0, b 1.5, relief steer 0.85, 40 ms window, restitution 0.1, friction 0.5, swell 1.4, 35 % size scatter).

Quick Start

Single-point PPV

import { computePPV } from 'blast-physics-js';

const ppv = computePPV(
  { x: 100, y: 200, z: 0 },       // observation point (m)
  deckEntries,                      // array of DeckEntry objects
  { K: 1140, B: 1.6, e: 0.5 }     // site constants
);
// Returns: number (mm/s)

Grid computation

import { computeScaledHeelan } from 'blast-physics-js';

const grid = computeScaledHeelan(
  deckEntries,
  holeEntries,
  { minX: 0, minY: 0, maxX: 200, maxY: 200, cellSize: 1.0, elevation: 0 },
  // chargeExponent is e in D/W^e; the mass exponent A = e·B is derived from it
  { K: 1140, B: 1.6, chargeExponent: 0.5, elemsPerDeck: 12 }
);
// Returns: GridResult { data: Float32Array, rows, cols, minX, minY, cellX, cellY, unit, model }

Low-level model API

import { ScaledHeelanModel } from 'blast-physics-js';

const model = new ScaledHeelanModel({
  K: 1140, B: 1.6, chargeExponent: 0.5,
  elemsPerDeck: 20, pWaveVelocity: 4500, poissonRatio: 0.25
});

const ppv = model.evaluate(point, deckEntries, holeEntries);
const result = model.computeGrid(deckEntries, holeEntries, gridParams);

Read a Kirra KAP and run the blast throw simulator

import { parseKAP, BlastMovementSimulator } from 'blast-physics-js';

const kap = await parseKAP(await file.arrayBuffer());   // { holes, decks, surfaces, products, raw }
const sim = new BlastMovementSimulator({ voxelRes: 1.5, maxVoxels: 30000, Pe: 1.0, maxSwell: 1.4 });
sim.load(kap);                 // throw directions, charge elements, confinement geometry
sim.generateVoxels();          // voxelise PREBLAST_VOLUME / VOXEL-BLK*, nearest hole, launch velocities
sim.run();                     // fixed 5 ms sub-steps until every fired block rests
const r = sim.results();       // vectors, comShift, swell, heightfield.surface (Kirra-style triangulated surface)

const cal = await sim.calibrate();   // secant-fit Pe to the surveyed POSTBLAST CoM throw

Ripple tank, frequency analysis, receptor PPV

import { RippleTankModel, fireTimesFromDecks, computeIDI, computeSpectrum,
         evaluateReceptor, decksFromEntries, poeFromPrediction } from 'blast-physics-js';

const ripple = new RippleTankModel({ K: 1140, B: 1.6, cp: 5000, cs: 2900, fP: 100, fS: 60 });
const field = ripple.computeGrid(deckEntries, { minX, minY, rows, cols, cellX, cellY, elevation }, 0.25 /* s */);

const { times, weights } = fireTimesFromDecks(deckEntries);
const idi = computeIDI(times, 1);                                   // Δt histogram, median, dominant intervals
const spec = computeSpectrum(times, { weights, maxHz: 200 });       // impulse-train FFT + peaks

const rx = evaluateReceptor(monitor, decksFromEntries(deckEntries), { superposeRMS: true, coherenceMs: 8, outputMode: 'A' });
const poe = poeFromPrediction(rx.value, 25 /* mm/s limit */, 0.22 /* site σ */);   // Blair 2011

Web Worker (Blair time-domain)

import { createBlairWorker } from 'blast-physics-js/workers';

const worker = createBlairWorker();
const strip = await worker.compute({
  deckEntries, holeEntries,
  gridParams: { minX, minY, elevation },
  modelParams: { K: 700, B: 1.5, bandwidth: 10000 },
  startRow: 0, endRow: 100
});
// strip: Float32Array

Data Structures

HoleEntry

Blast hole geometry and properties. Aligned to Kirra's Blast Hole Management.

{
  entityName,                     // Blast pattern name
  holeID,                         // Unique hole identifier
  collarX, collarY, collarZ,     // Collar position (m)
  toeX, toeY, toeZ,              // Toe position (m)
  holeDiamMm,                     // Borehole diameter (mm)
  holeType,                       // 'Production', 'Presplit', 'Buffer', etc.
  benchHeight,                    // Collar Z to grade Z (m)
  subdrillLength,                 // Grade to toe along hole (m)
  holeTime,                       // Surface initiation time (ms)
}

DeckEntry

One deck within a blast hole. Aligned to Kirra's Charging System with four typed deck categories.

{
  deckType,                        // 'COUPLED' | 'DECOUPLED' | 'INERT' | 'SPACER'
  topX, topY, topZ,               // Charge top position (m)
  baseX, baseY, baseZ,            // Charge base position (m)
  mass,                            // Explosive mass (kg, 0 for INERT/SPACER)
  density,                         // Explosive density (kg/L)
  vod,                             // Velocity of detonation (m/s)
  holeDiamMm,                      // Borehole diameter (mm) — from parent hole
  chargeDiamMm,                    // Effective charge diameter (mm):
                                   //   COUPLED:   = holeDiamMm (full contact)
                                   //   DECOUPLED: = product diameter (air gap)
  timingMs,                        // Total detonation time (ms)
  holeIndex,                       // Index into HoleEntry array
  primerFraction,                  // 0.0 = top, 1.0 = base
}

Why two diameters? COUPLED explosives fill the borehole — charge diameter equals hole diameter. DECOUPLED (packaged) explosives have an air gap — the charge diameter is the product's physical diameter, which is smaller. Pressure models need the borehole wall radius; mass calculations need the charge diameter. Both are carried per-deck.

From a Kirra KAP

parseKAP() returns { holes, decks, surfaces, products, raw }. Holes carry the extra Kirra fields burden, spacing, gradeZ, massPerHole, rowID and firstFireMs (earliest primer-resolved fire time). Deck timingMs is the primer's absolute fire time — electronic delayMs, or holeTime + delayMs + lengthFromCollar / deliveryVod for shock-tube / electric / cord cascades — and primerFraction locates the primer along the deck. Surfaces are { id, name, role, pos: Float64Array, idx: Uint32Array, np, nt } in world coordinates.

Monitor waveforms: parseMonitorCSV(text) reads Instantel Blastware / Micromate and Texcel Twf2CSV exports into { sampleRateHz, channels: { Tran, Vert, Long }, metadata }.

Vibration Model Hierarchy

The library provides five vibration models with increasing fidelity and computational cost:

1. PPV — Simple Site Law

PPV = K × (D / Q^e)^(-B)

Point-source evaluation at charge centroid. O(n) per point. Real-time.

2. PPV Per-Deck

Same physics, but evaluates at top/centre/base of each deck individually. Multi-deck holes show separate influence zones.

3. Scaled Heelan — Blair Non-Linear Superposition (RMS)

Blair & Minchinton (2006). Each deck subdivided into M elements with non-linear charge superposition:

Em = [m × w_e]^A − [(m−1) × w_e]^A
PPV_element = K × Em × R^(−B) × F(φ)

Heelan radiation patterns F₁(φ), F₂(φ). Viscoelastic attenuation via Qp, Qs. GPU-friendly (no time loop).

4. Blair Lite — Improved Radiation Patterns

Same RMS energy summation but with Blair's Vs/Vp-dependent radiation patterns:

sfacp = 1 − 2(Vs/Vp)² cos²φ     // P-wave: non-zero on axis
sfacs = sin(2φ)                    // SV-wave with fud=1.2 regularisation

Primer-aware element ordering. Vs derived from Vp + Poisson's ratio.

5. Blair & Minchinton — Full Time-Domain

Coherent waveform superposition with P-wave and SV-wave arrival times:

w(p) = (p^N − 2N·p^(N−1) + N(N−1)·p^(N−2)) × exp(−p)

Captures constructive/destructive interference. O(n × M × T) per point. Web Worker parallelism for grid computation.

Damage Models

Holmberg-Persson: Near-field PPV (mm/s) via sub-element integration, in the published form PPV = K·[Σ w·R^(−β/α)]^α — the sum is raised to α once, so the result converges in elemsPerDeck. Compare it against a critical PPV yourself: 700–1000 mm/s for new cracks in Swedish igneous rock (NIOSH p29), or PPVcrit = T·Vp/E (Persson 1994 via Onederra Eq 11). Changed in 0.3.0 — this returned peakPPV / ppvCritical as a unitless damage index before.

Jointed Rock: Combined intact rock fracture (σ_d / σ_t) and Mohr-Coulomb joint failure (τ / (c + μσ_n)).

Flyrock Models

⚠️ Corrected in 0.3.1. Lundborg and McKenzie both carried transcription errors. If you computed a clearance zone with 0.3.0 or earlier, recompute it — see Flyrock corrections in 0.3.1.

Four published algorithms. They are not a ladder of conservatism — they model different mechanisms and take different inputs:

| Model | Inputs it actually uses | Basis | |-------|------------------------|-------| | Richards & Moore (2004) | Burden, stemming, explosive density, K | Face burst + cratering + stem eject | | Lundborg (1974) | Hole diameter, bench/crater | Empirical upper bound, MK22 Eqs (1)–(2) | | McKenzie (2009/2022) | SDoB, hole diameter, stemming, density† | Chiappetta Scaled Depth of Burial | | Roth (1979) | Burden, mass/m, VOD, rock density | Gurney charge-to-burden-mass ratio |

† In McKenzie, rock density sets the fragment size that reaches the rim (Eq. 6), not the range — MK22 p.22 is explicit that density "does not affect maximum projection distance". Roth is the only model here in which rock density changes the range, and there it goes as L ∝ 1/ρ.

MODEL_INPUTS and usedInputsFor(algorithm, params) record which inputs a model actually consumed, so a saved shroud never claims a parameter that had no effect on it. K belongs to Richards & Moore alone; a McKenzie result recording K: 14 invites exactly the wrong conclusion.

Lundborg defaults to bench. Crater is the confined, fully-buried single charge (misfire assessment); bench is a normal production blast with a free face. Running Eq. (1) on a bench pattern is not "being conservative" — it is the wrong equation by a factor of 6.5. Conservatism belongs in the Factor of Safety, where it is visible and adjustable.

Stem eject can never set the Richards & Moore envelope. stemEject = cratering · sin(2θ) and sin(2θ) ≤ 1, so it never wins the max(); and its launch speed √(stemEject·g/sin2θ) collapses to √(cratering·g) exactly. The angle is reported for completeness but is not a dial — don't expose it as one.

3D shroud generation using the Chernigovskii ballistic envelope.

Site Law, Receptors and Probability of Exceedance

• fitSiteLaw — log-log least squares of PPV = K·(D/Q^e)^−B on monitoring observations → K50 / K90 / K95, B, R², residual σ, outlier flags.
• maxAllowableCharge / distanceForPPV — inverse site law for charge design and clearance.
• evaluateReceptor — every charged deck against a monitor: peak single-deck PPV, coherence-window RMS (±8 ms, gated by P-wave arrival), coherent seed-wavelet peak, dominant hole, contributors, compliance ratio and max allowable charge. Near-field clamp at SD = 1.0 m/kg^0.5 (Yang & Scovira 2007).
• probabilityOfExceedance — Blair (2011) P(V > V_β) from the log₁₀ z-score with the correct Abramowitz & Stegun polynomial forms (verified against Blair Table 1 in the tests; the circulated Kearney and XLSX restatements are wrong). normalQuantile / effectiveTargetForPoE give the inverse (design to 1 % PoE).

Ripple Tank

Coherent, phase-aware forward wave field: at time t every point sums the P and S contributions of every charge that has fired, with site-law amplitude and a causal wavelet at the arrival time. Fronts interfere constructively and destructively — the educational complement to the incoherent RMS heatmaps.

u(p,t) = Σ_i K·(D_i/Q_i^n)^−B · [ w(t − fire_i − D_i/cp, fP) + spRatio · w(t − fire_i − D_i/cs, fS) ]

Wavelets: causal Ricker (physical default), Gaussian bell, damped sinusoid, Berlage, or a measured geophone seed. RippleTankModel.computeGrid / timeSeries / rippleWaveFronts.

Signal Toolkit

| Module | Contents | |--------|----------| | signal/FFT.js | radix-2 FFT / IFFT, single-sided magnitude, band peaks | | signal/Wavelets.js | Ricker, causal Ricker, Gaussian bell, damped sinusoid, Berlage, two-term P+S, measured resampling, seed bundles | | signal/FrequencyAnalysis.js | inter-detonation intervals, impulse-train spectrum, dominant frequencies, MIC time-window histogram, structural-resonance bands | | signal/SeedSynthesis.js | signature-hole superposition (uniform / √Q / site-law amplitude, two-term P/S arrivals, Blair 2008 non-linear damage attenuation) | | signal/ForwardArray.js | L / T / V synthesis at a monitor with P, S and Love waves, polarisation, peak vector sum, Gao 2015 near-field S correction | | signal/SignatureDeconvolution.js | Li & Silva-Castro (2017) spectral-division extraction of the single-hole signature | | signal/Detune.js | reproducible timing dither (uniform / triangular / positive), nonel palette snap, rolling-window event-rate constraint |

Blast Movement (Phase 5 — implemented)

Physics-based blast throw / muckpile prediction — an open-source approach to the problem solved by Orica's OREPro 3D Predict. Ported from the Kirra blast-throw simulator (throw_4 generation).

Pipeline (BlastMovementSimulator):

1. parseKAP — holes, charging (mass per deck from geometry, primer-resolved fire times), and surfaces by role: PREBLAST_VOLUME / VOXEL-BLK* (material to blast), SHELL / *REMAIN* / *MINUS* (trusted confinement), PREBLAST_SURFACE / *TOPO* (fallback collision with lid/face exclusion), POSTBLAST* (survey reference)
2. Voxelise the blast volume by column ray-casting (auto-coarsened to the block budget); fragmentation-shaped block size scatter
3. Kinematic loading — Yang 3DMuck (Yang & Kavetsky 1990; Yang 2020): every explosive deck is split into charge elements; a block receives |ΔV| = Pe·ρe·d²·Δl / (4·r^b) from each element of every hole firing within the timing window of its dominant hole, summed vectorially. Confined momentum cancelled between cooperating charges is recovered and steered down the timing gradient (least-squares fit of fire time over neighbours → direction of relief). An energy-partition depth-zone model (v0 = √(2ηE·PF/ρ)) is available as an alternative.
4. Sphere DEM transport: fixed 5 ms sub-steps, gravity, spatial-hash sphere contacts (mass ∝ ρr³), static shell collision, ground plane, in-flight bulking to the target swell factor, rest detection with re-activation on impact
5. Results: displacement vectors (in-situ → final, world coordinates), volume-weighted centre-of-mass shift and bearing, achieved swell (prescribed and emergent), and a triangulated muckpile heightfield surface
6. Calibration: surveyTargets rasterises PREBLAST_VOLUME / SHELL / POSTBLAST onto 2 m columns (swell = muck volume ÷ in-situ, CoM throw); calibrate() secant-fits Pe with three coarse headless runs. On SWELLFACTOR.kap: survey swell 1.43×, throw 34 m @ 130° → fitted Pe ≈ 1.5

RapierEngine (@dimforge/rapier3d-compat, injected, not a dependency) swaps the transport for convex-hull rigid bodies with emergent swell. In calibration the sphere DEM reproduced the surveyed muckpile shape better, so it is the default.

Outputs: Displacement vectors (equivalent to OREPro 3D's SmartVectors™) for block model transformation, and predicted post-blast muckpile topography.

Package Structure

blast-physics-js/
  src/
    index.js
    core/
      DeckEntry.js             HoleEntry.js            RadiationPattern.js
      Waveform.js              RockMass.js
    vibration/
      PPV.js                   PPVDeck.js              ScaledHeelan.js
      ScaledHeelanBlair.js     HeelanOriginal.js       BlairMinchinton.js
      SiteLaw.js               ReceptorPPV.js          ProbabilityOfExceedance.js
      RippleTank.js
    signal/
      FFT.js                   Wavelets.js             FrequencyAnalysis.js
      SeedSynthesis.js         ForwardArray.js         SignatureDeconvolution.js
      GaoNearFieldCorrection.js Detune.js
    damage/
      HolmbergPerssonDamage.js JointedRockDamage.js
    pressure/
      BoreholePressure.js      PowderFactor.js         SEE.js
    detonation/
      DetonationSimulator.js   EmComputation.js
    flyrock/
      FlyrockTrajectory.js     FlyrockShroud.js        SDoB.js
      Ballistics.js
    movement/
      BlastMovementSimulator.js Voxeliser.js           InitialVelocity.js
      ThrowDirections.js       SphereDEM.js            ShellCollider.js
      SurfaceMesh.js           Displacement.js         RapierEngine.js
    io/
      KAPReader.js             ZipReader.js            MonitorCSV.js
    workers/
      BlairHeavyWorker.js      FlyrockWorker.js
  examples/
    index.html  throw.html  ripple.html  SWELLFACTOR.kap
  test/
  dist/

Breaking changes in 0.3.0

Every item here is a place where the code and the published equation disagreed. The corrected models are ported from Kirra's shader implementations, which are the reference — src/core/BlairScaledHeelan.js is a 1:1 port of Kirra's file of the same name, so the GPU and CPU paths cannot drift. Each source file keeps a ⏪ BEFORE 0.3.0 block with the old expression.

Sources. Blair & Minchinton (2006) Fragblast-8; Blair (2008) IJRMMS 45; Blair (2010) Fragblast-9; Blair & Armstrong (1999) Fragblast 3; NIOSH (Iverson, Kerkering & Hustrulid 2008); Onederra & Esen (2004).

| # | Change | Effect on published numbers | |---|---|---| | 1 | Holmberg-Persson sums first, then raises to α once (PPV = K·[Σ w·R^(−β/α)]^α). The old form raised each element to α and RMS-summed, which never converged. | ~34 % higher at 8 elements, and the answer no longer depends on elemsPerDeck. Pinned by the NIOSH worked example: a 3 m column at 1 kg/m, 2 m away at mid-column height → 476 mm/s. | | 2 | computeHolmbergPerssonDamage returns PPV in mm/s, not peakPPV / ppvCritical. ppvCritical is no longer a parameter. | Divide by your own threshold to recover the old ratio. computeGrid now reports unit: "mm/s". | | 3 | All models use the Blair patterns — blairPatternP (Eq 10) and blairPatternS (Eq 11, with α/β folded in). heelanF1/heelanF2 put P at zero and |SV| at maximum at φ = π/2, the reverse of the paper. | PPV was non-monotonic in distance — it read higher at 20 m than at 10 m. The old pair is still exported, marked as the pre-2026 pattern; nothing uses it. | | 4 | Blair 2008 Eq 22 replaces the one-sided primer approximation. The front leaves the primer in both directions, so paired elements share one increment until the shorter side runs out. | Telescopes to M^A exactly, for any primer position, so the result is independent of elemsPerDeck to within rounding. ScaledHeelan previously ignored primerFraction entirely. | | 5 | chargeExponent is Blair's A and now defaults to 0.8, matching Kirra. For a square-root site law, Blair 2008 Eq 14 gives A = B/2. | ~3.3× higher for an 80 kg deck. ⚠ Name collision: SiteLaw.js and PPV.js use the same name for the scaled-distance e, where 0.5 IS correct. The two are related by A = e·B. Check which you are passing. | | 6 | Q attenuation is GONE from both scaled models. The R^(−(B−1)) in the site law already IS the material attenuation (B&M p5). qualityFactorP/S are accepted and ignored. | Higher in the far field. Q still applies to HeelanOriginal, which has no site law to carry it. | | 7 | Elements sum linearly over per-element resultants, Σ sqrt(vP² + vSV²), not sqrt(Σ (vP² + vSV²)). | Conserves charge (Blair 2008 p237). With item 4, elemsPerDeck now moves the answer by < 0.1 % from 4 to 32 elements. | | 8 | HeelanOriginal rebuilt on B&M Eq 6: one constant for P and SV, C = a²·δL·b²·P_b·k6 / (2·μ·Vp) with μ = ρ·Vs² and k6 = (e/6)⁶/γ6 = 0.189887. Q is evaluated at the pulse's dominant frequency, 2π·0.0597·b, not VOD/(2a). | Very large. The old form used two different denominators, and its ω erased the far field — attenuation of 2.4e−5 at 100 m. It read 26 m/s at 5 m and 0.47 mm/s at 50 m; it now tracks a fitted site law within about 1.4–1.8×. | | 9 | Element mass comes from the deck's own mass in BlairMinchinton and BlairHeavyWorker, not from ρₑ·π·RAD²·dL built on the HOLE radius. | A decoupled deck was overweighted by (holeDiam/chargeDiam)² — about 2× at the DECOUPLED default. | | 10 | One named VOD fallback, DEFAULT_VOD = 5000, exported from core/Constants.js. | Was 5000, 5279 and 5500 in three different files. | | 11 | An explicit 0 is no longer replaced by the default in createDeckEntry or in BlairHeavyWorker's parameter reads. | Number(x || default) treated a legitimate zero as missing. |

Still uncalibrated

B&M p4 is explicit that the unscaled model "can only be used to predict normalised vibration values", because the true borehole wall load P_o is unknown. HeelanOriginal assumes P_b = ρₑ·VOD²/8, so its absolute mm/s is indicative and its SHAPE is the published one. Use ScaledHeelan, ScaledHeelanBlair or BlairMinchinton when you need calibrated numbers.

Flyrock corrections in 0.3.1

Two transcription errors, both in safety calculations, both ported from Kirra's corrected FlyrockCalculator.js. test/flyrockPaperParity.test.js now locks every model to a printed equation rather than to this library's own output — a snapshot test cannot catch a transcription error, and that is what these were.

Lundborg — wrong coefficient AND a spurious unit conversion

// ⏪ BEFORE 0.3.1
var Lmax_feet = 260.0 * Math.pow(holeDiamMm / 25.4, 2/3);
var Lmax_m    = Lmax_feet * 0.3048;

Lundborg published the same throw in two equivalent forms, and that they agree numerically is the proof the result is already metres:

CRATER  L'max = 260 × ø_in^(2/3)  =  30  × ø_mm^(2/3)    [MK22 Eq.1]
BENCH   L'max =  40 × ø_in^(2/3)  =  4.6 × ø_mm^(2/3)    [MK22 Eq.2]

260 × (229/25.4)^(2/3) = 1126        30 × 229^(2/3) = 1123

The old code also used the crater coefficient unconditionally, with no bench/crater choice. For a 229 mm hole it returned 343.3 m — neither published equation:

| | Range | vs old | |---|---|---| | Old code | 343.3 m | — | | Bench, Eq.(2) — the new default | 172.2 m | old was 1.99× too far | | Crater, Eq.(1) | 1122.9 m | old was 0.31× — 3.3× too short |

McKenzie — the 2/3 power reached SDoB

// ⏪ BEFORE 0.3.1
var Rmax = 9.74 * Math.pow(holeDiamMm / Math.pow(sDoB, 2.167), 2/3);

MK22 Eq.(5) is L'max = 9.74 × SDoB^(−2.167) × ø_mm^(2/3) — three separate factors. The old grouping pushed the 2/3 onto SDoB too, giving an effective exponent of −1.4447. The two forms agree only at SDoB ≈ 1, which is why it survived review:

| SDoB | Old | Correct | Ratio | |---|---|---|---| | 0.638 (under-stemmed) | 697.1 m | 963.9 m | 0.72× — 267 m short | | 1.037 | 346.0 m | 337.0 m | 1.03× | | 1.834 (well stemmed) | 151.8 m | 98.0 m | 1.55× |

The under-prediction is at the dangerous end — badly-stemmed holes are the ones that actually throw. rockDensity was also accepted, defaulted, and never read; it now drives Eq. (6) fragment size.

Also in 0.3.1

• Roth (1979) added — roth() and rothAtLaunchAngle().
• MODEL_INPUTS / usedInputsFor — so a result records only the inputs that moved it.
• Richards & Moore was already correct and is unchanged. It matches the reference workbook to 0.03 %.

Implementation Roadmap

| Phase | Scope | Status | |-------|-------|--------| | 1 | Core data structures + PPV site law + PPV per-deck | ✅ Complete | | 2 | Scaled Heelan + Blair Lite + Holmberg-Persson + Jointed Rock damage | ✅ Complete | | 3 | Blair & Minchinton time-domain + Web Workers + Heelan Original | ✅ Complete | | 4 | Detonation simulator + flyrock (R&M, Lundborg, McKenzie) + pressure + powder factor | ✅ Complete | | 5 | Blast movement: KAP import, voxelisation, Yang 3DMuck launch, sphere DEM (+ optional Rapier), displacement vectors, muckpile surface, survey calibration | ✅ Complete (v0.2.0) | | 6 | Kirra analysis suite: ripple tank, FFT / IDI / spectrum, seed & forward-array synthesis, signature deconvolution, site-law regression, receptor PPV, Blair 2011 PoE, SDoB / SEE, detune | ✅ Complete (v0.2.0) |

References

• Blair, D.P. & Minchinton, A. (1996). On the damage zone surrounding a single blasthole. Fragblast-5, Montreal.
• Blair, D.P. & Minchinton, A. (2006). Near-field blast vibration models. Fragblast-8, Santiago.
• Blair, D.P. (2008). Non-linear superposition models of blast vibration. Int. J. Rock Mech. Min. Sci. 45, 235–247.
• Blair, D.P. (2011). A probabilistic analysis of vibration based on measured data and charge weight scaling. EFEE 6th World Conf., Lisbon, 319–337.
• Blair, D.P. (2015). Wall control blasting. Fragblast 11, Sydney.
• Heelan, P.A. (1953). Radiation from a cylindrical source of finite length. Geophysics 18, 685–696.
• Holmberg, R. & Persson, P.A. (1979). Design of tunnel perimeter blasthole patterns to prevent rock damage. Tunnelling '79, London.
• Yang, R. & Scovira, D.S. (2007). A model for near-field blast vibration based on signal broadening and amplitude attenuation. EXPLO 2007, Wollongong.
• Yang, R. & Kavetsky, A. (1990). A three-dimensional model of muckpile formation and grade boundary movement in open pit blasting. Int. J. Min. Geol. Eng. 8, 13–34; Yang, R. (2020) 3DMuck.
• Anderson, D.A. (1989) / Hinzen, K.-G. (1988). Signature-hole linear superposition of blast vibration.
• Aldridge, D.F. (1990). The Berlage wavelet. Geophysics 55, 1508–1511.
• Li & Silva-Castro (2017). Spectral division deconvolution of blast vibration signals for signature estimation. ISEE 43rd Conf.
• Gao, Q.D., Lu, W.B., Hu, Y.G., Chen, M. & Yan, P. (2015). Comparison of the generation of shear wave with different simulation approaches. Fragblast 11, Sydney, 79–87.
• Chiappetta, R.F. & Treleven, J.P. (1997). Scaled Depth of Burial concept for flyrock risk assessment.
• Richards, A.B. & Moore, A.J. (2004). Flyrock control — by chance or design. Proc. 30th ISEE Conf.
• McKenzie, C.K. (2022). Flyrock model validation and application. Rock Fragmentation by Blasting (Fragblast 13), X.G. Wang (ed), Metallurgical Industry Press, Beijing. ISBN 978-7-5024-9269-4. Eqs (1)–(3) p.23; Eqs (4)–(7) p.24.
• Lundborg, N. (1974). Maximum flyrock throw, via McKenzie (2022) Eqs (1) and (2).
• Roth, J. (1979). A Model for the Determination of Flyrock Range as a Function of Shot Conditions. Management Science Associates for the U.S. Bureau of Mines, Contract J0387242. Equations pp.5–11.
• Siskind, D.E. et al. (1980). Structure response and damage produced by ground vibration from surface mine blasting. USBM RI 8507.

Related Projects

• Kirra — Web-based blasting pattern design application for mining and construction
• trimesh-boolean — Open-mesh boolean operations for Three.js

Author

Brent Buffham

• blastingapps.com
• kirra-design.com
• Buy Me a Coffee

License

MIT © Brent Buffham 2026