Fell Zone & Safe Distance Calculator

ANA›Life Services Authority›National Calculator Authority›Fell Zone & Safe Distance Calculator

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Fell Zone & Safe Distance Calculator

Estimate the fell zone radius and safe retreat distance when felling a tree, based on tree height and species lean characteristics.

Tree Height (m)

Trunk Diameter at Breast Height – DBH (cm)

Natural Lean Angle (°) (0 = perfectly vertical)

Crown Spread Radius (m) (half the full crown width)

Species / Wood Type

Softwood (pine, spruce, fir) Mixed / Unknown Hardwood (oak, ash, beech) Dense hardwood (hickory, hornbeam)

Ground Slope (°) (slope of terrain where tree stands)

Calculate

function felCalc() { var h = parseFloat(document.getElementById('fel-height').value); var dbh = parseFloat(document.getElementById('fel-dbh').value); var lean = parseFloat(document.getElementById('fel-lean').value); var crown = parseFloat(document.getElementById('fel-crown').value); var sf = parseFloat(document.getElementById('fel-species').value); var slope = parseFloat(document.getElementById('fel-slope').value);

var errors = []; if (isNaN(h) || h 150) errors.push("Tree height must be between 1 and 150 m."); if (isNaN(dbh) || dbh 500) errors.push("DBH must be between 1 and 500 cm."); if (isNaN(lean) || lean 45) errors.push("Lean angle must be between 0° and 45°."); if (isNaN(crown) || crown 30) errors.push("Crown spread radius must be between 0 and 30 m."); if (isNaN(slope) || slope 60) errors.push("Ground slope must be between 0° and 60°.");

var res = document.getElementById('fel-result'); if (errors.length > 0) { res.style.display = 'block'; res.innerHTML = '' + errors.join('') + ''; return; }

/* ── Core Formulas ───────────────────────────────────────────────────────── 1. Lean offset: The lean shifts the centre of mass horizontally. lean_offset = h × sin(lean_rad)

  1. Fell zone radius (R_fell): The maximum distance the tip of the tree can reach on the ground, accounting for lean, crown spread, species factor, and slope. On a slope the effective reach downhill is amplified.

R_fell = (h × cos(lean_rad) + lean_offset + crown) × sf × slope_factor

where slope_factor = 1 / cos(slope_rad) [downhill reach amplification]

  1. Safe retreat distance (R_safe): Industry standard (ANSI Z133, OSHA 1910.266) recommends a retreat distance of at least 2× the tree height, measured at 45° behind the felling direction.

R_safe = 2 × h × sf

  1. Danger zone arc: The fell zone is modelled as a full circle of radius R_fell centred on the stump (worst-case, accounts for unexpected kickback or barber-chair splits).

  2. Stump height recommendation: Stump height ≤ DBH / 3 (practical rule; lower stump = safer hinge) ─────────────────────────────────────────────────────────────────────────── */

var leanRad = lean * Math.PI / 180; var slopeRad = slope * Math.PI / 180;

var leanOffset = h * Math.sin(leanRad); var slopeFactor = 1 / Math.cos(slopeRad);

var R_fell = (h * Math.cos(leanRad) + leanOffset + crown) * sf * slopeFactor; var R_safe = 2 * h * sf;

/ Hinge width recommendation: 80% of DBH (cm → m) / var hingeWidth = 0.80 * (dbh / 100);

/ Stump height recommendation / var stumpMax = (dbh / 100) / 3;

/ Notch depth: 1/4 to 1/3 of DBH / var notchMin = (dbh / 100) * 0.25; var notchMax = (dbh / 100) * 0.333;

/ Escape route angle: 45° behind and to the side of felling direction / var escapeAngle = 45;

res.style.display = 'block'; res.innerHTML = '### Results ' + '' + 'Fell Zone Radius (Rfell)' + '' + R_fell.toFixed(2) + ' m' + 'Safe Retreat Distance (Rsafe)' + '' + R_safe.toFixed(2) + ' m' + 'Lean Horizontal Offset' + '' + leanOffset.toFixed(2) + ' m' + 'Slope Reach Amplification Factor' + '' + slopeFactor.toFixed(3) + '×' + 'Recommended Hinge Width' + '' + (hingeWidth * 100).toFixed(1) + ' cm' + 'Recommended Notch Depth' + '' + (notchMin * 100).toFixed(1) + ' – ' + (notchMax * 100).toFixed(1) + ' cm' + 'Max Stump Height' + '' + (stumpMax * 100).toFixed(1) + ' cm' + 'Escape Route Angle (from felling direction)' + '' + escapeAngle + '° to the rear' + '' + '⚠️ Clear all persons and obstacles from within ' + R_fell.toFixed(1) + ' m of the stump before felling. Retreat along your planned escape route to at least ' + R_safe.toFixed(1) + ' m once the back-cut is complete.

'; }

#### Formulas Used

1. Lean Horizontal Offset lean_offset = H × sin(θlean) Horizontal displacement of the tree tip caused by natural lean.

2. Fell Zone Radius Rfell = (H × cos(θlean) + lean_offset + Cr) × Sf × (1 / cos(θslope)) Where H = tree height, Cr = crown spread radius, Sf = species factor, θslope = ground slope angle. The term 1/cos(θslope) amplifies downhill reach on sloped terrain.

3. Safe Retreat Distance Rsafe = 2 × H × Sf Per ANSI Z133 and OSHA 1910.266, the minimum safe retreat distance is twice the tree height, adjusted for species density.

4. Hinge Width Whinge = 0.80 × DBH The hinge should span 80% of the trunk diameter to maintain directional control.

5. Notch Depth Dnotch = 0.25 – 0.333 × DBH Open-face or conventional notch depth of one-quarter to one-third of DBH.

#### Assumptions & References

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References

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