Tree Risk Parameter Explorer

Adjust sliders to see how each parameter feeds into the composite risk score (ISA TRAQ / QTRA framework)

Input parameters

Height H (m) 18

DBH D (cm) 30

Lean angle θ (°) 8°

Canopy radius (m) 4

Crown density Cd 0.60

Wind speed (m/s) 20

Distance d (m) 8

NDVI health 0.70

Derived geometry

Slenderness H/D

—

Fall radius

—m

Frontal area A

—m²

COG height

—m

Live formula outputs

Wind drag: F = ½ · ρ · Cd · A · U²
F = 0.5 × 1.15 × — × — × — = — kN

Wind moment: M_wind = F · h_eff (h_eff = 0.6H)
M_w = — × — = — kN·m

Gravity moment: M_g = m · g · sin(θ) · h_COG
M_g ≈ — kN·m (lean toward road)

Stem resistance: M_break = (π/32) · σ · D³
M_break = — kN·m (σ = 40 MPa)

Safety margin: M_break − (M_w + M_g) = — kN·m

Tree geometry (live)

Canopy size, lean angle, and fall radius update live with the sliders.

Risk score R = P_fail × P_impact × C

— —

LowModerateHighExtreme

P(failure)

—

P(impact)

—

Sensitivity — what moves the score most

Extracted assessments

Composite risk R = P_fail × P_impact × C_road (C=1 assumed).
ISA TRAQ bins: Low <5 · Moderate 5–25 · High 25–60 · Extreme >60.
ρ = 1.15 kg/m³ · σ = 40 MPa · m ≈ 150·H·D² kg (allometric).
References: GALES (Gardiner et al.), HWIND (Peltola et al.), ISA TRAQ (Dunster et al. 2017).

How the parameters connect — mathematical chains

Geometry chain

Height H and DBH D combine into the slenderness ratio H/D, which is the single strongest structural predictor — trees above H/D > 80 are broadly considered fragile. The lean angle θ and canopy radius CR determine whether the fall radius H · cos θ actually reaches the road distance d — this is the binary gateway to impact probability.

Wind loading chain

Canopy radius CR → projected frontal area A = π · CR² / 2 → drag force F = ½ · ρ · Cd · A · U² (F grows with U²). That force multiplied by the effective lever arm h_eff = 0.6H gives the wind overturning moment M_wind. Note F ∝ U² means doubling wind speed quadruples the moment — which is why wind speed dominates the sensitivity ranking.

Gravity chain

Lean angle θ adds a permanent gravitational overturning moment M_g = m · g · sin(θ) · h_COG, even at zero wind. The mass m is estimated from H and D via a simple allometric relation. This is why a leaning tree at moderate wind is far more dangerous than an upright tree in a storm.

Failure criterion

The stem's resistive moment M_break = (π/32) · σ · D³ is what the tree can withstand. When M_wind + M_g exceeds M_break, the safety margin turns negative — shown in red — and failure probability shoots toward 1. DBH has a cubic effect here, which is why a small increase in trunk diameter provides disproportionate structural strength.

Risk score

R = P_failure × P_impact × C_road. The sensitivity bars above show which parameter is currently moving the score most given your current inputs — useful for prioritising what to measure most precisely in the field.