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What Size Hail Dents a Car Roof?

Rand Simulation — Applications Engineering AI
Explicit transient dynamics · Ansys LS-DYNA · 8 min read

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Every summer the same argument breaks out on driveways and in claims offices: was that hail big enough to do this? Everyone agrees a pea bounces off and a golf ball ruins a panel — the fight is over the line between them. So we fired the whole hail-size ladder at the same piece of car roof in Ansys LS-DYNA, each stone arriving at the speed physics actually delivers it, and watched where the steel stops springing back. A 10 mm pea leaves 0.001 mm behind — nothing; a 45 mm golf-ball stone leaves a 25 mm dent you can feel with your palm; and the crossover sits right around the one-inch line the insurance industry already uses.

A 45 mm (golf-ball-class) ice sphere striking a generic steel roof section at its terminal velocity, solved in Ansys LS-DYNA and rendered from the solved shell field. The panel is colored by von Mises stress: on impact the flexural stress wave rings outward across the skin, the SPH ice sphere shatters into sliding debris, the ringing decays — and the dent stays, with the live readout settling at the residual 25 mm. The roof section is a generic, self-authored sedan-style panel (not any maker’s design); its out-of-plane deflection is exaggerated 3× so the wave and the bowl read on screen — the stress wave itself is carried by color at true scale.

Bigger hail falls faster, and that is the whole story

A hailstone is an ice sphere falling at terminal velocity, and terminal velocity scales with size. Drag balances weight when v_t = √(4 ρ_ice g D / 3 ρ_air C_d), so speed grows as the square root of diameter: a 10 mm pea arrives at about 14 m/s, a 25 mm quarter-sized stone at about 22 m/s, a 45 mm stone at about 29 m/s. That looks gentle until you count the energy. Kinetic energy is ½ m v²; mass grows as diameter cubed and v_t² grows as diameter, so the punch a stone lands scales as diameter to the fourth power. Between the pea and the golf ball that is roughly 400× the energy — which is why the ladder has a knife-edge in it rather than a gentle ramp.

Terminal velocity against hail diameter from the drag-balance closed form, with a drag-coefficient band and published hail fall speeds overlaid — Terminal velocity per size, from the standard drag-balance closed form with a hailstone drag coefficient of 0.5 (band 0.45–0.60 shown) and ice density 900 kg/m³. The curve is not tuned to our solve — it is the textbook relation, and it lands on published hail fall-speed data (NSSL/NWS guidance and Heymsfield-class measurements). Each stone in the study was fired at exactly its own v_t; this is the input to the impact, not an output of it.

How the roof was modeled

The roof is a self-authored, generic sedan-style panel: a shallow spherical crown (2.5 m radius — the curvature you see reflected in a parking lot) over a 600 × 600 mm section held at its edges, meshed with 22,500 fully-integrated shell elements and made of 0.75 mm bake-hardened autobody steel with a real hardening curve. The hailstone is an SPH (smoothed-particle) ice sphere — the right tool for a body that shatters — using the standard ice material model, with failed particles kept as fluid-like debris so the splash you see in the animation is physical, not decoration. The two meet through a contact that we gate on every run: the sliding-interface energy has to be non-trivial, because an impact deck whose energy balance reads a suspiciously perfect 1.0000 is usually a contact that silently did nothing. There is no mass scaling (it would fabricate kinetic energy on a hard hit) and no global damping during the strike; the panel rings, and a light structural damping only afterward lets the permanent dent settle out so we can read it cleanly.

“Where dents start” needs a definition, so we picked a physical one: the residual dent depth — the deflection left at the impact point after the panel stops ringing and springs back — read from the solver’s own nodal output late in each run and cross-checked against the retained plastic work in the steel. A dent is plastic strain that stayed; if the panel gave back all its energy, there is no dent, and the plastic-work number says so.

Pea bounces, golf ball dents — shown, not asserted

The pea is the control the whole argument needs. Fired at its 14 m/s terminal velocity, the 10 mm stone dimples the panel by a tenth of a millimeter for an instant, the panel springs back 98.8% of the way, only about 2 joules of plastic work is dissipated, and 0.001 mm is left behind — the stone rebounds off an essentially unmarked roof. Step up the ladder and the panel holds its composure until, right around the one-inch mark, it doesn’t: the 45 mm golf-ball stone drives a plastic hinge ring, its own ice crushes, and a 25 mm dent remains after everything settles.

The contrast on one screen, same roof, same stress scale, each stone at its own terminal velocity: the pea (left) barely stresses the skin and leaves it flat; the golf ball (right) sends a stress wave across the panel and drives a permanent bowl. Deflection exaggerated 3× for visibility; the dent readouts are the solver’s settled values.

The result: a generic 0.75 mm steel car roof leaves 0.001 mm behind from a 10 mm pea and takes a 25 mm dent from a 45 mm golf-ball stone. Visible denting (a 0.1–0.3 mm “just visible under inspection light” band) begins around 20 mm (0.8 in), and denting is unmistakable by the ~1-inch (25 mm) line the insurance industry already uses — a number readers can now see earned on a chart rather than asserted in a pamphlet.

Residual dent depth against hail diameter on a log scale, with the just-visible dent band, the onset region, and the one-inch insurance line marked — The chart the argument actually needs: residual dent depth versus hail diameter, each stone at terminal velocity. Below about 20 mm the panel shrugs the stone off; then the curve turns up steeply through the “just visible” band and the one-inch line into unmistakable denting. Common size names sit on the top axis, the assumptions are printed on the figure, and anyone who cares about a different visibility threshold can read their own onset straight off it.

Why ice is gentler than a steel ball — and what moves the line

Here is the part the pamphlets miss: a hailstone is not a ball bearing. Because ice crushes on contact, it caps the force it can deliver, spreading the blow over a longer, softer push. Fire a rigid ball of the same 25 mm size at the same speed and the panel takes a 4.5 mm dent — 2.3× deeper than the 2.0 mm the deformable ice sphere leaves. That gap is why steel-ball impact tests (the FM 4473 / UL 2218 lineage) are a conservative stand-in for real hail, and why modeling the ice as ice, not as a hard sphere, matters if you want the real number.

The onset is a band, not a single number, because it moves with the panel. Thicken the skin from 0.75 to 0.90 mm and the 25 mm dent drops five-fold, to 0.4 mm — the difference between a totaled roof and a car wash. A higher-strength steel grade trims it modestly (1.75 vs 1.96 mm). And the drag coefficient sets the arrival speed, so the same stone in a stiffer or calmer air column hits a little harder or softer. We also refined the ice-particle resolution to make sure the dent is a result and not an artifact: the number moved 3.3%, well inside our 10% gate.

Left: residual dent at 25 mm under each modeling change; right: the study's gates and receipts — Left: what moves the onset at the one-inch size — a rigid ball, a thicker skin, a stronger steel, a finer numerical resolution. Right: the receipts — the units gate, the terminal-velocity anchor, the pea-bounce gate, energy closure, the contact gate, the ice crush cap, resolution independence, and the read against the one-inch rule.

The same physics an automaker manages on purpose

Dent resistance is not a weather problem — it is a panel-engineering problem that automakers solve at design time, trading sheet thickness, steel grade, panel curvature, and adhesive support against mass and cost so a closing door, a leaning elbow, or a summer storm doesn’t leave a mark. The workflow here is the same one that answers those questions: build the panel, fire the real load at it, and read the permanent deformation from a gated, energy-audited explicit solve. Swap the ice sphere for a shopping cart, a stone off a truck, or a hand press, and the method does not change.

Honest scope. This is a generic, self-authored sedan-style roof section (0.75 mm bake-hardened steel, 2.5 m crown, 600 mm clamped span), not any specific vehicle; hoods, doors, aluminum panels, creases and panel edges behave differently, and the thickness/grade sensitivities bracket that spread rather than enumerate it. Stones fall vertically at calm-air terminal velocity — there is no storm wind, downdraft, or oblique strike, all of which make real hail hit harder, so the solved onset is a fair-weather-fall reading. Terminal velocity is a stated closed-form input (drag balance, published drag coefficient and ice density read against published fall-speed data), not part of the solve. “Visible” is a stated convention (a 0.1–0.3 mm inspection-light band); the chart carries the full curve so any threshold can be read off it. Dent depth is the steel substrate only — no paint or clear-coat fracture, no cosmetic claims-grade verdict. The hailstone is a smooth, homogeneous sphere at published density and strength (the standard test idealization), not a lumpy, layered, spinning real stone, and each size is a single center-of-panel strike — no multi-hit accumulation or storm statistics. Four further cases (a 0.65 mm thin-skin bound, two drag-coefficient velocity-band cases, and a halved shell-mesh refinement) were authored but scoped out of this run to stay inside the solve budget; the SPH-resolution check is the one that ran. Energy balance closed to within 0.02–0.2% across all twelve runs, with no mass scaling and no global damping; dent depths are the solver’s own settled nodal deflections, cross-checked against retained plastic work. The 3× deflection in the animations is a render-only visual exaggeration, stated on each clip.

Wondering how much punishment your panel, enclosure, or product can take before it’s permanent? The workflow behind this study — Ansys LS-DYNA solving the transient impact, crush, and springback of real materials end to end, gated on closed-form checks and anchored to published data — is how Rand Simulation turns “everyone knows it dents” into a number an engineering team can design against. That’s innovation through insight.