Heim Ratio and Runout Distance (Fahrböschung)

Albert Heim spent decades documenting Alpine rockfalls and in Bergsturz und Menschenleben (1932) gave the phenomenon its measuring stick. Draw a straight line from the crown of the source scar to the farthest point the debris reached. The vertical drop is $H$, the horizontal reach is $L$, and the angle that line makes with the horizontal Heim called the Fahrböschung — literally the travel slope. The ratio $H/L$ is its tangent. Given a drop and a ratio, the reach follows by division.

Heim's point was that this ratio ought to be the coefficient of friction, and for big landslides it is not. If a rock avalanche were simply a rigid block sliding down a slope and out across a valley floor, energy balance says it stops when the drop has been consumed by friction over the distance travelled, so $H/L = \tan\phi$. For broken rock, $\phi$ is around 30 to 35°, so $H/L$ should be roughly 0.6 to 0.7 no matter how much rock fell. Small rockfalls obey this beautifully. A few thousand cubic metres off a cliff makes a talus cone at the friction angle and stops. Large ones do not obey it at all: events of 10⁷ m³ routinely show $H/L$ near 0.2, a travel angle around 11°, meaning the debris ran two or three times farther than friction can account for. Some very large events reach 0.1.

That excess mobility is a genuine unsolved problem, and this page will not pretend otherwise. The candidate explanations are all serious and none is settled. Acoustic fluidisation proposes that violent grain vibration momentarily unloads contacts, letting the mass behave as a fluid. Trapped-air-layer models have the debris riding a cushion of compressed air. Self-lubrication by dynamic fragmentation has the rock breaking apart as it moves, and the energy of fragmentation producing a dispersive pressure. Mechanical fluidisation treats the whole mass as a dense granular flow with a low apparent friction. Undrained loading of saturated valley-floor sediment supplies pore pressure from below. Each accounts for some events and fails on others: the air-layer models are hard to reconcile with long-runout landslides observed on the Moon and on Mars, where there is no air, and fragmentation models struggle with events whose deposits preserve intact source stratigraphy. Ninety years after Heim, there is no consensus.

The travel angle is an arctangent, not a conversion. $H/L = 0.30$ means $\alpha = \arctan 0.30 = 16.7°$. There is no factor that turns a gradient into an angle, and reading 0.30 as "30 % of a right angle" or as 30° is the standard way to get this badly wrong. This site keeps them as different unit types on purpose.

And now the thing that matters most. This is a planning tool, not permission. A runout distance computed here does not define a safe location. It is a geometric consequence of a ratio you supplied, and any ratio you can supply is a statistical summary of where past events happened to stop — a description of history, not a prediction of the next event. Channelised paths run much farther than open slopes. A mass that entrains saturated valley-floor sediment can travel far beyond what its source volume suggests. Deposits from a previous event change the path for the next one. Hazard mapping, setback lines and land-use decisions are the work of a qualified practitioner with local event records, field mapping, and where the consequences justify it a numerical runout model. Use this page to understand the relation and to bound an order of magnitude. Do not use it to draw a line that someone will build behind.