Why do rocks from an erupting volcano fly more than a kilometre?
— Big ballistic rocks are "cannonballs" that the wind can't push around
Even more than a kilometre from a summit crater, an eruption can send rocks raining down from overhead. What launches them is steam and gas expanding violently inside the crater. The rocks can be flung out faster than a bullet train, and the bigger they are, the less air and wind can slow them down. That's why they trace the same curved path as a cannonball — and land far from where they started.
On a clear autumn Saturday, you've climbed a popular mountain to see the fall colours. Around lunchtime, lots of people are spreading out their packed lunches near the summit.
Suddenly, from a valley not far off, comes a loud boom, and grey smoke rises into the sky. The smoke still looks a long way off.
You think, "it won't reach here," and keep taking photos — and then rocks start falling from the sky. Something close to this actually happened during the eruption of Mount Ontake in September 2014, and many climbers lost their lives.
There are only two reasons rocks travel so far
When water inside the crater flashes instantly into steam, its volume expands more than a thousandfold. That force can launch rocks at speeds around 100 metres per second. Range grows with the square of speed, so doubling the speed quadruples the distance.
A rock's weight increases with the cube of its size. But the force the air exerts on it only increases with the square of its size. So the bigger the rock, the less it's affected by air or wind, and it keeps tracing a curve like a thrown ball.
Put these two effects together, and rocks bigger than a fist can come down at high speed more than a kilometre from the crater. Let's look at each in turn.
Double the speed, and the range quadruples
Everyone knows that throwing a ball harder sends it further. But the relationship isn't simple "proportionality." Ignoring air resistance, the distance travelled is proportional to the square of the launch speed. At 50 metres per second it's about 250 metres; at 100 m/s it's about 1 kilometre; at 200 m/s it's about 4 kilometres.
Try the slider in Figure 1 to change the rock's launch speed. Even a small increase in speed moves the landing point much further away. The furthest range is reached when the rock is launched at 45 degrees.
Just as important is how fast the rock comes back down. Ignoring air resistance, a rock lands at the same speed it was launched. 100 metres per second is 360 km/h — faster than a bullet train — and it comes down not straight above you, but at an angle.
Bigger rocks fly straight through the wind
In the same eruption, fine volcanic ash gets carried tens of kilometres by the wind. But rocks bigger than a fist fall in a parabola around the crater almost regardless of wind direction. Japan's weather agency calls these "large ballistic rocks," distinguishing them from "small ballistic rocks," which do get carried by the wind.
The difference comes down to a contest between weight and air force. If a rock's size doubles, its weight increases eightfold. But the area of the rock pushing against the air only increases fourfold. In other words, every time the size doubles, the air's force relative to the rock's weight is cut in half.
Look at Figure 2. The large ballistic rocks (solid line) from the crater on the left fall near the crater in a parabola even in wind. The small ballistic rocks (dotted line) get swept high up, then drift slowly to the right as they fall.
Even small ballistic rocks can reportedly fall more than 10 kilometres downwind of the crater. Because they fall more slowly, the damage is mostly things like cracked car windows rather than loss of life. It's the large ballistic rocks that mainly put lives at risk. If ash is falling, cover your mouth and nose with a mask or a wet cloth, and protect your eyes with goggles. If ash gets in your eyes, flush it out with water — don't rub.
A rock launched at 100 metres per second reaches a point 1 kilometre away in about 14 seconds. By the time you've noticed the ash plume and wondered what it is, the rock is already overhead. If you hear or feel an eruption, look for cover first — don't stop to watch.
A "phreatic eruption," where underground heat suddenly turns water to steam, can reportedly give less warning than an eruption driven by rising magma. The 2014 Mount Ontake eruption was this type. Even a small one can send large ballistic rocks flying around the crater.
So what should you do?
- Check the eruption warning level before you climbJapan's weather agency issues a level for each volcano. Don't enter areas where climbing is restricted. Check the map for the location of mountain huts and evacuation shelters in advance.
- Bring a helmetWearing a helmet is recommended on mountains with volcanic activity. If you don't have one, hold your backpack over your head for protection.
- If it erupts, take cover first, then move awayGet behind a large rock or into a hut right away, and once the rockfall stops, head away from the crater. If anyone is hurt, call 119 or 110.
Large ballistic rocks can fly in any direction around the crater, regardless of wind. Even a kilometre from the crater, the only sure protection is staying away. If an eruption warning or climbing restriction is issued, evacuate immediately — don't stop to take photos.
Summary
Rocks from an erupting volcano travel so far because the launch speed is extraordinarily high, and range grows with the square of that speed. On top of that, bigger rocks resist air and wind, keeping to a parabola and landing with a speed faster than a bullet train.
Ballistic rocks aren't just falling from the sky — they're being fired at you.
So don't wait to see them before you run. Take cover first.
For how eruptions themselves happen, see "Why do volcanoes erupt?"; for the hidden danger of invisible gas pooling around volcanoes, see "Why shouldn't you enter a 'hollow' near a volcano or hot spring?". For the force of falling rocks on a mountainside, see also "Why are falling rocks on a mountain dangerous even when small?".
- In a yard or park, hold a garden hose near ground level and aim it up at an angle. Slowly change the angle to find where the water reaches furthest. It should be close to 45 degrees.
- Next, keeping the angle at 45 degrees, pinch the hose nozzle slightly to speed up the water. Notice how much further the water reaches than you'd expect.
- Finally, throw a balled-up piece of paper and a small stone of the same size sideways with the same force. You'll find the lighter paper loses to the air and falls short.
※Make sure no one is in the direction you're spraying water. When throwing stones, use a wide open space with no people or windows nearby, and throw gently.
Want to know more? — Terms, formulas, and textbook connectionsFrom middle-school science to university-level courses, each section is labelled by level
- MSCovered in middle-school science
- HSCovered in high-school "Physics Basics / Physics" or "Earth Science"
- HS+Advanced high-school content, or textbook sidebar material
- UnivNot covered in high school — university-level specialist courses (volcanology, fluid dynamics)
- ResearchNot yet settled even at university level — an active research question
MSTerms: this phenomenon has names
- Funseki (ballistic rock): a fragment of rock ejected from the crater during an eruption. Japan's weather agency distinguishes "large ballistic rocks," which fly on a ballistic path unaffected by wind, from "small ballistic rocks," which are carried by wind.
- Phreatic eruption: an eruption where underground water is suddenly turned to steam by heat from magma or similar sources, and the pressure blasts apart ground and rock.
- Eruption warning level: information issued by Japan's weather agency for each volcano, showing on a five-level scale the area requiring caution and the action to take.
MSHSChecking with a formula: how far does a 100 m/s rock travel?
Ignoring air resistance, we calculate the distance and impact speed of a rock launched at 45 degrees. The value with no air resistance is a "rough ceiling" — the actual distance will be shorter.
| In symbols | R = v² × sin(2θ) ÷ g (if θ = 45°, then R = v² ÷ g) |
| In words | Range = (launch speed)² ÷ gravitational acceleration (at 45°) |
| Where it comes from | The rock keeps moving horizontally at constant speed while gravity decelerates and then returns it vertically (a combination of constant-velocity and constant-acceleration motion). Multiplying time in the air by horizontal speed gives the distance |
| Symbol | Meaning and unit |
|---|---|
| R | Range (metres) |
| v | Launch speed (metres per second) |
| θ | Launch angle (measured from the ground) |
| g | Gravitational acceleration (about 9.8 m/s²) |
| Launch speed (estimate for a phreatic eruption) | around 100 m/s |
| Gravitational acceleration | 9.8 m/s² |
| Volume of a 30 cm-diameter rock | about 0.014 m³ |
| Rock density | about 2500 kg per m³ |
| Speed squared | 100 × 100 = 10000 |
| Range R (m) | 10000 ÷ 9.8 ≈ 1020 |
| Speed squared at double speed (200 m/s) | 200 × 200 = 40000 |
| Range at that speed (m) | 40000 ÷ 9.8 ≈ 4082 |
| Weight of a 30 cm-diameter rock (kg) | 0.014 × 2500 = 35 |
| Impact energy (kinetic energy = mass × speed² ÷ 2), first half | 35 × 10000 = 350000 |
| Kinetic energy (joules) | 350000 ÷ 2 = 175000 |
| Impact speed converted to km/h | 100 × 3.6 = 360 |
Doubling the speed stretches the range from about 1 km to about 4 km — exactly four times. The 175,000-joule kinetic energy of a 30 cm rock is about the same as a 1-tonne car hitting something at roughly 67 km/h.
| Time for a 100 m/s rock to reach 1 km away | about 14 seconds |
| Impact speed | about 360 km/h (faster than a bullet train) |
HSHS+Why 45 degrees, and why bigger rocks resist air better
HSThis is the "projectile motion" covered in high-school Physics Basics. Increasing the angle lengthens the time in the air, but reduces the horizontal speed. The product of the two is largest at 45 degrees. Real ballistic rocks fly out in every direction from the crater, so the ones closest to 45 degrees travel furthest.
HS+The air force on a fast-moving rock is "inertial drag," proportional to the square of its speed and to its cross-sectional area. Since weight is proportional to the cube of diameter and cross-sectional area to the square, the ratio of air force to weight is inversely proportional to diameter. At 100 metres per second, air resistance isn't negligible even for a 30 cm rock, so the actual range is shorter than the no-air value. Rocks a metre or more across come closer to the no-air parabola.
UnivHow volcanology actually calculates this
Volcanology finds the trajectory of "ballistic ejecta" by numerically solving the equations of motion including gravity and air resistance. The drag coefficient varies with the "Mach number" (speed divided by the speed of sound) and the rock's shape, and models also account for the fact that, inside the eruption plume, the surrounding air itself is flowing outward from the crater, which can reduce the drag the rock experiences. These calculations, combined with surveys of the size and location of rocks that actually fell, are used to estimate hazard zones around a crater.
📖 For the derivation of the formulas and further detail: Projectile motion (Japanese Wikipedia) ／ Volcanic bombs and ballistic rocks (Japanese Wikipedia)
ResearchWhat's still not fully understood
- Predicting phreatic eruptions in advance. Eruptions not involving magma reportedly give only small precursory signs — such as earthquakes or ground swelling — making it still hard to know in advance when one will happen.
- Estimating launch speed. The speed at which a rock leaves the crater often can't be measured directly, so it's worked out backwards from where it landed and its size. Narrowing that uncertainty remains a challenge.
- How much protection shelters and helmets really give. Experiments are underway to test how well roofs and protective gear can withstand the size and speed of falling rocks.
In other words, this article too only reflects "what's understood so far." Actual hazard zones differ by volcano, so check information from Japan's weather agency and local authorities.
Connections to the curriculum (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| MS | Science Field 1, "Force and Motion" / Field 2, "Volcanoes" | Types of ballistic rocks; faster ones travel further |
| HS | Physics Basics, "Projectile motion" | Range proportional to speed squared, maximum at 45° |
| HS+ | Physics, "Air resistance" | Why bigger rocks are less affected by air |
| Univ | Volcanology / fluid dynamics | Numerical trajectory calculations including air resistance |
| Research | Volcanic disaster prevention | Predicting phreatic eruptions; strength of shelters |
| — | Everyday relevance | Checking information and wearing a helmet before climbing |
- Japan Meteorological Agency (気象庁) — explanation of eruption warning levels
- Wikipedia Japan (ウィキペディア), "Volcanic bombs" (ballistic rocks entry)
- Wikipedia Japan (ウィキペディア), "Projectile motion"
- Cabinet Office, Japan (内閣府) (Disaster Management) — materials on volcanic disaster prevention (guidelines for improving evacuation shelters)
- Fitzgerald, R. H. et al., review on hazard assessment of volcanic ballistic ejecta (published in Journal of Applied Volcanology and similar journals)
※This article is a general-audience science explainer. The figures given are approximations meant to illustrate the underlying mechanism. Actual hazard zones and climbing restrictions vary by volcano. Before climbing, check the eruption warning level from Japan's weather agency and follow the instructions of the agency, local authorities, and on-site staff.