Rodrigo Afonso

WHAT HAPPENS WHEN A 20,000-POUND LEARJET SLAMS INTO THE GROUND AT HUNDREDS OF MILES PER HOUR? Many people have been fascinated by the enormous crater left behind after the Learjet 60 crashed in Palm Beach County, Florida. Others doubt an aircraft could produce such destruction. But consider the physics. A Learjet 60 weighing approximately 20,000 pounds, descending at an extraordinarily steep angle at a speed potentially exceeding 600 mph, strikes asphalt and compacted soil. In a fraction of a second, an enormous amount of kinetic energy must be dissipated. The aircraft’s structure is violently crushed and fragmented. Some energy goes into deforming and accelerating the wreckage, but a substantial amount is transferred into the pavement and underlying soil, crushing, displacing and ejecting material to form an impact crater. Fuel released during the impact ignites, producing an enormous fireball. Wreckage is thrown outward. Other pieces separated before the aircraft reached the ground. The NTSB recovered pieces of the left elevator 1.3 to 3.8 miles from the crater. Residents found debris nearby. Tragically, human remains were also recovered. An intact aircraft at the bottom of the crater would be surprising. This animation illustrates the physics of a high-speed aircraft impact, including kinetic energy, deceleration, impact forces, ground pressure and crater formation. It’s worth watching. MY REVIEW OF THE PHYSICS AND MATHEMATICS I reviewed the calculations in this video. The principal mathematical calculations check out, and the overall explanation is consistent with established physics. However, several figures deserve clarification. Impact speed: The video uses a descent rate of 251 m/s and a horizontal speed of 123 m/s, giving about 280 m/s (626 mph). Published ADS-B data shows descent rates exceeding 30,000 ft/min. One analysis estimates a total speed of about 490 mph near 10,000 feet, although the aircraft’s velocity could have changed substantially before impact. The impact velocity remains unverified. Kinetic energy: A mass of 9,000 kg (about 19,800 pounds) at 280 m/s gives about 353 million joules. At 490 mph, it would be about 216 million joules. Still enormous. Stopping distance: The video assumes about 18 meters, roughly the length of the aircraft, giving an average deceleration of about 220 g. The math is correct, but the stopping distance is an assumption. Impact force: About 20 million newtons follows from those assumptions. This is a simplified average. Actual forces varied enormously as the aircraft fragmented and penetrated the ground. Ground pressure: The video assumes a contact area of about 3 square meters, giving roughly 6.5 million pascals. It compares that with typical allowable soil bearing pressures of a few hundred thousand pascals. But those values include safety margins and aren’t directly comparable to a dynamic impact. The calculation is illustrative, not a measurement. A FEW OTHER NITPICKS: A broken water main reportedly helped fill the crater, so it wasn’t all groundwater. The animated aircraft reaches the ground with its tail intact, even though the video itself says tail parts separated before impact. THE BOTTOM LINE The exact impact conditions remain uncertain, and this animation is not a forensic reconstruction of the accident. Nevertheless, its central explanation is physically sound. An aircraft carrying hundreds of millions of joules of kinetic energy into the ground can produce catastrophic fragmentation, tremendous ground deformation and an extensive debris field. For those who insist an aircraft couldn’t possibly create this crater or leave so little recognizable wreckage, this video provides a compelling illustration of the physics involved. There is nothing mysterious about the basic principles. The precise details of this accident remain a matter for the NTSB.