Jet crash math. #maths #learnwithsherlock #edutainment #interesting

Summary

The video estimates the speed and energy of a Learjet 60 crash using footage and GPS data. Its central point is that the aircraft was traveling extremely fast, but that does not mean it vaporized on impact.

Speed estimated from footage

The narrator says the footage runs at 30 frames per second and identifies a frame in which the plane is 441 pixels long. By comparing the plane’s position across consecutive frames, the narrator estimates that it moved about 251 pixels in one frame—roughly 0.57 plane lengths.

At that rate, the plane would travel its own length in about 1.75 frames, or 0.0583 seconds. Using the Learjet 60’s stated length of 17.9 meters, the estimated speed is:

• 307 meters per second
• About 687 mph or 1,105 km/h

Cross-check using GPS data

The narrator says GPS data shows a descent of 9,150 feet in 9.69 seconds, equivalent to about 944 feet per second vertically, or roughly 57,000 feet per minute. The plane was also moving horizontally at about 402 feet per second.

Combining the vertical and horizontal speeds using the Pythagorean theorem gives a total speed of about 1,026 feet per second, or 312.7 meters per second. The narrator says this is within 2% of the estimate from the footage.

Why the plane did not vaporize

The video uses the kinetic-energy formula ½ × mass × velocity² to estimate that the plane had about 47 kilojoules of kinetic energy per kilogram at the estimated speed.

It contrasts this with a stated value of 14,000 kilojoules per kilogram needed to vaporize aluminum, arguing that the aircraft did not have enough energy to vaporize. The narrator suggests the wreckage may appear limited because an aircraft contains substantial empty space, rather than because the whole plane turned to vapor.

Illustrative volume calculation

Using an empty mass of about 6,700 kg and an aluminum density of 2,700 kg per cubic meter, the video estimates that the aircraft’s mass would occupy about 2.48 cubic meters if treated as solid aluminum. That volume would fit in a cube about 1.35 meters (4.4 feet) on each side.

Speakers and sources featured

• Speaker: An unnamed narrator explaining the calculations.
• Sources and data referenced: Crash footage and its frame timing, GPS data, the Learjet 60’s stated dimensions and empty mass, and stated aluminum density and vaporization-energy values.