OK, I found another formula that got me a better result for the test case (Got me within an order of magnitude for human v(t).)
First, the
real surprise is just how dense an aircraft engine
isn't. The mass divided by the volume is slightly less than
0.1g/cm^3! If it were sealed in a plastic bag, it would float 9/10ths out of the water!
OK, takes sense once you think about it, by design, an engine is a mostly air-filled cavity. Boats float with most of their volume out of the water too.
As far as air resistance, one can assume the engine stops working fairly quickly as it falls, so the blades act more as a wall than a passage for airflow. Thus, the engine acts as a solid sphere as far as air resistance goes.
The formula for terminal velocity is:
v_t = \frac{.222 \cdot g \cdot (d_s-d_a) \cdot r^2}{n}
(
reference)
where
g = gravity 9.8m/s
d_s= density of object (.099g/cm^3)
d_a= density of air (.001239g/cm^3)
r is the radius of the "sphere" (210cm)
n is the "dynamic viscosity of air near the Earth's surface" (0.00018 g/cm/s)
I get a number of approximately 50m/s, which is a mere 100 mph.
That provides momentum of 315,000 kg-m/s. That is twice the momentum of a 3000kg car moving at 100mph.
One other factor: the engine is moving downward, not laterally. A house can deform laterally, but it will not deform vertically since the ground is immovable. This would
lessen the amount of damage it would do (since much of the impact would be transferred to the ground)
Conclusion:
I would conclude that a jet engine falling on a house would do amount of damage that is within 1x and 2x the amount that a car hitting it at 100mph would do.
Thus, the effect in the movie is pretty much bang on on the plausibility scale.
P.S. My wife
loves that movie.
