Downtown Chicago just got a little scarier. Besides the latest Loop rapist, now you can also be assaulted by inanimate objects.

Last week three Loop buildings hurled bricks and glass at the ground over a four-day period: 201 N. Wells spewed bricks from its 25th floor, 212 W. Van Buren followed suit, and 333 W. Wacker rained glass from its 31st floor. The only victims this time were three parked cars, but who can forget the hapless Wisconsin man cut down last winter by a killer slab of ice from the Neiman Marcus building?

Skyscrapers can turn relatively benign objects into dangerous projectiles (just as the proposed space station could be nearly blown apart by an orbiting space pebble because of the huge speeds involved). So what injury do we risk from being beaned by a construction worker’s fumbled lunchtime Twinkie or an office worker’s off-course paper airplane?

I asked Dr. David Slavsky, Loyola University’s assistant dean for mathematical and natural sciences (though you may know him better as WBEZ’s science expert), and Dr. James Kelly, director of the Rehabilitation Institute of Chicago’s brain-injury program.

“Ultimately what you’re concerned about is the force that’s generated when object hits skull,” says Slavsky. “You’ve got an object that’s falling, so it has momentum. It falls on your head. Your head will exert a force on that object to change its momentum. Conversely, that object exerts an equal and opposite force on your head. So ultimately what determines the amount of force is how much momentum that object had just before it hit you and–now this is the real tricky part–the time in which that momentum was brought to zero.”

Slavsky explained the tricky part with an example. Say you’re hit by both a one-kilogram lead ball and a one-kilogram beanbag. If they’re traveling at the same speed then they have the same momentum, which is mass times velocity.

“Which is gonna hurt more?” asked Slavsky. “Lead ball. Yet they have exactly the same momentum. The reason is the beanbag will deform around your head and the collision time is longer. In the collision of a head ball and your head the collision time is very rapid, because the lead ball is pretty nondeformable and your head is–kind of nondeformable, but will [deform] in this case. And so the amount of force in that [lead ball] will be sufficient to”–he paused–“challenge the structural integrity of your skull.”

Slavsky good-naturedly agreed to simplify his equations enough to approximate the forces pedestrians face from a variety of falling objects, and Dr. Kelly agreed to estimate likely injuries. We settled on a Twinkie and a Quarter Pounder, both possible missiles from the fumbling construction worker’s lunch; a paper airplane and a stapler from the irresponsible office worker; a brick; baseball; and a person, because 11 people have already jumped to their deaths in Cook County this year.

We assumed they would all be flung (or they’d jump) from the top of the Sears Tower. (Though the results would stand if the objects were dropped from any 30th floor, about the height needed to achieve terminal, or ultimate, velocity.)

“I have no idea how accurate these numbers are, but they’re close,” Slavsky warned. “I did some really sophisticated experiments, dropping baseballs and various things on my bathroom scale, watching how much they jumped, and trying to figure out from that the time of impact.”

“I want you to know that I get $300 a day for consulting on serious stuff!” he said, giggling. “Here I am calculating a Twinkie impact time.”

Projectile: Baseball

Dr. Slavsky’s Scientific Assumptions: “Baseballs deform a lot when you hit ’em.”

Force: 1,000-2,000 newtons (220-440 lbs)

Likely Injury: Linear skull fracture, concussion

Dr. Kelly’s Medical Comments: “This could include not just a brief loss of consciousness, but also a period of confusion or disorientation.”

Projectile: 5-pound brick

Dr. Slavsky’s Scientific Assumptions: “I’m calculating that the impact time of a brick will be at least as short as a baseball, probably even shorter.”

Force: 15,000 newtons (3,300 lbs)

Likely Injury: Death, depressed skull fracture, serious brain injury

Dr. Kelly’s Medical Comments: “Hard hats, as good as they are and as much as I advocate them, aren’t intended to stop bricks at terminal velocity.”

Projectile: Quarter Pounder

Dr. Slavsky’s Scientific Assumptions: “If it’s a Quarter Pounder of death we gotta tape the lid down, otherwise it’ll fly open and really slow it down.”

Force: 10-100 newtons (2-20 lbs)

Likely Injury: Headache

Dr. Kelly’s Medical Comments: “I recommend the usual headache remedies. Tylenol would probably be the best approach under the circumstances. You don’t want to use medications that are going to cause a potential for more bleeding, like aspirin or ibuprofen.”

Projectile: Twinkie

Dr. Slavsky’s Scientific Assumptions: “It’s going to have about the aerodynamic properties of a brick….[The force] is on the order of a Quarter Pounder, only because it has a lot less surface area. This is assuming the Twinkie hits broadside down. It could really haul if it comes down longways.”

Force: 10-100 newtons (2-20 lbs)

Likely Injury: Headache

Dr. Kelly’s Medical Comments: See “Quarter Pounder.”

Projectile: 150-lb person, falling spread-eagle

Dr. Slavsky’s Scientific Assumptions: “The human body is goping to deform more than a brick….I did not do experiments dropping people spread-eagle on my bathroom scale.”

Force: 36,000 newtons (8,000 lbs)

Likely Injury: Fractured neck, severed spinal cord, concussion

Dr. Kelly’s Medical Comments: This assumes “a top-end blow of a blunt heavy force like a person’s chest hitting the head of a person walking upright down the street.”

Projectile: Paper airplane

Dr. Slavsky’s Scientific Assumptions: “The biggest danger from a paper airplane is that if it hits you point side first it could take your eye out.”

Force: Negligible

Likely Injury: No head injury; could take eye out

Dr. Kelly’s Medical Comments: “It could also [take an eye out] at a football stadium where you have paper airplanes floating around. It could catch the wind so it turns around and comes back right into someone’s eye.”

Projectile: Stapler

Dr. Slavsky’s Scientific Assumptions: “Say you put a little weight on one end to make sure it falls [vertically]–a real stapler of death. I’ve got that it’ll go five times faster than your average baseball.”

Force: 5,000 newtons (1,100 lbs)

Likely Injury: Depressed skull fracture, stapler could get stuck in head.

Dr. Kelly’s Medical Comments: “By the way, if something penetrates the head it’s left in–and removed after images are taken of what’s there and the surgeons are ready to deal with the consequences of taking it out.”

Art accompanying story in printed newspaper (not available in this archive): illustration/Slug Signorino.