# The Assault capabilities of projectile Brussels Sprouts

This was a subject of some dispute at the dinner table last night.

“If a brussels sprout were dropped on you from a great height, could it kill you?”

I say not, since I believe that the sprout’s terminal velocity would be well short of the velocity which would make it … well, terminal.

This was then countered with:

“What if it was dropped on you from orbit. At great speed. Like, a significant percentage of c”

To which I counter that then the sprout would undoubtedly burn up in the atmosphere before it got anywhere near your head.

“Ahh, but if it were travelling at a REALLY significant fraction of c, then it wouldn’t have time to burn up before it got you.”

I thought I would throw this over to the Teeming Millions. Is Projectile Sproutocution theoretically possible? What would it take in terms of setup?

(Don’t need answer fast. We already bit the bullet and just ate the damn things)

it really doesnt have enough mass to do anything, similar things have come up on mythbusters with falling objects.

The other questions involve too much thinking… but if one was to come from space maybe it would confirm my brothers opinion that sprouts are 'Martian’s balls".

If it’s moving close to the speed of light all you’ll get is a thermonuclear explosion in the upper atmosphere. It still won’t make it down to where you’re standing.

Part of the problem is the weight and speed - part of the problem is “solidity”.

If you are hit by a rock, there is no “give”. The entire momentum of the rock is imparted to the point of contact.

Get your kids to try this simple experiment - drop a golf ball on their head from 5 feet up, then a mushy brussel sprout. Repeat from 10 feet up. Get them to explain why the golf ball hurts more, even though the weight is not that much different. (Add a 1-inch soldi metal ball bearing if they claim weight is the issue…)

Basically, the entire momentum of the golf ball is transferred to to point of contact. A golf ball may be about an inch and a half across, but the contact point is about a quarter inch or less, depending on skull hardness. (That can be tested with a ball-peen hammer ) A sprout, OTOH, you do not absorb all the momentum in an instant. The part that first hits you stops. The parts around it keep going until they hit your head too. The center and top keep going - since the way down is blocked, they deflect outward - hence… splat!! Some of the terminal velocity is transformed into diagonal or horizontal velocity, not all the momentum is cranially absorbed.

Then there’s the question of terminal velocity. An object that falls accelerates until wind resistance balances the force of gravity. For humans, terminal velocity is about 100mph. Terminal velocity depends on weight and the cross-sectional area presented to the wind, so in some way it’s related to density.

If you want to experiment with terminal velocity, video dropping various objects from a tall apartment building, and count the frames to the bottom to get a drop time within 1/30 second. Leave before the police arrive.

Otoh, baseballs and hockey pucks travel at about 90mph to 100mph in the best moments of the game. I doubt brussel sprouts terminal velocity is faster. However, while you don’t want to be beaned by a pitch or slapshot, the damage is bad but not in-your-head-and-out-the-ther-side bad.

There’s the story about how Boeing was testing aircraft windshield resistance to bird strikes. They built an air cannon and would shoot chickens from the grocery store (the humane way to do it) at the windshields are aircraft speeds. The <insert favourite minority> Aircraft Company decided to do the same tests, but kept breaking windows no matter how slow they flung the chickens. They asked Boeing for advice, and a tech came over to watch and said “thaw the chickens first”.

The very first “What If”, a new feature of XKCD:

What would happen if you tried to hit a baseball pitched at 90% the speed of light?

Terminal velocity is about area vs volume.

If a person lies flat on the ground, they are about 6 inches thick generally give or take, so 6 cubic inches of meat - which would be about the same weight as water - for every square inch making wind resistance. If they fall vertically, feet first or head first, the area-vs-volume ratio is even higher. A boiled brussel sprout is also about the same weight as water - but there’s probably about only 1 cubic inch per square inch of sprout, if even that.

Terminal velocity of a brussel sprout is probably quite low.

Only if it was in the belly of a goat shot out of a PVC cannon.

Here’s what happens when a small but significant mass travelling 90% of the speed of light approaches earth…

As it starts getting near the atmosphere, it starts hitting atoms of atmosphere, mainly, nitrogen and oxygen. These are floating free, getting thinner and thinner up to, let’s say, about 200 miles or more. (Remember Skylab was brought down in a matter of what, 6 years, from a 270mi high orbit, by “wind resistance”).

consider a collision between our RSBS and an atom of nitrogen. The collision should be perfectly elastic - the atom bounces off with about the speed of the RSBS and the RSBS slows down because it loses the momentum it imparts to the atom (really, not much- but real). That collision jars the mass of the RSBS creating heat. Now, the density is rising to say, 1/1000 the sea level atmosphere; the RSBS hits millions of atoms every meter it travels. Each imparts a bit of heat and slows it down.

Next, consider the atoms that are hit and bounce off. They travel until they hit another atom, and there is another collision. The second atom bounces away from the RSBS at the speed of the first atom, and the first atom stops dead - only to be hit again by the RSBS, bounce again, slow and heat the RSBS.

While the density is effectively zero up there compared to sea level, it is enough to have an effect.

What precisely is air pressure? 14.7psi at sea level means that there is a column of air above every point on earth such that a square inch times the distance to the edge of the atmosphere weighs 14.7 lb. What does a brussel sprout weigh? 1 or two ounces? By the time it gets close to the denser atmosphere it is already trying to ush out of the way far more than its own mass; basically it will come to a dead stop, and all that energy will be transofrmed into heat of the sprout itself and the air around it. Hence, the massive explosion.

If you want to kill someone with a brussel sprout, just have him eat one that my mother cooked.

One thing to consider in regards to hypervelocity brussel sprouts: Air resistance is based on the square of the velocity. So… if a sprout will burn up in the atmosphere at speed x, then it will burn up four times faster at speed 2x, and nine times faster at speed 3x. So, damage would increase with velocity only as long as the sprout is not burning up - once it starts burning up, increases in speed reduce it’s penetration.

(All said with a caveat that hypervelocity brussel sprouts are surely pushing the limits of simple air resistance equations.)

Yeah, I think the arguments in favour of the high altitude thermonuclear explosion have convinced me. Of course, you have to imagine that this in itself would have to be pretty unfortunate for the person standing directly underneath …

I think the formula is E=(mv^2)/2 for Newtonian caluations. (It’s been years since I did this.)

For v=.9c i think it requires the factor 1/SQRT(1-(v^2/c^2)) to account for relativistic apparent increase in mass.

1/SQRT(1-(.9)^2) = 2.294

E=(1/2)(2.294)(.81)(c^2) = 8.36x10^16 Joules