The physics of fairy impacts

Cafe Society
1

How’s that for a title?

Seriously, I do a webcomic and in one scene a fairy is swatted out of the air by one of the big bads. He flies across the room and impacts a wall before dropping to the ground.

Now the artist and I are arguing over how to portray the damage he took. Our own, at least I assume it’s him, Balance and I had a discussion in the comments about it and the physics was fun. But can you all help me out in making a determination.

I’m really not trying to self-promote here. Just to settle an artistic argument.

Anyway, the sequence in question begins here: http://low-forecast.com/?comic=686

2

Laws of physics are the laws of nature. Fairies are supernatural.

You already showed two fairies closing a window with some force while hovering. Why didn’t they get pushed up (they have much less mass than the window) instead of the window going down?

Damage from being swatted and hitting a wall would be unpredictable, and would be narrative-dependent. Whatever damage he sustains, physics is irrelevant.

3

Fairies are rather durable, but do tend to suffer somewhat from high impact. Usually they’re just dazed briefly and somewhat crumpled, but it’s usually temporary. Severe injuries have been known to leave them in a comatose state. But fairies life force is based on peoples belief in them. As long as enough people believe in them, they live. Clapping is a common method of expressing that belief.

4

Well, in terms of the window, the female fairy is later seen using magic to throw a board at the witch. I’ll presume that the issue of the window also features some magic. Sort of like how those wings can allow them to sustain flight.

But the blow and the impact weren’t under the male fairy’s control.

5

I don’t buy the argument that his magical nature means you can’t explain it. You don’t have to, magic or not; it’s your story. But what you seem to have is a collision of a small anthropomorphic flyer with a wall, not that different from if it happened to a bat or a bird or something.

Depends on the velocity, which does not seem well-defined here, but looks to be well below fatal splat range. Remember that small animals are traveling with low mass and thus collide with things with relatively low force. Also, he arced down to near the floor before hitting. He just wasn’t flying all that fast, really.

I’m thinking the worst of it might be some pretty severe wing trauma. How well do those regenerate? And I guess he hit his head or suffered whiplash, so there’s that.

So depending on how you play what looks like neck trauma, and how much wing trauma you think he took, he could end up with any of a variety of short-term and long-term outcomes.

6

Air resistance due to traveling through the air is a function of an objects size.

How quickly it slows down is a function of mass divided by air resistance.

Surface area is going to decrease slower than mass as something gets smaller. So, the smaller something is, the faster it is going to slow down as it moves through the air.

If you wack the crap out of something fairy sized, it is going to slow down pretty fast. So, the force you wack the crap out of the fairy with would probably do more damage to the fairy than the impact with the wall, because the fair will be slowing down quite quickly.

7

That’s getting to it. Alia and I have decided that Newton was knocked unconscious by the blow the witch dealt him. He has no apparent injury other than that from the blow. So the issue there is how much more he would have sustained from the impact. He hit with his back and wings so a severe sprain might be indicated.

Note, though, that it’s not a momentary lack of consciousness. When last we see them he’s still out cold in the nest.

8

Avoid the whole thing by having them eaten when the bird returns to the nest.

9

Oh, suuuure. This thing is just starting to build an audience. You want I should throw that good will away?

10

I think that you should depict the fairy as having been smacked clean through the wall, leaving a perfectly fairy-shaped hole in it. And the edges of the hole should be coated with just a little bit of sparkly fairy dust. The fairy himself would have bits of drywall all over him.

11

Yep, I was the one discussing Newtonian mechanics in the comics. :slight_smile:

My take is still that he would not have taken a whole lot of damage from either the punch or the impact with the wall. He just doesn’t have enough inertia. I’ve been pursuing further calculations (based, admittedly, on some SWAGs concerning heights, since the perspective in the relevant scenes make it hard to judge).

At her age, you’d expect Ellie to be around 5’ tall, but side-by-side shots with her mother suggest that she’s short for her age. Her mother doesn’t seem extraordinarily tall, and Ellie only comes up to her chest. Even if we assume Minerva is pretty tall, Ellie probably isn’t much over 4’. (Supporting this is that Will is significantly taller than Ellie; at age 12, boys average shorter than girls.)

Ellie’s head comes to the halfway point on the window, which is the conveniently about the same height at which the witch’s hand hit Newton. The strike was an upward backhand, so no downward vector was applied by the impact. To err on the conservative side, I’ll assume it imparted no upward vector either. That means that Newton was effectively in free-fall from the instant she hit him.

It appears that he hit the wall only inches above the floor–say, 6" (based on my estimates of Newton’s size elsewhere and Curry’s position in related frames). That means he fell 42" (3.5 ft) between the impacts.

d = 0.5 * g * t[sup]2[/sup]
3.5ft/(0.5 * 32ft/s[sup]2[/sup]) = t[sup]2[/sup]
t=0.47s

Again, to be conservative, let’s say his flight lasted 0.4s. Now we need to figure out how far he flew horizontally. After some measuring, and some more guessing, and some pondering of perspective, and some trig abuse I’m not going to try to reproduce here, I came up with a figure of about 8’ for the width of the room. Nudge it up to 10’ for the worst case, and to be mean to poor Newton.

So, now we can say that he traveled up to 10’ in as little as 0.4s. In that case, his average speed was 25ft/s. (For a point of reference, that’s around half as fast as you would expect Ellie to pitch a softball, if there were enough kids in town to make a team.)

Say Newton is roughly a foot tall; that means you’d have 3.3 Newtons/meter, so his spring constant is 3.3…er, never mind that.

Ahem. The point is, Newton is not hitting the wall all that fast, and he has very little momentum–only ~25 foot-pounds/second. Think of an adolescent casually lobbing a small beanbag at the wall. If he’d hit a person instead of a wall, he probably wouldn’t even have bruised them.

As for visible injuries–he might form visible bruising on his chest, centered where the witch’s knuckle hit. (With her hand open like that, it’s unlikely that more than one finger actually connected.) Probably no bruising on his back. Maybe a small bump on the back of his head, if that hit first, but my guess would be that his unconsciousness is actually the result of the initial strike hitting him at an angle that torqued his little brain around in his skull, the way a cross to the jaw can knock out a human.

My recommended depiction would be a sort of finger-shaped bruise on his chest and a really sore jaw that makes it hard for him to talk for a while.

12

I would say do whatever makes your artist happy.

13

Model them after a badminton shuttle. Moves fast when first hit, slows down quickly.

14

God, I love the Straight Dope. I truly do.

Tentatively, for art’s sake, Alia will give him some minor bandages. I have proposed that Curry nurse him with Hummingbird Noodle Soup. She seems to think that’s idiotic, or at least worthy of ignoring.

15

It is idiotic (sorry), but it could be used to have consequences along the lines of changing the way he flies…

16

That’s what started the discussion. What would be the changes in Newton’s abilities/attitudes based on his injuries?

17

Well, you sort of have to start backwards I think. Decide what consequences do you want, then stick bandages or hummingbird jokes in appropriate places.

18

Thats the analogy was I was also going to use in my first post but was too lazy to type. Compare how a baseball, a tennis ball, and a badminton behave when you give em a good knock. They have progessively lower mass to size ratios. The baseball keeps up a good speed for a while. A tennis ball less so. A badminton slows down pretty fast and in a pretty short distance.

A fairy is going to probably be a bit slower still than a badminton, depending on its size ( I am thinking of the pretty small fairies here myself).

Assuming its a human doing the wacking, the OP can take a badminton and throw it against a wall 10 feet away as hard as he can and get a good idea of how hard the fairy will hit the wall (or toss it up and swat it with his hand).

19

Cracked ribs would be plausible, and would account for bandages around his chest. They’d probably also make flying prohibitively painful for a while.

If he’s got broken bones, she ought to be making sure he gets plenty of calcium. You could have Key spot her carrying an absurdly outsized soup bone. (If she tells him Newton is going to eat it, he might abruptly reassess his position vis-à-vis fairies.) :smiley:

20

You might get some ideas from Lady Cottington’s Pressed Fairy Book. :slight_smile: