Comic for August 1,2020: Saved by the Spy

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Re: Comic for August 1,2020:Saved by the Spy

#16 Post by Technic[Bot] »

MuonNeutrino wrote: Mon Aug 03, 2020 12:06 am -Physics snip-
First i want to start saying that indeed. Biomechanics problems are really complicated as humans, and animals for that matter have too many moving parts and the relationship between forces and linkages is non-linear and does not have, most of the time. A closed form solution.
That being said I think you are over complicating the problem here Mr Moun.

As you point out drag is dependent on the object velocity squared, but also with the object shape, surface and interface. Normally an object and the medium, water in this case stay constant across a experiment but in this case Maddie is slowly getting out of water. So her contact surface is not constant. Hence this is a time-variant problem. Alas I doubt there is enough water, or speed for that matter, to have a significant effect on the mechanics of the situation. I think the friction between Maddie's lower body and the edge of the "pool" is more important, i think even the buoyancy has more effect on this than water drag which in any case would help Maddie not get pulled out of the pool as it works by opposing relative motion.

In this case we can simplify the issue, we can without loss of much precision, consider both Maddie and Karen as rigid bodies operating under the same relative plane. So we can reduce this to a two-dimensional problem, far easier than a general bio mechanics 3D problem.
The point of maximum torque is when Karen is perpendicular to the wall, as the distance is maximum to the fulcrum, her foot. If Maddie can generate enough force to pull her from that position she will be able to pull it from any other. The only forces on Karen are then Maddie's pull, her weight the normal from the wall and the friction. From there is is relatively issue to compute the strength on Maddie's arm by assuming equilibrium at that configuration by summing torque at Karen feet. This also allows us to compute the angle she is pulling from:

Code: Select all

 
 F =  m g x_l / (sin (a) (x_l + x_a)
 a = arctan(x_l mu / x_a)
 
Where F is the strength exerted on Maddie's arm a the angle she is pulling from, x_l the length from Karen center of gravity to her feet and x_a is the length from her center of gravity to her shoulder and mu is the friction coefficient between here feet and the wall.
Even if you ignore my assumption of a horizontal Maddies since we have the picture is is trivial, although a bit time consuming. To compute the angles required. After all we know Karen height and there is negligible effect on perspective here so using pixel measurements you can obtain a metric representation of the whole scene.
This approach does ignore the inertia Karen had at the beginning but i think it is small enough to ignore. Besides if we include that then this turn into a dynamic problem which is much harder to model and solve.

Finally as Mr Bell points out even if Maddies is not strong enough to pull Karen all she had to do is to bend her knees. Lay flat on the wall and there is no torque anymore Maddie only needs to pull her up.
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Re: Comic for August 1,2020:Saved by the Spy

#17 Post by MuonNeutrino »

Bellhead wrote: Mon Aug 03, 2020 1:05 am
MuonNeutrino wrote: Mon Aug 03, 2020 12:06 am
Bellhead wrote: Sun Aug 02, 2020 8:15 am Physics
More physics
Yet more physics
Entirely possible I suppose. I was assuming that one could treat Maddie and Karen as rigid bodies, but that was likely a mistake as you're correct that bodies are better represented as linkages. *Some* part of Maddie has to rotate CCW, but it's true that it doesn't necessarily have to be *all* of her. And once she's bent far enough that the pulling force is acting through the pivot point there won't be any net torque from that. There's still the net CCW torque from her weight (since her top half will have more mass than her legs), but if that causes her to rotate a little bit more then that'll just put the pulling force *below* the pivot point which makes its torque CW instead. As you point out, the trickier part is likely having enough strength to fling her over her head that way, but that much can be put down to comic book and/or basitin physics. :grin:
Technic[Bot] wrote: Mon Aug 03, 2020 1:45 amEven more physics
I agree that I don't think the water would have enough drag to do it. (And yeah the buoyancy would also screw things up.) I did some very ballpark back of the envelope calculations and was coming up with drag forces much too low to do anything with reasonable speeds and forces, especially given that the drag force's lever arm isn't that long and that Maddie's moment of inertia is way lower than Karen's in these poses. I just wouldn't be able to more rigorously prove it without doing a lot more work than I want to bother with, heh. :grin:

I did implicitly reduce it to a 2-d problem in my treatment, as noted the issue was treating them as rigid bodies. The problem isn't necessarily *Karen's* movement, though; I was already assuming that Maddie could generate enough force to at least hold her up just on a 'basitin are strong' basis. The problem is more that there isn't any real force to hold *Maddie* in place while she pulls, at least under the assumption of a rigid body. Her hips in contact with the pool edge can't exert a torque since any force there is acting through the pivot point and so has no lever arm, and there isn't going to be any friction between her legs and the pool wall since they're going to be rotated away from the wall. If you treat them both as rigid bodies the conclusion that Maddie has to rotate CCW is pretty sound I think.
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Re: Comic for August 1,2020: Saved by the Spy

#18 Post by Kyrit »

Maddie thinks you're all thinking to much about physics, which she enjoys actively defying. I recall there being much debate when she pulled off this stunt.

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Re: Comic for August 1,2020: Saved by the Spy

#19 Post by Yastreb »

Duh, Maddie is obivously wearing boots made of solid osmium. Standard spy equipment.

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Re: Comic for August 1,2020: Saved by the Spy

#20 Post by Emp_Dragon »

Yastreb wrote: Mon Aug 03, 2020 3:38 pm Duh, Maddie is obivously wearing boots made of solid osmium. Standard spy equipment.
Or just boots that can form a magnetic or vacuum seal against any surface.
;)
As for the physics part, I would suspect that pool is no more than sitting depth as in about 40 to 50cm of water along the edges with submerged sitting ledges or benches.
If the pool has submerged benches rather than a stepped ledge construction, it would be completely possible for Maddie to brace her hips and knees against the pool wall and her clawed feet against the submerged bench.

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Re: Comic for August 1,2020:Saved by the Spy

#21 Post by Ddraig »

MuonNeutrino wrote: Mon Aug 03, 2020 12:06 am
Bellhead wrote: Sun Aug 02, 2020 8:15 am I think you're mis-estimating where Maddie's getting her leverage from. Assuming she had just hit the water in panel 2 and was still moving slightly forward, she would have come to the point where her hips hit the glass at the end of the pool. Given that Karen is below that point, she could hold them both up fairly easily just by holding on and not letting her hips straighten out.

Pull hard enough with her arms at that point, and Karen would whip right around, pivoting on her own feet, landing pretty much right where Maddie started. And that could be done with a feat of Basitin strength, regardless of size.
The problem is that Maddie in this case doesn't have a purchase point. She's not holding *on* to anything except Karen, and that means that it doesn't matter how strong she is - the laws of mechanics are merciless, strength by itself isn't magic and without a purchase point all that being stronger does is let you pull *yourself* forward just as hard as you pull someone *else* backward. Due to Newton's laws, without a purchase point flipping someone backwards over your head also means flipping yourself forwards. Or, at least, at first glance. Thinking about this more carefully, the complicating factor is actually the presence of the water, which *might* let her pull this off but is *extremely* tricky to model.

I'm going to put on my physics teacher hat for a moment here, because the best way to explain this is with a free body diagram.
Spoiler!
Image
Since neither Karen or Maddie are holding on to anything except each other, both of them can be more or less treated as free bodies subject to only a few forces. And what we're mostly interested in here is rotation, so we're really looking for the torques around various pivot points and can neglect the support forces that only act *through* those pivot points. The light blue arrows represent the gravity force on each of them, which are roughly equal in magnitude (since they both weigh about 100 lb) and act downward through their center of masses (which are more or less somewhere in their torsos - exact locations aren't important). The purple arrows represent the forces they exert on each other through their grips, which are by definition equal and opposite due to Newton's 3rd law. The blue and red lines represent the lever arms of each force around their respective pivot points (her foot touching the wall for Karen and her hips touching the edge of the pool for Maddie), the green line outlines the rough position of Maddie's legs since we can't see them, and lastly the yellow lines represent forces between Maddie's legs and the water that I'll talk about in a moment.

The key question here is what the sum of the torques looks like on Maddie, but to figure that out we also have to consider Karen as well. A notable point is that her weight is acting pretty far from the pivot point, so it's exerting a large CCW torque. Maddie's pulling force is also pretty far from the pivot point, though, so it's also exerting a large CW torque. For her to not fall, those torques must be equal, so since the lever arms are roughly equal Maddie is likely pulling her with a force roughly equivalent to her body weight (i.e. pretty hard).

Moving on to Maddie, there are two obvious torques acting on her. First, the torque from the reaction force from her pulling on Karen, which is acting CCW with a pretty strong force and a relatively long lever arm and so exerting a pretty large CCW torque. Second, the torque from her weight, which is actually *also* going to be CCW because she's leaning out and so putting her center of mass beyond the pivot point. This torque is going to be smaller because its lever arm is shorter, but it's still an additional CCW torque. For Maddie to not rotate CCW (i.e. flip forward over the edge of the pool) there must be an equally large CW torque acting on her from somewhere. There are no other forces acting on the top half of her body, so if there's another torque it must come from her legs somewhere, and this is where the question of a purchase point becomes important.

If Maddie were able to brace her feet against something solid, she could exert a backwards force on it with her feet and so have it exert an equal forwards force on her by newton's 3rd law to provide a CW torque. The size of that force (and hence CW torque) would depend on how hard she pushed on it, so her strength would come into play and if she could push hard enough she could balance the CCW torques she's experiencing and not fall. However, Maddie is not bracing her feet against anything - she's hanging at her waist over the side of the pool (which we know is deep enough at the end to come up to at least mid-torso on several characters), so her legs aren't touching anything except the water and the pool wall. Thus, it doesn't actually *matter* how strong she is, because there's nothing for her to exert a force *on*.
[snip]
Personally, I think it's just possible from an estimation standpoint. I mostly agree, but have three counterpoints to your analysis:
The first is that on a female human the center of mass (CoM) is around the hips. That's why the 'pick up a stool' trick works. A Basitin's tail is going to pull that CoM even lower. This puts Maddie's CoM very close to the pool edge (aka the pivot point) or maybe below it, making it harder for lateral inertia to be converted into rotational inertia (because less of it will want to directly aid rotation; if Maddie's CoM is below the pivot point, some of it will even oppose rotation)

The second is that Karen's inertia at the point of the image is largely horizontal, and will not directly contribute to rotation because it's not terribly close to perpendicular to the radial from either Maddie's CoM or the pivot point ('radial' as in a line drawn directly out from either the pivot point or the Center of Mass) because F(rot)=F(pull)*DistFromCenter*sin(angle). That sin(angle) term make it primarily a pulling force and not a spinning force. There is a spinning component still that has to be counteracted somewhere, though, which bring me to my third counterpoint:

The pool appears to have a seating ledge running around the outside judging by how Sythe is positioned. This would give Maddie something to grip with her feet (a function of weight and the vertical component of Karen's pull on Maddie).
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Re: Comic for August 1,2020: Saved by the Spy

#22 Post by steelabjur »

Maddie is 4'10" (147 cm) and weighs 102 lbs (46 kg). Karen is 5'2" (157 cm) and 100 lbs (45 kg), both sets of numbers taken from their Character Ref sheets. If we're going to talk physics, we might as well get actual numbers in here.

As far as there being a ledge for Maddie to brace against, yeah we get a pretty good look at it here, probably made of glass from the look of it.

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Re: Comic for August 1,2020:Saved by the Spy

#23 Post by Technic[Bot] »

MuonNeutrino wrote: Mon Aug 03, 2020 5:32 am I agree that I don't think the water would have enough drag to do it. (And yeah the buoyancy would also screw things up.) I did some very ballpark back of the envelope calculations and was coming up with drag forces much too low to do anything with reasonable speeds and forces, especially given that the drag force's lever arm isn't that long and that Maddie's moment of inertia is way lower than Karen's in these poses. I just wouldn't be able to more rigorously prove it without doing a lot more work than I want to bother with, heh. :grin:

I did implicitly reduce it to a 2-d problem in my treatment, as noted the issue was treating them as rigid bodies. The problem isn't necessarily *Karen's* movement, though; I was already assuming that Maddie could generate enough force to at least hold her up just on a 'basitin are strong' basis. The problem is more that there isn't any real force to hold *Maddie* in place while she pulls, at least under the assumption of a rigid body. Her hips in contact with the pool edge can't exert a torque since any force there is acting through the pivot point and so has no lever arm, and there isn't going to be any friction between her legs and the pool wall since they're going to be rotated away from the wall. If you treat them both as rigid bodies the conclusion that Maddie has to rotate CCW is pretty sound I think.
Yeah I did ignore Maddie in my calculations but you are totally correct. Unless she can get some leverage under her feet not matter how strong she is she is gonna start spining as the is no force to balance out the torques.
steelabjur wrote: Tue Aug 04, 2020 1:08 am Maddie is 4'10" (147 cm) and weighs 102 lbs (46 kg). Karen is 5'2" (157 cm) and 100 lbs (45 kg), both sets of numbers taken from their Character Ref sheets. If we're going to talk physics, we might as well get actual numbers in here.

As far as there being a ledge for Maddie to brace against, yeah we get a pretty good look at it here, probably made of glass from the look of it.
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Re: Comic for August 1,2020:Saved by the Spy

#24 Post by Bellhead »

Technic[Bot] wrote: Tue Aug 04, 2020 2:58 am Yeah I did ignore Maddie in my calculations but you are totally correct. Unless she can get some leverage under her feet not matter how strong she is she is gonna start spining as the is no force to balance out the torques.
That was precisely the main focus behind my theory.

As Muon described far more elegantly than I managed to, we can think of Maddie as a lockable linkage rather than a rigid body. In such a case, she would end up at roughly the same angle she started at. If she straightened her arms away from her torso and locked her hips at an acute angle against the top of the glass, the moment of force Karen creates against Maddie's pivot point is essentially zero, which nullifies any effect angular momentum would have on her, regardless of speed, direction, or initial angular momentum at the start on the scenario.

She'd be, physically speaking, acting as a grappling hook. After Karen stopped falling, pulling her directly toward Maddie's pivot point (no leverage required, just strength) would cause her to flip upward just like we see here.
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Re: Comic for August 1,2020: Saved by the Spy

#25 Post by Techdragon »

So did anyone else notice that Karen's swimsuit changed color from purple in the previous strip to green in the first panel of this one, and then the straps went back to purple in panel 4?

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Re: Comic for August 1,2020: Saved by the Spy

#26 Post by Ville Saari »

Maddie is not a rag doll with freely articulating joints. She has muscles and probably pretty strong ones compared to a same size human. If you imagine Karen hanging from the pool edge by holding a Maddie shaped rigid hook, the situation turns perfectly stable.

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Re: Comic for August 1,2020: Saved by the Spy

#27 Post by Ville Saari »

Techdragon wrote: Tue Aug 04, 2020 8:04 am So did anyone else notice that Karen's swimsuit changed color from purple in the previous strip to green in the first panel of this one, and then the straps went back to purple in panel 4?
Re-read the entire oasis room section and you won't find her bikini the same color in two consecutive panels ;)

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Re: Comic for August 1,2020: Saved by the Spy

#28 Post by TheMasterOfOats »

Ville Saari wrote: Tue Aug 04, 2020 10:47 am
Techdragon wrote: Tue Aug 04, 2020 8:04 am So did anyone else notice that Karen's swimsuit changed color from purple in the previous strip to green in the first panel of this one, and then the straps went back to purple in panel 4?
Re-read the entire oasis room section and you won't find her bikini the same color in two consecutive panels ;)
Yeah, I saw that and was like "Is she wearing a rave bikini?"
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Re: Comic for August 1,2020: Saved by the Spy

#29 Post by James Polymer »

TheMasterOfOats wrote: Tue Aug 04, 2020 8:38 pm Yeah, I saw that and was like "Is she wearing a rave bikini?"
It could be. There's much we don't know about magic in this world; there could be articles of clothing enchanted to change color to match anything paired with them, or simply have them shift through the entire color spectrum at random. Having a color-coded outfit that changed shades every ten minutes would be a wonderfully garish way of showing off one's wealth.
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Re: Comic for August 1,2020: Saved by the Spy

#30 Post by Bellhead »

James Polymer wrote: Wed Aug 05, 2020 6:37 pm
TheMasterOfOats wrote: Tue Aug 04, 2020 8:38 pm Yeah, I saw that and was like "Is she wearing a rave bikini?"
It could be. There's much we don't know about magic in this world; there could be articles of clothing enchanted to change color to match anything paired with them, or simply have them shift through the entire color spectrum at random. Having a color-coded outfit that changed shades every ten minutes would be a wonderfully garish way of showing off one's wealth.
Most certainly. Don't know if that's what's happening here, but it would make a LOT of sense. Mana crystals are likely fairly expensive, and having them woven into fabric would be quite the expression of "I have money to burn". Could also be that Rose just felt like making something for the energetic childish Karen just because 'why not'.
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