Comic for August 1,2020: Saved by the Spy

[Rafe]

What is Maddie doing here?
Looking for male nudity, I'd say. Last time we saw her (http://twokinds.keenspot.com/comic/1087/) she was shocked by what she glimpsed looking from the door. I guess her curiosity won out over her Basitin morality.

[Bellhead]

Welp, Karen's safe. We can all breathe just a little bit easier.

But where was she that she got to that edge of the pool before Karen was out of reach? If the illusion was only for Karen, I could kinda see it, but if not, Maddie would have had to have been underwater right behind her. Then again, she's not even wearing a swim suit, so I think she just saw that Karen was heading for the edge.

And judging by the splashes near her, I'd wager she just ran down the edge and jumped in at the right moment. Probably was looking at guys, though.

[Rafe]

It's possible she's been lurking around the doorway/waterfall area for a while. Staying nearly invisible is one of her great talents, after all.

That thought (and the way she seemed to be eyeing Sythe in her last appearance), makes me wonder if she was listening in on Sythe hitting on Maren. She would have known that what Karen was seeing wasn't Maren, but now she'll have to explain why she knows that.

[Technic[Bot]]

Welp, Karen's safe. We can all breathe just a little bit easier.

But where was she that she got to that edge of the pool before Karen was out of reach? If the illusion was only for Karen, I could kinda see it, but if not, Maddie would have had to have been underwater right behind her. Then again, she's not even wearing a swim suit, so I think she just saw that Karen was heading for the edge.

And judging by the splashes near her, I'd wager she just ran down the edge and jumped in at the right moment. Probably was looking at guys, though.

I imagine she was underwater. Which considering how long the party and subsequent siege took she has some amazing lungs.
Also despite her curiosity getting the better of her morality i doubt she would be comfortable wearing anything more reveling than shorts and a shirt.

[Cosmacelf]

Tom's going to keep the suspense up as long as possible, isn't he?

[SomeBody]

Wasn't there a snorkel in an earlier scene?

[Eclipse]

Busted. Man, I didn't expect Maddie would actually show up at the party, of all the people to save Karen I didn't expect it to be her. Guess her Basitin morality isn't all that ironclad. Karen should thank her lucky stars it isn't.

[TheMasterOfOats]

Haha, this is a good page. I love in the last panel you can see Red and Raine trying to blow crap up and Natani and Keith actually blowing crap up.

Also, dang, Natani is straight up exuding lightning. It looks good on her .

[aitaituo]

Probably was looking at guys, though.

Poor Maddie was probably like a deer in headlights when all the male keidran got rid of their shorts at the party. Keith's furred, too. He could have been next!

[MuonNeutrino]

But where was she that she got to that edge of the pool before Karen was out of reach? If the illusion was only for Karen, I could kinda see it, but if not, Maddie would have had to have been underwater right behind her. Then again, she's not even wearing a swim suit, so I think she just saw that Karen was heading for the edge.

It was suggested during the stream chat that she was hiding on top of the awning-roof above the entrance, which I think makes sense for a lot of reasons.

First, it's probably the only place in the room it really makes sense for her to have been able to hide for so long. The oasis room is big, sure, but it's mostly wide open without much in the way of stuff to hide behind, especially trying to hide from the sightlines of multiple people spread around the room. Being on top of that awning she would have been able to spy on everyone without having to worry too much about being seen.

Second, it gives her a natural perch to have both seen what was going down with karen and the illusion and to have intervened as she did. The splash in the first panel can then be from her jumping from the roof into the pool, especially as her shirt doesn't look like it was already wet in that panel (compare to later panels) as it would have if she had been underwater.

Third, as Rafe points out, this would have given her an opportunity to have overheard Sythe and Maren's conversation before they left. This can not only help to explain how fast she reacted by having her know that it couldn't have been Maren (though she's also definitely observant enough to have noticed the actual inconsistency of the illusion-floor), but also gives her another reason to be embarrassed in the last panel given the... shocking (to a basitin) nature of what she'd have overheard, which Karen's question would have reminded her about.

On another note, Maddie's been selling herself short here, or else she's just too fixated on comparing herself with her mother. Being able to not only catch and halt Karen's fall but fling her over her head like that is no minor feat of strength. It's also a bit physics defying in this case; from their ref sheets they weigh about the same, and the poses there give Karen's weight a *ton* more leverage around the pivot point of the edge of the pool than Maddie's weight. It almost shouldn't matter how strong Maddie is, especially if she still has some forward momentum from lunging to catch Karen the scene really *ought* to end with Maddie flipping forward over the edge of the pool and falling too. But *that* is definitely a much too nitpicky objection for a comic strip.

[Bellhead]

On another note, Maddie's been selling herself short here, or else she's just too fixated on comparing herself with her mother. Being able to not only catch and halt Karen's fall but fling her over her head like that is no minor feat of strength. It's also a bit physics defying in this case; from their ref sheets they weigh about the same, and the poses there give Karen's weight a *ton* more leverage around the pivot point of the edge of the pool than Maddie's weight. It almost shouldn't matter how strong Maddie is, especially if she still has some forward momentum from lunging to catch Karen the scene really *ought* to end with Maddie flipping forward over the edge of the pool and falling too. But *that* is definitely a much too nitpicky objection for a comic strip.

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.

[Rafe]

Probably was looking at guys, though.

Poor Maddie was probably like a deer in headlights when all the male keidran got rid of their shorts at the party. Keith's furred, too. He could have been next!

She's still like a deer in the headlights! She let her teenage voyeurism take her over, and now her eyes are permanently bugged-out.
Her poor innocent mind is filled with things she can't un-see or (in the case of Sythe and Maren) un-hear.

Let's hope this condition is only temporary.

[steelabjur]

She might have still been out in the hallway and happened to peek in when Karen started toward the Maren illusion. Remember the hallway where these two met Stoneward? The door out disappeared there too, both are probably being hidden by illusion. Walls might be cloaked in illusion too, to make it look like they're not doing as much damage as they actually are and keep them trapped in with Evil Trace's Discount Stone Dragons.

[MuonNeutrino]

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.



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*.

Absent anything to brace against there are only CCW torques on Maddie's body, so she should start to rotate CCW around the edge of the pool. At that point her legs will try to move through the water as she rotates, so they will exert a force on the water to the right and the water will exert an equal force on them to the left by newton's 3rd law (represented by the yellow arrows on the diagram). This does provide a CW torque, which opposes the CCW torques of her weight and the pulling force. However, water isn't a solid. This force is a drag force, so it can't exist unless her legs are *moving* because drag is a function of velocity. Therefore that force cannot be large enough to provide a torque strong enough to keep her from rotating, because if she isn't rotating the velocity of her legs through the water is zero and so there can't be any drag.

As such, Maddie's body *cannot* be in static equilibrium, because if she's stationary there is a net CCW torque on her. What should happen is that as she exerts force on Karen, her body should begin to rotate CCW around the pivot point of the edge of the pool. This rotation will accelerate until her legs are moving through the water fast enough to produce a strong enough drag force for that CW torque to balance the CCW torques, at which point she will rotate CCW at a constant angular speed - at least until her legs break the surface of the water and that torque disappears and she just flips head over heels over the edge of the pool.

However, that's considering it as a more or less static (or, at least, equilibrium) problem. All the reasoning is still valid, but the conclusion we can draw from it is just that the situation must be dynamic and non-equilibrium. Specifically, we know two things - one, that Maddie must be rotating CCW, and two, that Karen is being pulled hard enough to not only hold her up, but reverse her motion and make her rotate CW. The question is then which happens first - Karen reaching vertical with enough angular velocity to flip her over the edge back into the pool (and dragging Maddie with her), or Maddie's legs breaking the surface of the water and thus removing the CW torque that allows her to actually slow her rotation and keep from flipping over the edge *out* of the pool. This question is a lot harder to answer. The harder Maddie pulls the quicker Karen's rotation will reverse, but also the quicker that *Maddie's* rotation will increase. In the absence of the water this would more or less completely cancel out because the air drag would be negligible, but drag in water is not only much larger but increases with velocity *faster* than linear (quadratic) for any large object moving at macroscopic speeds. Thus, Maddie pulling harder is still going to make her rotation increase, but not by as much as it will make Karen's rotation increase because the water drag becomes larger faster at higher speeds (relatively - i.e. 2x as much speed means 4x as much drag).

So the question actually becomes "How hard does Maddie have to pull to create enough extra water drag that Karen rotates back up to vertical before Maddie flips out of the pool?", which is unfortunately basically going to be impossible to answer with the information we have. My intuition (and a couple of very ballpark calculations) says "hell no", *especially* considering that both of their initial momenta are in exactly the wrong direction, but actually proving that would require some rigorous calculation (or, more likely, numerical modeling) unlike the simple analysis above. And I've already spent all afternoon on this, so that's about as far as I want to go.

[Bellhead]

Physics

More physics

I think you're assuming their relative rotation is what flung them over, while I'm thinking of a different approach. I'm going to start with what you've drawn, as I'm too lazy to bother figuring out Photoshop and my old imgur account at 9 pm on a Sunday night, but we'll see..

Now. Assuming the picture is before the point of equilibrium, where Karen stops falling, we can assume that the angle between the pink lines and the closest green line (their arms to Maddie's torso) is widening. My theory revolves around that scenario, wherein at the point where Karen stops falling, there's a triangle, not a trapeziod as your diagram suggests. In such a case, the three points are Karen's right foot, her left shoulder, and Maddie's hips which would come to rest against the glass. My theory is that at that point, she would lock her hips at an acute angle and allow her arms to straighten fully, thus turning her lower half not into leverage or angular momentum, but a hook. As long as her grip holds, and her body stays at that acute angle, she won't slip out, no matter how fast Karen is rotating, or falling, or pulling.

Pulling directly along that pink line, in that case, would cause CW rotation against Karen's foot, as well as upward force. Granted, Maddie would also have to exert a force near double Karen's weight to pull this off, pun intended, but I think this is more reasonable than superhuman speed vs. fluid dynamics.

Now let me change up the scenario just a bit...
Had she not had the strength to flip Karen, she could far more easily held her up using the same technique. Assume Karen slipped, and fell vertical against the wall. Maddie would have held her, but would have supported the weight solely from her hips, or whatever part of her was against the top of the glass, and that would be the only possible solution in that circumstance. No rotation would be needed on Maddie's part, as she would just pivot freely on the top of the glass as necessary.