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This is a successor of Little Mermaids: Will They Survive? and concerns the strength a little mermaid has to throw around.

You see, a little mermaid has enhanced strength; the strength of a typical mermaid packed inside a sardine-size frame. In other words, despite their size, they have the same strength as a regular-sized mermaid, and since they don't need to use most of that strength to move or support a large body, they can channel it into ridiculous feats. Please assume this is handwaved; the exact mechanics of how this work is beyond the boundaries of this question.

The idea here is to determine how strong a little mermaid is; if a regular mermaid is six feet tall, from the top of their head to the tips of their tailfin, and their strength is the same as an average American woman of that size, and a sardine-size (AKA little mermaid) has strength equal to their larger counterparts, how strong would a little mermaid be?

Clarification:

As Goodies pointed out, if the mermaids obeyed the square-cube law and were sardine-sized, they'd be weaker proportional to square of size, but if the power of a little mermaid was equal to that of a larger mermaid, the little mermaid would be much stronger than a sardine!

The entire point of this question is to determine how strong such a mermaid, with strength far beyond what her little frame should possess, would be considering the square-cube law. If this is not clear, please let me know.

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  • $\begingroup$ The question is unclear. You specified exactly how strong they are, and then want to know how strong they are. What is the actual question? $\endgroup$ Nov 20 '21 at 0:09
  • $\begingroup$ Muscles need some volume.. square-cube law sais a sardine should be weaker proportional to square of size.. when the power would be equal to the big mermaid, this little mermaid could be very much stronger than the average sardine ! (lol) $\endgroup$
    – Goodies
    Nov 20 '21 at 2:06
  • $\begingroup$ @coppereyecat: sorry for the confusion. Please see Goodie's comment below, as that is the point I was trying to make. A smaller version of a creature, with power equal to that of a larger counterpart, thanks to the square-cube law, would be stronger than the larger creature! That's what I'm trying to determine, how much stronger the little mermaid would be! $\endgroup$
    – Alendyias
    Nov 20 '21 at 4:01
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    $\begingroup$ @Goodies: thank you, I've been struggling to explain that very concept! I had the idea, but lacked the terminology necessary to explain. $\endgroup$
    – Alendyias
    Nov 20 '21 at 4:02
  • $\begingroup$ Just some clarrification... Are they exactly as strong as a normal mermaid(arm can lift 30 kg or so), despite their small size, or are they proportionately as strong as a normal mermaid, where an arm could lift(as an inaccurate example) 3kg? I know what you're asking, you're after their visually obvious strength, something you could describe to a reader without boring them too much with explanatory exposition like "she's lifting the helmet due to the (blahblahblah)!", but to give examples that'd be easily used to convey strength this clarification is necessary. $\endgroup$
    – Lemming
    Dec 5 '21 at 11:30
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Due to this comment...

would prefer knowing how strong they'd be if they were proportionately as strong as a regular mermaid

This answer shall now proceed to give information that disregards these statements.

You see, a little mermaid has enhanced strength; the strength of a typical mermaid packed inside a sardine-size frame. In other words, despite their size, they have the same strength as a regular-sized mermaid, and since they don't need to use most of that strength to move or support a large body, they can channel it into ridiculous feats

Little mermaid strength = normal mermaid strength, proportionately

Probable body weights of LM(little mermaid) vs NM(normal mermaid)...

You see, mermaids in my setting are capable of extreme dwarfism. How extreme? Well, if you've ever seen a sardine, or perhaps a neon tetra, that should give you a good idea.

The weight of sardine in Washington's fishery can be as small as 80 grams and as large as 300 grams but the average weight of sardine in our fishery is 150-175 grams. link

A Mermaid isn't a half-human, half fish. It is a human-orca-fish trifold chimera. -> accepted answer -> Human half will be focused on for strength determining purposes but weight will factor in

Many other events are listed between these examples and a number of events are found to share the same combination of height and weight (height 171 cm, weight 59-62 kg) swimming freestyle -> Age, height and weight of female Olympic finalists

... LM = 150g vs NM = 100kg(added weight for NM from orca-like aquatic tail, conservative and round approximation, bottlenose dolphins weigh 150-200kg so it's not like I'm making them fat)

Determining strengths... Focusing on female statistics due to female body specificity of previous questions...

The average woman should be able to deadlift a bit more than she can squat, at between 100% to 125% of her overall body weight

the average woman can only bench press between 50% and 75% of her total body weight.

women can squat near as much as they can deadlift. So the average woman is likely able to squat between 75% to 125% of her body weight.

link

Punching forces in amateur boxing are around 2500 N. If you weigh 70 kg (11 stone or 154 lbs), you’ll exert about 700 N of force on the ground just stood still. That makes punching force about 3.5 times body mass.

link... data specifically on average(non-boxer) females seems non-existent, or I'm blind, either way I tried to find it

For the purposes of this question I'll be translating average squat power into tail-only-ability-to-lift-things-upwards-underwater, TOATLTUU. Dead lifts will be halved due to only the upper body contributing to the lift, but being underwater may affect this number and have them be able to lift slightly more, incorporating the tail in this will help while underwater but it might as well be a mermaid squat at that point, see TOATLTUU for figures involving tail incorporation.

100kg NM approximate averages:

  • Dead lifts, 50-62.5kg - Upper body alone can lift very light humans
  • Bench press, 50-75kg - Arms are capable of holding up average but skinny humans
  • TOATLTUU, 75-125kg - Tail incorporation underwater allows the lifting up of heaver kinds of human, assuming the weren't buoyant(dead weight) and sank

Punch force, assuming your mermaids had the training of average boxers and could transfer the forces in a similar way while staying in one spot, 3500N. Swimming quickly will add to punch force as running does, (F = M x A) and all that.

University of Southern California estimates that a force of 3,300 newtons has a 1 in 4 chance of cracking the average person's rib

Congratulations, your normal mermaids are rib breakers, if they had boxer training.

150g LM approximate averages:

  • Dead lifts, 75-94.75g - A pack of crisps will be a great undertaking and will probably fail.
  • Bench press, 75-112.5g - That pack of crisps might just get held aloft.
  • TOATLTUU, 112.5-187.5g - Guaranteed crisp packet movement.

Punch force, assuming your little mermaids had the training of average boxers and could transfer the forces in a similar way while staying in one spot, 5.25N. - Might be good for tickles

If, however, you really, really want to pack the strength of a normal mermaid into a little mermaid...

They'll be able to move as much mass as a normal mermaid(assuming they can get a good enough and well-balanced grip), but take care that they don't try it with things as squishy as humans, unless you want them as combatants. They're more likely to pierce human flesh than help them in any regard from the combination of their strength and the amount of surface area they apply it through, and for that matter will be asolutely horrific against anything living, ripping and tearing everything they come across that doesn't happen to be made of bone or something much harder than flesh.

At least their swimming speed won't be too different(strength doesn't mean speed, you need more/better fast twitch muscles if you want them to be faster).

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  • $\begingroup$ Thank you so much! This is precisely what I was looking for, and I really appreciate the time and effort you put into this! Congratulations, you've earned a bounty! $\endgroup$
    – Alendyias
    Dec 8 '21 at 21:19
  • $\begingroup$ Well done, Lemming. $\endgroup$
    – Anon
    Dec 9 '21 at 1:48
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A sardine is about 22 cms long. A human might be 180 cms tall. They are 8 times bigger than sardines.

That means the sardine's volume will be 8^3 times smaller, 512 times. This is indeed true- a human might weigh 75 kilos, while a sardine might weigh 150 grams, 500 times less.

The strength of a sardine will be 8^2 times less. 64 times less. This is because strength is proportional to the area of the muscles.

As such, the little mermaid will be about 64 times stronger than a typical sardine.

A sardine can typically jump about 30 centimeters above water. The little mermaid might be able to jump 19 meters above water. A typical sardine can bench press perhaps two or three times its weight, 450 grams. A typical little mermaid can bench press 192 times their weight.

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  • $\begingroup$ Ooh, very nice, thank you! This is pretty much exactly what I was looking for! I would like a little more detail, however, as I'm not exactly good with math-if a little mermaid can bench press 192 times their weight, what does that mean in terms of moving things? Could they push a coconut around? Pry an eel's jaws open? That would be great, thanks! $\endgroup$
    – Alendyias
    Dec 2 '21 at 23:49
  • $\begingroup$ The typical bench strength of an adult is about 85 pounds, increasing up to about double with a lot of training. Humans can push around coconuts and pry open eel's jaws, so your little mermaid who is as strong as a human certainly could. $\endgroup$
    – Nepene Nep
    Dec 2 '21 at 23:52
  • $\begingroup$ One thing you might want to keep in mind is Newton's 3rd Law claims that every action has an equal and opposite reaction. According to your math the typical little mermaid can bench press 192 times her own weight, but the real question is whether her own body can actually withstand such an action. Keep in mind that creatures evolve in such a way that none of their normal actions cause self-inflicting damage, us egotistical humans clearly being the exception whenever we tend to over-estimate our capabilities. $\endgroup$ Dec 8 '21 at 20:42
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Extending the answer from Nepene Nep:

You've stated that they have mermaid-strength (which we're assuming is the same as human strength) and the size of a sardine (about 1/64th a human's).

They therefore have tiny fingers (which are presumably just as capable of handing loads as a human's). Therefore, they're able to apply all the force you could put into a chisel, but their hands are close to the size of a chisel-point. They can probably tunnel into the coconut, and break the eel's jaw. (In fact, they might have a high-risk hunting strategy of being swallowed by an eel while in body-armour, then punching through the roof of its mouth into its brain.)

For a more interesting comparison, a little mermaid would be able to fly in clear air with the aid of some Da Vinci stlye wings, provided that they can breathe air.

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  • $\begingroup$ Thanks for your elaboration! I found this very helpful! $\endgroup$
    – Alendyias
    Dec 3 '21 at 14:41

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