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This is about the same species as in e.g. How can humans coexist with an intelligent carnivorous species?

The culture of this intelligent, carnivorous, primarily quadruped species, in a sense despite the species' intelligence, is one that also favors physical prowess. That prowess includes, but is absolutely not limited to, both endurance and physical strength. One of the ways they measure themselves against one another is in ritualized games, not entirely unlike an ironman triathlon but including physical grappling matches as well as tests of endurance. These games are primarily to establish social standing but also to show off mating fitness.

A common part of the grappling contests is to attempt to throw your opponent; this would be measured (I hesitate to say "judged" as it's not guaranteed that there would be a referee) both on how well (including how far) one is able to throw their opponent as well as how well the opponent recovers (landing on feet vs back? getting back up quickly vs remaining on the ground? etc).

I have yet to decide on the exact rules, but to the extent that they may have bearing on answers, some general ones would be:

  • Both competitors are allowed to move about freely without artificial limits. That said, constantly running away from one's opponent is unlikely to be seen as a great display of physical prowess, especially considering that the grappling match isn't primarily a test of endurance.
  • Either competitor can choose freely at any time whether to attempt to grapple or try to avoid their opponent, and are free to take advantage of their opponent's actions in doing so.
  • Rough tactics are allowed, but not those that would cause permanent injuries (this is, after all, a ritual, as opposed to an actual fight, and it is among carnivores). So you might very well see one competitor grappling and throwing or pinning their opponent to the ground, but not clawing at their opponent's face.

Questions:

  • Realistically, what would be required in terms of physical ability for a reasonably large (big cat size) mammal to lob another of their kind a significant distance (to have a ballpark figure to work with, let's say more than three body lengths' worth) through the air?
  • As a bonus question, what particular evolutionary (not technique) adaptations are likely to allow an individual to take such a treatment better or worse than another? In other words, if these competitions were somehow the sole selection criteria in mating, which traits would be selected for or against?
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    $\begingroup$ Honestly, it sounds somewhat like a Scottish games festival! $\endgroup$ – Cort Ammon Jan 17 '17 at 16:35
  • $\begingroup$ @CortAmmon Well, if there are real-world examples that can provide for comparison, then only so much the better! $\endgroup$ – a CVn Jan 17 '17 at 16:39
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    $\begingroup$ Every action has an equal and opposite reaction. $\endgroup$ – Evil Dog Pie Jan 17 '17 at 16:46
  • $\begingroup$ I think they would have to be dwarves. $\endgroup$ – A. I. Breveleri Jan 17 '17 at 17:24
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    $\begingroup$ The problem in throwing a person (or similar creature) isn't so much the weight itself, but the fact that they are flexible, hard to grasp, and if conscious, likely to be squirming around while you're trying to get a good grip. $\endgroup$ – jamesqf Jan 17 '17 at 22:03
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Throw?

Throwing your opponent can mean a few different things: pick them up off the ground then throw them, knock them off balance then grapple on the ground or just body check them into submission. Depending on the body plan of the aliens in question, one of these three approaches will be the most useful. Determining which approach to take will depend on the vertical stability of the creature. Two legged creatures are better adapted to lift-and-throw while four legged creatures are more likely to use knock-over. Animals with essentially one huge leg (elephant seals for example) are more likely to use body checking.

Lift and Throw

This approach is unlikely for large (>human sized) mammals because lifting heavy things over your head is hard.

Consider the following:

  • Overhead Press: At 198 lbs, an elite male lifter can press 235 lbs. Also note that the 235 lbs in question is not a screaming, wriggling, highly motivated competitor. Lifting something over your head requires you to balance a heavy thing on essentially a long multi-jointed pole which is really hard.
  • Deadlift: This same 198 lb elite male lifter can deadlift 615 lbs. With sufficient grip strength, a wriggling competitor won't make much difference to being lifted.

In the two legged fighting domain, the competition can be won by being the biggest but because of the instability of moving on two legs permits a smaller competitor to be sneaky and use improved technique to beat a larger opponent....like this fight.

There aren't many species on Earth that can lift something really heavy over their heads. I can't think of any that compete by lifting and throwing a body-weight comparable object from an overhead position. It's just too hard and too specialized. There are other ways to compete.

Also consider that the more weight a structure (biological or mechanical) can lift, the more specialized it must be to that task. Cranes for skyscrapers can lift immense loads but they can't do anything else either.

Knock-over and wrestle

Throwing your opponent to the ground or unbalancing them is a common approach that usually leads to further grappling on the ground. Two legged and four legged creatures most often compete in this way. Human martial arts such as sumo, judo, karate, MMA, and others are examples of this kind of combat. The degree to which grappling happens on the ground will depend on the rules of the competition and the physical capabilities of the contenders.

A four legged creature won't be throwing things over its head since it's body is oriented towards movement parallel to the ground plane. Nor will it be lifting its opponent off the ground. However, knocking an opponent off balance and into a disadvantageous position (grasp around the throat, choke hold, etc) will be the focus. Observe how tigers fight each other. There's a brief series of blows attempting to off-balance the other tiger. Once the opponent has been knocked down, attempts are made to force submission.

Bump and Grind

For creatures that have essentially one big foot, a more likely approach will be body-checking, sumo style. In contrast to lift-and-throw, body-checking only requires the organism to accelerate quickly and survive an impact. Both characteristics are broadly applicable to general survival. Many ocean going mammals compete for social status and mates with this approach.

As an example of bump-and-grind, (bull elephant seals) fight by smashing into each other. The fights are often bloody though rarely lethal.

Conclusion

The only body plan that would support lift and throw competition would be simian or humanoid body plans. Humans in particular since they already have a vertically oriented body plan. However, for bump-and-grind competition, the available body plans are far more diverse, including the OP's reference to large cats.

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As has been pointed out, it's not a great idea to just pick someone up and chuck them over your head - it's much better to use momentum, both theirs and your own. In order for a reasonably sized mammals to do this, the best bet would probably to launch themselves at each other from a distance of, say, $1$m, for some explosive power into each other, such as here, at which point each would try to turn (for increased angular momentum) and fling the other into the direction that it's already facing, requiring technique, timing (OK, this is just technique again) and a bit of strength (though maybe not as much as you'd think). While the linked video shows one of the tigers leap vertically, they would probably stay on the ground and 'ground' themselves to the Earth in order to change directions of momentum more efficiently. (also, 1m is small enough that if it doesn't work the first time, they can just keep going at each other)

The point of this is that the 2 mammals move towards each other and connect, at which point the better fighter (the one that wins) transfers its momentum to the other by the process of turning its linear momentum into angular momentum and back into linear momentum of the other person - a bit like a bigger version of this moment, only with more movement involved - note the way that the woman twists herself to the side in order to get that conversion of momentum in.

If this was an actual fight, they would both grapple instead of throwing at this point for a short time, but that would negate the initial linear momentum of both of them, and the point isn't to fight, but to get the biggest throw.

Chucking in some maths:

You want the mammals to throw a distance of around $5$m (for ease of numbers), most the power of which would come from the initial 'leap towards each other' bit.

Assuming this to be the case, using the standard constant acceleration equations with final velocity $v = 0$ at the highest point, initial velocity $u$, acceleration $a = -g$ (due to gravity) and vertical displacement $s = 2.5 \tan\left(45\right) = 2.5$ when 'thrown' at an angle of 45 degrees; $v^2 = u^2 + 2as$ (in the vertical direction, immediately after impact of the mammals), the initial vertical velocity would be required to be $\sqrt{5g}$.

For this to happen, the horizontal velocity would also be equal to this (due to being 'thrown' at an angle of 45 degrees). Assuming that the change of direction of momentum is 100% efficient (or extra strength could be used to help this) and ignoring friction, each mammal begins with a momentum of $mu = m\sqrt{5g}$ and a kinetic energy of $\frac{1}{2}mu^2 = \frac{5}{2}mg$ Joules, which is also half of what the looser ends up with, to conserve momentum and energy.

In order to get to this speed over the distance of $s = 1$m, from the above equation with $u = 0$, $v = \sqrt{5g}$, you want an acceleration of $\frac{5}{2}g$ m$s^{-2}$, giving a force of $F = ma = \frac{5}{2}gm$ N, or being able to accelerate at about 7.5 times Usain Bolt.

At a bit of a guess, evolutionary adaptions would be reasonably strong hind legs and something a bit similar to elbows in the front legs. On top of this, they would need to be able to survive impacts of $5mg$ Joules at wherever they land (probably either on the back or legs).

To be thrown an arbitrary distance, $d$, you want an acceleration of $\frac{1}{2}gd$ m$s^{-2}$, or $\frac{3}{2}d$ times Usain Bolt's acceleration (for an acceleration due to gravity equal to that of Earth)

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If you look at large, fast land mammals, their strongest muscles are usually in their hind legs. Just watch a house-cat grab something in their front paws, roll onto their back, and start rabbit-kicking it, and you can imagine how far they could launch something from that position with a full-extension leg-kick. If you really look closely at it, it would resemble a leg-toss from judo or aikido. In short, an animal that has a vertical leap many times greater than it's own height would be capable of launching a similar-sized animal quite far with it's own leg strength directed at that foe.

There are also many forms and moves in martial arts that follow inspiration from the animal kingdom. This is probably the only time you could consider watching Kung-Fu Panda as valid research, since some of the forms are inspired by the capabilities of the animal performing the action.

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I'll give it a shot but some of this may fall more into biology. Lets take a male lion as the example: Mass = $190kg$ , body length $=2m$ Ignoring a struggling body, air resistance or anything we get the energy required is: $$E=\frac{m (V_{x}\cos(\pi/4))^{2}}{2}=\frac{m V_{x}^{2}}{4} $$

Where $ V_{x} = \frac{3 L_{body}}{T}$, $T=\sqrt{\frac{6L_{body}}{g_{0}}}$ and sticking them all together gives us an energy of $\approx 1400 Joules$, it also requires throwing the opponent at least 1.5 metres above the ground.

Comparing this to the caber toss it would seem ours is not an impossible feat. But it is important to note that in the caber toss both the arms and legs are used to provide the energy.

Several things could make this easier for your creatures:

  • Being able to lift their opponent high in the air (more throwing force into horizontal travel rather than fighting gravity).
  • Strong legs with a wide stance to balance them.
  • A powerful and flexible back meaning they can start off leaning back and move forwards into the throw.
  • Elbows like ours. They would need to be able to add the extension of the arms into the throw to provide power from all areas of their body.

I think those also fulfil the evolutionary traits that best adapt to this ability to throw. It ignores, however, being able to fight well enough to get your opponent in a position to be thrown. Though I would add that perhaps a smaller body would recover a little better from being thrown.

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Being able to throw someone of equivalent mass as yourself implies having the energetic capacity to jump/throw yourself that same distance. The only difference between jumping and being thrown is just a matter of positioning, grip, and support.

Your characters are throwing each other because they choose to do so (I hesitate to say "for intelligent reasons") but we can look at existing creatures for examples of biomechanical adaptations that allow animals to jump long distances for the principles required. Kangaroos, gazelles, and antelope, as well as smaller creatures like fleas, frogs, and grasshoppers, can jump long distances for 2 reasons:

  1. They have large amounts of their musculature and body mass devoted to jumping. Your mammals will likely not be walking around like inverted triangle cartoon body builders on spindly, short legs, and throwing each other with the massive arms that they use only for throwing people and working out so they can throw people farther. They will be throwing each other with the same muscles they use for daily locomotion and survival.

  2. They store energy for the jumping and throwing in elastic or compressible structures. All of the large mammals have long, elastic tendons which store energy for their jumps. Some insects compress air bladders or cartilaginous springs to store energy. Humans may not be able to jump very far or throw each other very far, but when we do, we run and jump (storing energy built up from the running in tendons) or store it in a tool like a pole vaulter's pole or a trampoline.

Your mammals are going to do something like hoist the other competitor into the air, and drop to their back, catch the opponent using their feet, and push them away.

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The best way to throw an opponent is by using the opponent's own momentum. The question becomes, how far can opponent leap? and how much can you help it along? Change the rules of the game so it's more like Judo meets a Sumo match fought by burly kangaroos. Sumo wrestlers attempt to resist being thrown out of the ring while attempting to throw their opponent. There are excellent examples of clever sumo wrestlers using their opponent's own weight and momentum.

https://www.youtube.com/watch?v=ErWyhXXk2iE

Judo also uses an opponent's weight and strength. I've seen very large men get thrown pretty hard by small women. Kangaroo judo matches could be quite entertaining (though they might need longer arms).

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A Finnish strong-man threw another 60 kg person 5.4 meters, according to the Guinness Book of World Records. That is three times a 1.8m height person, so that mostly meets your standards.

To be honest, I would suspect that our cave-man ancestors, who were generally stronger and more awesome than use, could accomplish this feat too.

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