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Assuming the information in this video by the Cambridge University is correct, Planthoppers can jump as far as a meter. Their size ranges from 1cm in cooler climates to 5cm in the tropics.

With disregard to further external influences such as diminishing returns, in theory they would be able to jump 50m when scaled to 50cm (from 1cm being able to jump 1 meter).

The video states that they accelerate to about 5m/s in the span of less than a millisecond, consequently experiencing g-forces of 500-700 g. Humans tend to die when subjected to g-forces greater than 100 g, so would this even be within the realm of plausibility to begin with?

Certainly, if scaled 50x without diminishing returns, the subjection of an organism to 25,000 g seems impossible. Not only does this g-force seem implausible but also the speed of acceleration, scaled up would be 250 m/s or 900 Kilometers per hour.

In theory, the insect would be the same size as dogs (50cm), therefore the air resistance will also be multiplied by around 50x. This would not lead to excessive heat build up as it would with a mouse the size of an elephant. assuming that internal densities and structural integrity were to achieve equilibrium and the organism may function correctly, would there be a way to consistently measure how much the acceleration speed would be affected by the upscaling?

If a Plant Hopper Nymph was to be scaled up to 50x its original size, to what extent would diminishing returns and other such laws affect the g-force, speed of acceleration, and jumping distance of the insect?

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    $\begingroup$ FYI: Square–cube law $\endgroup$ – Alexander Mar 14 '18 at 16:51
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    $\begingroup$ "Scaled 50x": now the animal is 125,000 times as heavy, but only 2,500 times as strong (because weight increases with the volume, or the cube of the length, while strength increases with the cross section of the muscles, or the square of the length): 50 times less strong per unit of mass. See the problem? Not to mention that insect physiology simply cannot scale to big animals -- their respiratory and circulatory systems cannot work in large animals. $\endgroup$ – AlexP Mar 14 '18 at 17:10
  • $\begingroup$ That's a very good point. Although if we were to conceive an organism, not an insect, yet sharing striated muscles in the legs like a plant hopper, is there a consistent way of determining force in relation to muscle mass? $\endgroup$ – Lutro Mar 14 '18 at 17:31
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    $\begingroup$ Relevant: Can you simply scale up animals? $\endgroup$ – Sec SE - clear Monica's name Mar 14 '18 at 17:40
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    $\begingroup$ Even if square cube law didn't apply here (which it does) the other impact of scalability that uniquely impacts insects is their lack of lungs. They rely on osmosis to absorb O2. Unless the atmosphere contains a LOT more O2, there's a theoretical limit to how big an insect can grow before suffocating in its core. Even just within such a theoretical limit, we can expect the insect to be very sluggish as O2 'consumption' is how the insect releases so much energy anyway. As the insect increases in size, O2 levels reduce, reducing energy output. $\endgroup$ – Tim B II Mar 14 '18 at 22:35
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Let's do some physics.

We know that the height that an animal can jump is equal to the starting height (leg length) $+\frac{v^2}{2g}.$

Therefore, if an animal can jump 50 meters, it should be able to reach a speed of $31.622\ m/s$ before it leaves the ground (i.e. before displacement $>$ leg length).

A planthopper's legs make up $65\%$ of the body length, or for our $50\ cm$ bug, $32.5\ cm.$

Therefore, if $v_{max}=31.622\ m/s$ and $\Delta h=0.325\ m$, $a=1538.462\ m/s^2$, or $156.8\ g.$

However, this is only sustained for $0.021$ seconds.

Note that in collaboration with John Stapp, Major John Beeding survived 83g for twice this time on a rocket sled when it crashed. A much smaller insect is likely to be able to survive this force.

Indy car drivers have survived impacts of 180 G or more (Society of Automotive Engineers. Indy racecar crash analysis. Automotive Engineering International, June 1999, 87-90.)

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