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So I have this android character that has super-human abilities. I like her durability level, speed, and everything else, but I feel her jump is a bit to short. She can lift around 12 1/2 times, or 2,000 pounds/1 ton, her body weight of 160 pounds. Currently she can leap vertically around 28 feet, but if she crouches, she may be able to jump 42 feet. Horizontally from a standstill she can jump around 36 feet, but running on 2 legs at 50 MPH she can reach about twice that, and if running on all 4s at full speed(100 MPH), she can leap to around 100 feet. How plausible is this, and if it is not, what is the more accurate jumping abilities?

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  • $\begingroup$ Does she have a 100% human body plan, or her legs, joints and ligaments are modified to boost jumping? $\endgroup$
    – Alexander
    Commented Nov 4, 2021 at 16:55
  • $\begingroup$ Pretty much human in shape, although her arms are as long as her legs to allow easier all 4 running and she is very flexible and is pretty much literally double jointed and kinda like an action figure in range of movement of her limbs.They are other deviations, but they are not really relevant to the topic of jumping. $\endgroup$ Commented Nov 4, 2021 at 17:06
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    $\begingroup$ That's not how people use language, Ivan. Try Google Image search for "female android". $\endgroup$
    – Sixtyfive
    Commented Nov 5, 2021 at 13:10
  • $\begingroup$ The important question is not how much the 'droid can lift, but how fast (and more). A human can deadlift 0.5 tons. Unfortunately, this does not translate into jump capabilities. With a lever, humans can lift much more, but the lever assistance does nothing for jumps. But there are devices to store energy, to improve human jumps. The pole in pole vaulting allows for a 6m high jump, a pogo stick for 3.2m. If your 'droid has such devices built-in, it could convert forward momentum into jumps (like a pole vaulter). Meanwhile: omnicalculator.com/physics/car-jump-distance $\endgroup$
    – Klaws
    Commented Nov 6, 2021 at 12:16

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This all depends on the mechanisms that give strength to your android. just saying your 12.5x stronger doesn't necessarily relate across the board. Even in humans this can vary a lot. In humans, we have different muscle tissues that help us excel in different ways. This article What Are Fast- and Slow-Twitch Muscles? talk about the different muscle fibers and what they do.

Basically, it comes down to what mechanisms your android has and how it's used. Your android might be able to lift 1 ton of something, but if its servos are designed for high capacity over time, it might not be able to jump 1 inch. Now, if it's designed to exert large amounts of force quickly, it could jump great distances, or run fast, but may not be robust enough to lift and hold large weight.

This is a balance that engineers deal with when designing any mechanical system. They determine the job the machine needs to do and balance the components that go into it to accomplish that job. It's all a give and take when it comes down to the benefits and draw backs on selected materials. Materials designed for heavy lift tend to be heavy, reducing speed and agility. Components designed for speed are slimmer. Plus having a servo move 1 ton quickly could cause high forces and may just fling its load around uncontrollably.

However, this is fiction. You can make the android have all the best components and not have any draw backs, so it could lift 12.5x more weight, can run 12.5x fast and jump 12.5x higher than any human can.

Here are some examples of how engineers are balancing components and function MABEL Bipedal Robot is Fast Enough to Run You Down 10 Humanoid Robots of 2020 KUKA Robotics introduces world's largest and strongest robot

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    $\begingroup$ As an extreme case, I used to run a logging forklift that could lift several tons of tree trunks, but couldn't jump worth a damn :-) It's not just the magnitude of the force, but how quickly it can be applied, and in what direction. $\endgroup$
    – jamesqf
    Commented Nov 4, 2021 at 17:40
  • $\begingroup$ Mostly talking about an arm lift. If you can lift 1000kg from the ground to 2m high, in 1 second, when you come to a stop, you will have an upward for to stop of several thousand kg of force. (I am not going to do that math at this time.) $\endgroup$
    – Sonvar
    Commented Nov 4, 2021 at 17:45
  • $\begingroup$ Right? A worm gear can make you N times stronger for generating a lifting force, yet it's not good for jumping, due to trading speed/distance. $\endgroup$
    – Kaz
    Commented Nov 5, 2021 at 6:20
  • $\begingroup$ Sonvar, thank you for writing this excellent answer and not just vaguely commenting "opinion-based" and VTC'ing the question :) $\endgroup$
    – KeizerHarm
    Commented Nov 5, 2021 at 8:07
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    $\begingroup$ Hydraulics are great for heavy lifting, but are difficult to make anything jump (exception is low-riders). Pneumatics are fast and can jump/flip things easily, but aren't generally used for heavy lifting (except for pillow jacks and some jaws of life). Magnetism/motors/linear actuators can be fast or slow, and have or lack power, but tend to get bulky and heavy fast. It's definitely not just about power, but also speed, weight ratios, and power requirements to run the system. Pick a setup and handwave the rest to save yourself from the nitpickers. $\endgroup$ Commented Nov 5, 2021 at 14:59
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The vertical jump distance appears unrealistically large to me. To be able to raise your CG by ~42 feet (13 m) would require leaving the ground at a velocity of around 16 m/s. If leaving from a crouch, it might be reasonable to assume that the maximum distance she is accelerating for is no more than 1 m (legs fully compressed to fully extended). To accelerate her 160 lb (73 kg) body to that velocity over that distance requires an average acceleration of 128 m/s^2 over that distance, so a continuous applied force of 9350 N. The latter is consistent with an ability to do a 'static' lift of 1 tonne, but during the push-off her muscles would need to produce an output power of around 150 kW, which is over 200 horse-power. Even during explosive exercise a human body can only output power of around 2-3 kW, so your android is exceeding that by a factor of 50-75 rather than 12!

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  • $\begingroup$ "your android is exceeding that by a factor of 50-75 rather than 12" About a factor of 100, actually. A single horsepower is defined as lifting 250kg/550lb 1 foot in 1 second, and the world record powerlifter lifted 500kg/1100lb about 3 feet in about 3 seconds (almost exactly 2hp). $\endgroup$
    – nick012000
    Commented Nov 5, 2021 at 2:14
  • $\begingroup$ Datapoint: A well ricked in motorcycle takes about 30 HP to ton. Similar ppwer for the android running probably reasonable. $\endgroup$ Commented Nov 6, 2021 at 11:10
  • $\begingroup$ ? Are you saying that the running speed for her is realistic? @RussellMcMahon $\endgroup$ Commented Nov 6, 2021 at 14:54
  • $\begingroup$ @Conan Highwoods The ability to lift weight is somewhat not linked to power. The ability to jump is linked to power and related to mass and rate of energy delivery. BUT running at high speed is dominated by air air resistance. Power increases with the CUBE OF AIR SPEED. YOU NEED about 30 HP to run at 100 mph. MAYBE. As little as 15 HP with very low profile streamlined design. $\endgroup$ Commented Nov 7, 2021 at 4:42
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Human vertical leap varies tremendously even between people the same height, weight, and leg press strength -- but the highest vertical leap I'm aware of in a human (male) is close to 49 inches (~125 cm). Assuming the 12.5x strength factor gives 12.5x the energy on leaving the ground (12.5x the force over the same distance), your android ought to be able to jump a simple 12.5x as high, other factors (including technique) being equal.

That's roundly fifty feet (about 15.25 m).

Long jump is more complicated, because not only does it involve vertical jump (hence flight time) but also horizontal sprinting speed. If she can get a similar amount of height as in a vertical leap, her air time would be about four seconds, giving a forward distance of up to roughly six hundred feet (about 190 m) from a 100 mph start.

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    $\begingroup$ That is a good point, essentially, if the android can both jump higher and run faster than a human, then it can jump much farther because the two effects multiply. $\endgroup$
    – quarague
    Commented Nov 5, 2021 at 9:55
  • $\begingroup$ i'm not 100% sure about that because air resistance is speed² - so making her 12 times as strong doesn't necessarily mean she'll be able to reach 12 times higher speeds (be it horizontal or vertical). $\endgroup$
    – stefs
    Commented Nov 5, 2021 at 13:15
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    $\begingroup$ @stefs Back of the envelope calculations virtually always ignore complicating factors like air drag, friction, etc. Hence "up to" -- just as there's no way a MLB pitcher can actually throw a baseball 200 yards, the same speed won't actually let the android fly that distance -- but it's a better first approximation than 100 feet, given the assumed values. $\endgroup$
    – Zeiss Ikon
    Commented Nov 5, 2021 at 13:43
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I assume you already ran the math, since your figures pan out, but just in case (or if anyone wondered),

  • How much high can she jump when running? Let that be X feet, or 0.3048*X meters. 28 feet is plausible since vertical acceleration is about eight times a human's. There is a slightly more complicated calculation to determine her jumping power from her legs' length and stance: she must not only be able to lift more mass than a human, she must be able to do it very fast.

  • Since the acceleration of gravity g = 9.81 m/s^2, this means she stays in air for a time t, such that s=0.5 * g * t^2, so 0.3048 * X = 0.5 * 9.81 * t^2, which means that t = SQRT(0.3048 * X/(0.5 * 9.81)) = approximately SQRT(X)/4. To get time in seconds from vertical jump height in feet, just extract the root and divide by four.

  • So, 28 feet means SQRT(28)/4 = 1.32 s in the air.

  • How far can she travel horizontally in 1.32 s?

  • 50 miles is 80467 m, one hour is 3600 s, so her speed is 22.35 m/s. In 1.32 s she can then cover 1.32 * 22.35 = 29 m, or 95 feet.

Now, vertical jump and horizontal speed are roughly related, and from that 28ft leap I would have expected a much faster running speed; she should be able to run at about 120 mph (almost parallel to the ground). Controlling her speed is a different matter, of course.

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