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For contextualization, in my world a phenomenon caused anomalous "creatures" (for a lack of a better term) to appear. Among these, I planned to have "creatures" capable of running at ludicrous speeds when compared to anything based on earth biology. However when researching about how animal movement and speed works, including on this SE, the main conclusion I got to is that any machine or organism that relies on limbs to move around and accelerate will always be necessarily less efficient than something that makes use of wheels or treads due to how friction works as well as other details (as a wheel will normally always stay in contact with the ground, being able to apply a constant force, differently from the paw system that naturally requires the limbs to leave the ground and has a smaller overall surface area at any given moment during the run). To attempt to mitigate that problem, I planned to make my creatures similar in overall anatomy to a house centipede, aka it would have multiple legs, each leg longer than the last one to avoid collision, so that it would always have at least one limb (or pair of limbs) on the ground at all times, essentially trying to get closer to a wheel's nearly constant contact with the ground (originally I planned for a total of 10 legs).

However, what I found on the movement and bodyplan of house centipedes stopped being useful to me, since I wanted my creatures to be much larger (around 2.5 meters long and ~1.5 meters tall, with a max weight no higher than 200 kg), and I couldn't really find anything to help me at such sizes. The fact that tiger beetles are proportionally much faster despite having only 6 limbs also made me doubt whether this approach would actually result in greater maximum speeds.

The ideal goal would be for the creatures to be able to maintain speeds of 150km/h for long periods, with max sprinting speeds closer to 500km/h (both assuming the creature is running on a straight line, unimpeded by obstacles). The creature's limbs end in 2 toes with claws and special rough skin used mostly to maximize traction. They predominantly live and run in terrain much like that of a flat Savanah.

Leaving worries such as the overheating problem and the resistance of the materials the creature is made of (these aren't my main concern, so as of now simply assume the creature is indestructible and fully capable of performing the necessary work without needing to worry about problems like overheating), is such an approach of having more limbs an effective choice to make my creature a faster runner overall? I couldn't really find whether the addition of limbs could provide any meaningful advantage or if a body plan of a centipede, with its hind(er?) limbs being longer than the previous pair, wouldn't cause drag-related problems given the creature's size and the speed it'd be running at, or at least not in the scale of approximately horse-sized (approximately 2 meters tall) animals.

If I've forgotten to add any important details, please let me know so I can add them.

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    $\begingroup$ Just from the energy perspective, your speedy centipedes may need to eat more that their body mass every day to be able to run around that fast. $\endgroup$
    – Alexander
    Oct 21, 2021 at 16:24
  • $\begingroup$ @Alexander - They'd most likely need to be carnivores to get the amount of energy they need. $\endgroup$
    – Paul
    Oct 21, 2021 at 16:31
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    $\begingroup$ @Paul from the 3 major nutrient classes, proteins are the worst in terms of energy. Sugars are fuels and fats are energy reserves, but proteins are meant to be building/repair blocks for the body, not fuel. I'd say the best diet for the speedy beast is corn, potatoes, sugar cane, rice, etc. $\endgroup$ Oct 21, 2021 at 16:49
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    $\begingroup$ Honestly if overheating is not a problem then you might as well just go for a better cheetah. $\endgroup$
    – Rubrikon
    Oct 21, 2021 at 17:17
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    $\begingroup$ @Paul "I don't think there's a food that could possibly supply the nourishment required" neither do it "... without having to stop every few minutes to restock" it may take a bit longer, but not much. A "a max weight no higher than 200 kg" traveling at 150kph requires 173kJ only to accelerate at that speed. That's about 20% of the energy intake of an average human per day. Scaling to a 200kg body, all the rest being equal, that would mean about 7-8% of the beast dietary energy per day. $\endgroup$ Oct 21, 2021 at 22:44

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The speed of an animal is a function of stride length and frequency, the greater both are, the greater the speed of the animal.

The stride frequency is a function of strength vs weight, with the limb acting a bit like a pendulum, so animals with a higher stride frequency tend to have limbs that concentrate their muscle mass high in the limb... think ostrich-like legs rather than human-like legs.

To use a mechanical example, consider a mechanical metronome. The closer the weight is to the pivot point,the faster the metronome will tick.

However, being strong enough to run means that the limbs must have a certain weight so that they won't break under the load put on them. To make the limbs lighter, the entire creature must be lighter.

Next is the matter of gait. When walking, an animal always has at least one foot on the ground. However, when running, there are periods in which all feet are off the ground. However, aerodynamic drag tends to slow the creature during these unsupported portions of their gait cycle, so an aerodynamic shape is of some importance.

The specifics of the gait cycle for creatures with more than 2 limbs affects the creature's speed and maneuverability. The fastest gait cycle is one in which the feet touch the ground sequentially with a minimum of overlap.

When considering animals with more than 4 limbs, the advantage that they give to the animal's speed depends upon how many limbs are necessary to support the animal's weight while running. The higher the ratio between number of legs and the number of feet required to touch the ground, the more distance each gait cycle will cover. Most insects with 6 legs have a ratio of 6:3, which is actually no better than 2:1, with the added disadvantage that insects tend not to have unsupported periods in their gait cycle. Arachnids also tend to have a ratio no better than 8:3 with no unsupported periods.

So, if we could have a six-footed creature with a 6:1 ground contact ratio, with long, light limbs, and a long unsupported period, you'd likely have a particularly fast creature. Eight legs with 8:1 ground contact would be even faster, but given the weight of all the limbs, this ground contact ratio may be unachievable without making the limbs overly bulky and slow.

There are yet more factors at play. Take, for example, a cheetah, Earth's fastest living land animal. Even its spine plays a role in its great speed. By flexing and extending its spine while galloping, it gains about 5kph to its running speed due to the effect that has on the angles of its pelvis and shoulders relative to its spine. However, that is specific to a mammalian body plan. Other creatures may have other features that may allow greater speed.

So, just adding more limbs isn't necessarily going to make a creature faster. Centipedes are quite fast, but millipedes, with more legs, are actually slower. It all depends on the factors I have mentioned above.

There is just one circumstance which would allow a greater speed than any creature with limbs: rolling motion.

A creature capable of rolling - perhaps a serpentine creature which can roll itself into a hoop, or perhaps a roundish creature - could propel itself by distorting its shape so that gravity was pulling it down and leading it to roll forwards. The speed at which it could move would depend on its size and the speed at which it could change the shape of its body, as well as the local gravity and the local slope. The impact of centripetal forces on its body would also be important.

However, this would be a relatively niche means of locomotion, dependent upon having quite smooth, flat ground over which to roll. Obstacles could easily prove injurious or fatal at the speeds achievable.

The advantage of rolling locomotion is that there is (probably) no reciprocating limb motion consuming lots of energy, and the range of motion required is relatively small. The creature should be able to coast for considerable distances and achieve higher maximum speeds than creatures using multiple limbs.

This is probably the only reasonable way to achieve the speeds mentioned in the OP's question without requiring a ridiculously high energy input and having an unreasonably low endurance level.

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Centipedes are fast because they 's' their bodies like snakes not because they have so many legs.

More legs isn't any bonus to speed. It's not the amount of legs that matters as much as the length of the legs and other factors.

What you need is just a faster more durable horse or gazelle. Or a kangaroo built for speed with longer more powerful hind legs. Once a kangaroo gets going it can go pretty fast for a long time because most of the time it's in the air.

The Red Kangaroo can run at 70km/h and is the most efficient land animal we know of for covering distance quickly.

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    $\begingroup$ Nearly all examples in nature show that a quadrupedal animal adapted for running will have greater maximum speeds when compared to a bipedal one. The comparison between the max speeds of Ostriches, kangaroos and other bipeds (max speeds around 70km/h) VS cheetahs, horses and other quadrupeds (max speeds closer to 80 km/h, with maximum speeds close to 100km/h present) comes to mind. $\endgroup$ Jan 7 at 0:15
  • $\begingroup$ No... just, no. I don't know where to start detailing the errors in this answer. Every paragraph contains some sort of error... $\endgroup$
    – Monty Wild
    Jan 7 at 2:14
  • $\begingroup$ @MontyWild not many paragraphs, name some errors. Is a red kangaroo not able to run at 70kmph as the link says? Or are you just blowing wind? $\endgroup$
    – Kilisi
    Jan 7 at 2:45
  • $\begingroup$ Centipedes are faster than millipedes because their legs are a lot longer than those of millipedes. Having snakelike bodies makes no difference as they don't slither. $\endgroup$
    – Monty Wild
    Jan 7 at 2:49
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    $\begingroup$ Kangaroos don't run at all... they hop. Their efficiency is due to their elastic ligaments storing a lot of the impact energy of hitting the ground every gait cycle. $\endgroup$
    – Monty Wild
    Jan 7 at 2:52
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More legs can work as a means of going faster, but only to a certain extent. The most efficient model would launch the animal forward with one pair of legs, then launch again when deceleration begins to take effect. Whether this is by another pair or the same, as long as it has the speed to achieve this the animal will get the most speed out of it's legs. Other factors with speed are dependent on shape or strength of the legs.

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There are two ways this could go -

The first is that these limbs contribute to speed, like extra legs or longer limbs so it could move faster. Many four legged animals move faster than two legged animals, because they can have longer stride distances. Humans top out in speed alot shorter than most quadrupedal animals, for example.

The second way this could go is bay making them slower. These extra limbs are extra weight, which could considerably slow them down. For example, even though an elephant is stronger than an antelope, the antelope will move faster because it has a lot less weight.

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