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Is it possible for a land organism to break the sound barrier via running?

I may make an organism that can move faster than the speed of sound, however on this planet the main components of air is Hydrogen Chloride and the speed of sound in hydrogen chloride is 964 ft/s, 294 m/s, or 657.2 mph.

Something that could help you with this is the tiger beetle, it moves an astounding 120 body lengths per second. However a Southern California mite is much faster than the Australian tiger beetle and it is the current record-holder for running speed as measured in body lengths per second.

By this measure, the mite runs 20 times faster than a cheetah and the equivalent of a person running 1300 miles per hour.

One last thing, make it plausible and I would also appreciate if you could tell me the fuel requirements of such a beast.

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    $\begingroup$ Broadly, if we're limited by realistic physiology, no. Are we bound by physics, or do we get to use magic? $\endgroup$
    – jdunlop
    Sep 19, 2021 at 18:24
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    $\begingroup$ Well, an eleven-ton all-metal kerosene-eating jet-powered being reached a speed of 1228 km/h (763 mph) over land in October 1997; that is indeed faster than sound. The highest speed achieved by a wheel-powered land vehicle is 649 km/h (403 mph); its engine developed about 4400 horse-power or 3300 kW. $\endgroup$
    – AlexP
    Sep 19, 2021 at 19:36
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    $\begingroup$ Ignoring the square-cube law and talking about speed, etc. as proportional to body size is great for making cheesy SF movies, but not much help in consideration of the actual laws of nature. Ants are not many times stronger than humans, they are the benefactors of the square-cube law when prorating strength by size. $\endgroup$
    – Gary Walker
    Sep 19, 2021 at 21:16
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    $\begingroup$ "the main components of air is Hydrogen Chloride" Hydrocloric acid, but without the water to dilute it. Right... at this point: screw physics and and magic it, because making anything biological exist in an atmosphere of HCl, is another — but equally indigestible — kettle of fish. To make this — the atmosphere, and the extreme speeds... all achieved by something biological — plausible, you need magic. $\endgroup$
    – MichaelK
    Sep 20, 2021 at 10:48
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    $\begingroup$ Movement speed as multiple of body lengths per second is a very grotty way to measure speed. A helium atom, using no legs at all, in room temperature air on Earth, moves 8 trillion "body lengths" per second, just by existing. $\endgroup$
    – PcMan
    Sep 20, 2021 at 16:47

6 Answers 6

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Not just by running

The fastest wheel-driven vehicle was the Bluebird CN7 which reached 403mph. It has been suggested that its theoretical top speed could be as high as 500mph. This is still a long way off the speed of sound in air (761mph) or the speed of sound in the OP's question (657mph). More recently, the Spirit of Rett achieved 414mph.

The Bluebird CN7 his was limited partly by aerodynamics but also partly by its ability to lay down power at the wheels; and that power came from a gas turbine engine rather than internal combustion. The Spirit of Rett used an internal combustion engine. All vehicles exceeding this speed have been jet-powered.

Even considering that a creature could replace the pistons of an internal combustion engine with muscles, it seems implausible that they could lay down greater power with muscles than an internal combustion engine can manage (in a similar mass/volume package). This means that even the Bluebird CN7's or Spirit of Rett's speed would not be achievable by a creature.

Does your worldbuilding allow jet-powered creatures?

There is no plausible way that a creature could evolve a jet turbine, as used by post-war aircraft and by land speed record vehicles from the Bluebird CN7 onwards. The mechanics of evolving the compressor stage just aren't possible.

Pulse jets are simple enough though that a creature could conceivably evolve them. V1 flying bombs achieved 400mph and were primarily limited by the control technology, so we're getting towards the right kind of ballpark. Since jet turbines are a mature technology and superseded pulse jets, research on improving pulse jets has been relatively limited, so we can speculate that it could be possible to do better.

But then they're more likely to be flying creatures

If you've got jet power, there's no need to stay on the ground. And more than that, there are evolutionary pressures to not stay on the ground. Running at high speeds, even just on a horse, needs flat surfaces. Nature isn't like that, so if you want to go fast then you need to be in the air, otherwise you die just from hitting a pebble at high speed.

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    $\begingroup$ It do allow the jet-powered creatures. $\endgroup$
    – JelliPapi
    Sep 20, 2021 at 12:00
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    $\begingroup$ I think that i'm going to have to make a flying creature that flies faster than the speed of sound rather than a land animal running faster than it. $\endgroup$
    – JelliPapi
    Sep 20, 2021 at 12:06
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    $\begingroup$ @JelliPapi pehaps you should alter your question then, it specifically mentions running. (Before anyone says it, I used a wheeled vehicle as an example to illustrate my answer). $\endgroup$
    – Demigan
    Sep 20, 2021 at 13:13
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Simple answer: no.

When a car or person is speeding up, their speed eventually stops increasing. This is why cars for example have a maximum speed even at maximum throttle: the combination of inefficiencies of the engine and air drag will increase the faster you go.

Lets assume that you have a perfect engine with unlimited horsepower and only air-drag being a factor, then you are still limited. Even a car pushes off the ground with its wheels. So the contact of the wheels with the ground is what lets it move forwards. This contact is based on the normal force and the friction this can generate with the surface, as well as the materials of the contact surfaces.

Normally a friction coefficient is something like 0.9 (rubber on dry asphalt). This coefficient goes down when the asphalt or rubber is wet, causing the wheels to slip sooner. So lets assume a perfectly ideal situation with a coefficient of 1. This means that you can get the maximum speed out of the friction, which uses the normal force, which uses gravity in its equation.

In that idealized scenario your maximum speed will the equal to the maximum speed you can achieve by gravitational pull. This would be the same as terminal velocity.

A human in belly position reaches around 200km/h. If your creature is more aerodynamic we can equate it to a human terminal velocity when facing straight down: around 290km/h. So you would not exceed that limit.

Some notes:

  • biological beings push off from the ground more than a rotating wheel does, meaning you would essentially be jumping rather than running (not surprising, a jaguar or tiger is essentially making low jumps when running). This means the ideal speed would be lower.
  • you could improve by using reverse wings to push yourself against the ground and increase that maximum speed, this is what spoilers on cars do.
  • you could increase the speed by using and sticky surfaces to increase friction. That does mean the surface is not like sand or similar.
  • pushing off will also mean deforming the ground at higher speeds, reducing the maximum speed further.
  • keep in mind we eliminated things like efficiency and power generation per second. Unless you can burn enough biological fuel per second to push a +/-100+ kilogram being away this cant happen.
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    $\begingroup$ Coefficient of static friction can exceed 1 (silver on silver is 1.4), some of the stickiest tires exceed even that. SAE paper #942484 mentions tires with 1.8 at 120 MPH (3.0 at 0 MPH). This does not even factor in downforce (that you mention) or using Casimir force or other possible refinements. Running over natural surfaces, instead of wheels over engineered surfaces will significantly limit the amount of friction force. Given that drag would vary as speed squared, an effective friction coefficient of perhaps 10+ would be needed for Mach 1. $\endgroup$
    – Gary Walker
    Sep 19, 2021 at 21:01
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    $\begingroup$ I don't see the logical leap that free fall terminal velocity is the limit for landspeed. If I were falling at terminal speed next to a cliff face, conceivably I could do something to thrust off the rock and move slightly faster for a bit. Maybe if I were a real exotic creature, something I could repeat several times a second and with great force. $\endgroup$
    – BMF
    Sep 19, 2021 at 21:37
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    $\begingroup$ @BMF - the assumption is a CoF of 1. In that case, the limit to the force that can be applied from contact with the surface is equal to the normal force - that is, gravity. So the fastest you can go is the fastest that gravity can make you go, because terminal velocity is the point where drag forces exactly match the force of gravity. No logical leap, just math. $\endgroup$
    – jdunlop
    Sep 19, 2021 at 21:46
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    $\begingroup$ @jdunlop if I can swing my arms faster than the cliffside is moving past, then I should be able to gain momentum. It's not obvious to me why that motion would be physically impossible. Without atmosphere, it would be totally possible. But the introduction of any atmosphere will prevent me from swinging my arms that fast? It would also be easier to swing in the opposing direction, due to the direction of the wind. Hypothetically, I should be able to swing my arms at terminal velocity in the opposite direction. That could mean a good deal of force. $\endgroup$
    – BMF
    Sep 19, 2021 at 22:14
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    $\begingroup$ This answer seems to suggest that the terminal velocity of a supersonic vehicle is supersonic. That seems unlikely. What am I missing here? $\endgroup$
    – Jordi Vermeulen
    Sep 20, 2021 at 13:00
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I foresee two main problems:

  1. breathing: supersonic and subsonic flows in a tube behave in different ways, the creature's airways would need to be able to support both regimes and the shockwaves produced by supersonic flow. Kind of tricky, if you want to allow both resistance to shockwaves and gas exchanges.
  2. propulsion: if the creature uses legs or something similar to move, the structure will continuously oscillate between supersonic (leg going forward) and infrasonic/subsonic (leg going backward) speeds. Once again, shockwaves will become an issue here. And you can't squander in protection, because that would mean additional mass to move.
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    $\begingroup$ Not to mention that no wheel-powered vehicle has ever broken through the sound barrier. It seems that wheel-on-ground (or foot-on-ground) traction cannot provide enough thrust. $\endgroup$
    – AlexP
    Sep 19, 2021 at 19:42
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    $\begingroup$ "Gas exchanges"... What about... breathing air in, explode it, and... erm... excrete it towards behind? A flatulent jet engine... (Well, it's not running, though.) $\endgroup$
    – Pablo H
    Sep 20, 2021 at 14:31
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    $\begingroup$ @AlexP Ah, but they have - just not on Earth. The speed of sound on the moon is zero, easily surpassed by the Apollo Lunar Rovers. If Elon Musk's Star Child Tesla were to actually make it to Mars and safely land there, it might be able to break the Martian sound barrier. (A regular car probably couldn't because you need air to run a gas engine.) $\endgroup$
    – Darrel Hoffman
    Sep 20, 2021 at 16:56
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Let's do it anyway

Giant Alien Ostriches

Let's minimize the speed requirement a bit. Say, your atmosphere would consist of Sulfur hexafluoride (11ºC) the speed of sound would be reduced to 133m/s, which is 479km/h. Now suppose your creature can breath that atmosphere and be as fast as an ostrich (70km/h), it would need to be at least 7x an ostrich height, which winds down to a running bird about 7x2.5 or ca. 17.5 meters tall. See below.

enter image description here

On your planet, with a speed of sound more than 2x my example value, it would stand about 35-40 meters tall.

As far as "fuel" is concerned (I prefer "food" for organisms) this is quite modest for ostriches. An earth ostrich needs about 3 pounds of food per day, mainly vegetables and some insects.

NOTE: taking into account the Square-cube law, my giant ostrich would of course be ca 50x the weight. It needs more food, thicker legs, slowing it down. Maybe somewhere is an optimum to be found ? Or you could lower gravity of course.. Another, more secundary issue is: my Ostrich does not have any incentive to run that fast. You'd probably need a ca 40m cheetah to hunt them.

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    $\begingroup$ SF6 is about 5 times as dense as air, 8 times as dense as HCL gas. This implies you need 5 times as much power to travel at the same velocity as you would through air, or 8 times that for HCL You are going to need more power to run through SF6 at Mach 1 than you do thru HCL. Power vs. speed is not strictly V**2 in the compressible regime (Mach > 0.7), but comparing Mach 1 in both cases makes the comparisons similar. $\endgroup$
    – Gary Walker
    Sep 21, 2021 at 16:27
  • $\begingroup$ The no's win.. ok.. it becomes clear this is a hopeless exercise (maybe you have noticed I reason starts out with a minimal requirement. Meeting the OP requirments would mean the Ostrich would be 40-50m, when taking into account the square cube law AND atmosphere density it would become even bigger. $\endgroup$
    – Goodies
    Sep 22, 2021 at 6:20
  • $\begingroup$ I also did a calc. on the amount your muscles would heat up for the 100m dash - under generous assumptions would generate enough heat to boil - can't be a good thing. $\endgroup$
    – Gary Walker
    Sep 22, 2021 at 12:45
  • $\begingroup$ Well, now you claim something else, Gary.. this is a science-based question.. I'd like to see that calculation, please put an answer. Leopards have a heat problem while running at top speed, but I've never seen an actual calculation, not for predators and also not for ostriches. I know ostriches are quite energy-effective. What would be an appropriate model yielding the boiling point of water, for a giant ostrich ? $\endgroup$
    – Goodies
    Sep 22, 2021 at 16:27
  • $\begingroup$ Simple enough. About 2.1 MJ useful output (see James. McKlellen's answer). Max. efficiency of muscle is about 35%, so at least 3.7 MJ of waste heat . Avg. human muscle mass is about 5 kg or 5,000 g. Water would heat by about 740 degrees (ignoring the large heat required for boiling, etc.). Total travel time of 0.3 seconds does not allow a significant dump of the waste heat. $\endgroup$
    – Gary Walker
    Sep 22, 2021 at 17:20
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Not on Earth.

But it might be possible on a planet with a thinner atmosphere. The speed of sound (unlike light) is not a constant - it depends on the medium the sound is moving through. On Earth, in air at sea level, that's about 340 meters/sec. But on Mars, it's only 240 meters/sec, much more likely to be achievable.

Obviously you'd need to explain how a creature can breathe in such a thin atmosphere, and how it can breathe methane instead of oxygen - or your planet could still have have an oxygen atmosphere, just less dense than on Earth.

The thinner you make the atmosphere, the slower the speed of sound. Obviously when you get as thin as "no atmosphere", e.g. on the Moon, the speed of sound is just zero, so astronauts walking on the Moon during the Apollo missions easily outpaced the speed of sound there. (Of course, with no atmosphere, the "sound barrier" isn't even a thing.)

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  • $\begingroup$ Perhaps it may be possible to have places with very low pressure/density, with lower sound speed. Other areas would have normal pressure/density, allowing breathing. $\endgroup$
    – Pablo H
    Sep 20, 2021 at 14:36
  • $\begingroup$ @PabloH Well, we have that here on Earth, mostly just based on elevation. The atmosphere at the top of Mt. Everest is much less dense than at sea level, which presumably results in a slower speed of sound up there. If one were to build a suitable road at that elevation, perhaps a land vehicle could break the sound barrier. (Note that supersonic planes generally fly at much higher altitudes, partly for that reason.) A planet with more extremes in terms of elevation could fit that bill. (e.g. Olympus Mons on Mars, higher than Everest, and with overall thinner atmosphere, seems ideal.) $\endgroup$
    – Darrel Hoffman
    Sep 20, 2021 at 15:01
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A Very Interesting Question

The speed of sound in salt water (which is what muscles and the body is mostly comprised of) is around 1,500 meters per second. The speed of sound in air is a much more leisurely 343 meters per second. And, for your world, you are asking to beat an even more casual 294 meters per second.

On paper, then, it sounds very plausible.

Some Limiting Factors

  • Nerve conduction speed for muscles is, on average, 80 to 120 meters per second. Humans make a round-trip to the brain when running, but a hypothetical animal might not require brain involvement.

  • Aerodynamic forces ($F = C_D A {1\over2} \rho v^2$) increase with speed and peak at the formation of the normal shock wave at Mach 1.

The density of air $\rho$ is 1.225 kg/m3. These fine folks have calculated the $C_D A$ for a subsonic bicyclist to be 0.39. I'm going to estimate A is 1 m2, to pull from this measurement a $C_D$ of 0.39. And this stack exchange question includes an image from Horner's 'Fluid Dynamic Drag' which shows several bodies and gives the shockwave + other drag for a body at around 0.4.

Putting in the numbers for 294 m/s and 343 m/s, the drag force is 21 kN/m2 to 28 kN/m2.

  • Counteracting drag is our ultimate source of thrust : friction. The equation for friction is $F = \mu_k F_N$ where $\mu_k$ is the friction coefficient, a number between 0.0 and 1.0, usually less than 1.0. And $F_N$ is the part of the animal's weight that is normal to the ground, which is related to the animal's weight and the tug of gravity $m g$.

enter image description here

What Would It Take For An Animal to Generate 21 kN of Thrust?

To overcome supersonic drag, an animal would need to generate 21 kN/m2 of thrust (21,000 N). To do this using the ground as a power source, $\mu_k m g >= 21,000$. Is that even possible?

For a $\mu_k$ of 1.0, a g of 9.8, and an A of 1 meter square, the animal would need to weigh almost two tons (2,100 kg).

However, area scales as the square of cross-section. For an animal half this cross-section, the mass required drops by a factor of 4 to: 525 kg.

Scaling one more time to an animal with a $1 \over 4$ meter cross-section : 131 kg.

This Answer Does Only Does the Rough Analysis of Biomechanics at the Top. Speed of muscles could be in the regime of the speed of sound in seawater (1,500 m/s). Nerve conduction is much slower at 80 to 120 m/s. But, it appears possible that some animal design may exist that could conceivably go supersonic.

How Much Does This Thing Eat?

Energy is a function of force and distance. If this animal runs in 100 meter bursts, then, it would consume at least 21 kN x 100, or 2,100 kilojoules of energy. Converting to calories, that’d be around 500 kilocalories, or what we usually just call calories.

A similar-mass animal (humans) consumes about a 2,000 kilocalorie per day diet. If this animal could do several bursts per day (maybe a dozen), it would only about triple the animal’s calorie needs compared to a human.

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  • $\begingroup$ To speed up the potential in your answer: we can send timed signals for certain actions, like throwing a ball or walking. As long as no adjustments are necessary (tough chance at high speeds) you can have the entire walking sequence send before your brain even receives the first feedback. $\endgroup$
    – Demigan
    Sep 21, 2021 at 10:45
  • $\begingroup$ Man, I was gonna check an answer and now I cant decide. $\endgroup$
    – JelliPapi
    Sep 21, 2021 at 11:16

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