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I have a bipedal kaiju-style monster that walks upright on two legs and weighs 20,000 metric tons. Supposing, of course, that it can carry its own weight, its muscles can support the stress, and the ground can support it, does anyone have any idea how to calculate how many seconds it might take for this creature to decelerate from the respective speeds of 15 and 30 mph to a complete standstill?

I tried using freight train emergency braking times as a reference, but I imagine the two stopping methods are very different and therefore might yield very different results.

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    $\begingroup$ I hope the answer will include a drawing with vectors. $\endgroup$
    – Willk
    Apr 21, 2018 at 16:56
  • $\begingroup$ I suspect the answer to this lies in some details not provided. How does he stop himself? Back pedaling, just digging his feet in? What terrain is he in? Something like a marsh might stop him quicker than smooth stone $\endgroup$
    – Lio Elbammalf
    Apr 21, 2018 at 17:01
  • $\begingroup$ I suppose I'm imagining two different types of terrain. The first is an open field and the second is a paved city road. I'm picturing him slowing himself as any rubber-suit style monster would: in the most conventional looking way imaginable- just like a person youtube.com/watch?v=1J1wzMnFGXk $\endgroup$
    – Joseph Rouleau
    Apr 21, 2018 at 17:58
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    $\begingroup$ American football players sometimes do a "front flip" to quickly slow down when they reach the end zone at full speed. Forward momentum is translated into vertical motion, and you stop within 5-6 yards. $\endgroup$
    – RonJohn
    Apr 21, 2018 at 18:35

2 Answers 2

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Great question, here comes the mother of all spherical cow estimates

Proposal: The limiting factor is force the ground can absorb.

I propose that what keeps a kaiju from decelerating too fast is the amount of pressure it can put on the ground before the ground shatters into....whatever the ground shatters into under a kaiju's foot. If it 'shatters' the ground, the foot slips, and it won't be able to stop quickly, so that will be our limit.

We'll assume the monster's body is sufficiently muscled to do anything a human can do, including taking the same strides relative to the body.

How much force can the ground take?

Based on a powerpoint on building foundations, lets assume that the bearing stress on good quality bedrock is 10 MPa.

How much force does a monster put out?

A human sprinter generates a ground reaction force of ~3000 N for a 60 kg sprinter, while accelerating at 3 m/s$^2$ over 10 strides each of 2 meters.

The monster is 20,000 tons or lets round to 300,000 times the mass of the sprinter. If the monster is the same shape as a human, by cube law, it should be 70 times longer in each length dimension.

First, lets make sure the monster can stand on the ground. Two human feet are 200 cm$^2$; a kaiju's equivalent feet would be about 100 m$^2$. Lets say its got big Godzilla feet, so that is really 200 m$^2$. $2\times10^{7}$ kg times $g$ over that area is 1 MPa; well under the bedrock strength.

An equivalent human full force footfall is 5 times more force than standing force (3000 N versus 600 N for a 60 kg person); the kaiju's standing 1 MPa times five is 5 MPa; still below the bedrock limit, though perhaps barely.

How long does that take to stop

A kaiju with roughly human dimensions and feet with twice and much surface area proportional to its body size could accelerate and decelerate at the same rate a human could.

Usain Bolt can get to just under 30 mph in 6 seconds, so he could decelerate in roughly the same. He gets to 15 mph is half that: 3 sec.

Therefore, it is reasonable for the ground to support a kaiju doing the same. Of course, it takes 60 strides for Usain Bolt to come to the full stop, while we are assuming that the kaiju has the musculature to do it in about one stride.

Conclusion

The force required to stop a 20,000 ton kaiju whose running mechanics are similar to a humans should be low enough to allow the kaiju to stop within about 6 seconds from 30 mph and 3 seconds from 15 mph.

This is assuming a good, strong bedrock surface that the kaiju is walking on; the kind you need to support tall buildings in Manhattan or Tokyo, in case your kaiju is into that. On softer ground, no promises. And of course, everything between the kaiju's foot and the bedrock should be thoroughly pulverized.

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    $\begingroup$ +, because this kaiju is actually a giant spherical cow. HOW DID YOU KNOW?? $\endgroup$
    – Willk
    Apr 21, 2018 at 17:26
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    $\begingroup$ @JosephRouleau I added a conclusion to answer your question better. As for friction, on a smooth hard rock surface that would be a problem, but there should be plenty of pavement, topsoil, trees, squishy humans, buildings, and whatever else underfoot to give him good traction. $\endgroup$
    – kingledion
    Apr 21, 2018 at 18:23
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    $\begingroup$ "mother of all spherical cow estimates" should get multiple upvotes! Thanks for the smile! $\endgroup$
    – Paul TIKI
    Apr 21, 2018 at 19:58
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    $\begingroup$ Now actually, the feet probably end up digging into the soil on an angle and producing a compressive force normal to an inclined plane... but when that transmits down to the soil/bedrock interface it will form an angle with the horizontal bedrock, possibly resulting in sliding at the soil/bedrock interface and the "mowing up the ground" that NL mentioned. In other words, it will act like gigantic earth-moving equipment. $\endgroup$
    – Ben Voigt
    Apr 22, 2018 at 2:54
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    $\begingroup$ @BenVoigt If you look at the paper in my second link, you see that the forces along the (x, y, z) axis are broken down by the authors. The vertical force of the footfall goes up to 3000 N, and the anterior-posterior force (y-direction) maxes out at about 800 N of the first step of the sprint, and thereafter is more like 500 N. I don't doubt that some asphalt will get torn up, but I don't see that much slipping. $\endgroup$
    – kingledion
    Apr 22, 2018 at 10:54
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The problem here is that you can't have a 20,000 ton biped (indeed, the number of legs is largely immaterial). An elephant weighs in the order of 10 tons, you want an animal that is in the order of 1000 times that. This will mean that it will need to be 10 times as tall, wide and long (10^3 = 1,000). Its legs though will have to carry 1000 times the mass, despite only having a cross-section 100 times that of an elephant (ignoring for a moment the fact it has half as many). That means that each leg will have to be 10 times as large in cross-sectional area, or for a simpler way of looking at it, you'll need 10 times as many.

Now picture in your mind an elephant that is proportionally the same as a normal-sized one, but with 40 legs (each proportionally the same size as a normal one) - you end up with much more leg cross-section than you do elephant (alternative explanation - think of an ant with legs that are proportionally very spindly, but can carry far more mass relative to the creature than an elephant can - then reverse the logic).

Even if you ignore the leg strength issue, you're going to have a similar issue with the feet - with a ground pressure ten times that of a real animal, it's going to sink.

Given that the basic physics of your creature aren't really possible without a lot of hand-waving, how long it takes to stop can largely be a product of your imagination.

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    $\begingroup$ (There's a lot of high grade phlebotinum involved), but that's not really pertinent to the question, considering the parameters I've set. "Supposing, of course, that it can carry its own weight, its muscles can support the stress, and the ground can support it...". $\endgroup$
    – Joseph Rouleau
    Apr 22, 2018 at 16:35
  • $\begingroup$ But the problem is that as far as I can tell, the limiting factor is deceleration will be the strength of the legs; and they can’t support the animal anyway. So trying to establish the exact physics seems a little pointless, you might as well just fit the capability to the narrative. $\endgroup$
    – Matt Bowyer
    Apr 22, 2018 at 19:14
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    $\begingroup$ (Notwithstanding the fact that it will probably sink into any ground it’s placed on, meaning that the stopping distance will be “very short and very dramatic”) $\endgroup$
    – Matt Bowyer
    Apr 22, 2018 at 19:24
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    $\begingroup$ Frame challenges (questioning the OP's premise) aren't wrong, but they're not preferred. Answers are expected to be provided within the OP's context. In this case, considering humans can run through ground (soggy, peat, sand, etc.) in which we sink, the premise isn't simply ignorable. Remember, half of "science fiction" is fiction. $\endgroup$
    – JBH
    Aug 17, 2018 at 2:16
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    $\begingroup$ Please attempt to answer the question as it is written. Non-answers to questions may be deleted. $\endgroup$
    – Monty Wild ♦
    Aug 17, 2018 at 3:00

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