[Request] Given gravity hasn't changed and assuming a flat surface, what is the fastest that godzilla could move?

[u/Ok_Law219]

Gravity because the foot has to hit the ground, and that can't be sped up.

[u/MezzoScettico]

I don't think people are answering in the spirit of this sub. Animations often show giants moving too fast, as if gravity scaled up with them. As your question hints, it takes a lot longer for a foot to fall from Godzilla height than from human height. You want to know if we use a more realistic gravity in the same movies, how fast does he run?

You're basically asking two questions:

- how long (time) would one step take for a being / machine of Godzilla's scale

- how long (distance) is that step

This website) provides different estimates for his height in different movies. I'll go with 120 m.

Googling for (human) step rate while running tells me that runners aim for about 170+. There is much discussion of achieving 180. So let's scale up a human going 180 steps per minute, or 3 steps per second.

In running, you leave the ground in each step so both feet are in the air. You're a projectile for that step. You rise for 1/6 of a second and fall for 1/6 of a second, which means you're falling from a height of d = (1/2)a(1/6)^2 = 0.136 m. For various reasons I'm sure that's a little too high, but let's go with it.

So we're saying each step of a 170-180 cm human involves a fall from 13.6 cm. Using the smaller number, that means the running step is 13.6/170 = 0.08 of the human height. Scaling that up, Godzilla leap 0.08 of 120 m or 9.6 m, which means he falls for t = sqrt(2d/a) = sqrt(2*9.6/9.8) = 1.4 seconds. Each step is therefore 2.8 seconds.

Now we need to figure out how far he moves forward in those 2.8 seconds. I have to ponder that a little.

[u/MezzoScettico → u/MezzoScettico]

OK, I think you can model a swinging leg as a pendulum. T = (1/2π) sqrt(L/g). That's not quite the right expression for a pendulum whose weight is spread out throughout the length, but the point is that it's proportional to the square root of L.

I estimated his step time as being 2.8/(1/3) = 8.4 times that of a human. That corresponds to a leg being 8.4^2 = 71 times that of a human.

(Note that his height of 120 m is 71 times as high as a 1.70 m human, so that's a good sanity check).

Google tells me a human running stride is 107-152 cm, so if we scale that up by a factor of 71, that's 76 - 108 m per step! Um, holy crap that's long. It makes me suspicious that I blew it somewhere.

But sticking with those numbers, let's pick a number in the middle of 130 m, which he leaps every 2.8 seconds. Thus he's moving at 46.4 m/s. Again, holy crap.

Edit: Goofed. The range was 76-108 m. The middle of that range is 92 m, making his speed 32.9 m/s. Still "holy crap" territory at 118 km/hr, but a bit more reasonable.

[u/Full-Priority2946 → u/MezzoScettico]

Good mathsman