Why would anyone ask if Godzilla could ice skate? Let's just think of it as a challenge.

The first thing to consider is the compressive strength of ice. I really don't know everything that goes on when someone (a human) ice skates, but I do know something. If an object has a super large pressure on the ice, the ice is going to break or crack or have some type of destruction. It's only ice and it can't take an infinite pressure on it.

The maximum pressure a material can withstand is called the compressive strength. Here are some compressive strength values for some materials (but not ice). The best value I could find for ice was from this US Geological Survey document on the strength of ice in rivers. It gives an average ice strength at about 200 pound/inch2 which would be 1.4 x 106 N/m2. But this is ice compressed in a river. Maybe the ice you skate on is even stronger.

What about a human on ice skates? I know this can happen, I've seen it in real life. What would be the pressure these blades exert? That would depend on the length and width of the ice skate blades. I don't really know very much about skates, but this is a pretty awesome video from Smarter Every Day in which Destin looks at some of the interesting aspects of skating. Even though it's not completely true (apparently), I will say that the bottom of a skate blade is flat (but watch the video, it's great).

The point is this: ice skates exert pressure on the ice. If this pressure goes over the compressive strength, I am going to guess that bad things would happen. The pressure depends on the area of contact and the weight of the skater. That seems fairly straight forward.

So, what's the problem with Godzilla skating? The answer: scale. Bigger things are not the same as smaller things. That's obviously true, but we humans make mistakes all the time. Take a big Godzilla. Has long as he looks humonioid-ish, and has correctly scaled skates he should be fine, right? Well, probably not. Here's why. Let me start with a spherical human on skates and a giant that is twice as tall also on skates (bigger skates).

Since I'm interested in the pressure on the ice, I can calculate the pressure as:

The force on the ice will just be the weight of the person. If I assume that these spherical humans have the same density (ρ), then that would just be the volume of a sphere multiplied by this density.

Now for the area. I said that the skates for the normal human have a length of L, but what about the width? For now, I will just say that the width is some fraction of the length and this fraction will be represented by a. This means that if I double the length of the skates, the width also doubles. The area for the human-sized and double sized skates would then be:

The double sized skates are both twice as long and twice as wide. This means that they will have 4 times the contact area. Now, what about the pressure for both the human and the double human?

The weight depends on the volume. So doubling the height of the spherical human increases the weight by a factor of 8 (2 cubed). Doubling the size only increase the area by a factor of 4. If I find the ratio of pressures on the ice, I get:

If I remove the factor of two and replace it with some scaling factor s, you can see that increasing the size by s also increase the pressure by s. Big deal, right? Yes, it's a big deal. Oh, before we go on, there are two points. First, I am assuming the humanoid density is constant. If a large human is made of the same stuff as a normal human then wouldn't they have the same density? I think so. Second, human's aren't spheres. Yes, that is totally true but it still doesn't matter. No matter what shape you pick (in the past I have used cylinders for humanoid shape) the volume will be proportional to the cube of the height as long as the ratio of dimensions are the same.

How about some numerical values? A typical human might have a mass of 65 kg and wear skates that about 30 cm long and 4 mm wide. If this human was only using one foot at a time, this would produce a pressure on the ice of about 5.3 x 105 N/m. This is well under the compressive strength of ice in the USGS study (for river ice).

Now, let's increase the scaling factor. Here is a plot of pressure on the ice vs. human scale (remember, everything has the same proportions for larger humans).

Suppose the ice used in ice skating is actually 10 times the reported value from USGS. In that case, a correctly proportioned human with the same density as a human could be 26 times the height of human (with correctly scaled ice skates) before cracking the ice. If a normal human is 1.8 meters, then this biggest skating human would be 46 meters tall. This is around half the height of a Jaeger from Pacific Rim and also the 2014 version of Godzilla. Don't forget that the size of Godzilla in the movies gets bigger over time.

Since the 2014 Godzilla is probably around 130 meters tall (and bulkier than a humanoid). I am going to guess he could NOT ice skate with normal scaled (even though huge) ice skates. But could he skate at all? Well, he would need to decrease the pressure on the ice. This can be accomplished by increasing the contact area. What would these skates look like?

Ok, let's just pretend that Godzilla is human shaped - just pretend. This would mean that we could use the same model above with a scale factor of 72. If a human has skates that are 30 cm long, Godzilla's would be 21.6 meters long. Now, what about the compressive strength of ice? Let's just guess a value of 2 x 106 N/m2. How wide would the skate blades need to be? Since the pressure on the normal looking skates is 3.7 times greater than this max pressure, the pressure needs to be reduced by a factor of 3.7. This means that the skate blades need to be an extra 3.7 times wider.

A correctly scaled set of ice skates would have blades that are 72 times wider than a human sized skate - about 28 cm. In order to account for the increased pressure, they would need to be about 1 meter wide. Yes, that is huge - but not as huge as I would have thought. If a human had skate this wide, they would only be about 1.5 cm.

Ok. I guess Godzilla could ice skate after all.