Well, we’re going to have to assume that our protective clothing is magical, because as far as I know, when you’re dealing with something hot enough to vaporize iron, I don’t think the type of protection you’re hoping for exists. But we can certainly ignore the melting factor when looking into whether or not you could go surfing on the Sun.
Surfing on the Earth works on a few principles; first, we have waves in our oceans; and second, surfboards are very good at floating on our oceans. It’s the second one of these that’s going to cause us the most trouble. Not only does the Sun have solar flares, but solar tsunamis also appear occasionally on the surface of the Sun. Solar tsunamis are usually triggered by some kind of solar flare-up, and can rise thousands of kilometers above the surface of the Sun - these tremendous shock waves are bigger than our entire planet.
But could you surf one? Ignoring the inadvisability of such an endeavor on so many fronts, let’s look at the physics of floating on a surfboard. Most surfboards are made of very light materials - which makes them much, much less dense than water. They have to be, because the surfer would like their surfboard to still remain above water when they’re standing on top of it, and so the surfboard has to resist sinking well enough that the weight of the board, plus the weight of the surfer, doesn’t submerge the board. The average human is slightly more dense than fresh water, so the surfboard is stuck doing all the heavy lifting.
The buoyancy of an object is the fundamental piece of physics which determines if something sinks, floats, or hangs neutrally in the middle. This last is the goal of a scuba diver, but a surfer wants to float. Buoyancy is usually described in terms of liquid displacement; if you take an empty 2 liter bottle, and submerge it in water, you had to move 2 liters worth of water to make room for the bottle. 2 liters of water weighs about 4 and a half pounds (2 kilograms exactly), so you could fill that bottle with anything you like, as long as it weighs less than four and a half pounds, and it will float. Fill it with something (rocks, for example) which weighs more than 4 and a half pounds, and it’ll sink.
Surfboards are often filled with polystyrene (packing peanut material), so they’re pretty close to the empty 2 liter bottle end of our experiment above. If you submerge a surfboard that displaces 65 liters of water, on the Earth, you get a buoyant force of some 638 Newtons in the 'out of the water' up direction. Gravity pulls down on it with only 29 Newtons of force (assuming a 3 kilogram / 6 pound board), so buoyancy wins, and it floats.
If we want to go surfing on the Sun, we still need to float. Here’s the problem: the Sun is way less dense than water. Particularly at the surface, where you get your solar tsunamis and your solar flares, the density of the solar atmosphere is a million times less dense than air at sea level. It is a billion times less dense than water.
If you take a normal surfboard and a normal human male according to the 1960s, the average density between them is 554 kilograms per cubic meter. This is significantly less than the 1000 kg per square meter for water, so you’re safe to float in water. But 554 is ten million times too dense for the solar atmosphere. You have no hope of floating on the surface of the Sun. You would drop like a very heavy rock, deep into the Sun.
What to do? If you wanted to get the same buoyant upward force from the Sun, clocking in at a density of 10-6 kilograms per cubic meter, as you did from water on Earth (which has a density of 1000 kilograms per cubic meter), how big would your surfboard need to be? Well, let’s plug things back into our equation. We know the gravitational force at the surface of the Sun, the density of the solar atmosphere, and we need the volume of the solar surfboard. This works out to needing a surfboard which has 36 times the volume of a standard surfboard. It means a surfboard which is 2.5 inches deep by 4 feet wide by 86 feet long.
And that’s just to get the same upward force - it says nothing about whether the surfboard sinks or floats. How light would it have to be to float in the solar atmosphere? To match the density of the solar photosphere, our 86 foot surfboard would have to have a mass of less than 2.3 milligrams, and that’s without a rider. 2.5 milligrams is approximately the weight of a mosquito, or a few grains of sand. To add an 80 kg rider, and give yourself another 80 kg for surfboard infrastructure, you’re looking at a barge 5cm thick, and 54 kilometers square - just shy of trying to surf Manhattan Island. Once again, this one is a non-starter- you’d have a hard time catching any kind of wave on a craft like that.
No surfing the Sun.
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