Molten iron is much like water, and it will run off without having a chance to burn, unless it goes into the top of your shoe or boot, in which case you have a serious problem.
The slightest amount of moisture will cause iron to explode out of the mold, and this happened to me one time, and I had iron strike my leather jacket, run down the arms, and into my gloves.
3rd degree burns on both hands, but nothing really to be concerned with; ie: no limbs were lost.
The bigger problem is radiant heat, mostly from IR.
If you look at 4:35 in the video, the radiant heat from the open furnace, and from the sides of the crucible are supremely hot, and will start to burn you in short order.
I guess the loose clothing act sort of as a heat shield.
I can speak from experience, standing that close to a crucible that big with no gear on is really amazing, and I am not sure really how they get away with it. The heat on the face is incredible.
And you can quickly burn your eyes with IR without shaded glasses. I guess they don't look at the crucible or open furnace, either that or get cataracts. I burned my eyes after one melting session without the proper eye protection.
The scoop-out ladle would not be very dangerous or difficult to handle, as long as you made sure it was super dry before dipping it in the crucible.
I will attach some photos of my iron experience.
The slightest drop of iron vaporizes the skin almost instantly, and creates a large burn zone around the contact area.
I pour aluminum without much protection. The main thing to protect are the eyes.
If you splash in the eyes, it is game-over.
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