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Found an answer by Minnesota's Department of Natural Resources. For new, clear ice, 4 inches should be good for ice skating or any activity involving just a person's weight. They recommend double that thickness (8 inches) for white ice which has about half the strength.
Think about it: one to two thousand pounds (450-900 kg) falling about five feet (1.5 metre)? Of course it's going to hurt the cow.
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