A Donkey dick is actually a 'combi plug' (trade name). Its called a donkey dick because it looks a bit like a donkey's dick

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Used for tread repairs only and fills the void left by the nail or whatever in the tread - it has rubber cement/solution applied to all surfaces in contact with the tyre carcass, then pulled through the hole and finished off on the inside using a roller to smooth the mushroom shaped head against the inside of the tyre.
Hope that explains it for you Thor
