Yes, eucalyptus burns remarkably well when it is adequately seasoned. It generates a lot of heat and burns very quickly, which may lead to overheating. However, because of its high resin and oil content, it is susceptible to sparking and splitting when burned.
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.Eucalypts are evergreen trees. They're shedding and regrowing their leaves constantly. They do have major shedding in summer and you find a lot of dead leaves under and around them, but the trees don't look any different, the process is invisible