I'm posting this here in case anyone searches Google for help aerating clay soil and needs ideas. This worked great for me and I'd like to share it. We have dense clay soil and, while applying gypsum helps somewhat, I've been told that aerating is necessary too to loosen it up. I've tried using hand aerators:
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the soil is too dense and the coring tines are almost impossible to push into the ground, even after watering it to soften it. I tried renting an aerator, but the machine they called an "aerator" was really a cultivator, with spinning tines designed to rip up the ground, not pull plugs out. I called 5 different gardening services and none of them offer aerating services; most hadn't even heard of the process. I also searched Google and the Yellow Pages under lawn aerating and nobody offers this in the Los Angeles area. Our lawn is far too small for those tow-behind aerators:
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finally worked great was to use a 1-inch auger drill bit with my power drill:
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need an auger bit, not a paddle bit, because you need the dirt to be pulled out of the hole.) Using this, I was able to properly aerate the front and back lawns in about 4 hours. Hope this helps anyone else in a similar dilemma!