For larger cutouts use a bi metal hole saw. Make sure you are sizing your drill bits to match your screws.
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Can you drill into fiberglass. Coarse blades will grab and chip the gelcoat. The problem with drilling through fiberglass is that the drill bit has a tendency to chip the edges of the hole. If you simply attempt to drill a hole into the fiberglass you will have extreme difficulty in drilling holes without cracking the gelcoat. I dont think it is a good idea to drill holes in your fiberglass door because it probably is a hollow door and it will be difficult to keep the screws from falling out from the weight of the rod. Fiberglass is harder and stronger than wood but can just as easily be drilled into using wood drill bits. Use the lowest speed possible to start the bit.
I read some things like you need to champher the hole drill backwards first drill with a uni bit use masking tape over the hole before you drill it and such things to avoid cracking the fiberglass. Step 1 mark where the drill holes are going to go using a tape measure and a pencil. You want to start with a drill bit thats about 50 between the major and minor diameters. Screws have major and minor diameters. Is there anything special about drilling into fiberglass. A drill and a jigsaw.
The method i use which works about 999 of the time is to put the drill in reverse drill through the gelcoat then put the drill in forward and drill through the rest of the laminate. The fiberglass will dull drill bits out fast and generally require pilot holes when drilling holes any bigger than 18 inch. Use sharp fine tooth blades. Standard drill bits will do for holes under an inch in diameter. Drilling fiberglass can be a time consuming procedure if you wish to drill a perfect hole. As it begins to dig into the fiberglass increase the rotational speed.
Either using your hand or if you have clearance the drill running in reverse lightly score the fiberglass inside the bilge by applying pressure rotating the hole saw bit. Slowly begin to drill a hole through the surface of the fiberglass. Now youre ready for the big moment lets finish drilling the hole from the outside of the boat. This is because fiberglass has a gel coated surface and the edges of a drill bit tend to get underneath this surface and then chip it off. This will result in a cleaner hull when the hole saw finishes the cut.