Would anyone know the thickness of the head gasket on the HP500 540 Bull Dog?

Don't know for absolute but I would assume .039 for a thickness. That is pretty common for most head gasket thickness. Why are you asking for the thickness.

I am looking into raising the compression currently 8.6 to1
I would like to be 9.3 to 9.5 to 1 but did not want to change out the pistons. I will be going to dart pro 1 heads if I do this mod.

You would need to take about 10 cc of combustion chamber volume out of the heads to do this. The heads can be milled to accomplish this but I would be careful with the Pro-1, my experience is the deck surface is not real thick to start with. I'd rather start with Brodix or Racing Head Service (old Top Line) heads. Be sure any combustion chamber porting is completed before making the chambers 109 cc.

You might be able to get 9.0 to 1 by milling the heads and using a slightly thinner gasket, but thats about it.

I thought you were selling the Bulldogs????? They need head gaskets and springs with the hours you have on them anyway.
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