I have built many arches over the last 10 years. I did quite a few roman arches before I did my first gothic one. That was in collaboration with Dan Snow in 2005 at the second Canadian dry stone festival in Port Hope Ontario. We had a heck of a time trying to figure out what the correct angles for the vousoirs would be. He admitted that it was his first gothic arch too.
Dan took a while and figured something out and drew some lines for us on the wooden form, where he thought they should be, but as we built over it we realized the guide lines were not looking like the correct angles at all.
When Im building a 36 inch wide arch, I still use that form sometimes and smile when I look at the old pencil lines drawn on it. Gothic arches, it turns out, are actually a bit easier to construct and as far as I can tell produce a much more stable structure than roman dry stone arches. I build mostly gothic arches now.
Sometimes a client wants a door in an arch I will be building them. Most of the time they are for decoration, as this one in Oakville, Ontario. Actually the door was the form in this example. ( It was doubled up and had plywood bent over the top to support the stones). We lowered it an inch after the stone arch was built, and left it there to look like a door. It didn't go anywhere. (Neither the door, nor the arch)
Speaking of not going anywhere, many of the doors to the arches I have built don't have handles, as is the case with this one above that we built in Uxbridge Ontario in 2008. They don't need door knobs if they are just decoration. They often have keys though, which is kind of amusing.
In a Gothic opening if the door is actually going to be used and is to open properly at all, it needs to be hung flush with the outside or inside wall (the pintles can't be located in the middle of the wall), otherwise the top of the door catches on the top of arch (unless the door is hung much lower) Who knew? These are little things you discover as you go. Sometimes you find out the hard way.
Below is a door we placed in an arch we built for Mariposa Gardening at the 2009 San Francisco Flower and Garden Show. I borrowed the door from a vendor at the show who had several rustic hand-made doors on display. We met up during the show and decided one of his doors would look good in a photo standing inside the arch. This door has a handle, but clearly doesn't have hinges....... It's held there by 'hand'.