In all the "RUNS" over all the years , I've never got to run wide open for the length of the Dragon.  

There is always a rolling Road-Block around one of the corners .

That's not to say we have never done stretches of it "Really Fast"   and maybe a little "Wild" ...  

About 4 years back we got to run from the overlook almost all the way to Dragon Central (200-220 curves) with-out a road block !   My brother  who lives there was trying to show me his power house bike (V-65 Honda) could leave the little Savages.   ,   Turns out that 100HP don't mean much in the twisties , but Tork and light weight does . I had to brake in the truns to keep from hitting him but didn't have HP enough between the turns to get ahead.  
The next day I was in front and he was keeping up perty good till we came up behind a couple of 600cc sport bikes , the first one we came up on made the mistake of glancing in his mirrow to see what "What-The-Heck" had cought up with them , he drifted into the other lane a little --- That's when I shot past him !       He did his best to keep-up , and his buddy who seen me coming did his best to keep me from passing him.   Well the "Buddy" had me running my best and I never gained or lost any ground to him ... Then we came up behind a PACK of Harleys ridding double --- so it was Race-Over , The first Sport Bike caught up ,... Then Brother caught-up with  the rest of Our guys right behind him.   But what a RIDE !  

I like to have at least one RIDE like that every year !  

There are some Dragon Runs on U-tube ! https://www.youtube.com/watch?v=iDS4FfzXRzEhttps://www.youtube.com/watch?v=bi...

I don't go realllllly fast on the straights, as there is always the chance of a radar speed check - but I do ride the corners pretty quickly with a bit of reserve left for avoiding someone drifting into my lane.

If I ride the entire length briskly and non-stop without anybody slowing me down....it takes about 20 minutes.  I was talking to some sport bike fellows with racing slicks and full leathers...they make the run in about 13 minutes (and had large scrapes on their leathers to show they don't always make it without stopping somewhere).

I believe there are some professional riders that have done it in 9 minutes with the road being closed so they can apex corners and use both lanes.  

I like to imagine that I ride the Tail of the Dragon a bit like this:

https://www.youtube.com/watch?v=LuBxU7WnrL4

The videos remind me of the road outside Asheville, NC that my stepson took me on in his tricked out and supercharged Miata..... (I wonder if he ever got the stain out of the seat??)