If you have been watching his video series then this would go with video No.9. I don't plan to give instruction on how to carve the volute since Curtis' decades of experience shown in his video is far more useful.
The above photo is of the tool set for the carving. You can see the sweep stamped at the base of the blade or handle. Note that there are two different no.7 sweeps. Keep in mind that sweep varies from tool maker to tool maker. And the sweep varies based on the width of the gouge from the same maker. So I have shown a ruler to judge the size. (These are actually metric gouges.) I am showing this not so that you can buy the exact tools but it will give you a better idea of the tools to look for when buying.
The best thing to do is take the volute pattern you are wanting to carve and then match up the sweep of the gouge to the pattern until you have a set of gouges to carve that pattern.
Below is a photo showing generally where the gouge is used. The blue marks are the line where I worked up to using that particular numbered gouge in doing the initial defining of the volute line. You can see that the no.3 gouge is used only at the very first then follows with the no.5 for a large portion of the rest and so on. It is nice to see though that two of the same gouges can be used in carving the recessed area with the exception of the larger no.7 and no.8.
The orange lines follow the same pattern but are in regard to the recessed area that is carved out. Of course this is not an exact reference on how to carve this but just some guidelines that could aid you when starting to carve one of these for the first time.
Take your time. Use a good solid mallet that doesn't bounce and feel the wood respond as you carve. Remember that oak splits well for getting that straight grain fibers we want for almost every other chair part but it can split when we don't want it to when carving. Keep an eye at the top and bottom of the volute portions where the short grain can quickly break off.
Now get out there and do some carving! Keep a smile on your face... you do better work that way.