I did a rebuild of the GPR a couple years ago for my buddy Brian Dancey. We had no intension of making it look like a Hawken, I don't think, but it ended up that way. Probably because Hawken's geometry is so much more pleasing to the eye than the Lyman rifle's. I took out most of the perch belly, greatly altered the curve of the wrist from the breech to the comb, lock panels, cheek piece, and forearm. I exchanged the escutcheon plate for pure silver, and added some other inlays per Brian's taste. I don't know what the wood is - walnut of some kind - but is harder than anything I've ever carved before or since. Oh yeah, I browned the barrel, rib and thimbles, triggers and guard, and butt plate, and case hardened the nose piece and screws.
There isn't much you can do to improve the butt plate...it has much too short a heel. that's perhaps the single biggest complaint I have of this design, and of the design of Hawken plates that are currently available on the market today. Don Stith has the only plates of which I am aware, that are correct. Perhaps someone else can suggest other venders that have correct plates.
In answer to a diminishing number of requests, I have erased the photobucket images and replaced them using our new service, and added a few more from my files.
Regarding the profile of the GPR, I think the single most important improvement that you can make is to take the standing breech tang out of the stock, straighten out that terrible hump, rebend it closer to the break-off, reinlet it and file away those two bevels along the edges ( I don't know what they were for). This will make the top curve of the wrist more gentle, more pleasing, and more like a Hawken rifle.
Someone made a great observation regarding Hawkens and other fur trade era plains rifles. There were lots of builders, right in St. Louis that were contemporary to the Hawken boys, and they made some wonderful rifles. Volume III of Gordon's books on this subject has pages of rifles by other makers and most are very neat, rivaling Hawken's design. So don't be afraid to let your imagination loose.
As an example, I have included an image of the stock barrel slide escutcheon which is a skinny football shaped piece of steel pressed into a too-large hole filled with soft putty. I made new escutcheons out of pure silver and I think they add a great deal of interest to the otherwise fairly plain rifle.
I used the factory sights. The rifle also has L & R's replacement flintlock. It works very well whereas I was unable to get the factory lock to make ANY sparks. But I have seen other GPRs whose stock locks work well...go figure.
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