One frequently discussed problem with vintage three speeds is high gearing. Raleigh et al usually mounted 18 tooth cogs on their rear hubs, which often makes going uphill a chore. The best way to lower the gearing (and make hill climbing easier) is to swap that small cog with a larger one. Nola Wilken of Restoring Vintage Bicycles from the Hand Built Era recounts her experience of doing so on her 1950 Raleigh Sports Tourist:
Born and bred in the diminutive State of Connecticut, adventurepdx (aka Shawn Granton) has been living in Portland, Oregon, Cascadia, for two decades. Freelance artist and writer by trade. Self-publishing comics since 1996, first TEN FOOT RULE and now NEW OLD STOCK. Involved with the bicycle community in town and rides almost everywhere he can, but also loves riding trains. Loves bike touring! Occasionally puts on Bike Touring Workshops. Lives in a modest house somewhere around the North Tabor neighborhood of NE Portland. And now someone in love with film photography.
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I agree that Sturmey Archer 3 speed hubs are geared very high. There is also the caveat that the drive chainring has to be big enough to give a greater that 1:2 advantage so the torque being applied to the hub planetary gears wouldn’t break them. The overgearing was so bad that if 2nd was geared for good all around flat land performance you really only had a 2 speed bicycle. The 3rd gear was still a very high downhill, downwind gear. I solved all of this by violating the torque specification and mounting a smaller front sprocket and a large rear sprocket. Now 3 gear is a good all around flat land riding gear. 2nd is a good stoplight startout gear and 1st is great for going over freeway overpasses and going up hills. Haven’t broken the hub yet and have had it geared this way for years now.
Society Of Three Speeds 
Reblogged this on Urban Adventure League.
I agree that Sturmey Archer 3 speed hubs are geared very high. There is also the caveat that the drive chainring has to be big enough to give a greater that 1:2 advantage so the torque being applied to the hub planetary gears wouldn’t break them. The overgearing was so bad that if 2nd was geared for good all around flat land performance you really only had a 2 speed bicycle. The 3rd gear was still a very high downhill, downwind gear. I solved all of this by violating the torque specification and mounting a smaller front sprocket and a large rear sprocket. Now 3 gear is a good all around flat land riding gear. 2nd is a good stoplight startout gear and 1st is great for going over freeway overpasses and going up hills. Haven’t broken the hub yet and have had it geared this way for years now.