Let's look at the figures here. The Refractometer(Brix) to specific gravity calculation is a standard that is published all over the place. I just googled around to find one of the many calculators on the web and came upon this one.
http://onebeer.net/refractometer.shtmlFirst, if you want to use a Refractometer as your standard tool, vs. A hydrometer, get used to taking the OG with it to. Without that, you are introducing the error from your hydrometer calibration in 20C distiller water to the error from your reading on the optics of the Refractometer.
Your OG of 1.051 is probably around 12.4 Brix. 12.5 works too, but is farther over than 12.4 is under. You need this original value to get the final gravity. Given the original 12.4 Brix and a final 7.1 Brix yields the 1.014 FG that you calculated.
I may be going off on the wrong tangent here, but the beer smith Value is spot on too, this being a simple calculation. So the problem is calibration.
- did you calibrate with distilled water or tap water? Both for hyrdo and Refractometer.
- did you read the devices at the right way ? Look at the hydro instructions to see where on the meniscus you were looking.
- did you temperature compensate for the hydro ? The Refractometer may be temperature compensating, but your need to put the wort sample on there and wait a while before taking the reading to let it compensate.
- lastly, given that the hydro is quoted at 1 part per thousand roughly, and the Refractometer is onle read at 1 per hundred, you can see that 0.006 is really trivial given all the other areas where error can be induced.
Don't get me wrong, a Refractometer is a great tool to have in the brew kit, but it is not the most accurate if you are aiming for a target gravity and want to be spot on. Your need to get used to reading between the lines (literally on the graticule) to get that kind of accuracy.
It is a great device for checking to see whether the gravity is changing and fermentation is over, but you may want to get a bottling hydrometer with it's expanded scale (Williams brewing has one, but calibrate it and be careful of it's fragility) to get the FG, and don't forget to compensate for the temperature.