It's about the dough and the challenges of high altitude and low humidity

Okay, the short story here is that for to get the dough to come together properly, I had to add an additional ¼ cup of water and if my bakers math is correct this says it is a 84% hydration.  The dough however is performing like a normal 66% dough.  I am a relative newb, but serious in my baking.  Am I making a math calc error?  Is anyone else baking in a similar dry environment having to make this large an adjustment?  The rest of the story:

Julia’s French loaf, take 3

When I got my bag of bakery bread flour, I thought I would use Julia Child’s classic French loaf recipe as a base and then figure out adjustments.  I have also started weighing the ingredients to track my baker’s math.

Recipe:

16 oz. or 31/2 cups of flour, (my flour weighs 140 grams/cup, so 3 cups less 2 Tbs)

1 Tbs whole wheat or rye flour

11/3 cup water

2 tsp yeast

21/4 tsp salt

When I mixed this 66% recipe I could not even get the dough to form a ball, there was excess flour in the bowl.  I needed to add 1Tbs water and mix with wet hands, just to get the dough to form a ball.  I live at an altitude of 4,400 feet and the ambient humidity inside rarely goes above 50% and the humidity outside is 25%, so very low.

On my second crack at the recipe, I added an additional 2 Tbs water and the dough came together very well.

This is my third test of the recipe and I have added an additional 4 Tbs of water and this is the best working dough from this batch of flour.  It stretched and folded nicely and was not difficult to work with.  When I did the baker’s math the dough is 84% hydration:

454 g bread

12 grams WW

Total flour 466 grams, 392 grams water = 84%

In my environment this dough is just beginning to look like the dough featured in this King Arthur flour video an mixing and folding:

http://www.kingarthurflour.com/professional/videos.html

I am a little surprised with the hydration number and can’t help think I am making a calculation error.  As they say, it is about the dough and my dough likes a lot more moisture and I figure the altitude and low humidity are the reason.  Here is how things looked after the first 1 hour bulk ferment:

My plan is to bake the next batch with an additional 2 Tbs water above this formula and continue adding water to subsequent batches until I get dough resembling something like Peter Reinhart’s ciabatta or pain ancienne photos from BBA and ABED.

 The adventure continues . . .