I would like to grow mushrooms on oak trees I can harvest from my property. I've read that the best results will be when the sap is rising but the tree hasn't budded yet. The mycelium feeds on the sugars in the logs.
I would love to be able to measure the sugar content so I could accurately asses the sugar content. Here in Southern Oregon the winters are mild and the leafing out of the oaks varies quite a bit from year to year.
How can I measure sugar content of the sap in a tree?
The difficult step will be getting samples of sap: have a look at the WP page for maple syrup for ideas about methods of tapping into the xylem of your trees.
You will then need to assay sucrose in the sample of sap. There are many commercial assay kits available (Google: sucrose assay), which rely on an enzyme, invertase, to convert the sucrose to glucose + fructose. The released glucose is then measured by a glucose oxidase assay. You would need some kind of colorimeter/spectrophotometer for quantitative results but there is a visible color change, so you could probably get a rough idea of what is going on by visual comparison with a set of glucose standards.
An alternative would be to measure sugar concentration by refractometry: see here and here.