Sap Flux Heat Calculations

By: Brett Stoddard


By far the most annoying part of designing a thermal sap flux probe sensor is the “thermal” part. Without a proper heat pulse, there is no sensor. The problem is generating heat requires raw energy. According to my calculations, the heater makes up ~99% of the total energy requirements for this sensor. One of the goals of this project is to make the sap flow sensor as energy efficient as possible which will require a lot of testing to find the most efficient way to send out a heat pulse.

The Knobs

To find that maximum efficiency, there are a couple of design “knobs” that can be adjusted to find the maximum efficiency. Unfortunately, due to the short amount of time on this project, not all of these are going to be tested. Here is a list with what I believe are going to be the most important factors first:

  • Energy Delivered (joules)
  • Time of Pulse (second)
  • Depth into Tree (inches from the edge of the tree’s cambium)
    • There’s a possibility that a “wrap” sensor could be possible like Dynamax’s Dynagague which uses thermojunctions on a flexible PCB
  • Size of the Probe

The *IDEAL* Physics

I’ve put together a simple spreadsheet of a few different heater resistance values. Since this sensor is primarily being designed to integrate into other OPEnS Lab projects (namely the Evaporometer) a 3.7 voltage supply is assumed (uses 3.3V logic but runs off of a 3.7V battery, the heater will draw power from the battery).

Linked here is a google sheets file that I’ve been using to estimate the heat increase of the tree directly around the probe, and calculate the power requirements from the total resistance of the heater. 

One thing that should be noted when finalizing the resistance: the wattage rating for the resistor. There exists a lot of SMT resistors on the market, Digikey lists near 50 thousand, however, only a small minority possess the wattage requirements to provide that much heat (this can be seen in the “wattage” column of the attached table). If a resistor is chosen that does not satisfy the wattage requirements it will most likely fail. If a specific resistance is desired that is not available at this wattage, two identical resistors can be placed together in series, essentially halving this wattage requirement.

The temperature delta was calculated assuming that the heat capacitance of sapwood is 8 joules/C. This is an estimation. Further research into the exact heat capacitance of sapwood should be conducted.