Instruction manual

6
be inserted radially into the plant stem, with the temperature being measured at a point far
enough below the surface of the stem to avoid the unknown losses of heat which had
previously reduced the usefulness of Huber’s method. Marshall’s (1958) work was based
on an analytical solution to the idealized heat flow equation. He used this theory to
calculate the temperature rise at any point in the sapwood following the application of an
instantaneous line source of heat. Thus, Marshall’s contribution was an important first
step in establishing a sound theoretical basis for the heat-pulse method.
Swanson (1962) was one of the first to utilize Marshall’s analytical solutions, by applying
them to the analysis of the ‘compensation’ heat pulse method in which two temperature
sensors are placed asymmetrically either side of a line heater source (Fig. 1). Swanson
showed that if the temperature rise following the release of a pulse of heat is measured at
distances
X
u
[m] upstream and
X
d
[m] downstream from the heater, then the heat-pulse
velocity can be calculated from
V
X
X
t
=
d
u
z
+






2
(1)
where
t
z
[s] is the time delay for the temperatures at points
X
d
and
X
u
to become equal. In
effect, Eq. (1) implies that following the application of an instantaneous heat-pulse, the
centre of the heat-pulse is convected downstream, from the heater, to reach the point mid-
way between the two temperature sensor after a
t
z
. Equation (1) is particularly well suited
to data logging since it only requires electronics to detect a null temperature difference
and an accurate timer to measure
t
z
. The
t
z
’s are the only data that need to be recorded,
since the distances
X
u
and
X
d
remain constant. We refer to this estimate of
V
[m s
-1
] as the
‘raw’ heat -pulse velocity.
1.3 Wound Corrections to the Heat-Pulse Velocity
The calculation of
V
from Eq (1) is based on Marshall’s (1958) idealize d theory and
assumes the heat-pulse probes have no effect on the measured heat flow. In reality,
convection of the heat pulse is perturbed by the presence of the heater and temperature