HDF during the drive
In this newsletter we
continue the previous study of the Handle Drag Factor HDF (RBN
2020/01). HDF is not dimensionless and similar to the boat, blade
and ergometer DF, has the dimension kg/m:
DF or HDF = P/v3
= (kg m2/s3)/(m3/s3) = kg/m (1)
This is a consequence of
general equation for drag coefficient Cd of a body
moving in a liquid or gas:
Cd = 2 Fd
/ (ρ A v2) (2)
where Fd is
the drag force, ρ – mass density of the liquid or gas, A
–reference area of the body, v – velocity of the body movement. Cd
is truly dimensionless and depends on the shape of the body and the flow
characteristics (laminar or turbulent). Combining the equations above,
DF = Fd/v2
= Cd ρ A / 2 = (kg/m3) m2 = kg/m (3)
Therefore, DF
is a combination of the shape (Cd) and the size (A)
of the moving body and density of the environment (ρ). It could
be interpreted as a mass of the liquid or gas displaced for each meter of the
body travel. DF and HDF have the same dimension and
meaning: they are both indicators of ratio of the resistance force to the
velocity of movement.
Equation 3 allows us to derive instantaneous HDF values during the drive phase from the measured handle force and velocity (Fig.1):
HDF is not defined (equal to infinity ∞)
at catch (1), when the handle velocity crosses zero. Then HDF
decreases, when the handle velocity rapidly increases (2), while blade enters the
water (3). After about 8-10% of the drive time, HDF has a pit (4),
which coincides with the moment of full blade immersion (5). The handle
velocity curve bends here (6), its growth becomes slower, and HDF
increases to achieve its peak value (7) at 18-20% of the drive time. The
peak HDF happens straights after the legs velocity peak, when trunk and
arms start working (8) and the boat acceleration has its first peak. This
moment could be felt by a rower as “the blade locks on” (Prof. Volker Nolte
expression). After the peak, HDF continuously decreasing (9), because
the dynamic oar gearing gets lighter. HDF became negative just before
finish (10), when the handle force becomes negative (because of oar inertia)
and the blade exits the water (11). At finish (12), HDF is not
defined again (=-∞), when the handle velocity crosses zero.
The pattern of HDF is quite consistent across various stroke rates and rowing styles (Fig.2):
In this
sculler, the catch angle gets shorter at higher rates, so HDF magnitude
decreases, which was mentioned before (RBN 2020/01). However, the pit is happening
at the same 8-10% of the drive time and 3-4% of the stroke length, the peak is achieved
at a similar time and position, and HDF values look similar at
the end of the drive.
In the calculation
of average values of HDF over the stroke cycle, using average force
Fav in Eq.3 would give higher figures compare to power
P in Eq.1, because Fav is derived only during
the drive phase, but rowing power P is distributed
over the whole duration of the stroke cycle. Therefore, Fav
must be multiplied by the rhythm value (ratio of the drive time to the total
time of the stroke cycle) to get average HDF numbers published in
RBN 2020/01.
It is interesting how the stiffness of the oar affects HDF pattern and the rower’s qualitative boat feel (Fig.3):
The softer oar has more bend
after the catch, when the force grows up, which makes handle velocity slightly
higher, HDF lower (1) and rower’s feelings lighter. When force
decreases during the second half of the drive, the softer oar recoils more and later,
which makes handle velocity slower, HDF higher (2) and a rower
feels more pressure. This means, a softer oar makes HDF and rower’s
feelings of pressure more evenly distributed during the drive.
Acknowledgements. Thanks for Prof. Volker Nolte
for productive discussion and reviewing this article.
©2020 Dr. Valery Kleshnev www.biorow.com