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HDF during the drive

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