# HDF during the drive

In this newsletter we
continue the previous study of the Handle Drag Factor ** HDF** (RBN
2020/01).

**is not dimensionless and similar to the boat, blade and ergometer**

*HDF***, has the dimension**

*DF***:**

*kg/m**DF or HDF = P/v ^{3}
= (kg m^{2}/s^{3})/(m^{3}/s^{3}) = kg/m (1)*

This is a consequence of
general equation for drag coefficient ** C_{d}** of a body
moving in a liquid or gas:

*C _{d} = 2 F_{d}
/ (ρ A v^{2}) (2)*

where ** F_{d} **is
the drag force,

**– mass density of the liquid or gas,**

*ρ***–reference area of the body,**

*A***– velocity of the body movement.**

*v***is truly dimensionless and depends on the shape of the body and the flow characteristics (laminar or turbulent). Combining the equations above,**

*C*_{d}*DF = F _{d}/v^{2}
= C_{d} ρ A / 2 = (kg/m^{3}) m^{2} = kg/m (3)*

Therefore, ** DF**
is a combination of the shape (

**) and the size (**

*C*_{d}**) of the moving body and density of the environment (**

*A***). It could be interpreted as a mass of the liquid or gas displaced for each meter of the body travel.**

*ρ***and**

*DF***have the same dimension and meaning: they are both indicators of ratio of the resistance force to the velocity of movement.**

*HDF*

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**

*∞***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.**

*HDF***The peak**(8)

*HDF*happens straights after the legs velocity peak, when trunk and arms start working**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,

**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 (=-**

*HDF***), 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

**values look similar at the end of the drive.**

*HDF*In the calculation
of average values of ** HDF** over the stroke cycle, using average force

**in Eq.3 would give higher figures compare to power**

*F*_{av}**in Eq.1, because**

*P***is derived only during the drive phase, but**

*F*_{av}**rowing power**

**is distributed over the whole duration of the stroke cycle. Therefore,**

*P***must be multiplied by the rhythm value (ratio of the drive time to the total time of the stroke cycle) to get average**

*F*_{av}**numbers published in RBN 2020/01.**

*HDF*

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,

**higher (2) and a rower feels more pressure. This means,**

*HDF***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*