# Balance of forces on the boat hull

Experiments with comprehensive
force measurements were conducted recently with new the ** BioRow**
instrumented C-bracket, which was mounted on a wing rigger (Fig.1) and measured
3D force at the pin: in horizontal

**, side**

*Fp*_{H}**and vertical**

*Fp*_{S}**directions. Forces at the gate were measured with the**

*Fp*_{V}**2D instrumented oarlock at the normal to the oar axis**

*BioRow***and axial direction**

*Fg*_{N}**.**

*Fg*_{A}The stretcher force was determined
at three points with ** BioRow**
v.2009 sensors (RBN 2013/08), which measured the horizontal force components

**only (Fig.2).**

*Fs*_{H}Other biomechanical variables
were measured with the standard ** BioRow**
system (Fig.3): oar angles in horizontal

**and vertical**

*Ah***planes (RBN 2009/10), seat and trunk movements (2014/12), boat speed, acceleration and rotations (2012/03), wind speed and direction (2013/06).**

*Av*A male sculler (1.84m, 84kg)
performed 8 short rowing pieces of ~200m each, increasing stroke rate from 17.2
up to 41.5 spm. The data for each sample was processed using the standard ** BioRow** method (RBN 2017/12),
and the penultimate sample of 35.5spm is presented below (Fig.3).

The sum of three stretcher
forces ** Fs_{H}** was subtracted
from the sum of horizontal components of both pin forces

**, which resulted in propulsive force applied to the boat hull**

*Fp*_{H}**(Fig.4):**

*Fb*_{H}The propulsive force at the
boat ** Fb_{H}**
is the sum of the boat inertia force

**(**

*m*_{b }a_{b}**=16.7kg is the full boat mass,**

*m*_{b}**is its acceleration) and drag force at the hull**

*a*_{b}**, which could be determined directly from our measurements.**

*F*_{d}*F _{d} = Fb_{H}
- *

*m*_{b}

_{ }

*a*_{b}

*(2)*This drag force calculated
with our force measurements ** F_{d}(F)** was compared with
the drag force calculated from the boat velocity

**and drag factor**

*v***:**

*DF***, and the difference was determined as**

*F*_{d}(v)=DF v^{2}**.**

*D*_{Fd}= F_{d}(F)- F_{d}(v)The curves of the drag force
calculated with different methods appeared to be quite close (Fig.5). The small
difference could be explained by the force on the slides, which arises from two
factors: gravitation and friction. After the catch, the boat pitch has maximal
negative values of about -1deg (stern â€“ down, bow - up), plus a 1deg slides
pitch relative to the boat. The rowerâ€™s mass moves slightly upwards, which
creates forward force at the slides ** F_{sl}=sin(A_{p}) m_{r}g**.
At the total slide angle

**=2deg and the moving rowerâ€™s mass**

*A*_{p}**=60kg (weight of legs subtracted), a force**

*m*_{r}**of ~20N pushes the boat forward at slides, but it was not measured and accounted for here in the force balance. Therefore, the drag force**

*F*_{sl}**was calculated higher than its real value (Fig.5,1).**

*F*_{d}(F)During the drive, the boat
pitch became positive up to +1deg (stern goes up, bow â€“ down), so the slide
angle became close to zero and only the friction force at the wheels of the
slide affects the total balance of forces. At the finish, this creates a few fluctuating
peaks (2), when the seat moves fore-aft and may hit back-stops. During the recovery,
the friction force at the seat pushes the boat backwards, which shifts the
measured balance of forces in a negative direction (3).

The average drag force **Fd**
over the stroke cycle was compared with the average boat speed

**for each of eight samples. It was found that the best fit equation is different from the traditionally used:**

__v__**(R**

__Fd__= 2.59__v__^{2.1726}^{2 }= 0.989). In fact, the average

**was found to be ~12% higher than**

*F*_{d}(F)**. This will be further discussed in future publications.**

*F*_{d}(v)Concluding: **For the first time, the drag force on the
boat was determined directly with BioRow**

**measurements, which can be used for evaluation of rowing technique and equipment quality**.

**Â©****2019 Dr. Valery Kleshnev ***www.biorow.com*