Energy cost and efficiency of Venetian rowing on a traditional, flat hull boat (Bissa)

Abstract

The total net metabolic power output ($\dot{E}$, kW) required to scull a traditional, flat hull boat—the “Bissa”, 9.02 m long and weighting about 500 kg including the crew—was assessed at different constant speeds (ν) ranging from 2.44 to 3.75 m s⁻¹. $\dot{E}$ increased with the speed: $\dot{E}$ = 0.417 × e ^0.664v; r ² = 0.931. The amount of metabolic energy spent per unit distance (C, J m⁻¹) to move the “Bissa”, calculated by dividing $\dot{E}$ by the corresponding ν, was a linear function of ν: C = 0.369 ν –0.063; r ² = 0.821. The hydrodynamic resistance met by the boat in the water—drag (D, N)—was estimated by analysing the decay of the reciprocal of ν as a function of time measured during several spontaneous deceleration tests carried out in still water and by knowing the total mass of the watercraft plus crew. D increased as a square function of speed: D = 12.76 v ². This allowed us to calculate the drag efficiency (η_d), as the ratio of D to C: η_d increased from 8.9 to 13.7% in the range of the speeds tested. The “Bissa” turned out to be as economical as other flat hull, traditional watercrafts, such as the bigger Venetian gondola, and her η_d was similar to that of other modern and traditional watercrafts.

Appendix

The drag of the boat with the crew was measured by applying the method proposed by Bilo and Nachtigall (1980). This method, originally developed to estimate the floating drag and the drag coefficient (C _D) of penguins gliding underwater, is based on the analysis of the spontaneous deceleration. In the following paragraphs, a short description of the approach is reported.

Water drag (D) is described by the following equation:

$$ D = {{C_{\text{D}} \times A \times \rho \times v^{2} } \mathord{\left/ {\vphantom {{C_{\text{D}} \times A \times \rho \times v^{2} } 2}} \right. \kern-\nulldelimiterspace} 2} $$

(3)

where A (m²) is the characteristic area of the moving object in water, ρ is the water density (kg m⁻³) and ν (m s⁻¹) is the speed of the moving object.

In turn, C _D can be expressed, by manipulating Eq. 3, as:

$$ C_{\text{D}} = {{2D} \mathord{\left/ {\vphantom {{2D} {\left( {A \times \rho \times v^{2} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {A \times \rho \times v^{2} } \right)}} $$

(4)

During spontaneous deceleration of the boat in the water, the reciprocal of the speed (ν⁻¹) is a linear negative function of the time t of deceleration. Indeed, in this context, the inertial force F(t) always counterbalances D:

$$ F\left( t \right) = - D\left( t \right) $$

(5)

According to the second principle of the Newtonian dynamics, F(t) is given by:

$$ F\left( t \right) = ma\left( t \right) $$

(6)

where, m is the overall mass of the object and a is the acceleration—negative acceleration in this case: a = dv/dt. Since, at the speeds investigated the present study—i.e., at rather large values of the Reynold’s number, D is adequately expressed by Eq. 3, the combination of Eqs. 5 and 6 yields:

$$ ma\left( t \right) = {{ - C_{\text{D}} \times A \times \rho } \mathord{\left/ {\vphantom {{ - C_{\text{D}} \times A \times \rho } {2v^{2} \left( t \right)}}} \right. \kern-\nulldelimiterspace} {2v^{2} \left( t \right)}} $$

(7)

Equation 7 is a differential non-linear equation that, however, can be simplified as follows: we can describe a(t) proportional to the square of the speed ν:

$$ a\left( t \right) = - {\text{c}}v^{2} \left( t \right) $$

(8)

where

$$ c = {{\left( {C_{\text{D}} \times A \times \rho } \right)} \mathord{\left/ {\vphantom {{\left( {C_{\text{D}} \times A \times \rho } \right)} m}} \right. \kern-\nulldelimiterspace} m} $$

(9)

By integrating Eq. 8, we easily obtain the following equality:

$$ v\left( t \right) = {1 \mathord{\left/ {\vphantom {1 {\left( {y_{\text{0}} + {\text{c}}t} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {y_{\text{0}} + {\text{c}}t} \right)}} $$

(10)

where 1/y ₀ = v _o at t = 0, i.e., the initial speed at the beginning of the deceleration. Equation 10 is liable to be easily transformed into a linear equation:

$$ y\left( t \right) = {\text{c}}t + y_{\text{0}} $$

(11)

where y(t) = 1/ν (t). The slope c is obviously obtained by fitting the data pairs of t _i and v _i recorded during the first 10–13 s of spontaneous deceleration by means of a linear equation. Provided we know m, A and ρ of the water, the dimensionless C _D can be now calculated as:

$$ C_{\text{D}} = c\left( {{{2m} \mathord{\left/ {\vphantom {{2m} {A\rho }}} \right. \kern-\nulldelimiterspace} {A\rho }}} \right). $$

(12)

In the present investigation m was the overall mass of the boat with oars and full crew (489.4 kg), A, the characteristic area of the object, was the maximal frontal submerged area of the boat, (0.092 m²) and ρ was the distilled water density (998 kg m⁻³) prevailing at a water temperature of 21°C. Therefore, D of the boat could be finally estimated by means of Eq. 3 assuming that it was strictly proportional to the square of the speed of progression.