### 1. Penalty curve

As in reality, the maneuvers and sail changes times are variable in Virtual Regatta, depending on the force of the wind and the boat used.

On this page , we find the different maneuvering times for each boat as well as the following curve :

On global way, the maneuver time $T_m$ is equal to :

- the minimum maneuvering time $ T_ {min} $ if the wind speed (TWS) is less than 10 knots,
- the maximum maneuvering time $ T_ {max} $ if the wind speed (TWS) is greater than 30 knots (until exception),
the result of the following calculation : $$T_m(tws) ={ {{(T_{max} - T_{min}) \times f(tws)}\over 100} + T_{min}}$$

With :

- $T_m(tws)$ : Maneuver time
- $T_{min}$ : Minimum maneuvering time
- $T_{max}$ : Maximum maneuvering time
- $f(tws)$ : Normalized contribution from 0 to 100% of the reference curve

### 2. Reference curve $f(tws)$

Using the curve provided by VR, we created a reference curve..

To do so, the curve provided was printed in large format on graph paper..

Finally, the equation of the raised curve was approximated using a spreadsheet..

In green, the raised curve.

In red, the curve resulting from the equation.

$$f(tws) ={8,21565 \times 10^-15 \times tws^6 + 0,00025679 \times tws^5 - 0,025678992 \times tws^4 \\+ 0,956690978 \times tws^3 - 16,3150717 \times tws^2 + 130,3637174 \times tws - 397,862533 }$$

Thanks to this equation as well as to the reference values of the various maneuvers contained in the polars of the game, ** ITYC.fr ** is able to calculate for each 1 / 10th of a knot of wind, the value of the penalty that will be applied for all types of boats.