Coefficients and ratios
From KayakWiki
Meaning of Variables
| A | Area. |
| B | Beam. Also BWL - Beam at the waterline |
| C | coefficient. |
| D | Displacement. |
| F | Freeboard - the height of the sheer above the waterline. |
| FA | Freeboard aft. |
| FF | Freeboard foreward. |
| FM | Freeboard midships. |
| H | Draft or depth of a hull underwater. |
| g | Acceleration due to gravity |
| L | Length. Also LWL, Length at the waterline. |
| V | Velocity or speed. |
| WS | Wetted surface area. This is the area of the hull that is in contact with the water. |
| ν | Viscosity |
| ∇ | The volume of the hull that is below the waterline. This is also an indication of displacement, since the displacement is this volume times the density of water. |
[edit] Ratios
- Beam/Length ratio
- B/L The ratio of the beam to the length, both being measured at the waterline.
- Length/Beam ratio
- L/B The ratio of the length to the beam, both being measured at the waterline.
- Speed/Length ratio
- V/√L See Hull speed
[edit] Coefficients
Coefficients are dimensionless values that are used to compare, qualify and quantify properties in hydrodynamics. They are dimensionless because the dimensions of the variables in the numerator and denominator cancel each other out. By being dimensionless, they can be compared without regard to the physical size, speed, weight or other parameter. In this manner, kayaks with different properties can be compared objectively.
- Block Coefficient
- Cb = ∇/LBH The ratio of the volume of the hull underwater to the volume of a rectangular solid with the same submerged length, width and depth as the hull.
- Froude Number
- Fn = V/√gL The ratio of inertial forces in a fluid to the gravitational forces. Two kayaks with a similar shape and the same Froude number will have similar wave patterns forming even if their lengths are different. This, in turn, results in them having wave-making resistances that are proportional.
- Prismatic Coefficient
- Cp = ∇/AxL The ratio of the volume of hull underwater to the volume of a solid with the same submerged length and cross section as the hull at its widest point.
- Reynold's Number
- Re = VL/ν The Reynold's number reflect the ratio of inertial forces to the viscous forces. It represents resistance exclusive of wave-making resistance.
- Section Coefficient
- Cx = Ax/BH The ratio of the area of the largest cross section underwater to the area of a rectangle having the same beam and draft.
- Volumetric Coefficient
- Cv = ∇/(L/10)3 The ratio of the volume to the cube of one-tenth of the length. This is a measure of the fatness or fineness of the hull. It is a better indication of fineness than the Beam/Length ratio, since the resistance felt has more to do with moving a volume through water than the width.
- Wetted Surface Coefficient
- Cws = WS/√(∇L) This coefficient allows us to compare two kayaks with different lengths and displacements.
[edit] Notes
- Note that the block coefficient, prismatic coefficient and section coefficient are related: Cb = CpCx.
- Note that the speed/length ratio is equal to the Froude number times √g
References:
