So...in our world, ie. racing sailboats, if you are going upwind, you are being Sucked. If you are going downwind, you are being Blown.
Sucked or Blown, that is the question. And here's some light math for you to figure it out:
value of effort
The plots of air strike sail on both sides so:
On the windward side efforts are atmospheric pressure, wind pressure, and virtually no depression due to wind.
On the leeward side efforts are atmospheric pressure, a bit of depression and almost no wind pressure.
To simplify the manipulation of these forces, the forces are summed into a single force and that the entire surface of the profile (sailing) in a simple formula (valid for airplane wings like a rudder, a sail, an anti Plan -drift) [7]:
[8]
with
E = effort that can give up the wind (see Max Q);
C = coefficient Aerodynamic
According to the Bernoulli, the maximum stress of wind or density of kinetic energy maximum for the entire surface of the sail:
The full expression of the force is:
with
F = lift, expressed in Newton
ρ (rho) = density air (ρ varies with the temperature and the pressure) ;
S = typical surface, for sail, it is the sail area in m²
C = coefficient Aerodynamic. Aerodynamic coefficient is unit-less, it is the sum of two percentages: the percentage of recovered energy leeward side + percentage of the recovered energy into the wind. For this reason, the coefficient aerodynamics can be greater than 1. It depends on the angle of upwind sailing.
V = Speed is the speed of the wind relative to the sail (Apparent wind) in m / s.
The sail is deformed by the wind and takes a form named Airfoil. When the flow of air around the profile is Laminar [9], the factor against depression in the wind becomes crucial. This effect is then called lift. Studies and theory to draw a sail [10] that:
Depression on the upper (leeward side) represents two thirds of the lift,
The pressure on the lower surface (facing the wind) represents one third of the lift.
[edit] Lift effect on sail
The study effect of lift can compare cases with and without lift [11]. A typical example is a gaff sail. The sail is rectangular and is approximately vertical. The sail has an area of 10 sqm, with 2.5m of foot by 4m of leech. The apparent wind is 8.3 m / s (about 30 km / h). The boat is supposed to uniform velocity, no wave. It does not heel, does not pitch. The density of air is set at: ρ = 1.2kg / m3
[edit] turbulent flow or downwind
The boat is running downwind. The shape of the sail is approximated by a plane perpendicular to the apparent wind.
The depression effect on the sail is second order, and therefore negligible, it remains:
On the windward side, efforts are atmospheric pressure and wind pressure
On the leeward side, there remains only the atmospheric pressure
Efforts to atmospheric pressure cancel out. There remains only pressure generated by the wind.
Roughly speaking, shock of parcel on the sail forward all their energy from wind in 90% of the surface of the sail. This means that the Cz or aerodynamic lift coefficient is equal to 0.9.
[edit] laminar flow
The boat is Close hauled. The wind has an angle of about 15 degrees with chord of the sail.
Because the setting of the sail at 15 ° relative to the apparent wind, the camber of the sail creates a lift. In other words, the effect of depression on the leeward side is not neglected. As air pressure forces cancel out, efforts remain are:
On the windward side, wind pressure,
On the leeward side, wind depression.
The only unknown is the drag coefficient to be estimated. Curve takes a good adjustment of sail is close to upper shape NACA 0012[12][13]. A sail less well adjusted or older technology (old rig), will be more hollow, more camber. The coefficient of aerodynamic lift will be higher but the sail will be less efficient (lower finesse). The profiles would be more suitable profiles as NACA 0015, NACA 0018 [14].
For a given profile, there are tables which giving the lift coefficient of the profile. The lift coefficient (Cz) depends on several variables:
Incidence (angle: apparent wind / Profile)
The lift hill of the sail, which depends on its extension,
The surface roughness and Reynolds number, which affect the flow of fluid (laminar, turbulent).
The coefficient is determined for a fluid stable and uniform, and a profile of infinite extension.
The Reynolds number is:
with
U - fluid velocity or apparent wind [m / s]
L- characteristic length or foot of the sail [m]
ν - kinematic viscosity fluid: ν = η / ρ [m / s]
ρ - density air [kg / m³]
μ - dynamic viscosity air [Pa] or Poiseuille [pl]
so for this sail about Re = 106
Under an incidence of 15 ° and a Reynolds number to one million, reached a NACA0012 Profile Cz 1.5 instead of 0.9 for 90 ° incidence.
The lift has increased by 50%. This also corresponds on sheet an increase of 50% effort for the same apparent wind.[15][16]
