Trans RINA, Vol 152, Part B1, Intl J Small Craft Tech, 2010 Jan-Jun Z
z-plane (deck plane)
φ (negative) CL Y CD z-plane
Figure 1: Lift and drag coefficient and effective angle are defined in the heeled z-plane (deck plane)
insensitive to the flow component along their span (i.e. along their mast) and that only the flow component along the chord produces the lift and drag forces. Jackson [8] discusses this further and reiterates that it is therefore feasible to model the sails as only being influenced by the flow component in the deck plane (z-plane) shown in Figure 1, which heels with the yacht. The flow in the z- plane is called the effective flow and is calculated from its geometric relationship to the apparent flow in the horizontal plane. The effective wind angle (βeff) and speed (Veff) are calculated from the apparent wind angle (βA) and the heel angle (φ) with
βeff = − () [ and
tan tan1 eff = A A cos , A sin V V −1 sin 2β φ2 , β φ βeff ∈ 0 ,180 ] (1) (2)
where VA is the apparent wind speed in the horizontal plane. In this study βeff and Veff are calculated at the geometric centre of sail area height above the water while the true wind speed (VT) is given at the standard reference height of 10m above the water.
By employing the effective angle concept CL, CD and the centre of effort position are modelled relative to the z-
plane as functions of only βeff instead of βA and φ. CL and CD, as force coefficients (CF), relate to the respective force (F) through
F C A q C A ρ= = F S eff F S
2 eff air
V 2 , (3)
where AS is the reference sail area, ρair is the density of air and qeff is the effective dynamic pressure. The reference area is taken as the rated International Measurement System (IMS) sail area defined by Poor [9], as
A ASmain 1.16
S = +
I J , 2
(4)
where ASmain is the mainsail cloth area and I is the fore triangle height and J is the fore triangle length. Note that the total IMS sail area is used to calculate force coefficients even if the sails are reefed.
In this study the position of the centre of effort is defined as the intersection of the central axis with the centreline plane of the yacht according to Hochkirch [10]. The central axis is aligned with the force vector (F) and F can be applied anywhere along the central axis to produce the
X βeff
same moment vector (M). The point (a) on the central axis that is closest to the origin can be determined from
a F M×= F
2 . (5)
The intersection of the central axis and centreline plane is the centre of effort defined by the longitudinal position (xCoE) and the height (zCoE), which can be calculated from
xCoE = −a F Fa x
Y y
Y y
X ,
zCoE = −a F Fa z
Z . 3. EXPERIMENTAL PROCEDURE
The experimental study was carried out by conducting force measurements in the Twisted Flow Wind Tunnel of The University of Auckland on a scale model of a 10m IMS cruiser/racer as shown in Figure 2 utilising the Real- Time VPP. The forces were measured by a six- component force balance, located under the turntable of the wind tunnel, to which the model was attached. From calibration measurements a mean error in the x-direction of ±0.09N is obtained. In the y-direction the mean error is ±0.11N and in the z-direction it is ±0.27N. For typical measurements this results in an accuracy of ±1% in the x and y-direction and ±5% in the z-direction.
(6) (7)
Figure 2: 1:6.67 scale wind tunnel model of a 10m IMS cruiser/racer yacht used for the investigations
©2010: The Royal Institution of Naval Architects B-11
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60