A ship travelling in still air experiences air resistance on its above-water hull and superstructure. The level of air resistance will depend on the size and shape of the superstructure and on ship speed. Some typical values of air resistance for different ship types, as a percentage of calm water hull resistance, are given in Table 3.6.
The air drag of the above-water hull and superstructure is generally a relatively small proportion of the total resistance. However, for a large vessel consuming large quantities of fuel, any reductions in air drag are probably worth pursuing. The air drag values shown are for the ship travelling in still air. The proportion will of course rise significantly in any form of head wind.
The air drag on the superstructure and hull above the waterline may be treated as the drag on a bluff body. Typical values ofCDfor bluff bodies forRe>103 are given in Table 3.7.
When travelling into a wind, the ship and wind velocities and the relative velocity are defined as shown in Figure 3.25.
Table 3.7.Approximate values of drag coefficient for bluff bodies, based on frontal area
Item CD
Square plates 1.1
Two-dimensional plate 1.9
Square box 0.9
Sphere 0.5
Ellipsoid, end on (Re2×105) 0.16
VA VT
VS
β γ
Relative wind velocity
Figure 3.25. Vector diagram.
The resistance is
RA=12ρaCDAPVA2, (3.51) whereApis the projected area perpendicular to the relative velocity of the wind to the ship,VAis the relative wind and, for air,ρa=1.23 kg/m3, see Table A1.1.
It is noted later that results of wind tunnel tests on models of superstructures are normally presented in terms of the drag force in the ship fore and aft direction (X-axis) and based onAT, the transverse frontal area.
3.2.2.2 Shielding Effects
The wake behind one superstructure element can shield another element from the wind, Figure 3.26(a), or the wake from the sheerline can shield the superstructure, Figure 3.26(b).
Figure 3.26. (a) Shielding effects of superstructure.
Figure 3.26. (b) Shielding effects of the sheerline.
CD
90° 180°
Relative wind
angle β
CD = 0.6–0.8 based on relative wind velocity
Head wind
Figure 3.27. Typical air drag data from model tests.
3.2.2.3Estimation of Air Drag
In general, the estimation of the wind resistance involves comparison with model data for a similar ship, or performing specific model tests in a wind tunnel. It can be noted that separation drag is not sensitive toRe, so scaling from model tests is generally acceptable, on the basis thatCDs=CDm.
A typical air drag diagram for a ship model is broadly as shown in Figure 3.27.
Actual wind tunnel results for different deckhouse configurations [3.44] are shown in Figure 3.28. In this particular case,CXis a function of (AT/L2).
Wind drag data are usually referred to the frontal area of the hull plus super- structure, i.e. transverse areaAT. Because of shielding effects with the wind ahead, the drag coefficient may be lower at 0°wind angle than at 30°wind angle, whereCD
is usually about maximum, Figure 3.27. The drag is the fore and aft drag on the ship centreline X-axis.
0
−8
−4 0 4 8 12
Deckhouse configuration a b c d
• (sharp edges)
• (round edges R = 2.7 m)
• (round edges R = 4.2 m)
30 60 90 120 150 γR(•) 180
Cx ã103
Figure 3.28. Wind coefficient curves [3.44].
In the absence of other data, wind tunnel tests on ship models indicate values of aboutCD=0.80 for a reasonably streamlined superstructure, and aboutCD=0.25 for the main hull. ITTC recommends that, if no other data are available, air drag may be approximated fromCAA=0.001AT/S, see Chapter 5, whereATis the transverse projected area above the waterline andSis the ship hull wetted area. In this case, Dair=CAA× 12 ρSV2. Further typical air drag values for commercial ships can be found in Shearer and Lynn [3.45], White [3.46], Gould [3.47], Isherwood [3.48], van Berlekom [3.49], Blendermann [3.50] and Molland and Barbeau [3.51].
The regression equation for the Isherwood air drag data [3.48] in the longitudinal X-axis is
CX =A0+A1 2AL
L2
+A2 2AT
B2
+A3 L
B
+A4 SP
L
+A5 C
L
+A6(M), (3.52)
where
CX = FX
0.5ρaATVR2, (3.53)
andρais the density of air (Table A1.1 in Appendix A1),Lis the length overall,Bis the beam,ALis the lateral projected area,ATis the transverse projected area,SPis the length of perimeter of lateral projection of model (ship) excluding waterline and slender bodies such as masts and ventilators,Cis the distance from the bow of the centroid of the lateral projected area,Mis the number of distinct groups of masts or king posts seen in the lateral projection.
The coefficients A0–A6 are tabulated in Appendix A3, Table A3.1. Note, that according to the table, for 180°head wind,A4 andA6are zero, and estimates ofSP andMare not required. For preliminary estimates,C/Lcan be taken as 0.5.
Examples ofCDfrom wind tunnel tests on representative superstructures of fast ferries [3.51] are shown in Figure 3.29. These coefficients are suitable also for mono- hull fast ferries.
3.2.2.4 CFD Applications
CFD has been used to investigate the flow over superstructures. Most studies have concentrated on the flow characteristics rather than on the forces acting. Such studies have investigated topics such as the flow around funnel uptakes, flow aft of the super- structures of warships for helicopter landing and over leisure areas on the top decks of passenger ships (Reddyet al. [3.52], Sezer-Uzolet al. [3.53], Wakefieldet al. [3.54]).
Moatet al. [3.55, 3.56] investigated, numerically and experimentally, the effects of flow distortion created by the hull and superstructure and the influences on actual onboard wind speed measurements. Few studies have investigated the actual air drag forces numerically. A full review of airwakes, including experimental and computa- tional fluid dynamic approaches, is included in ITTC [3.57].
3.2.2.5 Reducing Air Drag
Improvements to the superstructure drag of commercial vessels with box-shaped superstructures may be made by rounding the corners, leading to reductions in drag.
The aerodynamic drag coefficient CD is based on the total transverse frontal area of superstructure and hulls
CD = 0.88
CD= 0.67
CD = 0.50
CD = 0.56
CD = 0.55
CD = 0.64
CD= 0.50 No. 0
No. 1
No. 2
No. 3
No. 3a
No. 4
No. 5
Superstructure shape Drag Coefficient
Figure 3.29. Drag on the superstructures of fast ferries [3.51].
It is found that the rounding of sharp corners can be beneficial, in particular, for box-shaped bluff bodies, Hoerner [3.37] and Hucho [3.58]. However, a rounding of at leastr/BS=0.05 (whereris the rounding radius andBSis the breadth of the super- structure) is necessary before there is a significant impact on the drag. At and above this rounding, decreases in drag of the order of 15%–20% can be achieved for rectan- gular box shapes, although it is unlikely such decreases can be achieved with shapes which are already fairly streamlined. It is noted that this procedure would conflict with design for production, and the use of ‘box type’ superstructure modules.
A detailed investigation into reducing the superstructure drag on large tankers is reported in [3.59].
Investigations by Molland and Barbeau [3.51] on the superstructure drag of large fast ferries indicated a reduction in drag coefficient (based on frontal area) from about 0.8 for a relatively bluff fore end down to 0.5 for a well-streamlined fore end, Figure 3.29.
3.2.2.6Wind Gradient Effects
It is important to distinguish betweenstill airresistance and resistance in a natural wind gradient. It is clear that, as air drag varies as the relative air speed squared, there will be significant increases in air drag when travelling into a wind. This is discussed further in Section 3.2.4. The relative air velocity of a ship travelling with speedVsin
Vs
Figure 3.30. (a) Relative velocity in still air.
Vs Vw
Figure 3.30. (b) Relative velocity in head wind.
still air is shown in Figure 3.30(a) and that of a ship travelling into a wind with speed Vwis shown in Figure 3.30(b).
Normally, relative wind measurements are made high up, for example, at mast head or bridge wings. Relative velocities near the water surface are much lower.
An approximation to the natural wind gradient is V
V0 = h
h0 n
(3.54) wherenlies between 1/5 and 1/9. This applies over the sea; the indexnvaries with surface condition and temperature gradient.
3.2.2.7 Example of Gradient Effect
Consider the case of flow over a square box, Figure 3.31.V0 is measured at the top of the box (h=h0). AssumeV/V0=(h/h0)1/7andbandCDare constant up the box.
Resistance in a wind gradient is R= 1
2ρbCDV02 h0
0
h h0
2/7
dh
V0
b
Figure 3.31. Illustration of wind gradient effect.
i.e.
R=1
2ρbCDV02 h20/7
h9/7ã7
9 h0
0
and
R=12ρbCDV02ã79h0= 79R0=0.778R0. (3.55) Comparative measurements on models indicateR/R0of this order. Air drag correc- tions as applied to ship trial results are discussed in Section 5.4.
3.2.2.8Other Wind Effects
1. With the wind off the bow, forces and moments are produced which cause the hull to make leeway, leading to a slight increase in hydrodynamic resistance; rud- der angle, hence, a drag force, is required to maintain course. These forces and moments may be defined as wind-induced forces and moments but will, in gen- eral, be very small relative to the direct wind force (van Berlekom [3.44], [3.49]).
Manoeuvring may be adversely affected.
2. The wind generates a surface drift on the sea of the order of 2%–3% of wind velocity. This will reduce or increase the ship speed over the ground.