Page 96 - The ROV Manual - A User Guide for Remotely Operated Vehicles 2nd edition

84 CHAPTER 3 Design Theory and Standards
perpendicular to the water flow) is warranted. This so-called Von Ka´rma´n shedding begins to
Based on the above discussions, the total drag of the system is defined as:
Total drag 5 1=2σAvV2Cdv 1 1=2σAuV2uCdu ðwhere v 5 vehicle; u 5 umbilicalÞ
A simple calculation can be performed if it is assumed that the umbilical cable is hanging straight down and that the tether from the end of the umbilical (via a clump or TMS) to the vehicle is horizontal with little drag (Figure 3.20). For this calculation, it will be assumed that the ship is stationary keeping in a 1 knot current (1.9 km/h) and the vehicle is working at a depth of 500 ft (152 m). The following system parameters will be used:
Unfaired umbilical diameter 5 0.75 in. (1.9 cm)
A, the characteristic area of the vehicle 5 10 ft2 (0.93 m2)
Based on the above, the following is obtained:
Vehicle drag 5 1=2 3 64=32:2 3 10 3 ð1:689Þ2 3 0:9 5 25:5 lb ð11:6 kgÞ
Umbilical drag 5 1=2 3 64=32:2 3 ð0:75=12 3 500Þ 3 ð1:689Þ2 3 1:2 5 106:3 lb ð48:2 kgÞ
Note: Computations will be the same in both imperial and metric if the units are kept consistent. This simple example shows why improvements in vehicle geometry do not make significant changes to system performance. The highest factor affecting ROV performance is tether drag. The following discussion will consider the drag of individual components.
Drag computations for the vehicle assume a perfectly closed frame box. Drag computations for the tether are in the range of a cross-section of ROV systems sampled during recent field trials of small observation-class systems.
By varying the tether diameter, the relationships in Figure 3.23 can be developed. Figure 3.24 shows that by varying the speed with a constant length of tether, the vehicle will display a similar curve, producing a drag curve that is proportional to velocity squared.
The power required to propel an ROV is calculated by multiplying the drag and the velocity as follows:
Power 5 Drag 3 V =550
The constant 550 is a conversion factor that changes foot-pounds/second to horsepower. As dis- cussed previously, the drag of a vehicle is proportional to the velocity of the vehicle squared.
appear with Reynolds numbers approaching 90 (Figure 3.19) and disappear once the Reynolds 4
number approaches 10 . Vortex shedding is a real problem as the flow speed increases. The turbu- lent vortex cells on either side of the cylinder can be either symmetrical (Figure 3.22(a)) or (much more often) asymmetrical (Figure 3.22(b)). As the flow increases, and the asymmetrical oscillations begin, the cylinder is pulled back and forth with the oscillations further exacerbating the drag and causing structural stresses. Engineers for large offshore structures mount strakes on the skin to inhibit the formation of these vortexes. ROV operators have the choice of either fairing the tether cable or accepting the problem.