Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014
Where the term,
is the wetted girth, which increases with the deadrise angle, .
As maximum operating speed increases, the main recourse that a designer typically has is to move LCG aft to reduce frictional resistance. This results in a slight increase in trim and pressure resistance at high speeds, but
a very large reduction in frictional resistance.
Moving LCG aft also results in a very large increase in resistance at hump speed (Fn=0.5). Variation in LCG is constrained by arrangement considerations, hydrostatic trim, and porpoising--the
coupled oscillation in heave
and pitch that occurs when a planing hull operates at too high a trim angle.
Savitsky and Morabito [2] have provided a clear method of illustrating when stepped hulls may be advantageous. Their approach is to observe the running trim and compare it with the optimum trim value of approximately 4-degrees demonstrated by Savitsky [6]. When the hull runs significantly higher than 4-degrees, the pressure component dominates and a stepped hull design choice.
is a foolish When the hull runs well below the
optimum trim angle, the friction component dominates and a stepped hull can be used to raise the trim and reduce wetted area.
Nearly all high speed planing craft are fitted with trim control devices, such as trim tabs, adjustable outboard motors, or variable surface propeller immersion. These features allow the operator to optimize running trim for a given speed and loading; however they are often best suited for creating bow-down pitching moments at high speeds, and cannot be relied upon for major reductions in wetted length at pitching moments).
high speeds (which require bow-up
Generally, once a designer has moved LCG as far aft as possible, and performance is still unsatisfactory, an advanced hull form, such as a stepped hull, becomes an attractive alternative.
2.2 PATROL BOAT EXAMPLE
To illustrate the strong effect of LCG on patrol craft performance, the following example was developed for a notional
parameters: Length Beam
Deadrise
high speed patrol = 25m
= 5m
Displacement = 60 MT Speed <
= 15 degrees = 65 knots
Calculations were made using the Savitsky method [6], assuming the thrust line passes through the center of gravity. Figure 3 shows the results of these findings. At speeds less than 40 knots, the forward LCG hull has substantially lower resistance because the boat operates at a lower trim angle,
©2014: The Royal Institution of Naval Architects boat with the following
minimizing pressure drag. At speeds above 50 knots, the craft with the aft LCG has significantly lower resistance because the wetted area is smaller.
From a design standpoint, it would be ideal to have the best elements of both LCG positions by locating the LCG at 25% and using trim control devices to reduce trim (and pressure resistance) at the low speeds. However, trim control devices like trim tabs or interceptors often have very little effect at very low speeds. Also, it is usually impractical to get the center of gravity so far aft. Thus, the modern
planing boat designers must find a
compromise between LCG position and size of trim control devices.
Figure 3: Effect of LCG on Resistance to Weight Ratio versus Speed for Notional 60 MT Patrol Boat
2.3 STEPPED HULLS FOR MODERATE SPEEDS
For the heavily-loaded naval craft given in the previous example, a practical solution may be to utilize a stepped hull, in which the step is located fairly far aft. At low speeds, the afterbody (portion of hull aft of the step) would provide necessary hydrostatic buoyancy, giving the hull a bow-down trimming moment and inherently low hump speed resistance. At high speeds, the flow would separate from the step, leaving the afterbody mostly dry, and reducing frictional resistance substantially.
Figure 4 shows a sketch of a stepped planing hull intended for moderate speeds.
Unlike stepped hulls
intended for higher volumetric Froude numbers, there is no need to have a step located far forward, when only a small shift in effective LCG position is needed.
The primary advantage of this arrangement is that most of the load is placed on the forebody instead of split between forebody and afterbody. This allows the running trim
angle and resistance of the forebody B-89
to be
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