Speed/Power Analysis > Planing Hull Savitsky Prediction

Planing hull drag prediction using the Savitsky method

Planing is a hydrodynamic state where a hull is dynamically supported by pressures that are developed by the forward motion of the vessel. Before addressing the state of planing, let's consider what a boat needs to do before getting up on plane.

At rest, a hull is supported by buoyancy. The static water pressure surrounding the hull holds it in place. This hydrostatic state is completely a function of the hull's volumetric shape.

When a boat begins to move, however, it forces water around and under the hull and it is no longer in a hydrostatic state. It is now in hydrodynamic motion. As a boat moves at low speeds, the water typically follows flow lines that return more-or-less to their original position behind the hull. This is traditionally called the displacement hull mode.

The boat accelerates as a we give it more throttle into what is called the semi-displacement or pre-planing modes. In this mode it will also tend to sink a bit and trim up by the bow due to suction forces at the stern. The boat is now approaching the hump, that point where the sinkage and trim are greatest.

The trim that is inherent in this mode gives us the critical piece that allows for planing to occur. The suction that previously pulled the stern down now turns to a pressure as the boat runs faster and faster. The pressure - caused by the motion of the hull through the water at a particular angle of attack (its trim) - begins to lift the hull and typically reduce the trim somewhat. The final state of lift and trim is a complex equilibrium of forces and moments. The boat will remain in this state so long as nothing changes its speed, trim or weight distribution. The boat is now fully planing, or on plane.

Components of planing hull drag

The planing hull equilibrium described above shows us that trim and lift are interrelated. Trim affects lift, and it also affects drag. In fact, trim determines drag, as we will see below.

(Note: This describes the drag on the hull only. A boat in service will have additional drags due to appendages, seas, and shallow water. It might also have devices such as trim tabs that will also affect drag. These are not treated here.)

Planing hull drag is made up of four principle components:

Pressure + Friction + Spray + Windage

Windage drag is the air resistance of the exposed hull that is driven through the air. It has the tendency to increase trim. More windage area means more drag and also more trim.

Spray drag, sometimes called whisker spray, is the drag of the hull driving through the mass of the spray that is produced ahead of the boat. Evaluating the effect of spray is complicated and is often neglected, as well-designed spray rails or strakes can be effective in moving the spray away from the hull rather than leaving it in front of the hull. Like windage drag, spray drag would contribute to greater drag and trim.

This leaves Pressure drag and Friction drag as the two parts of our planing drag analysis. The planing hull analysis that is used here is a modified version of the well-known Savitsky prediction method.

Savitsky prediction method

The Savitsky method poses the bare-hull planing drag as

Bare-hull drag = Pressure + Friction = L tan(t) + CF ½ r S V2 / cos(t)

where,

L = lift on the planing bottom (nominally the boat weight)

t = dynamic trim angle

CF = frictional drag coefficient across the wetted planing surface

r = mass density of the water

S = wetted planing surface area at the particular dynamic trim angle

V = mean water velocity across the wetted planing surface

The Savitsky prediction calculations solve for all of the above variables at a given trim angle. The prediction, therefore, must solve for the proper trim angle so that the equilibrium is maintained.

This implementation of a Savitsky prediction includes the effect of the boat's CG location (as it is about this point where the equilibrium is centered), as well as the thrust line vector. For example, a thrust line that is pointed above the CG will tend to lower trim, while a vector below the CG will bring the bow up.

One important consideration when using the Savitsky method is that it was developed for prismatic hulls, meaning that the hull is a prism of a pure wedge shape. These hulls had linear sections from keel to chine with constant deadrise (no warp), and no strakes or rails. HydroComp has developed and implemented a number of modifications to the Savitsky method for warped hulls, as well as for hulls of non-linear sections with strakes and rails.

Evaluating drag at pre-planing speeds

The methodology described above is for a boat past the hump and settled into its fully planing hydrodynamic mode. The calculations employ a version of the Blount/Fox pre-planing hump speed correction to better model the shape of the drag curve at pre-planing speeds.

Differences in Savitsky methods

You must not expect that all calculations built upon the basic Savitsky formula to produce the same prediction results. Some reasons for this are:

•	Use of an equilibrium trim analysis. Some predictions do not consider the effect of the lift and drag components on trim. For example, if the thrust line vector is assumed to pass through the CG (which Savitsky called the simple case), the predicted trim and drag will not account for this.

•	Definition of deadrise angle. Unfortunately, there is no standard rule for the calculation of appropriate deadrise angle. Differences in how the deadrise is calculated produce differences in the prediction results.

•	Definition of the chine beam. The outer chine beam defines the shape of the wetted planing surface. A different beam gives a different result.

•	Variable deadrise. Warped hulls of varying deadrise need a dynamic calculation of a suitable effective deadrise.

This implementation of the Savitsky prediction accounts for all of these variables.

Drag reduction analysis

This planing hull analysis also provides design feedback. Four hydrodynamically significant hull parameters - deadrise, LCG, thrust line shaft angle, and chine beam - are evaluated for their effect on drag. A sensitivity index number provides a measure of the significance of the parameter on drag. By reviewing the indices, you can see a measure of the parameter's influence on drag and then use this information to optimize your designs.

References

The following are three important references about the Savitsky prediction methodology.

•	Savitsky, D., "Hydrodynamic Design of Planing Hulls", SNAME Marine Technology, Oct 1964.

•	Savitsky, D. & Brown, P.W., "Procedures for the Hydrodynamic Evaluation of Planing Hulls in Smooth and Rough Water", SNAME Marine Technology, Oct 1976.

•	Blount D.L. and Fox, D.L., "Small-Craft Power Prediction", SNAME Marine Technology, January 1976.

About effective power

Effective power is a function of resistance. It is simply resistance converted to power units by multiplying by the boat’s speed.

Effective power = Resistance * Speed

Effective power is NOT engine power, as only a fraction of the engine’s rotational energy can be converted into thrust at the propeller. Between engine power (at the engine) and effective power (at the hull) are a number of places where energy is lost. These losses can be defined by individual efficiencies:

Transmission efficiency = 96% to 98% (gear friction and heat)

Shafting efficiency = 97% to 98% (bearing friction and shaft torsion)

Hull efficiency = 90% to 100% (pressure regions affecting the hull)

Propeller efficiency = 50% to 70% (hydrodynamic losses)

Multiplying these together gives us the ratio of effective-to-engine power. This figure is known as the Overall Propulsive Coefficient, or OPC. OPC varies with hull type, speed range and propeller style, and is typically in the range of 50% to 65%. Some applications can push the OPC to 70%, while heavily loaded, slower hulls can see OPC reduced to 40% or less.

Estimating engine power

As we can see from the effective-to-engine power figures of 50% to 65%, your engine power is likely to be in the range of twice your effective power – sometime more. To estimate engine power, you can use the following table to find a multiplier to estimate engine power from the predicted effective power.

First, remember that the predicted effective power is for the bare hull only. You will need to add an appropriate service margin for additional hull roughness, appendages, windage, and seas. So, match service margin and OPC to find an engine power multiplier.

Table of engine-to-effective power multipliers

	Service margin
OPC		0%	10%	20%	30%
	50%	2.00	2.20	2.40	2.60
	55%	1.82	2.00	2.18	2.36
	60%	1.66	1.83	2.00	2.17
	65%	1.54	1.69	1.85	2.00

Please note, however, that a reliable estimate of service margin and OPC requires a thorough propulsion analysis, which is beyond the scope of these calculations. Before selecting an engine for your design, we strongly recommend that you prepare a proper propulsion analysis, either by consulting with an experienced professional or with comprehensive propulsion analysis software.