What A Drag
Naval
Architect Chris Cochran from Morrelli & Melvin Design &
Engineering has put together this fascinating look at drag. No,
not how you dressed for Halloween, but as it relates to going
fast. Give a big thanks to Chris for providing a great piece of
info for all of us. -Ed.
Part
1 Decomposing Drag
One
of the more important aspects of yacht design is the fundamental
understanding and determination of drag. Where does it all come
from? How is it estimated? To begin with, the total resistance
of a yacht moving through calm water can be divided into 3 major
categories: friction drag, residuary drag and induced
drag. If desired, the residuary drag can be further subdivided
into viscous pressure (form) drag and wave-making
drag. The viscous pressure drag can then be combined with
friction drag to obtain viscous drag. All other components
of drag - heel drag, appendage drag, air drag, etc - are some
combination of the big three. The only exception is added wave
resistance, which is the additional drag caused by oncoming waves.
Most
sailors are fully aware of friction drag: the resistance
caused by the skin friction of a surface moving through a fluid.
As the yacht (the surface) moves through the water (the fluid),
it develops a boundary layer, or region of interrupted flow, surrounding
the submerged surfaces. The water immediately touching the hull
(the base of the boundary layer) is actually moving at the same
speed as the hull. The hydrodynamic no-slip condition occurs
all along the base of the boundary layer, due to the viscosity
of the fluid. Further away from the hull surface, the water gradually
returns to its normal flow, which occurs at the edge of the boundary
layer. This transition of flow within the boundary layer causes
inter-molecular shear stresses, which requires a certain force
to overcome. This friction force is dependent on the properties
of the fluid, the wetted length, wetted area and speed of the
moving body. For example, more wetted surface produces more friction
drag, as does increased speed.
Examples of the various drag contributions |
As
mentioned earlier, residuary drag is actually the combination
of the wave-making and viscous pressure drag (form drag). The
wave-making drag is just as it sounds; the resistance caused by
the creation of bow and stern waves. As the boat moves forward,
it pushes water out of the way. Due to conservation of energy
(remember that law from physics?), the moving boat must use some
of its own energy to push the water out of the way. This loss
of energy would tend to slow the boat down, which means that more
energy is required to keep the boat moving at the original speed,
in other words an increase in drag. Wave-making drag is dependent
on hull shape, since fine hulls create smaller waves than fat
hulls, and boat speed, since wave size and length increases with
speed.
Viscous
pressure drag, or form drag, is the additional
pressure drag due to the shape of the hull. The position of the
center of buoyancy, the shape of the stern, the shape of the bow,
all have important effects on form drag. Now you’re probably
saying wait, I thought hull shape had more to do with wave-making
drag!? You’re right; form drag and wave-making drag go
hand in hand. It is sometimes difficult to distinguish between
the two, which is why they are often paired together as residuary
drag.
Induced
drag can be a difficult concept to understand. It is the
unfortunate bastard son of lift, the necessary force that keeps
the boat from slipping to leeward. Without going much into the
theory or physics behind it all, it is important to know that
lift creates a byproduct in the form of trailing vortices. These
vortices are caused by the existence of circulation, a phenomenon
required to create lift. Induced drag occurs because the energy
required to create the vortices is taken from the total energy
of the moving yacht, and so additional energy is required to keep
the boat moving at a steady speed. Since lift is usually increased
with leeway, we can say that induced drag increases as leeway
increases.
All
other types of drag are some sort of combination of the above.
Appendage drag is simply the friction drag, form drag and induced
drag of the foils and bulb. Since most foils operate below the
free surface of the water, their wave making drag is neglected.
Heel drag is just the change in drag (sometimes negative) that
occurs due to the change in the hull shape below the surface.
The added resistance from oncoming waves is a slightly different
type of drag. The additional waves can increase or decrease the
drag of the yacht, depending on whether the yacht is beating into
them or surfing down them.
So
to recap, the three significant types of calm-water drag are friction
drag, residuary drag and induced drag, or alternatively viscous
drag, wave-making drag and induced drag. Most other types of
drag are different combinations of the big three. Now that we
are familiar with the various types of drag, we can investigate
ways that naval architects and yacht designers estimate them and/or
determine them by experimentation.
Part
2 Determining Drag
Last
time we learned about the various types of drag: friction drag,
residuary drag (wave-making drag and viscous pressure form drag)
and induced drag. Now we will investigate some of the methods
that naval architects and yacht designers use to estimate these
different contributions of drag. Friction drag is easily computed
numerically, and there are three typical methods used in the yacht
design industry to determine the remaining drag: model testing,
computational fluid dynamics (CFD) and numerical prediction.
Friction
drag is the simplest to evaluate. It is more convenient to separate
total friction drag into hull friction drag, keel friction drag,
rudder friction drag, etc The friction drag of each component
can then be determined using an empirical formula, called the
ITTC Friction Line. Using only wetted length, speed and
water viscosity (i.e. the Reynolds number), the non-dimensional
friction coefficients can be determined from the ITTC line. The
wetted surface, speed and water density is then used to convert
the non-dimensional coefficient to physical drag.
Tank
testing of geometrically scaled models is a fairly accurate, albeit
expensive way to determine form drag, wave-making drag and induced
drag. To begin with, a bare hull (without appendages) is towed
upright at zero leeway, to obtain the total upright drag at various
speeds. The friction drag at each speed is calculated using the
ITTC friction line, and since the hull is towed upright at zero
leeway, there is no induced drag to consider. Naval architects
then have a neat little trick for further separating the residuary
drag into form drag and wave-making drag, obtaining a form factor
for the yacht. This form factor is then applied to the friction
drag to obtain the viscous drag, which is then subtracted from
the total measured drag to obtain the wave-making drag. The upright
bare hull drag then serves as a base-line to compare additional
induced drag from leeway, heeled drag, appendage drag, etcUsing
various scaling techniques, the results can then be extrapolated
to full scale drag values.
Computational
fluid dynamics (CFD) is another way to predict the drag of yachts,
and is usually used for high-end racing and performance cruising
designs. Using advanced computer programs, the exterior surfaces
of yacht are meshed, or subdivided into tiny triangles, quads
and polygons. The local water surrounding the yacht is meshed
as well. Each corner of the mesh, called a node, represents a
point where a specific set of equations is solved. The value
of each node has a relative impact on the surrounding nodes, so
the complexity in CFD comes from keeping track of the values of
all of the nodes as they are updated consecutively. There are
many different types of CFD, but the common types used for hull
drag analysis are Reynolds Averaged Navier Stokes (RANS) codes
and potential flow codes. RANS codes are the most accurate, as
they attempt to solve for the turbulent flow existing in trailing
edges, wakes, etc, and is usually reserved for appendages, where
the flow is in the absence of a complicated free surface. For
free-surface calculations, i.e. hull drag, potential flow codes
are typically used. These codes obtain results by solving the
inviscid potential flow equations at the various nodes. Depending
on the complexity of the code used, the results can be divided
into residuary drag, wave-making drag, heeled drag, etc CFD is
proving more and more to be a reliable method for predicting drag,
and increases in computing power and speed will only improve the
accuracy. Though not as expensive as tank testing, the costs
of reliable CFD predictions are beyond the budgets of most production
cruiser/racer designs.
When
tank testing and CFD is out of the question, a convenient database
of existing hulls and keels is available for reasonable drag prediction.
The Delft Series is an ongoing collection of various hull and
keel types tested since 1972. It was started at the Delft University
of Technology in the Netherlands, as one of the first methods
used to estimate a yacht’s performance, paving the way for
commercial velocity prediction programs (VPP). The tank testing
data for all of the yachts tested in the Delft series has been
thoroughly regressed into various tables and equations, as functions
of certain non-dimensional hull speeds and parameters. So given
a list of hull parameters, a yacht designer can use the Delft
coefficients and equations to predict the drag of the yacht.
The ITTC fiction line is again used to determine friction drag,
while the residuary drag, induced drag, heeled drag and appendage
drag is determined by the Delft equations. The Delft series is
surprisingly accurate for most conventional hull forms. Since
it uses data based on similar hulls, the main requirement is that
the hull in question fits inside the guidelines set out by the
Delft series. If the hull parameters are outside of the Delft
range, then the estimated data must be extrapolated, which is
always a dangerous maneuver and could lead to false results.
Using
the methods listed above, yacht designers and naval architects
can reasonably predict the different types of drag for sailing
yachts. Friction drag can be easily computed numerically, and
form drag, wave-making drag and induced drag and can be determined
using the towing tank or CFD. As an affordable alternative, the
Delft series is available to estimate residuary, induced and heel
drag using regressed data obtained from testing similar hull types.
Once the yacht’s drag budget is determined, the designer
can better understand what aspects of the hull design are worth
changing in order to decrease overall drag.
01-Nov-2004
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