Subject: Problem Definition
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Date: Fri, 12 Sep 2003 10:37:27 -0700

ENME 489E
Hull Design
Team
Final Report

by Glen Roberts

December 12, 1995

Instructor: Dr. Neil Wright
Department of Mechanical
Engineering
University of Maryland, Baltimore
County

Overview

This project was one of five in an integrated effort to design a superior
craft for competition in the Solar Splash solar and electric powered boat
competition. My particular task was to create the hull that will be the most
obvious sign our the team's effort.

An initial decision was made concerning the design focus of the project. The
Solar Splash competition consists of two main events - a sprint of 300 meters
and a two hour long endurance event. Our options were to optimize for one event
at the expense of the other or to pursue a more balanced approach. We chose a
middle ground by agreeing to construct a single hull but to evaluate its
performance using two motors, each optimized for one of the events. My insight
into this approach was that the best design in general was a displacement
type hull that had been designed with some consideration of planing
characteristics. Predictions of the hull's performance at various speeds
indicate that a design speed of 4.6m/s (10.4 mph) corresponding to a Freud
number of 0.725 was in certain ways, optimum for the endurance competition.
Operation at that speed consumes power in the region of 700 W or slightly less
than one horsepower. Calculations indicate that we should have adequate power to
do so. Similarly, in the sprint competition, our projected speed of 11.6m/s (26
mph) is quite close to the times of last year's winning design.

Quite a few materials options exist ranging from traditional plank on frame
construction to modern composite fabrication. I am proposing a sculpted foam
approach reinforced with a fiberglass skin for surface hardness and stiffened
overall with an internal composite beam. Polystyrene foam is very light, easy to
work, and is generally available at a reasonable cost. Because of the ease with
which it can be worked and repaired, it is suitable for amateur builders. As a
stiffener, I proposed a "stress-skin" molded beam set into the hull so that its
strengths will combine with those of the Styrofoam. The shaped beam will
additionally provide a base for motor mounting. The cost of materials for the
hull alone will be under one thousand dollars.Problem Definition

The general formulation of the task addressed by this project was to design a
hull for the 1996 Solar Splash competition. In order to do so, a number of
criteria were to be met. The first was the absolute requirement that it conform
to the stated limits and requirements of the competition. These included size
and power constraints as well as mandatory safety features. A brief list of the
rules that pertain specifically to the hull follows.

Length is not to exceed 6 meters (19ft 8in)

width is not to exceed 2.4 meters (7ft 10 1/2in)

height is not to exceed 1.5 meters (4ft 11in)

depth is unrestricted

cross-sectional area is unrestricted

materials must be nonpolluting

visibility must be unrestricted for at least 100 to each side

minimum stability is guaranteed by restricting heel to 15 when a
10kg

mass is placed at the sheer line

shielding must be provided for all revolving or otherwise dangerous
parts

cockpit must be excitable in under 5 seconds

reserve buoyancy must be sufficient to make the craft unsinkable

tow fittings must be attached bow and stern.

In addition to
the specific design parameters above, several other criteria had to be
addressed. Obviously, the hull should be strong enough to resist the loadings
associated with its normal use in the water. It will also have to survive
transportation to the competition and, once there, to and from its staging area.
Durability is essential if it is to be extensively tested prior to the event.
Since displacement is a critical factor in performance, it should also be as
light as possible without risking structural failure. The hull's interior must
be large enough to fit its components, chief among which is its operator. The
outer surface must be composed of a hard, smooth, maintainable material for
minimum drag. A practical boat must be kept within budget as well as being
within the skills of amateurs to build.

The Solar Splash competition includes at two primary events. The first is a
sprint in which the general objective is to cover a 300m straight course
in the minimum time. The particular objective is to finish ahead of the
other competitors in a given heat. In this event the design goal is to achieve
maximum speed over a short period of time (about 30 seconds). The second event
is one of duration in which the object is to cover the maximum distance in two
hours time. While speed is obviously important, the design objective here is to
use the available energy as efficiently as possible. The limiting parameter is
the amount of battery and solar generated electrical power. If the battery is
depleted before the conclusion of the event, performance will suffer. The boat
that will win this competition is the one with the least resistance at the
greatest operating velocity.

There is a conflict in emphasis implied in the two different design
objectives mentioned above. The properties of a hull that generate highest speed
are not always compatible with optimum low speed operation. For example, those
properties that allow a boat to plane easily - a flat, wide stern and hard
chines - create drag that is largely avoided in optimal low speed displacement
hull designs. The initial design decision, then, was one of focus. We had to
chose between the following options:

design exclusively for the endurance competition

design exclusively for the speed competition

design predominantly for one or the other

design an more or less equally weighted compromise

design a separate hull for each competition.

The decision was
reached to attempt a balanced approach that would result in a "good" all round
boat that would perform well in both events (but would not be expected to win
either since the were not optimized for a certain kind of performance). In the
actual development stage, the form of the design came to emphasize the duration
aspect of the competition somewhat more than the speed aspect. There sere
several reasons for this. Primary among them was that the information acquired
indicated that a displacement type hull designed to operate at moderate Froude
numbers (between 0.5 and 1.0) could perform well in higher ranges (between 1.0
and 2.5) if sufficient power was available. Conversely, a planing type hull does
badly in the lower speed ranges. Calculations by several members of the design
team over the course of the design period confirm that the discussion was a good
one. A hull designed for speeds typical of the best boats in the endurance event
( 4.0 to 4.6m/s or about 9 to 10mph) should reach speeds typical of the winners
in the speed event (11.6m/s or about 26 mph) when powered by our larger motor.

As a practical matter, once a design philosophy was established, the hull was
crafted to conform to a number of empirical parameters derived from extensive
testing on displacement type hulls operating at moderate Froude numbers.
However, when choices presented themselves between purely displacement design
and one that was more like a planing hull, the decision was usually in favor of
the planing characteristic. Such a path was to some extent forced by the test
data itself. At faster speeds, certain hull characteristics tend to produce
planing behavior, I particular, a degree of dynamic lift. In testing, the hulls
with these characteristics tend to produce desirable results at Froude numbers
between about 0.5 and up. Thus the these "semi-planing" test hulls skew the
empirical relations to select in their favor of their characteristics at higher
operating velocities. So, for example, our long and narrow displacement hull has
much more of its width placed farther aft than symmetry would dictate in the
hope that our hull will emulate semiplaning behavior. In that respect, ours is
more like a planing hull. Likewise, the transom of our craft is cut at right
angles to the water line rather than canoe shaped. This stimulates sharp flow
separation at planing speeds and reduce frictional drag. Many of the design
parameters associated with the hull were chosen to emphasize the high speed
performance of a displacement type hull. These choices are enumerated in the
following section.
Analysis

There were several levels of possible approaches to take toward the
development of an optimum hull for the competition. As illustrated above, the
choice concerning the operational goals of the hull and the dichotomy between
the requirements for the two primary events is one level at which alternatives
had to be considered. Further elaboration of these choices is included below.
However, there is a broader issue that presented itself early in the research
phase of the report that deserves highlighting. It is the choice among design
methodologies.

Specifically, the choice was to design using a computational fluids approach
or a parameter based approach. The first method relies heavily on solutions to
basic fluid dynamic equations usually in some sort of finite element
environment. The second uses empirically and experientially based relations
between a handful of nondimensional parameters. Each of these parameters
captures a certain characteristic dimensional relation in the geometry of the
hull and correlates it to performance, often through graphical means. In theory,
the two methods should give similar results since they are two ways of
describing the behavior of a single physical entity. Normally, a preliminary
form is designed using empirical rules of thumb and subjected to mathematical
analysis as a first stage of testing. As it came to pass, the necessary
expertise as well as the computing power for the computational fluids approach
were beyond my means this semester. In retrospect, this was not altogether
detrimental to the project. The result has been a hull designed to empirical
guidelines but still needs to be tested. What follows is a brief discussion
concerning the motivation behind empirical coefficients and an explanation of
those that are critical to our hull design.
Design Parameters

A major design task in the development of a hull design is the calculation of
its resistance at speeds in the range in which it is intended to operate. The
results of these calculations determine power requirements, maximum velocities,
etc.. There are two primary components in hull resistance: frictional drag
(sensitive to Reynold's number) and residuary resistance (sensitive to Froude
number). While most sources present similar calculations for frictional
resistance, each source recommends a different formula for residuary resistance.
To estimate the resistance of the hull design proposed in this report, I used
the general equations from Principles of Yacht Design. These equations
were the most recent I could find, they were applicable for Froude numbers up to
0.75 (about 4.6 m/s), and, since they were intended to be used with metric
measurements, they contained no unwieldy conversion factors typical of many
formulas based on English units. The formula for hull drag is :
Rtotal = Rfriction +
Rresiduary

where: Rtotal is the total drag on the hull,

Rfriction is the portion of the drag originating from the
surface friction of a body moving through the water,

Rresiduary is the portion due to all other factors,
primarily form drag and energy losses due to wave making.

The equation for the frictional resistance is:
Rfriction = CF SW
(1/2V2)

where: CF is the hull coefficient of friction defined as
CF = 0.075 (log Rn -
2)-2

where: Rn = VL/

and: V is the hull's speed

L is 0.7 times the hull's waterline length

is the dynamic viscosity of water

(1x10-6m2/s)

SW is the wetted surface of the hull

(1/2V2) is the dynamic pressure of the water.

The equation for residuary resistance is a big one and relies on a number of
empirically derived coefficients. I simply included a copy of the figure from
Principles of Yacht Design on the next page. (Note that the formula
results in the residuary resistance times a factor of 103/weight.)

The results for our hull at a design speed of 4.6m/s (10.4 mph) are:

Rfriction = 115 N

Rresiduary = 35 N

Rtotal = 150 N.

These values vary gradually with speed. For example, at 9 mph the total
resistance is 132N and at 8 mph it is 112N. As can be seen from the graph below,
the variation is not linear. Due to the influence of wave making effects, the
generally increasing curve contains a series of "humps and hollows" where the
data deviates above or below the trend of the larger curve. In the region of the
"hollows" an increase in speed does not cause as much of an increase in
resistance as elsewhere. Thus, these regions can be considered design points.
The region around Fn = 0.725 (4.6m/s, 10.4mph) is such a spot. Interestingly, on
typical displacement hull performance graphs (such as the one in Principle of
Naval Architecture), there is no such region at a similar location. Partly
because of this, and also because the dip is particularly sharp at Fn = 0.725, I
believe that this region corresponds to the onset of planing in the test hulls.
If this is true, then that operation in that region is a particularly desirable
goal since at that point, the resistance characteristics of the hull change for
the better. The beginning of planing should be apparent in the prototype when
tested. Whether or not it occurs where predicted, speeds just above the onset of
planning are the most efficient speeds in terms of moving the boat a maximum
distance in a timed event.

Power can be calculated by multiplying velocity and resistance. To travel at
the endurance design speed of 4.6m/s (10.4 mph), our hull will consume almost
700 watts or just under one horsepower. Discussions with other members of the
design team suggest that it would be possible to produce that much power over a
two hour period with a contribution from the solar cells. To attain the sprint
design speed of 11.6 m/s (26 mph) will require in the range of 12 to 15 kW (15
to 20 HP). This amount of power also seems to be available over a thirty second
race.

Many of the terms in the equations above, like LWL/BWL,
are dimensionless hull coefficients. These express special characteristic
relations between hull parameters that have been statistically shown to make
significant contributions to hull performance in various controlled tests. A
list of some of these coefficients as well as several other important parameters
appears on the following pages. The process of designing the underwater shape of
the hull is essentially an iterative one of selecting values for these
interrelated parameters that results in the desired performance. Certain
parameters, for example overall length, are for all intents set by external
requirements. Others, like maximum beam, can be varied and tested for their
effect on hull resistance. To arrive at the hull presented in this report, I
used as primary variables (those that express the dimensions of hull geometry)
waterline length, beam, and draft, as well as the location of the hull's center
of buoyancy. I also tested the effects associated with displacement volume as
well as various shape coefficients - such as CB (block coefficient),
CP (prismatic coefficient), CM (midship coefficient), and
AW (waterline area) - all of which depend on the primary variables. A
descriptive reference of important design parameters is included the appendices.

Since the hull parameters are interdependent, the process of designing the
underwater section is a cyclic one of choosing parameters - both primary
parameters and shape coefficients - and using some numerical technique like
Simpson's Rule to calculate the resulting secondary parameters that describe the
hull geometry. Once all of the parameters are calculated, I compared them to
their suggested ranges according to empirical rules of thumb. If the values were
not suitable, I would redraw the hull shape and recalculate the remaining
parameters using numerical techniques. Once the values came within limits, I
used them predict hull resistance in a spreadsheet included in the appendices.
The fourth and (so far) final set of drawings are also reproduced in the
appendices. The next step, and one which I have not yet attempted, is to reduce
the hull geometry to mathematical equations in order to reconcile the three
views of the drawing with one another and produce a "faired" hull consisting
only of smooth curves.

A listing of the final values for the parameters appears below. For an
explanation of each parameter as well as typical ranges for each, refer to the
appendices.

Primary hull characteristics:

target speed

4.6m/s (10.6mph)

corresponding Froude Number

0.725

Reynold's number

106 to 108

displacement weight

1700N (380lbf)

displacement volume

1.7m3 (6.0ft3)

waterline length

6m (19.7ft)

beam

0.5m (1.6ft)

draft

0.13m (0.4ft)

Derived coefficients

length to bean ratio

12.0

beam to draft ratio

3.9

Dimensionless Shape (or Geometric)
coefficients

block coefficient

0.53

prismatic coefficient

0.70

midship coefficient

0.74

waterplane coefficient

0.68

location of center of buoyancy

12.4%

waterline entrance half-angle

6

Location of Components

Once the basic shape of the underwater hull is set and the hull parameters
established, we are in a position to make certain observations. One is the
expected resistance curve. Another, is the location of the center of buoyancy of
the hull. It is the same as the centoid of the volume of water displaced by the
hull. This is the point through which the buoyant forces of the hull combine to
act much as the center of gravity of the hull is the point through which its
weight acts. It is apparent that, unless these the forces due to buoyancy y and
gravity are equal and acting through the same point, the hull will tend to move
in the direction of equilibrium. To balance, or "trim," the hull at rest
requires that the individual components about the boat be located in such a way
that the two centers are the same.

From an analysis of hull characteristics, we know the location of its center
of buoyancy (LCB). The value given - 12.4% - means that the LCB is positioned
12.4% of the total waterline hull length behind the midship line. For a 6 meter
long hull, the LCB is somewhere in a vertical plane 3.74 meters aft of the
fowardmost point. Since the lateral center of buoyancy is very close to the
longitudinal centerline of the hull due to symmetry, we can say that the hull CG
must be located on a vertical line through the same plane. The overall hull CG
can be found though an application of Varignon's Theorem which states that the
sum of the moments of the individual centers of gravity of each component about
some locus is equal to the moment of the composite center of gravity about the
same point. I estimated the weights of the primary hull components and
positioned them in various ways until I came upon an arrangement that satisfied
the requirement that the CG align with the LCB.

The hull components could be positioned an infinite number of ways. Some ways
had compelling reasons to suggest them. For example, I placed the motor directly
over the LCB (and, therefore, the CG) in order to minimize the effect of any of
its misaligned forces on the hull by reducing their moment about the CG. Since
different motors will be used for each of the events, this will also reduce the
impact of the change in characteristics on handling. The drop from the motor to
the propeller will also act as a relatively neutral pivot when turning and not
as a fin (which would resist a change in direction).

Similarly, there are good reason to locate the battery compartment near the
motor compartment (for ease of access and to minimize wire runs) and behind the
pilot (to keep the pilot away from vented fumes). This is especially true
because the batteries are to be utilized as an adjustable weight for and aft
hull trim. The pilot is the heaviest component and is the one with the most
potentially to vary. With the pilot ahead of the CG, it is necessary to adjust
the balance with a similarly sized weight behind the CG. The diagram below shows
schematically the placement of each of the major components. Their weights are
found in the appendices on a spreadsheet used to calculate hull CG.

The final CG and LCB of the hull will undoubtedly differ from the idealized
diagram above. That is why there is adjustability built into the design. For
example, in their positions above, the batteries have a moment of 290 Nm about
the CG. The pilot exerts a 275 Nm moment. A change in the weight of the pilot of
44 N (10 lbf) results in only a 4 cm shift in the position of the batteries.
Since the battery farther from the CG has more effect on trim, we could move the
two batteries independently of one another giving, in effect, coarse and fine
trim capabilities. As we come by better estimates of weight for the various
components, slight repositionings will occur. The diagram above can not be
considered the final word.

Once the components are located, it becomes possible to define the internal
structure of the hull. Certain requirements must be met. For example, the
batteries must be housed in their own vented compartment, the cockpit should be
at least 1.2m (4ft) long to accommodate the pilot's extended legs, there must be
positive floatation built into the hull to make sinking impossible, all working
parts must be accessible for installation and repair, etc.. Between the
compartments will be bulkheads (walls) that stiffen the hull laterally as well
as sealing the areas from one another. Any area of the hull not dedicated to
some specific purpose, is available for floatation. The floatation volume built
into the hull must be greater than a volume of water equaling the weight of the
hull. An 1800N (400 lbf) hull would displace 1.8m3
(6.4ft3) of fresh water if completely submersed. We must include more
than that volume of sealed airspace in the hull in order for it to float above
the water. The diagram below shows the position of various compartments within
the hull. Note that, for clarity, the hull's beam is greatly exaggerated.

With the compartments situated as above, there will have to access through
the deck to service the components. In particular, the motor, batteries and
steering mechanisms must be easily reachable. A diagram showing the placement of
access panels through the deck is shown below.

Construction

An issue that is distinct from the physical placement of components is that
of the method and materials used in the construction of the hull. There are a
number of criteria to be met by the combination of construction materials and
techniques. The first is, obviously, that the result is a hull that will perform
without failure. Here, failure could mean catastrophic failure or, less
seriously, a degradation of performance due to insufficient strength or some
other flaw. Another criterion is that the hull be constructable by essentially
amateur builders perhaps with some help from others in possession of tools or
techniques unavailable to the amateur. Construction should take into account
design criteria such as proper hull shape and minimal weight. The construction
process must be safe for those engaged in it.

The choice of materials often determines the construction techniques. Plank
type wooden hulls, for example, require that a form be built around which strips
of wood bent and meticulously fitted to one another. While such a technique can
result a durable, beautiful, and surprisingly lightweight hull, it takes an
experienced craftsman to do so. Neither long term durability nor beauty are high
on our list of priorities for this year's boat. Wood veneers can be overlaid
around a mold to make a very light, very strong shell. Again, this technique
mandates the existence of a level of skill perhaps beyond that of the assembly
team. Plywood can be molded over a frame to make a strong shell. However, even
thin plywood can bend primarily in a single direction making complex curves
difficult to execute. Fiber reinforced resin (fiberglass) construction is the
current technique of choice in the boatbuilding industry because fiberglass can
be made to conform to any shape and it is easy, if messy, to use. However,
fiberglass construction necessitates an original mold on which the material is
applied. Building the mold is, itself, a process a multistep process requiring
boatbuilding skills. Also, fiberglass has only moderate strength to weight
properties. Finally, aluminum skin construction has been suggested. Its
drawbacks are difficult construction and the likelihood of permanent deformation
(denting) if the hull is subjected to impact.

I propose to use polystyrene foam (Styrofoam) blocks as the primary hull
material. Styrofoam is very lightweight, easily worked an repaired using common
tools, readily available, and reasonably inexpensive. Pieces can be joined
together to make a monolithic block of the necessary dimensions and then
essentially carved out to form the hull's interior and exterior shapes. Because
Styrofoam is so easily dented, it will be necessary to cover the shell with a
single layer of fiber reinforced resin - probably e-glass in a nonpolyester
epoxy - to give the hull a degree of surface hardness. Internal bulkheads serve
both to stiffen the hull and to form compartments. They can be constructed using
foam sections attached to the hull interior wall and glassed in for rigidity.
Since Styrofoam is so light, it would not be necessary to provide sealed
floatation compartments. Whatever foam does not need to be removed amounts to
floatation. This can simplify construction and strengthen the hull.

While Styrofoam is strong for its weight, it is unlikely that the wall
thicknesses we will be using (2in - 3in) possess the strength to support 1800N
(400 lbf) weight along a 6 meter beamlength. It will, therefore, be necessary to
treat the hull simply as a strengthless shell and to build a structure that will
support the expected loads with a reliable safety margin. This structure will
also have to contain provisions for mounting the motor and rudder assemblies and
must prevent puncturing of the hull from the inside. One candidate for such a
structure is a "stress-skin" beam.

Stress-skin beams are lightweight composite constructions normally consisting
of a thin plywood skin over a frame made of dimensional lumber. The name stems
from the fact that the strength of these structures comes from the shear
strength of the glue between the plywood skin and the lumber. Their resistance
to bending is many times that of wood of a similar thickness. A typical
stress-skin panel is diagrammed below. Note that the location of the individual
lumber frame members is noncritical - it is primarily the gluing surface area
that determines the strength of the assembly.

The structure I propose is a sandwiched beam, rather than a simple panel,
constructed using the same techniques as the stress-skin panel. It will
constructed, fitted in the hull as shown in the following diagram, and joined to
the interior of the hull using a combination of throughbolts and epoxy.

In stress-skin construction, areas that require extra support or sections to
which items will be mounted can be easily reinforced by including a continuous
mesh of dimensional lumber as shown in the diagram below. The areas in our
design that will require such support are the motor throughhull and the rudder
throughhull. These locations will feel the effects of associated with motor and
rudder actions. There will be permanently mounted hardware bolted to these
reinforced sections to which the motor and rudder will be in turn attached. In
addition to the extra material internal to the sandwich construction, additional
layers of lumber can be added as needed to the exposed upper face of the beam in
order to distribute the loads even more. The added support will be particularly
necessary around the motor mount and will not add much weight. The following
view shows schematically the reinforcement scheme within the stress-skin
assembly.

Note that the bow section is left without the additional support of the
stress-skin beam for its first meter. This region will support little weight
either in operation and so has been left as floatation volume. The main hull
generated bow wave normally resides about one forth of the way back from the bow
leaving the forward section with reduced loading. In a planing regime, the bow
should be clear of the water for the most part. During transportation, the hull
will be supported closer to its center than this.

One drawback to engineering with stress skin beams is that there is very
little reference information available that would aid in predicting strength of
a particular assembly. Experience indicates that they are very strong for their
weight. We will have to test the beam after its construction in order to
determine its strength. To that end, I have included a brief analysis of hull
loadings.

If we model the motionless hull as a beam, we can locate the gravity loads as
per the hull CG analysis. In addition, there will be the buoyancy force (the
reaction force) acting as a distributed load. Although it is in fact more
complicated, buoyancy can be taken as an evenly distributed upward force along
the entire length of the beam. Similarly, the weight of the hull itself can be
taken as a distributed downward force of 22N/m. The maximum force of the motor
can be modeled as a forward act force along the length of the beam (which
contributes no moment to the system) and a torque operating at the LCB (because
that is where the motor has been placed). If the larger motor has a peak output
of around 30HP (22.4kW) and the boat is traveling at 26mph (11.6m/s), the force
generated at the propeller is 433 lbf (1925N). This force is generated about 12
inches (0.3m) from the hypothetical beam and so creates a torque of 5,200
poundinches (575Nm). The force vector created by the rudder is complicated.
However, in normal operation it contributes little to the bending of the hull in
the plane represented below as the surface of the page, and so is dropped in
this analysis. A loading diagram describing this situation is:

As can be seen from the, the maximum shear is 682N and occurs under the
pilot's seat. The fact that the pilot's weight is actually distributed tempers
this value somewhat. However, it can still be expected that the maximum shear
exists in that region. The maximum moment appears to occur near the center of
gravity. The moment diagram is problematic, however, in that it indicates some
"residual" moment at the right end (corresponding to the stern). This is due to
the simplifying assumption of equally distributed buoyancy. The hull, in fact,
has significantly more buoyancy located rearward where it will have a relatively
large effect on the moment because it is far from the point about which the
moment is taken. The un balanced moment diagram implies that the hull can not
actually exist in the state described. However, for illustration and estimation
purposes, I believe the simplified description of the hull is adequate.

Note that the effect of placing the propeller beneath the hull in the way
that is planned would also be to increase the buoyancy toward the rear of the
hull. The clockwise torque created on the hull by the force of the propeller
acting at a certain distance below the hull CG forces the stern to sink until
the increased buoyancy toward the stern equilibriates. The performance effect of
this is twofold. Initially, at lower speeds, the hull simply sinks by the stern
creating more resistance to motion than if the hull remained upright. If,
however, there is sufficient power available to overcome the resistance, the
hull will begin to plane earlier than if the hull had remained trimmed. The
resistance calculations above seem to indicate that there will be marginally
enough power available to operate in the planing region over a two hour period.
As mentioned earlier, if sufficient power exists it is best to invest it at the
low end of the planing region.
Costs

To estimate costs using the foam block hull described above, I specified
enough foam to occupy a prism the size of the hull's orthogonal dimensions.
Since a good portion of the boat will consist of empty space, this method should
result in extra foam. This extra can be used for bulkheads, repairs,
experimentation, and as filler for floatation space. Similarly, I specified
several yards of e-glass beyond a conservative estimate of what is required.
With the exception of the large blocks of polystyrene, the materials listed
below are readily available should a shortage develop.
Projected Costs for the Solar Splash Hull

Quantity

Item

Cost

Extension

5

10" x 24" x 96" extruded polystyrene blocks
[PSF102]

110.00

550.00

15 yd

3.7 oz E-glass in 60" width [FG1522]

3.05

45.75

2

1 gallon Epolite 2410 resin kits [POXYI3]

54.50

109.00

3

1/4 ply cut to 24" wide widths (fir or better)

15.00

45.00

6

1" x 4" x 10' lumber

4.00

24.00

misc.

parts

50.00

50.00

TOTAL

823.75

Note: Prices and catalogue
numbers of foam, fiberglass, and resin are from Alexander Airplane Company 1993
catalogue. Lumber prices are estimated. Miscellaneous parts could include eye
bolts for towing, foamcore for test forms, application brushes, etc..
Summary

The initial stage of design is one of determining the useful ranges for a
number empirically significant parameters corresponding to certain
characteristics of the underwater surface of the hull. Once accomplished, there
is an iterative process in which the chosen values of these parameters determine
the geometry of an underwater hullform. The geometric characteristics of the
drawn hull are determined and compared with the initial values of the
significant parameters, adjusted to fit, and the hull is redrawn. When the hull
parameters converge to reasonable values, they are used in empirical formulas to
compute hull resistance at various speeds. Our rather optimistic design speeds
for the two events were 4.6m/s (10.4 mph) for the endurance event and 11.6m/s
(26 mph) for the sprint competition.

In order to trim the hull for most efficient operation, it was necessary to
compute locations for each of the major hull components (including the pilot).
Because trim will vary, a degree of adjustablitiy was designed into the system
by allowing the batteries to move some distance along the boat's length.

The proposed method of construction uses joined polystyrene blocks from which
the interior and exterior of the hull will be sculpted. Since Styrofoam is a
soft material, it will be necessary to cover the hull with a thin fiberglass
skin. Because the strength characteristics of Styrofoam are suspect, the hull
will include a beam-like structure that will serve as a stiffening agent as well
as a mounting platform for components such as the motor.

The materials cost of constructing the hull will be in the neighborhood of
$800 to $1,000.
An Abbreviated Bibliography

Basic Naval Architecture

Barnaby, K. C.

Hutchinson and Co., LTD: London; 1949 (1967 edition).

Marine Hydrodynamics

Clayton, B. R.

Gulf Publishing Co.: 1982.

The Aerohydrodynamics of Sailing

Marcaj, C. A.

International Marine Publishing: Camden, Maine; 1979 (1991 revised edition).

Principles of Naval Architecture

Comstock, J. P. (Ed.)

Society of Naval Architects and Marine Engineers:

New York; 1969 (1983 edition).

Principles of Yacht Design

Larsson, L.; Eliasson R. E.

International Marine Publishing: Camden, Maine; 1994.

Some important hull parameters

Symbol

Name

Formula

Range

Description

Re

Reynold's number

VL/

106 to 108

ratio of motion forces to viscous forces

found in skin friction and form drag descriptions

L is representative linear dimension (e.g., waterline length)

, the kinematic viscosity, is / (density over dynamic viscosity) -
at STP = 10-6 m/s

Fn

Froude number

V/gL

.35 to 1.5

ratio of motion forces to gravity forces

found particularly in wave making formulas

L is some linear dimension (e.g., length,
volume1/3)

g is gravitational force

LOA

length over all

L

6m
(20 ft)

actual length of the hull from stem to stern

LWL

length waterline

fraction LOA

4.2 m to 6m
14 to 20 ft)

length of wetted hull at the waterline

sometimes approximated as 0.7 LOA

varies with speed, waves, and planing conditions

B

beam

B

.6m to 2m
(2 to 6.5 ft)

maximum width of the hull (often maximum waterline beam is
used)

T

draft

T

.05m to .5m
(2 to 20 in)

depth of the hull below the waterline

usually calculated for canoe body, i.e., without appendages like the
keel

displacement volume

.15 to .2 m3
(5.2 to 7 ft3)

the volume of water displaced by the hull in static conditions

this volume of water weighs the same as the boat

varies with water density (as between fresh and salt water)

displacement weight

1350N to 2225N
(300 to 500lbs.)

the weight of the water displaced by the boat

same as the weight of the boat (Archimedes principle)

CB

block coefficient

/ LWL*B*T

.4 to .6

ratio of displacement volume to the volume of the rectangular prism
formed from the waterline length, waterline beam , and draft
dimensions

a gauge of the slenderness of the hull

CP

prismatic coefficient

/ LWL*Amax

.55 to .7

a refinement of the block coefficient that relates displacement
volume to the volume of a cylinder which conforms to the hull's maximum
cross-sectional area and is LWL in length

helps in assessing the longitudinal placement of hull
cross-sections

CM

midship coefficient

Amidship / B*T

.7 to .9

ratio of the area of the midship cross-section to the maximum beam
and draft

note that the maximum beam and draft are generally aft of midship,
therefore CM indicates the slenderness of the foreward hull
section

CWP

waterplane coefficient

AWL / B*LWL

.65 to .85

ratio of the waterline planview area to its circumscribed area

LCB

location of center of bouyancy

2% to 7%

distance aft of midship of the hull's center of bouyancy (the
centroid of the displacement volume) usually in a percentage of the
hull's total length

measure of the fullness of the stern sections and the volume
distribution in general

iE

waterline entrance half-angle

4 to 15

angle between the hull's longitudinal centerplane and the tangent to
the bow's foremost section (in degrees)

enumerates the sharpness of the bow section

Rf /

frictional resistance

CF Swet (1/2V2)

ratio of skin friction to displacement weight

depends on Re (because of CF)

dimensionless because it is a ratio of forces

displacement is the most important pararmeter in hull drag

CF is flat plate resistance of a board of length L

Swet is wetted surface area (underwater surface)

RR /

residuary resistance

(BIG empirical formula)

sum of rsistances sensative to Fn

generally includes wave making resistance and form drag

displacement most significant variable

RT

total resistance

RF + RR

sum of previous two ratios times displacement weight

sometimes expressed as a fraction of displacement weight (RT
/)

balances propulsion forces at a given speed (under ideal
conditions)