The Effects of
Boat-generated Waves vs. Wind Waves on Ada Lake
Constructed
by: Scott Allen
University of
Wisconsin-Madison
Department of Civil and
Environmental Engineering
Introduction
Objectives:
We have studied waves from natural sources
(wind), but never from anthropogenic sources
(boats). For this project, I will show the effects
of boat-generated waves when compared with
wind-generated waves on:
Wave height
Wave power
Sediment resuspension capabilities
Importance:
Wave power can have drastic effects on shoreline
erosion. As waves hit the shore, they break apart
the soil and carry sediments into the water. This
results in shoreline recession which can create a
loss of beach area or an instability of coastal
structures. Waves can also have impacts on the
shoreline biota, changing the environment in which
plants and animals live.
When sediments are resuspended into the water,
they can be transported and deposited to other
places in the lake. This can cause problems related
to loss of sediments or the accumulation of
sediments, changing the bathymetry of the lake.
Sediment resuspension can also allow hazardous
particles that may have settled to the bottom to
re-enter the water column, causing problems for fish
and plants.
Ada Lake Info
Ada Lake (red star) is a small, glacial lake in
northeastern Wisconsin, about 70 miles northeast of
the city of Wausau. The western shore of the lake
is dominated by houses and cabins of private
landowners and the eastern shore is undeveloped land
of the Nicolet National Forest, including a state
campground. Ada has a maximum depth of 18.3 meters
and an average depth of 4.9 meters. The lake covers
73 acres, has 1.6 miles of shoreline, and is home to
a healthy population of panfish, bass, and northern
pike.
Ada Lake was chosen for two
reasons. Firstly, my uncle owns a cabin on Ada
where I have spent many relaxing days fishing and
swimming. Also, gas-powered motors are currently
prohibited on the lake for aesthetic, noise,
pollution, and environmental reasons such as
shoreline erosion. By using Ada Lake in this study,
I can show if the introduction of motorboats will
have significant negative impacts on the lake.
Boat Info
Three different boats will by analyzed for this
study.
1. The MasterCraft ProStar 205V is a
premier fiberglass sport boat used for water
recreation. It was chosen to represent boats that
will use Ada Lake for waterskiing and tubing, two
very popular water sports. Pictured to the right is
a typical wake produced at a speed of 15.2 m/s.
Length - 6.27 m
Weight - 1383.48 kg
Draft - 0.56 m
Capacity - 12 people
2. The MasterCraft X-Star is a
premier fiberglass sport boat used for water
recreation. It was chosen to represent boats that
will use Ada Lake for wakeboarding, a sport that
requires a large wake. Pictured to the right is a
typical wake produced at a speed of 8.5 m/s.
Length - 6.27 m
Weight - 1383.48 kg
Draft - 0.56 m
Capacity - 12 people
3. The 1989 Smoker Craft Magnum is
an outdated aluminum fish/ski boat. It was chosen
to represent older boats that will cruise Ada Lake
for fishing or other purposes. It was also chosen
because my parents own one which I have used on
numerous occasions and I was curious to see the
types of waves it generates. Pictured to the right
is a typical wake produced at a speed of 8.5 m/s as
well as me about to get huge air on my wakeboard.
Length - 4.88 m
Weight - 362.9 kg
Draft - 0.3048 m
Capacity - 5 people
Calculations
The calculations for
this study can be divided into three sections.
First, I needed to find the wave heights generated
by both wind and boats. Then I could use those wave
heights to find the power the waves produce and
their capabilities for resuspending sediments.
Please click on the links below for details on each
section.
To find the height of the waves
generated by the boats, I used the equation
summarized by Sorensen and developed by Bhomik,
Soong, Reichelt, and Seddik. This equation was
produced by measuring the waves produced by 12
different recreation-type vessels. It should be
noted that the type of boat hull (V-hull, Tri-hull,
Jon boat, etc) was not taken into account.
Hm = 0.537*V-0.346*x-0.345*LV0.56*D0.355
where Hm = maximum
wave height in meters, V = velocity in m/s, x =
distance from shore in meters, LV =
length of vessel in meters
D = Draft of vessel (how deep it
sits in the water) in meters
Boat length and draft
are shown in the table below.
ProStar 205V
X-Star
Magnum
LV
6.27
6.78
4.9
Draft
0.56
0.71
0.3048
Wind
Wave Height:
s
for varying wind speed (U) according to the
following equations:
Hs/U2 =
0.0016*(Fs/U = 0.286*(F1/3
where F*=gF/U2
The wind was
estimated to be coming from the southwest, making
the fetch 685.8 m, which is the largest fetch
possible on Ada Lake.
For vessel and wind
speeds varying from 1 to 20 m/s, and for boat
distances from shore varying from 10 to 100 meters,
the wave heights are shown below.
The distance of x = 30.48 m
corresponds to the distance of 100 ft, which is the
closest boats can travel to the shore with a wake in
the state of Wisconsin. From the graphs you can see
that the wave height observable from shore increases
as the boat gets closer to shore. It is noteworthy
that the wave heights decrease with an increase in
speed, which is a result of the planning effect of
boats. Also evident is that the wind wave height
increases with wind speed.
2. Wave Power
Wave power is
important because as waves generate more power, they
have a greater capacity for eroding the shoreline.
The total wave power can be calculated by first
finding the wave energy density using the following
equation:
E =
1/8*ρ*g*H2
where ρ = 1000 kg/m3
and g = 9.81 m/s2. When boats produce a
wake, they create more than just one wave. Sorensen
estimated that boats create 13 measurable waves of
different amplitudes as shown in the figure below.
Therefore, to find
the total wave energy produced by one passing boat,
we must sum up all the energies resulting from each
wave in the figure. Then we must multiply that
amount by the number of passing boats per day. I
will assume that there are an average of 5 boats on
Ada Lake each day and each boat will travel around
the lake 15 times per day.
Similarly, since the
wind speed being used is a long term average, we
will assume that the wind is blowing all day long,
resulting in 24 hours of waves. The wave energy
calculated per wave must then be multiplied by
86,400 seconds since the period of the waves is
about 1 second.
Wave power,
calculated by dividing the wave energy by the wave
period (assuming shallow water), is shown in the
graph below. This graph is only for boats at a
distance of 30.48 m (100 ft) from the shore, but the
graphs for other distances will look similar.
Note: The wave power due to wind
is only visible for speeds less than two because of
the scale of the graph. The power produced from
wind is orders of magnitude greater than the power
produced from boats.
3. Sediment Resuspension
Sediment resuspension is important
because when sediments from the lake bottom are
resuspended, they can be eroded or transported.
This can result in deposition of sediments and the
resuspension into the water column of hazardous
particles that had settled out.
To estimate the potential of boat
waves to resuspend sediments when compared to wind
waves, I calculated the bottom velocity produced by
various wave heights. From the CEE 514 lecture
notes, the equation for bottom velocity, in its
simplified form, is:
Ub = π*H/(T*sinh(kd))
where k = 2π/L
Shown in the graph below is the
bottom velocity generated by waves created by both
wind and boats. The boat waves are from a distance
of x=30.48 m from the shore (the edge of the no-wake
zone).
Discussion of Results
Wave Height:
The MasterCraft X-Star boat produced
the largest wave height of the three boats studied.
This is not surprising since the X-Star is mainly
used for wakeboarding, a sport that requires a large
wake. At low wind speeds, the wind wave height was
less than the boat wave height for all boats. As
the speeds increased, however, the wind wave height
eventually surpassed the boat wave heights, since
boat wave heights decrease with speed and wind wave
heights increase with speed. The wave height from
boats could be greater than or less than those from
the wind based on the boat type, the boat distance
from shore, the boat speed, and the wind speed.
Wave Power:
The results show that the wave power
produced from wind waves far exceeds the power
produced by boat waves, which is due to the duration
of the waves. Boats usually only operate during the
daytime and there is a limited number of boats that
can fit comfortably on Ada Lake, especially when
skiing or wakeboarding. I estimated a total of 75
boat wakes per day, composed of 13 waves each.
However, with the wind assumed to blow all day long,
it creates 86,400 waves per day, which results in a
much greater daily wind power.
Sediment
Resuspension:
While time duration is an important
factor in wave power, it is not important in
calculating sediment resuspension capabilities
because the bottom velocity equation greatly depends
on wave height. The bottom velocity due to wind is
less than the bottom velocity due to boats at low
velocities, but greater than the bottom velocity due
to boats at high velocities. This is due to the
fact that boat waves decrease with speed and wind
waves increase with speed. However, the average
wind speed in the Ada Lake area is only 4.37 m/s.
So with the exception of storm events, boat waves
will have more impact on bottom velocity than wind
waves.
Causes for
Error:
There are many potential sources for
error in this project.
I only used three different
types of boats in my analysis, and different
boats will produce different size waves.
However, I chose boats that will likely be
common to Ada Lake if the lake is opened up to
motorboats. Also, I analyzed the MasterCraft
X-Star, a wakeboarding boat that produces a
larger wake than the vast majority of
recreational boats.
I assumed the wind direction to
be from the southwest, making the fetch of the
lake 685.5 m. This is not always true since the
wind changes direction, but it is a good
assumption because it represents the largest
fetch possible on the lake.
I estimated the number of boats
per day (5) and the number of passes per boat
(15) on a typical day. I feel that these are
reasonable assumptions, but the number of boats
and number of passes will vary from day to day.
I assumed the wind to be blowing
for 24 hours a day. This is obviously not
always the case as wind speed will vary daily.
I analyzed sediment resuspension
by calculating the bottom velocity produced by
the waves. While I believe the velocity
calculations are correct, they do not directly
correspond to sediment resuspension due to
factors such as particle size and cohesion.
Turbulence can also play a role
in sediment resuspension and would be worth
considering if I had more time.
On a final note, this project is not
meant to be an all-encompassing, study to end all
studies on boat-generated waves. I made several
assumptions and used fairly simple equations in my
analysis. However, I hope that I have shown trends
in the significance of boat waves compared to wind
waves on wave height, wave power, and bottom
velocity for Ada Lake.
Sorensen, Robert M. (1997).
Prediction of Vessel-Generated Waves with
Reference to Vessels Common to the Upper
Mississippi River System. Upper Mississippi –
Illinois Waterway System Navigation Study, ENV
Report 4. US Army Corps of Engineers.
Wu, Chin. (2003). Notes for
CEE 514- Coastal Engineering. University of
Wisconsin-Madison.
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