1. Humpy Dumpster Project
What: a chute carrying fish waste is supported on a
floating metal cylinder which rises and falls with
tidal variations against a pile. A dumpster, moored
to the float, catches the waste from the chute. When
full, the dumpster is towed out to sea and emptied.
Where: Fish processing plant, Valdez, Alaska
Who: designed by an engineering company in the
Puget Sound &
built by Shoreside Marinas of Bellingham, WA.
WCC: D.Sluys
Humpy Dumpster: Daphne Sluys:

2. with tidal fluctuations
Humpy Dumpster Schematic
(as designed with placement errors)
Pile Hoop about
12” above water line, on diameter of float, around Pile.
wastechute *
Water Line
with tidal fluctuations
Dumpster
attached to float 12” above hoop
Float
Pile, driven into ground
Note: Some diagrams and slides are adapted from Dan Sweet’s
Co-Operative Learning Project in Winter 2005 at WCC
WCC: D.Sluys

3. Placement of pile hoop needs to be corrected.
Objectives :
Find how far the float will be pushed down in the water by the weight of the whole chute structure.
Placement of pile hoop needs to be corrected.
(Incorrect as drawn on the plans – cylinder floating too high)
2. Find center of buoyancy of float; according to specifications weights need to be attached below the center of buoyancy.
i.e. find the center of mass of displaced fluid
(No ready-made formula in available engineering texts)
WCC: D.Sluys

4. Dimensions of float: radius = 2.5’; length = 10’
Known & Basics:
Dimensions of float: radius = 2.5’; length = 10’
Load on float = 6400 lbs + 200lbs ballast to level
Density of sea water approx. 64 lbs/cubic ft.
Volume of water displaced by the loaded float
= total load of /density of sea water
= cubic foot.
Cross-sectional area submerged
= volume displaced / length of float
= sq.ft.
proportion of cross-sectional area submerged
= submerged area / total area =
WCC: D.Sluys

5. First Objective Finding d, the depth of submersion: using geometry
Diagram adapted from Dan Sweet’s work

6. Diagram adapted from Dan Sweet’s work
Finding d, the depth of submersion: using calculus (trig substitution; trig identities) y
(d-r) d d x O dy -r
Diagram adapted from Dan Sweet’s work

7. Common sense check for 3 obvious cases
The cross-sectional area A is given by:
where d = depth of submersion
r = radius of floating cylinder
Common sense check for 3 obvious cases
Fully submerged: d = 2r
Half submerged: d = r
Not submerged: d = 0

8. where d = depth of submersion r = radius of floating cylinder
A = cross-sectional submerged area pi
0.5252pi
d = 1.022r

9. calculator (2nd CALC: Intersect ) or
Use graph or
calculator (2nd CALC: Intersect ) or
Newton-Raphson (calc I application)
to find d = 1.022r
where r = 2.5 feet.
Float more than halfway submerged
Plan indicates pile hoop attached on diameter,
about 1’ above water line and 1’ below dumpster attachment
Corrosion problems
Dumpster attachment problem (1’ above pile hoop)
Need to raise pile hoop to about 3.55 feet (i.e. 2.5’ + 1’)
to maintain 1 foot above water level
WCC: D.Sluys

10. Second Objective Finding the center of area formula:y
(d-r)
Water line d d x O dy -r
Diagram adapted from Dan Sweet’s work

11. Center of Submerged Area result: (Check three common sense cases)

13. “Experts” may not admit they goofed
Possible Lessons:
“Experts” may be wrong
“Experts” may not admit they goofed
Check all work against common sense
Ready made formulae may not be at hand
Rely on basic principles and concepts
Not all equations can be solved algebraically
Use multiple techniques to check your work
Real problems often require skills from multiple fields
Details, details, details, details, details.
WCC: D.Sluys

14. Log raft made of parallel logs diameter D
Possible Extension:
Log raft made of parallel logs diameter D
How does diameter of logs affect the free board (height of
raft above water level)?
free board D
Water level
WCC: D.Sluys