1. School of Naval Architecture and Marine Engineering — College of Engineering
Shane Bruce — E-mail smbruce1@hotmail.com — 504-756-6934 — Graduate Student
1
NAME 4177 Fall 2009: Instructor Chris McKesson - Assignment #3 – What are AMV’s good for?
Issue Date: 23 Sep 2009
Due Date: 7 Oct 2009
1st
of Assignment Set: Kennell’s Transport Factor
Background
Transport Efficiency was a study of Engineer named Theodore von Karman who published a map of the
cost of speed in 1950. The value of speed then could be quantified in relationship with many concerns
such as economical efficiency or even speed areas and barriers of certain types of technology.
ߟ
்ୀ
ௐ௧ ௗ ௌௗ
௪
In 1998 Colen Kennel introduced a variation of the von Karman/ Gabrelli metric and named it Transport
Factor still using English Units, which is defined as:
ܶܨ ൌ ܭ
ܹ
ܵܲܪ
ܸ݇
݁ݎ݄݁ݓ ܭ ݅ݏ ܽ ܿݐ݊ܽݐݏ݊ ݂
1
550
Or
ܶܨ ൌ
ܹሺ݈ܾݏሻ כ ܸሺ݂ݏሻ
550ܲܪܵݔሺ݄ሻ
, ݏ݅ܭ
1
326
݄݊݁ݓ ܸ ݅ݏ ݅݊ ݇݊.ݏݐ
SHP (Shaft Horse Power) being a function of how much HP is delivered to the shaft of a propeller,
another term can be introduced call the EHP (Effective Horse Power) which is the power required to
‘tow’ a ship without it’s intended or other propulsion.
As weight is distributed, Transport Factor may also be distributed.
TF = TF(SHIP) + TF (cargo) + TF (fuel)
Question Set
1a.) How many units of TF is required for a ship to voyage 10,000 miles?
Of course the first question that come to the front is “how fast”, von Karman’s method of calculating
transport efficiency showed one thing. Speed is expensive.
Assuming this question is poised for a sea vessel in average calm waters, and that is neither wind nor
externally propelled, but is a question that can be answered in Watts of a diesel engine that the vessel
carries aboard, and that the vessel is neither refueled or uses alternatives to power.
Further assumptions:
2. School of Naval Architecture and Marine Engineering — College of Engineering
Shane Bruce — E-mail smbruce1@hotmail.com — 504-756-6934 — Graduate Student
2
NAME 4177 Fall 2009: Instructor Chris McKesson - Assignment #3 – What are AMV’s good for?
1. Average speed of vessel maintained.
2. Constant displacement (despite fuel being used)
3. Endurance speed is the service speed (rated power)
4. Ship service is negligible.
5. All fuel used, no point of return.
Actually plotted Transport Factor to Fuel, another concern of course emerges, type of vessel (technology
wise that is used).
One can see that an airplane, 10,000 miles would require a TF8, while a conventional monohull steam
ship would require a TF17. I imagine that diesel is the boat of choice in this matter, being the most
common and efficient way of transporting power, being a TF12.
Now, the interesting question was McKesson asked how what kind of TF factor would be required for
himself to travel 10,000 miles. I stipulate that the weight required of calories couldn’t be carried, food
being less power dense than diesel. McKesson, I estimate weighs about 180 lbs, and could maintain a
3. School of Naval Architecture and Marine Engineering — College of Engineering
Shane Bruce — E-mail smbruce1@hotmail.com — 504-756-6934 — Graduate Student
3
NAME 4177 Fall 2009: Instructor Chris McKesson - Assignment #3 – What are AMV’s good for?
rather long gait walking. Looking up on various charts McKesson would burn about 276 calories per
hour at a rate of 3 mph, or 4.3x10-4
HP during three miles and one hour.
ܶܨሺெ௦௦ሻ ൌ
ሺଵ଼௦ሻሺଷ௧௦ሻ
ሺଷଶሻሺ.ସଷுሻ
՜ ܶܨሺெ௦௦ሻ3852
So McKesson has a really high Transport Factor, and such a number is assuming that he gains sustenance
from his environment along the way. In this case the way being 10,000 miles. How much does food
weigh?
ܲሺெ௦௦௦ሻ ൌ
ሺ10000݉ሻሺ276݈ܿܽݏ݁݅ݎሻ
3݉
ൌ 920,000 ݈ܿܽݏ݁݅ݎ
To ensure that the calories are used for transportation purposes and not used to gain weight (constant
displacement), we’ll use beer, as according to Prof. David J. Hanson, Ph.D of the State University of New
York of Potsdam, calories from alcohol are not associated with weight gain, and causes the metabolic
rate to increase significantly while reducing loss of fat. (i.e. the acetate released into the bloodstream
replaces fat as the source of fuel).
We’ll use an Anchor Porter having 209 calories per 12 ounce (the Flying Dog Horn Dog have a more
optimal beverage at 314 calories per 12 ounce and better than the Anheuser Busch Natural Ice at 157
calories per 12 ounce). Thus McKesson fuel consumption would be 52823 ounces or (at 0.0295735
L/ounce) 1562 liters of Anchor’s Porter. Though Flying Dogs Gonzo would match nicely with 269
calories at one can per hour.
ܹሺெ௦௦௦ሻ ൌ
52823ݖ
16ܾ݈/ݖ
ൌ 3301݈ܾݏ
So McKesson would have to carry 3301lbs of Anchor Porter beer with no more exertion than walking
normally. His total weight being now 3481lbs, we emerge with a new TF(McKesson).
ܶܨሺெ௦௦ሻ ൌ
ሺଷସ଼ଵ௦ሻሺଷ௧௦ሻ
ሺଷଶሻሺ.ସଷுሻ
՜ ܶܨሺெ௦௦ሻ74497
Though our factors of speed and SHP cancel out and the TF(fuel) depends on SFC (specific fuel
consumption as seen above and as approximates:
ܶܨሺ݂݈݁ݑሻ ൌ ݇ሺܵܥܨሻሺܴܽ݊݃݁ሻ
The weight of the vessel ranging widely, one could hardly assume the weight was 94.9% fuel, of course
with a denser beer we could reduce the TF(McKesson) to a manageable factor. Of course the answer could
be a wide range from a low TF at low speeds if there is no opposing wind to a higher number, but with
the above assumptions a 12-17 is expected for an ocean going vessels of size.
4. School of Naval Architecture and Marine Engineering — College of Engineering
Shane Bruce — E-mail smbruce1@hotmail.com — 504-756-6934 — Graduate Student
4
NAME 4177 Fall 2009: Instructor Chris McKesson - Assignment #3 – What are AMV’s good for?
1b.) So if the Vessel was State of the Art, 40 knots with the above assumptions and needed to go
10,000 miles, what is the T Factor?
State of the Art:
Usually I would devise State of the Art for naval vessels into areas of expertise:
1. Hull Design
2. Propulsion
3. Control systems
4. Materials and Composites
5. Etc.
But I only have a few days for this assignment, so the advantage of the gross or macroscopic approach of
the Transport factor is perfect for the management or contract administration as for ORN or NAVSEA.
Simply charting in all the characteristics, what patterns emerge in a deterministic universe, where do
bifurcations occur (overstablized areas that would appear to be excitable) and which branches occur
from such behaviors that will best suit our needs.
Research Administration, rather than attempting a new state of the art idea, can make inferences based
on the foundation of previous work, simply correlate all possible relevant data and see if any such work
has already been accomplished. McKesson’s, Kennel’s, and von Karman type graphs of “world of known
vessels” is a macroscopic approach to logistics of finding our State of the Art. What are they?
McKesson defines the transport factor as being dependant on Lift/Drag. How and Why?
In Hull Design, Efficiency Horse Power is the power dependent upon the hull design, the power required
to for the ship to be moved. Shaft Horse power can be seen from the Effective Horse Power by the
Overall Propulsion Coefficient.
ܲܪܧ ൌ
ோ௧ሺ௦ሻכሺ௧௦ሻ
ଷଶ
and ܵܲܪ ൌ
ாு
ை
So Transport Factor itself does not have to contain a velocity factor as the TF Component of “SHP/VK” is
to be found:
ܵܲܪ
ܸܭ
ൌ
ܲܪܧ
ܱܲܥ
ܸሺ݇݊ݏݐሻൗ
ൌ
ܴݐሺ݈ܾݏሻ
326 כ ܱܲܥ
ܶܨ ൌ ܭ ൬
ௐ
ௌு
ൗ
൰ ൌ ቀ
ଵ
ଷଶ
ቁ ቀ
ௐ
ோ்
ቁ ሺ326ሻሺܱܲܥሻ ܶܨ ൌ
ሺைሻሺௐሻ
ோ்
So by the above equation, we’ve moved from less weight and less velocity of Kennels TF, to a higher
optimization, less weight and less resistance of McKesson, who states by OPC=1, TF=Lift/drag.
5. School of Naval Architecture and Marine Engineering — College of Engineering
Shane Bruce — E-mail smbruce1@hotmail.com — 504-756-6934 — Graduate Student
5
NAME 4177 Fall 2009: Instructor Chris McKesson - Assignment #3 – What are AMV’s good for?
First speed, how fast is a ship? Speed is a relative term and perceived in various ways, from a
bystanders point, velocity of an object going by is speed, no matter what the size is. Size is a factor only
in displacement or momentum, so unless one has such velocity or has to interact with an object of some
velocity, size doesn’t matter. From the perspective of operation and being on a vessel, size does matter.
The perceiver’s speed of a vessel probably best described as mass time velocity, or in the case of naval
vessels, speed times displacement volume. How fast is what going? When gives us the Froude Number.
Size being length or volume, Froude numbers for both (though I suppose the volumetric Fn has a unit of
length:
݊ܨ௧ ൌ
ܸ݈݁ݕݐ݅ܿ
ሺ݃ݕݐ݅ݒܽݎ כ ݐ݄݃݊݁ܮሻ
ଵ
ଶ
݊ܨ௨ ൌ
ܸ݈݁ݕݐ݅ܿ
ሺ݃ݕݐ݅ݒܽݎ כ ሺܸ݁݉ݑ݈
ଵ
ଷሻ
ଵ
ଶ
Lift for a displacement and/or dynamic lift within a single medium can be written as generically and
broadly as:
ݐ݂݅ܮ ൌ ߩܣሺ݄݃
1
2
ܸܮܥଶ
ሻ
Where CL is a coefficient and the Velocity of the 2nd
half of the equation is dynamic lift.
All that being said, what is state of the Art?
From data the best lift/drag ratio is a 17.28, which assumes perfect effectiveness of propulsion, and
the equation of the best lift/drag state of the art has been plotted against graphed dated as:
ݐ݂݅ܮ
݃ܽݎܦ
ൌ 5 40݊ܨ௩
ଷ
Finally all put into place, we at least have the variable we need to know to find “what’s the TF?”
Curves show the best current ships that do about 40 knots have about a 22% used in fuel weight
according to Kennel’s findings on TF devoted to fuel, and from HSSL an expected range of OPC to be
0.65-0.75. With all this we still have to either know or guess the weight of this red herring, as with the
given equation we can set weight equal to the displace volume of a model.
6. School of Naval Architecture and Marine Engineering — College of Engineering
Shane Bruce — E-mail smbruce1@hotmail.com — 504-756-6934 — Graduate Student
6
NAME 4177 Fall 2009: Instructor Chris McKesson - Assignment #3 – What are AMV’s good for?
Let’s just make up one. A 102,870 Tonnes (that’s metric tons) ship (my birth date) has a volume of
102,870m3
(very efficient don’t you think?) at 40 knots which we’ll just call 17.88m/s and 64.37km/hr
has Froude number
݊ܨ௨ሺ௧ሻ ൌ
17.88 ݉/ݏ
ሺ9.81݉/ݏଶ כ 102870݉ଷ
ଵ
ଷሻ
ଵ
ଶ
ൌ 0.084
` Which means our lift to drag ratio is:
ݐ݂݅ܮ
݃ܽݎܦ
ൌ 5 40݊ܨ௩
ଷ
՜ ݃ܽݎܦ ൌ
ݐ݂݅ܮ
5 40݊ܨ௩
ଷ
102,870,000݇݃
5 40ሺ0.084ሻଷ
ൌ ܴܶሺ݃ܽݎܦሻ ൌ 6206 ݇ܰ
Sounds like a tanker, but where chugging along here with an OPC of 0.70 (state of the art), so:
ܶܨ ൌ
ሺܱܲܥሻሺܹሻ
ܴܶ
ൌ
ሺ0.7ሻሺ102,870,000݇݃ሻ
6206݇ܰ
ൌ 11.60
1c) How much does of the weight can be for the ship and cargo?
Like McKesson, let’s assume a 0.4 lbs/hp-hr as a 0.24 Kg /kW*hr, then 16,093 kilometers at 17.88 m/s or
4.96km/hr.
Then 16,093km at 64.4 km/hr, we have 250.0 hours.
Also, to overcome the drag of 6206݇ܰ ܽݐ 17.88 ݉/,ݏ we need 110 MW which means 6,750,652 kg of
fuel. Data shows a trend of TFfuel/TFtotal at 22%, while my ship has 6,750,000/102,870,000
fuel/total ratio of 7%!!
So, 96,120,000 kg or 96,120 tonnes is available for Lightship and Cargo.
7. School of Naval Architecture and Marine Engineering — College of Engineering
Shane Bruce — E-mail smbruce1@hotmail.com — 504-756-6934 — Graduate Student
7
NAME 4177 Fall 2009: Instructor Chris McKesson - Assignment #3 – What are AMV’s good for?
Assignment Set #2: Plot Kennel’s Transport Factor, Re-plot using Froude Number
1d) What is the SHP of the ship?
Since I chose a OPC of 0.7 we can find SHP using the equation:
ܵܲܪ
ܸܭ
ൌ
ܲܪܧ
ܱܲܥ
ܸሺ݇݊ݏݐሻൗ
ൌ
ܴݐሺ݈ܾݏሻ
326 כ ܱܲܥ
Since SHP probably is expected in actual Horse Power, probably have to “put some English on it”.
ܵܲܪ ൌ
ܴݐሺ݈ܾݏሻሺܸܭሻ
326 כ ܱܲܥ
ൌ
6,206,370ܰሺ17.88݉/2ሻ
ሺ754 ܹ/ܲܪሻ326 כ 0.7
ሺ݅݊ܿ݅݀݁݊ݕ݈݈ܽݐ ݃݅݃݊݅ݒ ݏݑ ܽ ݉݁ܿ݅ݎݐ ""ܭ ݂ 254804ሻ
SHP = 645 HP (ok 645 horse power sounds a little shy for a 102870 metric tonne ship.)
