Does any one have an approximate mathematical relationship between
hull displacement and fuel consumption? Consider a 40' trawler
displacing 20,000 lbs and a 46' trawler displacing 40,000 lbs, similar
hull, same engines, both cruising at 7 knots.
Larry Cruzen
"Larry Cruzen" larrycruzen@gmail.com writes:
Does any one have an approximate mathematical relationship between
hull displacement and fuel consumption? Consider a 40' trawler
displacing 20,000 lbs and a 46' trawler displacing 40,000 lbs, similar
hull, same engines, both cruising at 7 knots.
I highly recommend "The Propeller Handbook", by Dave Gerr. All you ever
wanted to know, and more. See http://tinyurl.com/gerrprop for details.
Scott Welch
FirstClass Product Manager
www.firstclass.com
Those who make no mistakes rarely make anything.
Larry:
Bebe's book (the revised edition with modern, Nordhavn oriented chapters)
gives horsepower versus speed graphs for several displacement trawlers. What
you will find from these graphs is that at hull speed (defined as 1.34 *
sqrt (lwl)) an average boat will require 2 horsepower per 1000 lbs. This
rule of thumb works pretty good for 32' to 50' displacement trawlers.
Also looking at these graphs you will see that if you slow down to about 1 *
sqrt(lwl) then the horsepower drops by 1/3 to 2/3 hp per 1000 lbs.
So the point is that the horsepower depends on two variables: the speed to
length ratio, ie speed/sqrt(lwl), and the displacement.
So once you figure the horsepower using the rules of thumb above then the
fuel consumption is pretty straightforward. For slower reving, non
turbocharged engines (the kind in displacement trawlers) fuel consumption is
about 16-20 horsepowr per gallon per hour. The factor is on the low end for
older engines like the Ford Lehman and maybe on the high endfor modern,
common rail engines like the John Deere.
Back to your original question. The 40' trawler with maybe a lwl of 37' at 7
kts has a speed to length ratio of 7/(sqrt(37)) = 1.15. So maybe it will
need about 1 hp per 1000 lbs at that speed or 20 hp. BTW I doubt that there
are any 40' trawlers that weigh 20,000 lbs. The 46' trawler has a speed to
length ratio of 7/(sqrt(43)) = 1.06. So maybe it requires 0.8 hp per 10000
lbs or 32 hp. These are rough top of my head approximations, but they are in
the ball park.
Then applying the fuel consumption rule of thumb and taking 18 hp per gallon
per hour as an average, the 40' trawler will require 20/18 = 1.1 gph and the
46' trawler will need 32/18 = 1.8 gph.
You can read Gerr's books and you can read Bebe but I suspect you will come
to the same rough conclusion. Slow speed to length ratios (well under 1.34)
gives very economical cruising horsepower and fuel consumption. But
displacement is an important factor as well.
David