Cruising 'Uphill' and efficiency

Hello from Marineland FLA, where we are hanging out for a few days. Our last 2 days cruising northwards involved many hours of going 'uphill', or against an opposing current. As we slogged along at reduced speed I had time to think about what engine rpm would achieve maximum efficiency when pushing against opposing current. Since today is gray and cold (60's !!) it seems a good time to crunch some numbers.

 

[Warning ! The analysis below relies on many rough estimates and a few WAG's. Hopefully any errors in the input numbers do not impact the conclusions reached.]

Normally a displacement boat (non-planing hull) like Spray gets better fuel mileage (mpg or since we measure speed in knots we'll use nmpg = nautical miles per gallon) when you go slower. When I bought Spray I was told that when cruising at 1600 rpm she makes 6.5 knots and burns 1.5 gallons of diesel per hour (much cruising since then has verified those numbers), but that increasing engine speed to 2000 rpm brings speed to 8 knots but at the cost of double the fuel use, or 3 gal/hr. Going to full throttle yields 2400 rpm and top speed of 9 knots but again doubles the fuel use to 6 gal/hr.

Here's a table that summarizes all this and includes a slow cruise rate of 1200 rpm:

Spray performance in still water

rpm    speed in knots    fuel use in gph

1200         5.0              0.75

1600         6.5              1.5

2000         8.0              3.0

2400         9.0              6.0

Here is the fuel use data graphed, with rpm on the horizontal axis and gph on the vertical axis. (A cubic polynomial has been fit to the data points)

The non-linear aspect of this performance is obvious. Basically what happens with a displacement hull is that when you reach a 'hull speed' based primarily on hull length (at waterline), pushing harder makes a bigger wake and uses more fuel, but gives very little added speed.

 

What about efficiency, as measured in nmpg ? It's easy to calculate since nmpg = nmph (aka knots) / gph, so for our basic cruise speed we see 6.5 nmph / 1.5 gph = 4.33 nmpg. Now 4+ miles per gallon stinks for a car but its pretty good for a cruising boat (we see many that are yielding 1 nmpg or less).

 

Here's the table from above with nmpg data added :

 

Spray performance in still water

rpm    speed in knots     fuel use in gph      Efficiency in nmpg

1200        5.0                 0.75                   6.7

1600        6.5                 1.5                    4.3

2000        8.0                 3.0                    2.7

2400        9.0                 6.0                    1.5

Now lets graph this efficiency data :

This confirms what was stated earlier : for a displacement hull slower speeds yield better fuel mileage and at higher speeds (especially above hull speed), fuel mileage suffers badly.

 

Why don't we cruise at 1200 rpm and yield nearly 7 nmpg ? It's a matter of compromise between efficiency and making progress. 6.5 knots is slow enough. 5 knots would seem glacial. I have met boaters who cruise that slowly though.

 

Next lets look at the effect of opposing current with water speed v (we'll use negative v's for opposing current). If you pick an extreme case of v = -6.5 knots, you yield zero efficiency at 1600 rpm since Spray would be effectively motionless as it fought such a current, and to get any forward motion at all you'd need to push rpm > 1600. So there's a case where you need higher engine rpm for better efficiency, which is the reverse of what we see in still water.

 

I took the table above and repeated it 6 times, each time adding v values of -1, -2, -3, -4, -5, -6 knots to the 'speed in knots' columns. The resulting nmpg numbers are graphed below :

The still water case (v = 0) is shown in blue for reference. As I study the plots, here is what I notice.

 

A) All the plots are below the v = 0 reference plot, so opposing current always reduces nmpg (Duh!).

 

B) The hit on nmpg is biggest at low rpm and smaller at high rpm.

 

C) For opposing currents up to 3 knots, the plots always slope downwards, which means that slowing down the engine rpm will still increase fuel mileage.

 

D) But for opposing currents of 4 knots or greater, there is an optimum rpm above 1200 that will yield best fuel mileage.

- For 4 knot opposing current it looks like 1600 rpm yields best efficiency.

- For 5 knot opposing current it looks like maybe 1800 rpm yields best efficiency.

- For 6 knot opposing current it looks like just under 2000 rpm yields best efficiency.

- (it should be noticed that at these high opposing current speeds, even the optimum efficiency stinks)

 

E) At high opposing current speeds and low rpm we see 'negative' nmpg values. This means we are burning fuel but Spray is moving backwards relative to land. Obviously not a good situation.

 

So what conclusions do I draw from this, and should I change how I drive Spray uphill?

 

1) I mentally knew that this analysis would yield the 'optimum' rpms to run at for opposing currents (thinking about the v = -6.5 knot extreme case) but I didn't predict that it would occur only for such large opposing currents, which we rarely encounter. For the 0.5 to 2.0 knot currents we regularly do encounter, the old rule of still slowing rpm for better nmpg still applies.

 

2) What I had been doing was this : when cruising at 1600 rpm and saw that opposing current slowed Spray to below 6 knots, I would bump the throttle up to maybe 1750 knots, adding a few tenths of a knot to our speed. This helps to keep us near schedule for a day's travel but what does it do to nmpg? For a 1 knot opposing current the red curve above yields the following:

2.1) Keeping at 1600 rpm we see nmpg reduced from still water value of 4.3 to about 3.7. A hit but not a huge one.

2.2) Moving down the red curve to 1750 rpm reduces the nmpg value further to about 3.1. We have gained some of the lost speed back but at the cost of a double-whammy to nmpg.

 

Conclusions :

 

I) Avoid extended runs into opposing currents above 2 knots, if at all possible. Better to drop the anchor and wait for the tide to change.

 

II) If time allows, when running into opposing currents of 1-2 knots, just keep the rpm at normal cruising value of 1600. Fuel mileage will drop somewhat but we won't be making it even worse. Besides, what's our hurry?

 

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