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Author Topic:   Fuel Consumption Calculations
jimh posted 08-10-2001 09:48 PM ET (US)   Profile for jimh   Send Email to jimh  
Here is a little metric I picked up recently (from where I cannot remember):

Compute your engine's fuel consumption at wide-open-throttle (WOT) as approximately equal to HORSEPOWER/10 = GallonsPerHour (gph).

Then, approximate the fuel consumption at a particular throttle setting as a linear percentage of the wide-open-throttle consumption.

Let's try this out with my boat:

Engine Rated Power = 70 hp
Est. Fuel Consumption WOT = 7 gph

At WOT the engine is turning about 5500 RPM.
At cruise of 4400 RPM, the fuel consumption should be about:

7 gph * (4400/5500) = 5.6 gph

At 4400 RPM we are doing about 28 MPH and burning about 5.6 * 2 = 11.2 gph, giving us a Mileage of about 2.5 Miles per Gallon (mpg).
(I had to double it because we have twin engines.)

So we are getting 2.5 mpg from our fairly low-powered set up of twin 70 HP engines.

Taking this same approach, I approximate LHG's fuel consumption, running a larger boat with bigger engines. He comes in like this:

200 HP --> 20 gallons per hour at WOT (6000).

Now for him to cruise at 28 MPH he is only running his engines about 2200 rpm, so he is burning about:

20 gph * (2200/6000) = 7.3 gph

Thus his fuel consumption is about 14.6 gph while making 28 mph, for a mileage of about 1.9 miles per gallon.

This was quite surprising to me! I thought I would would be much farther ahead with a smaller boat and smaller engines, but it turns out my fuel economy is only 0.5 mpg better, and that is only an approximation!

After cruising together for a week, it almost seemed like we were using about the same amount of fuel, implying that the fuel mileage was closer than shown above.

I also think that the approximation for fuel consumption versus engine speed is a little off. The fuel consumption is probably not linear with crankshaft speed, and it is likely lower at lower speeds than would be suggested by a linear approximation. This would again work in favor of the boat with larger engines running at lower speeds.

Comments and other observations welcomed,

--jimh

Dick posted 08-10-2001 10:43 PM ET (US)     Profile for Dick  Send Email to Dick     
jimh
Very interesting, I was aware of the HP to consumption rate at WOT but not how to compute it down to a cruise RPM. I haven't run a scientific consumption on my Montauk with a Merc 50 4 stroke but at WOT I am sure I am not burning 5 gph. Is it possible that that these formulas change 2 stroke vs 4 stroke?
Dick posted 08-10-2001 10:55 PM ET (US)     Profile for Dick  Send Email to Dick     
jimh
I just thought through my last post.
It takes X fuel to produce X Hp. Therefore a 350 hp inboard could suck 35 gph a 50 outboard 2 or 4 stroke could suck 5 gph.
I had a brain fade. Common for me at this age.
Dick
Dr T posted 08-11-2001 12:11 AM ET (US)     Profile for Dr T  Send Email to Dr T     
Nice rule of thumb if it works.

Let's try it with mine.

1982 13 ft sport with 1982 35 hp Johnson 2 stroke and 11x9 prop.

Location for calculation: Stagecoach Reservoir near Steamboat Springs, Colorado. Elevation about 7400 ft.

At WOT, the rule of thumb gives me about 3.5 gph or about an hour and 45 minutes for a 6 gallon tank.

Last weekend, I took the boat out and pulled kids around the lake on a tube for about 3 hours total time including pit stops, trips to the picnic area to change out groups of kids, and the down time associated with putting the kids out on the tube. Figure that I spent half the total time in pulling the kids and puttering around. All in all, estimate I went about 20.5 miles (measured) at an average 15 MPH (estimated 1.36 hours) and used about 5 to 5.5 gallons of fuel.

This implies at the altitude of the lake (7400 ft) with sea level jets I would get about 6.28 MPG. At sea level, I used to get about 8 to 9 MPG cruising around (with a 10x13 prop).

Rule of thumb seems to work.

Great find. Thanks a lot.

Terry


johnk posted 08-11-2001 12:27 AM ET (US)     Profile for johnk  Send Email to johnk     
A very simple calculation used for gasoline powered internal combustion engines in aircraft is 5% of rated horsepower equals optimum cruise fuel burn rate per hour.

This formula also works well for marine use, as both aviation/marine applications are constant load, as opposed to vehicular land use which typically is not.

Using this formula:

90 HP motor burns ~ 4.5 gph at optimum (4000) cruise.

225 HP motor burns ~ 11.25 gph at optimum cruise.

Of course, the assumption has to be made that the engine is in proper tune, correct prop, and average load, etc. (both marine and AV). The GPH for dual applications generally is a little lower per ..total.. horsepower due to the additional parasitic loss of 2 drivetrains.

This guideline actually works out virtually exactly to real-world numbers in both my Montauk/90 and my 25'/225.

Hope it helps..

john


bdb posted 08-11-2001 07:21 AM ET (US)     Profile for bdb  Send Email to bdb     
Jim,

Neat formula; thanks!

As I read through it I was amazed at how uncanny it was. My consumption figures have been seat-of-the-pants/gut feel with a dose of simple math. The formula verifies actual so close it's scary!

Please change your profile to "The Amazing Kreskin."

Respectfully,

Harpoon 7gph Harry

Peter posted 08-11-2001 07:29 AM ET (US)     Profile for Peter  Send Email to Peter     
The performance reports that I have seen published by Yamaha suggest that the burn rate relationship for its 2 cycle outboards is not linear. They are more efficient at mid-range rpms than a linear calculation suggests.

There is quite a bit of performance data at www.yamaha-motor.com/01marine/perfbull/bulletins_frame.html

jimh posted 08-11-2001 07:45 AM ET (US)     Profile for jimh  Send Email to jimh     
Peter's link to the Yamaha website is a good one. I came across that site yesterday and last night I was just studying their data for about a dozen applications, trying to fit a formula to what their tables show.

The WOT consumption does seem to be on the order of 10% of horsepower (GPH), but it does not decrease linearly. In many cases the fuel consumption is reduced to half of the WOT rate by just backing off 1000 RPM, so this would be consistent with the rate mentioned by johnk for "optimum cruise" (5% of HP).

The big surprise in all of this to me was how small the difference in fuel consumption there was between a pair of 200 HP engines and a pair of 70 HP engines when pushing their boats along at cruising speeds.

--jimh

Peter posted 08-11-2001 08:47 AM ET (US)     Profile for Peter  Send Email to Peter     
The old rule of thumb I've known for years is that two-thirds to three-quarters of WOT throttle is usually the most efficient operating range. The old rule seems to correspond exactly to the Yamaha data assuming percent of WOT throttle converts directly to percent of WOT RPM.

For my 22 Revenge powered by a 225 Yamaha EFI, RPM at WOT is about 5200-5300, 2/3 to 3/4 throttle yields an RPM range of about 3500 to 4000. Speed at 3500 RPM is approximately 26 MPH and speed at 4000 RPM is about 30-31 MPH. According to Yamaha's burn rate performance data for the 225 Yamaha EFI, it burns about 8 GPH at 3000 and 11 GPH at 4000. So for simplicity sake, assume that it burns about 9.5 GPH at 3500. According to my calculation, My revenge is getting about 2.7 MPG at 3500 and 2.7 MPG at 3900~4000 RPM. Interestingly, this RPM range is exactly where the boat seems to be its ideal element in terms of cruising comfort and where I naturally find my self operating most of the time without thinking, conciously, about fuel economy.

Peter posted 08-11-2001 08:56 AM ET (US)     Profile for Peter  Send Email to Peter     
I should also add that the 225 is turning a 17 inch Yamaha Saltwater Series stainless steel prop.
jimh posted 08-11-2001 09:31 AM ET (US)     Profile for jimh  Send Email to jimh     
I have been drinking some coffee this morning and honing my fuel calculation formula, using a spread sheet for analysis and the Yamaha charts for data. Here is my second iteration on the fuel consumption formula.

For 2-stroke engines, compute WOT fuel consumption:

Fuel (GPH) = Horsepower/9.1

For 4-stroke engines, compute WOT fuel comsumption:

Fuel (GPH) = Horsepower/10.5

To approximate consumption at lower throttle settings, use this formula:

(GPH@WOT) * ( (RPM/WOT)^EXP )

For 2-cycle engine EXP= 1.5
For 4-stroke engine EXP=1.7

Using an exponential factor gives a much better curve fit than using a linear factor.

You can roll this into a simple spreadsheet and have some fun. Generally I was able to get within 5% of the actual numbers shown on the Yamaha charts with the method described above. The simple linear method is accurate to about 10% at the higher speeds, but begins to get way off at lower speeds, sometimes as much as 50% or more.

Dr T posted 08-11-2001 10:09 AM ET (US)     Profile for Dr T  Send Email to Dr T     
Two items:

1. In my earlier calculation, I assumed a WOT speed of 22 MPH at the high altitude. It is probably in the low 30's at sea level.

2. My first reaction of the failure of jimh's curve fit at the lower speeds is that it may be due to hull effects as the boat comes down off of plane. Thoughts?

Peter posted 08-11-2001 11:14 AM ET (US)     Profile for Peter  Send Email to Peter     
Very interesting formula. For those who have a Yamaha EFI V6, the formula probably applies for 2000 RPM and above.

The Yamaha performance reports provide data for both the carburated and EFI versions of its 225. It shows a significant difference between the 225 carb and new EFI models from 2000 RPM and below but not as great a difference above with the difference in favor of the EFI seeming to decline as WOT is approached. The big difference below 2000 RPM is caused by the fuel management program run by the EFI model. Below ~850 RPM, fuel is supplied to only five cylinders and between 850 and ~2000 RPM, only four cylinders are supplied.

I imagine that if you plotted the entire curve for this model, it might be discontinuous at 850 and 2000 RPM due to a change in operating mode.

Bigshot posted 08-13-2001 01:14 PM ET (US)     Profile for Bigshot  Send Email to Bigshot     
Confused now from all the linear vs non stuff. I use the old 6 gal tank trick. Fill it and see how far you go at cruise before she runs out. My 17' Montauk 90hp Yamaha from this burns about 4gph at 36-3700rpm @28-29mph. Interesting thing is the 100hp 4stroke compared to the c90 is usually about 1 gph @ cruise(from the Yamaha site). Therefore it would take about 1000 hours to break even on the price difference, hmmmmm.
Dr T posted 08-13-2001 11:10 PM ET (US)     Profile for Dr T  Send Email to Dr T     
The way it works for me, I fill up the 6 gallon tank and see how many weeks it lasts. Unfortunately, the boat is usually sitting in the garage during this time, so it is hard to compute the milage :-(.

Hank posted 08-13-2001 11:32 PM ET (US)     Profile for Hank  Send Email to Hank     
Beware of DATA. In reviewing some of the data on the Yamaha website, I was struck by the variability of the fuel consumption as a function of RPM in different applications.

Specifically, I looked at the GPH vs. RPM for the c90TLRZ engine on several different boats. There is no way one can draw any precise conclusions about fuel consumption vs RPM for this particular engine from this data. The "non-linearity" of the data for one boat appears less than the variation from boat to boat at first glance. Trying to fit a curve to this data seems like an exercise in futility.

If you believe this data then engine fuel consumption as a function of RPM is partially dependent on the application and is not simply dependent on the engine.

JimH
If you want to do some curve fitting, pick one YAMAHA engine and plot the data for several boats (RPM vs. GPH)on one graph. I'm sure you'll find a broad scatter diagram. Put a best fit straight line through this and that's about the best you'll get for that particular engine.
I looked at three examples of the c90TLRZ and the data is all over the lot.

Bigshot
The six gallon test sounds like a good approach. Your 4 GPH figure sounds a little too good. At 29 MPH you're getting 7.25 MPG. There might be something off in your calculations. None of the 90HP Yams on the website show anywhere near 7.25 MPG. They seem to use only 4.0 GPH at engine speeds under 3000 RPM.

Hank

Bigshot posted 08-14-2001 10:03 AM ET (US)     Profile for Bigshot  Send Email to Bigshot     
Hank I know that is why I said what I do. I ran for a little over 1.5 hours on a 6 gallon at cruise, easy to do in FL. Honestly I think it might burn a bit less. I will do it again this weekend just for S&G.

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