Average Fuel Mileage: Proper Weighting Factors

[jimh]

Please use this discussion for follow-up questions or comments about my article which appears in the REFERENCE section at

Average Fuel Mileage: Proper Weighting Factors
http://continuouswave.com/whaler/refere ... geMPG.html

The articles demonstrates the proper method for estimating the average fuel economy of a boat which is operated at various speeds with different rates of fuel consumption.

Note: there was a prior discussion in the OLD FORUM about the article, but I am creating this new thread to renew the discussion in an active forum.

[jimh]

As mentioned in the REFERENCE article, the proper weighting of data about fuel economy to develop an average fuel economy figure is not by time or by distance, but by the the amount of fuel burned at each data point.

I will use some real-world data from my own boat to illustrate how proper weighting works.

In recent testing (see http://continuouswave.com/forum/viewtopic.php?f=7&t=4698) I obtained this data:

SOG   RPM  MPG
24.5  3536 2.76  
2.9   503  10.2

Let's assume a 60-40 division of running the boat at these two speed, favoring the low speed. We run for six hours at 2.9-MPH and four hours at 24.5-MPG. What is the average fuel economy?

6-hours × 2.9-MPH = 17.4-miles
17.4-miles ÷ 10.2-MPG = 1.7-gallons

4-hours × 24.5-MPH = 98-miles
98-miles ÷ 2.76-MPG = 35.5-gallons

Total gallons = 1.7 + 35.5 = 37.2-gallons
Total miles = 17.4 + 98 = 115.4-miles
AVERAGE FUEL ECONOMY = 115.4/37.2 = 3.1-MPG

We see that even though most of the time the boat was underway was at a slow speed that gave 10.2-MPG, the average fuel economy is only 3.1-MPG, much closer to the MPG at the faster speed.

To see this outcome derived in another way, we weight the MPG factors at the two speeds by the percent of fuel consumed at those speeds. The total fuel consumed was 37.2-gallons, so the percentages are

For high speed: 35.5/37.2 or 0.9543 weight
For low speed: 1.7/37.2 or 0.0457 weight

Now we apply those factors as weighting to the MPG at each speed:

For high speed 2.76-MPG × 0.9543 = 2.634-MPG
For low speed 10.2-MPG × 0.0457 = 0.466=MPG
AVERAGE = 2.634-MPG + 0.466-MPG = 3.10-MPG

This example again shows how great fuel economy at idle or low speed generally tends to have only a minor influence on the overall fuel economy of the boat, even when the majority of the time the boat is being run at the slower speeds. The proper weighting factor when averaging fuel economy data in MPG at various speeds is not the time or distance run at those speeds, but weighted by the percentage of the total fuel burned that was consumed at those speeds.

I mention this because I do not think most boaters are aware of the proper influence of fuel economy at low speed on overall boat fuel economy. Now, if you are a boater who operates their boat 100-percent of the time at low speeds, then the low-speed fuel economy figures are going to be very important. But if you are a more typical boater and operate the boat on plane for a significant amount of the time underway, the amount of fuel burned at the higher boat speed is going to be more influential on overall fuel economy than you probably thought.