## Average Fuel Mileage: Proper Weighting Factors

### by James W. Hebert

The fuel economy of boats varies greatly with boat speed, and the ratio between fuel economy numbers at various boat speeds can be 4:1 or higher. Because boats tend to be operated over a wide range of speeds, their overall or average fuel economy will be a blend of many different rates of fuel consumption at different speeds. What weight should be given to each different rate of fuel consumption? This article answers that question.

### Weighting Factors: Time or Distance?

The two most obvious factors which could be considered as variables for the weighing of fuel consumption rates are time and distance. Let us explore how these influence the aggregate fuel economy of a boat. To illustrate the problem we consider a hypothetical boat which gets the following fuel economy at two different speeds:

```Hypothetical motor and its fuel economy:

5-MPH  = 1.0-MPG
25-MPH = 2.0-MPG```

To test the influence of distance, we go a fixed distance (25 miles) at the two different speeds:

```At 5-MPH
25-miles/5-MPH   = 5-hours
25-miles/1.0-MPG = 25-gallons

At 25-MPH
25-miles/25-MPH = 1-hour
25-miles/2-MPG  = 12.5-gallons

Combined fuel economy
25 + 12.5   = 37.5-gallons
25 + 25     = 50-miles
Average MPG = 1.33```

If distance were the proper weighting factor, we would expect that the average fuel economy would be the average of the two factors, that is (1+2)/2 = 1.5-MPG. However, we see that this is not the result. The average is weighted toward the 5-MPH fuel economy. Distance is clearly not the proper weighting factor. However, if you will notice, we spent much more time at the 5-MPH rate of consumption, and the average is weighted that way, so perhaps time is a factor.

Next we explore the influence of time on the aggregate fuel economy. We go a fixed time (five hours) at the different speeds:

```At 5-MPH
5-hours X 5-MPH  = 25-miles
25-miles/1.0-MPG = 25-gallons

At 25-MPH
5-hours X 25-MPH = 125-miles
125-miles/2-MPG  = 62.5-gallons

Combined fuel economy
25 + 62.5   = 87.5-gallons
25 + 125    = 150-miles
Average MPG = 1.7-MPG```

Now the average fuel economy is weighted toward the 25-MPH rate. Clearly time cannot be the proper weighting factor, either.

### Proper Weighting Factor

If neither time or distance is the proper factor for determining how to weight the influence of different rates of fuel consumption, what other factor is there? The answer: the amount of fuel burned at the various rates. Again, we use our hypothetical boat to test the theory. We burn the same amount of fuel at two different speeds:

```At 5-MPH
10-gallons X 1-MPG = 10 miles

At 25-MPH
10-gallons X 2-MPG = 20 miles

Combined fuel economy
10 + 20 = 30 miles
10 + 10 = 20 gallons
Average MPG = 1.5-MPG```

Finally, we have discovered the correct weighting factor. It is neither the time or distance at which we operate at a particular rate of fuel consumption, but the amount of fuel burned at that rate. This leads to some interesting observations.

### Real Boats

For real boat data we turn to our favorite boat, the Boston Whaler, and from their many published fuel consumption rates we pick those for the 200 DAUNTLESS with a 175-HP Verado motor as a random choice. Here is the data collected by the careful test drivers in Edgewater, which I think all will accept as being accurate and reliable:

```SPEED       MPG   GPH
4.4        8.8   0.5   "no wake" speed
24.2        4.9   4.9   "cruise" speed
```

To keep the analysis simple, we will use just these two speed. Now we arbitrarily say that we use the boat in such a way that 40% of the time we are at "no wake" speed and the rest of the time, 60%, we are at "cruise" speed. I think this is a reasonable use pattern for many boaters, at least for boaters like me who are not avid fisherman and who do not troll for long periods with their main motor. With this use pattern we can calculate the aggregate fuel economy as follows:

Assume we go four hours at "no wake" and six hours at "cruise". Our fuel consumption will be:

```4 hours X 0.5 GPH = 2.0 gallons
4 hours X 4.4 MPH = 17.6 miles

6 hours X 4.9 GPH  =  29.4 gallons
6 hours X 24.2 MPH = 145.2 miles

TOTAL GALLONS =  31.4
TOTAL MILES   = 162.8
AVERAGE MPG   =   5.2
```

The results are somewhat surprising for most people. Even though the fuel economy at "no wake" speed is quite good and almost double the other rate, the average fuel economy is much closer to the "cruise" speed mileage because so much more fuel was burned at that rate. We burned about 15-times more fuel at the "cruise" rate than we did at the "no-wake" rate, and thus this weighs much more heavily on the average fuel economy.

An even more accurate estimate of the average fuel economy could be found if more speeds were used and the amount of time at each speed was alloted according to the ICOMIA Duty Cycle. We leave this as an exercise for the reader or for a future installment.

### Conclusion

The surprising outcome that the weighting of different fuel consumption rates is by the amount of fuel consumed at that rate, not the time or distance at that rate, also has an interesting effect. For boats and motors which show extremely good fuel economy at low speeds, in some cases as much as five times greater than at higher speeds, the fact that so little fuel is burned at these rates causes their influence on the aggregate or average fuel economy to be reduced. Going back to a hypothetical boat for a moment, let's say we have a boat and motor that perform like this:

```SPEED       MPG   GPH
5.0        10.0   0.5   "no wake" speed
25.0         3.0   8.3   "cruise" speed
```

There may be a temptation to judge the average fuel economy as being somewhere around (10+3)/2= 6.5 MPG. However if we apply the same 40/60 time split as above we find the actual average will be much different:

```4 hours X 0.5 GPH = 2.0 gallons
4 hours X 5 MPH   = 20 miles

6 hours X 8.3 GPH = 49.8 gallons
6 hours X 25 MPH  = 150 miles

TOTAL GALLONS = 51.8
TOTAL MILES   = 170
AVERAGE MPG   = 3.3
```

This results shows that even though the engine has very impressive fuel economy at low speeds, the fact that so little fuel was consumed at that speed makes its overall influence on the average fuel economy have much less weight. In the use pattern of 40/60, we see that the average fuel economy is overwhelmingly determined by the "cruise" rate because so much more fuel (25-times more) was burned at that rate. The actual average fuel economy, 3.3-MPG, turns out to quite a bit less than what might have been assumed, 6.5-MPG, if the two factors were given equal weight.

When estimating average fuel economy for a boat used at several different speeds and rates of fuel consumption, the proper weighting factor for the different rates is the amount of fuel consumed at that rate. Computation using this method will yield accurate and surprising estimates of aggregate fuel economy.

### A Crazy Example

To further demonstrate how the weighting can vary, consider this strange hypothetical motor, one that gets 100-MPG at trolling speeds:

```SPEED    MPG   GPH
5.0      100   0.05
25.0       3   8.3
```

Let's assume this motor is used by a guy who trolls a lot, and 80% of the time he is at the low speed, and only 20% of the time at cruise. This ought to really help with the fuel economy. But here is his average fuel economy:

```8 hours X 0.05 GPH = 0.4 gallons
8 hours X 5 MPH    = 40 miles

2 hours X 8.3 GPH = 16.6 gallons
2 hours X 25 MPH  = 50 miles

TOTAL GALLONS = 17
TOTAL MILES   = 90
AVERAGE MPG   = 5.3
```

So even though the motor gets fantastic fuel mileage at trolling speed, and we spend almost all of our time trolling, the average fuel economy is 5.3 MPG, and much more influenced by the rate at cruise than the rate at trolling speed.

### Further Discussion

Questions and comments on this article can be posted to a discussion reserved for that purpose.

DISCLAIMER: This information is believed to be accurate but there is no guarantee. We do our best!

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Copyright © 2007 by James W. Hebert. Unauthorized reproduction prohibited!

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Author: James W. Hebert
This article first appeared September 7, 2007.