We currently are underway on a 3,650nm non-stop run from St. Helena to Barbados. Prior to this passage, our longest non-stop run without fueling was 3,023nm from Dampier, Australia to Rodrigues, Mauritius. The current 3,650nm passage is at the very limit of Dirona’s range and we are, naturally, monitoring fuel economy closely to ensure we have sufficient fuel to complete the run.

Calculating the fuel economy seems straightforward—you just divide the miles traveled so far by the fuel consumed. The amount of fuel remaining, less reserves, must be sufficient to cover the distance remaining at that particular fuel economy. (We typically use a 300-gallon reserve on longer passages, but currently are using 400 gallons to be more conservative at the start of this passage.) The closer you get to the details of fuel calculations over long distances, however, the more messy fuel calculations become.

It’s complicated to predict the fuel economy of a vessel floating in a moving fluid where the depth of immersion is changing, the fluid movement is changing, and the parts of the vehicle not floating are in a lower density but still very powerful fluid also moving. Further complicating the calculation, fully 15% of the weight of Dirona was in fuel when we left St. Helena. As we proceed and that fuel burns off, economy will improve slightly. Messy.

The difficulty of precisely measuring the amount of fuel on board makes the calculation even more complex. We have three sources of on-board fuel levels: 1) sight sensors, 2) pressure gauges, and 3) ECU fuel burn readings. The sight gauges rely on gravity and, as a consequence, require some skill to read in a moving seaway. Like all gauges, if the sight gauges are not calibrated by filling the tank slowly in small increments and marking off the level, they are not very accurate at all. But with careful calibration they are pretty good.  Our estimate is they are +/- 5%-7% of the fuel load.  The challenge here is that 7% of our maximum fuel load of 2,707 gallons is 189 gallons, which is a very large margin of error. Perhaps with care you could get the error down to 5% but that is still 135 gallons.

Another problem with sight gauges, at least on Dirona, is they don’t read the bottom 50 gallons or the top 185 gallons of each side tank. Since that problem applies to both tanks, the sight gauges don’t read 470 gallons or about 17% of the fuel load.  The sight gauges not reading the top 185 gallons is a real problem when carrying deck fuel. For stability reasons, you don’t want to be operating with low main tanks and deck fuel above. As the below-deck tanks go down sufficiently to accommodate the above-deck fuel, we need to pump the fuel down below. The impact of replenishing the main tanks from the bladders is that the boat will spend roughly two weeks of the current four-week trip in the top area where the sight gauges don’t read. This makes sight gauges a good redundant check that we really like, but they aren’t ideal as a primary source of measurement data in our configuration.

Our second fuel-measuring option is pressure sensors in the bottom of the tank. These are effectively measuring the weight of the fuel above the sensors and, knowing the density of diesel, they produce a surprisingly accurate level measure. We display these readings on our Maretron N2KView display, along with a total fuel level that includes deck fuel. The pressure sensor measurements are our primary source of data, but they still are far from perfect. The sensors are +/-3% accurate over their range (0 to 3 PSI). When we compare the levels measured by the sight gauges and the pressure sensors in flat water, the pressure gauges appear to be delivering results far better than +/-3% but, generally, banking on more is probably a mistake.

Other sources of error on the pressure based sensors are: 1) as the boat heals, the distance between the sensor and the fuel surface changes, and 2) the density of diesel changes with temperature. We limit the impact of heeling partly by averaging over short time periods to find the “central” position. In addition we track boat trim (this central averaged value) and select the tank to pump fuel from to maintain zero heel. The second issue, changes of fuel density due to temperature, could easily be taken into account using fuel temperature level corrections. But the other sources of error appear to dominate, so we don’t bother to do this. The net after all the errors aggregate is the pressure based level sensors are +/- 3%-4% accurate. This is relatively good but, absolutely, still represents 81 to 108 gallons of uncertainty over 2,707 gallons.

The third measure available to us on Dirona is the engine control unit (ECU) estimate. Modern electronically-controlled high-pressure common-rail diesels are incredibly precise and know exactly how many injections events have happened and precisely how much fuel was injected on each event.  Amazing. We have found that at rated RPM, the ECU produces a number you can take to the bank. The ECU-reported fuel consumption just about exactly matches the fuel measured at the pump on a subsequent fill. But there is a problem here as well.

You would think that, with the ECU answer, the problem is solved and we know our exact mileage. Sadly, it’s not that easy. Engine manufacturers measure their engines very precisely at the rated RPM and power output and use these numbers to market the engines. Consequently, the data produced at these power levels is quite precise. In fact, impressively so. At lower power levels, however, the tables used by the ECU to produce estimates are checked much less carefully. (See Fuel Economy and Range for details.) So, on our engines down around 1500 RPM, the ECU estimate is off by 13% to 14% which, on our current fuel load, is 352 gallons to 379 gallons. Fortunately it reads conservatively so you won’t run out, but you also won’t be able to successfully push the limits of crossing distance as we are right now. You need the “missing” 352 gallons.

Where does that leave us?  With experience we learn that the variability of the pressure sensors is roughly evenly distributed. So, over time, this estimate doesn’t accumulate error. It’s always around 3%-4%. The ECU number is very precise at full engine load but not at all precise at the low loads used to go very long distances. But the ECU error is nowhere close to evenly distributed. Most of the error is functionally dependent upon RPM and load and appears to be near linear with RPM. Since we are using a fixed pitch prop, load is functionally dependent upon RPM. By running for multiple days at 1500 RPM, we know the ECU reading at that RPM (and load) is reading just over 13% conservative.  We know that at 2100 RPM it is reading just about precise. And sampling shows us that it’s close to linear in between. We suspect the error continues to increase at lower RPMs but we haven’t investigated down there.

Using the observations on the nature of ECU error being mostly functionally dependent upon RPM, we produce a 4th fuel level measure. We take the ECU based estimate, the current RPM, and the error measurements we have determined above to produce an estimate of fuel burn that is, by far, the most accurate we have. We take ECU fuel burn and RPM and use linear curve fit to produce a corrected number where at 2100 RPM and above there is no correction. At 1500 RPM and below, the correction is a fixed 13%. In between 1500 and 2100 we use a linear model.

This computed fuel economy based upon the ECU number and RPM is remarkably precise and it is the primary data point we use for setting boat speed to get the needed economy. As a backup to verify the accuracy of this number and to detect engine problems that could cause more fuel to be burned, we use the pressure sensors to detect any accumulating computed fuel economy error. And, as a final check, we use the tank sight gauges.

The above approach gives us a fairly accurate measure of real time fuel economy. We use the computed ECU number to set the boat speed to the needed RPM. In fact, we have two lights on the dash that both show green. If conditions change and the economy starts to slip, then a red light will come on saying “slower”.  If currents turn favorable over time or other conditions improve, the other light will come on orange and say “faster”. The lights makes driving the boat easy. We set the reserve fuel we want to complete the trip, the length of the trip, and the system computes needed speed and lets us know when the speed could be changed.

The numbers we show on the web site are based upon the fuel tank levels measured using pressure sensors. These numbers are shown below in tabular form, which we use to monitor fuel economy during the trip. We can generate all the table data automatically, except the trip miles remaining and the ECU-calculated fuel consumption. These we enter manually at irregular intervals during the day and shift changes, which is why the web site fuel burn numbers are displayed on somewhat irregular intervals.

In the table, “tank nm/g” is the current fuel economy estimate based on the distance covered so far divided by the difference between the fuel levels at the start of the trip and the current tank pressure sensor tank level readings. (The fuel level at the start of the trip was 2,691 rather than the full load of 2,707 due to generator consumption after fueling at St. Helena.) The “nm/g needed” is based on the distance and fuel remaining, less reserve. The current fuel economy number is red when it is less than the needed nm/g.

We were always on target to cover trip distance based on the ECU-computed fuel economy described earlier. Over time, the tank numbers converge on that number and help confirm it. But the tank numbers do show more variability and, early on when the amounts of fuel consumed is relatively slight compared to the error of the measurement, there were long periods when the tank levels showed us as not making it.

The pressure sensors have wide enough error bars that they work well over longer distance where the errors average out. But as a real-time measure of fuel economy, the variability makes them much less useful. To give more real-time insight into the current fuel economy, the table also shows the ECU-computed fuel economy for each leg (table row) and how the overall ECU-computed fuel economy compares to tank level deltas.

When working on a passage that pushes out towards the limits of the boat’s range, you would think the primary focus would be on fuel economy. But having crossed the equator once without air conditioning, we’ve decided we’ll not do that again. We now run the master stateroom and pilot house air conditioning 24×7 on these longer runs. By the time the run is completed, the power consumed to run the A/C will represent a material portion of our overall fuel burn. But we don’t regret it. The two things we avoid are 1) when spending weeks at sea with the doors all open the entire boat gets a thin surface of salt on all windows and walls and 2) since the master stateroom portals have to be closed at sea, it can get really hot down there right beside the engine room. We don’t like running the generator 24×7 on low load, so the main engine on Dirona has 9kw of alternator on it and a 240v inverter that happily runs all the A/C units. (See A More Flexible Power System for Dirona for details.) In fact, that inverter is a beast. It’s capable of running any of the appliances on the boat including the oven, dryer and scuba compressor. With this system, we use the main engine to produce power underway. And when plugged into shore power, even as small as 15 amps or 50 cycle, we use shore power to run everything on the boat. Consequently, we only need to run the generator when not plugged into shore power or underway. 24×7 A/C for a month represents a substantial diesel burn, but we would rather arrive a day later, smiling and well-slept, than dripping in sweat in a dirty boat.

We’re generally happy with our current fuel tank measures, but continue to think that more precision should be possible and we will investigate fuel flow sensors in the future. Better data means less worry so we are always looking for more precision.