mph vs range(duration)?

[bwilson4web]

Hi,

I picked up the EPA roll-down coefficients and plotted the hp, range, and duration as a function of speed:

• Used "Test Car Database" from EPA.gov for roll-down coefficients
• 18.7 kWhr - traction battery usable capacity, 85% of 22 kWhr
• 746 W - estimated vehicle electronic overhead
• 34 hp - clamped the range extender engine output

This gives a set of curves that suggest:

• 30 mph -> 150 miles (5 hrs)
• 50 mph -> 105 miles (2 hrs)
• 60 mph -> 85 miles (1.5 hr)
• 65 mph -> 75 miles (1.2 hrs)
• 70 mph -> 70 miles (1 hr)
• 75 mph -> 62 miles (0.8 hrs) above 75 mph the range extender runs out of power and draws from traction battery

Now this is just a math model and I had to make some educated guesses. For example, the usable traction battery energy comes from the BMW technical specs and the vehicle electrical overhead from typical Prius values. But any math model needs validation from benchmarks.

Has anyone run any constant speed, range (duration) tests with the i3-Rex? I would use those data points to adjust the math model until we have something useful for trip planning.

Thanks,
Bob Wilson

 

[alohart]

Tony Williams of Quick Charge Power has measured the ranges of several EV's at a constant 100 kph (62 mph) on a level highway loop in southern California. I can't find a link to his results, but I know that he measured the 62 mph range of an i3 BEV at 88-89 miles. The REx is a bit heavier (shouldn't affect constant-speed range significantly) and has a slightly worse drag coefficient, so its 62 mph range should be a bit less than that of the BEV. So your theoretical i3 REx range at 62 mph is pretty close to what was measured.

 

[bwilson4web]

Thanks!

I sent him the chart and a pair of Prius charts, one SAE and the other standard units.

Bob Wilson

 

[justanotherdrunk]

Has anyone run any constant speed, range (duration) tests with the i3-Rex? I would use those data points to adjust the math model until we have something useful for trip planning.

Thanks,
Bob Wilson

What exactly are you asking for?

I have unused lease mileage and time to play ...

:lol:

 

[bwilson4web]

Has anyone run any constant speed, range (duration) tests with the i3-Rex? I would use those data points to adjust the math model until we have something useful for trip planning.

Thanks,
Bob Wilson

What exactly are you asking for?

I have unused lease mileage and time to play ...

:lol:

What I'm looking for is some measurement of how much energy is consumed per mile at a constant speed. I've put in an offer for a BMW i3-Rex but have not picked it up, yet. But getting credible numbers takes time:

• constant speed - use cruise control to hold velocity
• flat, 10 mile route, two runs opposite directions or a 10 mile loop - this removes altitude and wind effects
• measure start energy level and ending level - this gets tricky because we need either range extender ON the whole time or OFF the whole time. Then accurately record the starting and ending values. Please excuse my ignorance but I suspect "miles remaining" may be the best metric for range extender OFF. But then we run into a rounding problem. If the miles remaining are not to the 1/10th, the actual miles remaining could be 9.5-10.4 over a 10 mile segment. But there may be a better, more accurate metric, perhaps % SOC? It is even more difficult with the range extender since we need an accurate measurement of how much fuel was burned.

This is the type of anal-engineering problem that I'm curious about. Now it happens I have a plan on how to gather more accurate data using an OBD based, recorder, or adding my own instrumentation, a recording clamp-on amp sensor. For example, recording MAF flow lets me get the range extender fuel consumption. The clamp-on amp sensor can measure electrical load on the battery.

The used i3-Rex I've put out an offer is about 800 miles away from Huntsville AL along the Gulf Coast. Noting the winds, I'll be able to adjust the metrics over segments of the return trip and get a crude estimate. Better than nothing, it will give a first set of data about the car performance.

I use these metrics to adjust the math model so I will have a more accurate chart to plan my trips. Occasionally I have to drive to Nashville, TN, ~120 miles away. But I also plan to use this car for more intercity, day trips. We are keeping our 2010 Prius for longer trips but there is an overlap between the i3-Rex and Prius and knowing the capabilities of each, we can choose the vehicle that best meets our trip requirement.

Any private or commercial pilot understands what I'm after.

Bob Wilson

 

[alohart]

measure start energy level and ending level - this gets tricky because we need either range extender ON the whole time or OFF the whole time. Then accurately record the starting and ending values. Please excuse my ignorance but I suspect "miles remaining" may be the best metric for range extender OFF.

The i3 will report its average energy consumption/distance from starting and ending points of your choice. This would almost certainly be more accurate than trying to calculate the amount of energy used as you have described. And this is independent of whether the REx engine is running, so you wouldn't have to worry about how much energy the REx generator is providing.

You could also measure the fuel consumption rate of the REx engine, but it runs at several different speeds and thus at several different fuel consumption rates depending on various things like the remaining battery charge, the rate of energy consumption while driving, whether the REx engine is fully warmed up, etc. So generalizing on a gasoline consumption rate might be challenging.

 

[i3Alan]

[*]flat, 10 mile route, two runs opposite directions or a 10 mile loop - this removes altitude and wind effects

No, it does not remove wind effects. Wind effects are non-linear. A 5 MPH headwind will cost more energy than a 5 MPH tailwind will save. Even a side wind causes some energy loss (in both directions!).

This test would need to be done in near zero wind to be reasonably accurate.

 

[bwilson4web]

. . .
The i3 will report its average energy consumption/distance from starting and ending points of your choice. This would almost certainly be more accurate than trying to calculate the amount of energy used as you have described. And this is independent of whether the REx engine is running, so you wouldn't have to worry about how much energy the REx generator is providing.

Thanks! I am working on getting the Owner's Manual and discovering it appears to be App based. Old school, I like paper but haven't found a PDF version, yet. Still, this sounds like what I'm after. Once I understand the units, I can convert the spreadsheet to use the same and validation should be fairly straight forward.

You could also measure the fuel consumption rate of the REx engine, but it runs at several different speeds and thus at several different fuel consumption rates depending on various things like the remaining battery charge, the rate of energy consumption while driving, whether the REx engine is fully warmed up, etc. So generalizing on a gasoline consumption rate might be challenging.

Thanks, I plan to take a close look at the engine-generator operation. In particular, I hope to plot the generator-engine specific fuel consumption, the kW / fuel-flow.

[*]flat, 10 mile route, two runs opposite directions or a 10 mile loop - this removes altitude and wind effects

No, it does not remove wind effects. Wind effects are non-linear. A 5 MPH headwind will cost more energy than a 5 MPH tailwind will save. Even a side wind causes some energy loss (in both directions!).

This test would need to be done in near zero wind to be reasonably accurate.

About the wind effects, not only does the drag increase by the square, a cross-wind has a vector that is additive on each run. So I typically run my high-speed benchmarks between midnight and the crack of dawn when surface winds and traffic are at a minimum. For ordinary, 1st order metrics, bi-directional runs at and under 45 mph and given the accuracy of car-based instruments, these are usually close enough. Just doing a single direction run induces worse errors. Some examples might help:

• 60 mph + 10 mph head wind ~= (60+10)**2 = 4900
• 60 mph - 10 mph tail wind ~= (60-10)**2 = 2500
• average of above = 3700
• 60 mph ~= (60)**2 = 3600
• error (3700-3600) / 3600 = 2.8% error

A gentle reminder, there are three drag coefficients and aerodynamic is just one along with vehicle overhead, rolling, and stirring drag. These tend to dilute but not eliminate the aerodynamic drag effects.

Personally, every car manual should include a graph of fuel (energy) consumption as a function of speed. I'm typically looking for a 'knee in the curve' (not expected in the i3-Rex). However, the generator output as a function for fuel consumption may have some non-linear effects.

With rare exception, Otto engines do not behave well at partial throttle so I'm interested in the output generator power as a function of fuel consumption. Knowing the energy needed at different speeds, we can then identify optimum, cross-country speeds to maximize fuel-to-electrical operation.

Bob Wilson

 

[I33t]

Knowing the energy needed at different speeds, we can then identify optimum, cross-country speeds to maximize fuel-to-electrical operation.

Sounds simple, but it is far more complex than that. You would need the gradient profile of the cross country trip you are going on, as well as your driving style, selected mode, (Comfort, Eco-Pro, Eco-Pro+), traffic, speed limits, wind speed and direction, temperature, traction, passenger and luggage load, Cabin temperature setting, use of lighting, etc, etc.

A far easier method would be to just measure your energy use on actual trips in an actual i3. Recording trips over time would give you a more accurate personal profile of energy use which would include all of the above.

 

[websterize]

… I am working on getting the Owner's Manual and discovering it appears to be App based. Old school, I like paper but haven't found a PDF version, yet.

Bob, PDFs of manuals are at http://www.bmwusa.com/Standard/Content/Owner/dgh.aspx

Click the 2015 tab for the i3s'.

 

[bwilson4web]

Ok,

Now that I've had time to do a first pass through the owner's manual, hopefully this will be more useful. FYI, updated to reflect more recent data:

• mi/kWhr - changed the energy consumption to match readouts from the i3-REx
• range - assumes an 18.7 kWh pack, 100% charged. Aged or partial charged packs will have shorter range.

For now, disregard range as this is a function of the battery pack health and status. The energy consumption, mi/kWhr, as a function of cruise-control set speed is the most interesting. Now the Prius (2001-2015) has a lower limit of 23 mph and if the car dips under, it cancels cruise control. Is there a lower limit for the i3-REx that I missed in the manual?

Understand these charts are for a 'standard' day model, the best case. The goal is to manage user expectations and give some rules of thumb, insights, to how adjusting one's speed can change distance and duration. Everyone is aware of the EPA range number, 72 miles, but we don't have the speed since it is derived from a set of standard, variable speed, tests.

When we pick up our used, i3-REx, we'll have between Houston TX and Huntsville AL to do some benchmarks. Once home, I'll have the time and tools to continue my studies. But in the meanwhile, these charts are good enough to plan optimum routes and measure critical data points.

Now if you have the time (and music to listen,) there are some interesting data points:

• 20 mph - close to the maximum mi/kWhr, easily accomplished doing loops around a large shopping center parking lot. Also insights to the vehicle overhead.
• 30 mph - another excellent point part of the slope
• 40-55 mph - second point on the slope, helps with the roll-down coefficients
• 75-95 mph - gives insights for high-speed falloff

Bob Wilson

 

[jadnashuanh]

The minimum set speed on the cruise control of the i3 is 20mph/30kmph per the user's manual.

 

[I33t]

Still can't see the point of this Bob.

How many people drive an i3 at constant speed? The i3 is a city car, that puts it into traffic and intersections requiring plenty of stop and go.

The EPA range system is a lot more realistic than driving at a constant speed in daylight, ignoring acceleration and traffic.

 

[bwilson4web]

The minimum set speed on the cruise control of the i3 is 20mph/30kmph per the user's manual.

Perfect! One of the harder Prius benchmarks are those under 24 mph.

Still can't see the point of this Bob.

How many people drive an i3 at constant speed? The i3 is a city car, that puts it into traffic and intersections requiring plenty of stop and go.

The EPA range system is a lot more realistic than driving at a constant speed in daylight, ignoring acceleration and traffic.

It has to do with my primary requirement to be able to drive 120 miles between Huntsville AL and Nashville TN without having to take a charging break. We have a physician in Nashville and it is important to make our appointment. But there are two cities, in the 120 mile range that are important:

• Birmingham AL - nearest airport served by SouthWest Airlines
• Nashville TN - next nearest airport served by SouthWest Airlines and cross-country carriers

The 150 mile range, somewhat lower in freezing weather, is why I looked but was not tempted by any earlier EVs. Heck, I'd even considered a Leaf with a home-grown, mod to carry a pack-bus booster on a rear, modified bike carrier. But it kept looking too kudgy even for this 'red-neck' engineer.

Bob Wilson

 

[jadnashuanh]

A major factor in your situation would be temperature and your willingness to rely only on the seat heaters verses the cabin heater when cold. The BEV uses a heat pump, the REx always uses resistance heating while the BEV might end up using it if it is really cold. That can suck up lots of battery charge, then, the battery capacity does decrease fairly significantly when really cold out there. If you can precondition the batteries prior to leaving, it can help minimize some of that cold temp battery degradation, but not if it sits part way through the trip and can cool off enough to be an issue. You could make that trip using the REx, especially with the 2017 model, you might make it most of the way without running the REx at all, and if you did need it, could stop and refuel, then keep going. While some people use the i3 as a long distance car, especially in the USA where the CCS network is so small and spotty in coverage, you're at a big risk, or it will require lots of planning. One charging station out of service could ruin your day, or someone or more than one person waiting in line ahead of you to use it.

You can gain about 10% of nominal range with each step in the ECO modes verses comfort, but if you drive very conservatively, that number will be smaller since you're doing much of what the computer would be doing in those modes.

 

[justanotherdrunk]

Datapoint: don't know if this helps

I wanted to know the maximum electric only range on the freeway

fully charged overnight
76F
60 mph cruise control
eco pro+ mode
no accessories other than radio
flat no wind

93.8 miles until rex started at 6.5% soc

 

[bwilson4web]

Excellent!

Datapoint: don't know if this helps

I wanted to know the maximum electric only range on the freeway

fully charged overnight
76F
60 mph cruise control
eco pro+ mode
no accessories other than radio
flat no wind

93.8 miles until rex started at 6.5% soc

• 4.2 mi/kWh @60 mph - from my model
• 93.8 mi / 4.2 mi/kWh = 22.2 kWh
• 100%-6.5% = 93.5%
• 22.3 kWh / 93.5% = 0.238 kWh/%
• 100% * 0.238 kWh/% = 23.8 kWh

What this suggests is the 18.8 kWh capacity listed by BMW may be 'sandbagged.' Understand we have to be very careful about making such claims BUT it is always nicer to find more than expected. Just remember VW TDI drivers used to claim 'better than EPA' because of the cheat-software.

Bob Wilson

 

[i3an]

In my BEV I have gone 93 miles (with 1 mile left on the GOM) at 5.0 m/kWh out-and-back from San Francisco on Bay Area highways, so some loss for head and side winds during our "summer". 2 people, preconditioned, EcoPro+, a/c off, set at 56 mph (90 kph) on assisted cruise control (aka 54 mph real-world): 18.8 kWh x 5.0 m/kWh => 94.0 miles, it figures. I could go slower and further, I am guessing getting 5.1 at 50 mph => 96 miles or even 5.2 at 45 mph => 98 miles, but those speeds would be a wee bit risky on some freeways. I have never dared run it flat, so I don't know how honest the lower end range-to-empty is since the software update.

 

[bwilson4web]

I've had a chance to run a series of charge sustaining, REx benchmarks:

32 MPG @75 mph, loses 20% SOC
40 MPG @65 mph
44 MPG @55 mph
. . .
45 MPG @35 mph

During the 35 mph test, I had a ScanGauge II connected:

• HPR - horse power
• GPH - gallons per hour
• fWT - water coolant temperature
• RPM - revolutions per minute

The Scangauge II does not record the data but one observation was the engine ran all the time at ~2,400 rpm when at 35 mph. The HPR and GPH varied proportional to the grade of the loop. Descending it would drop to 9.3 HPR and 0.57 GPH. But on upward grades, I saw up to 15-20 HPR and up to 1 GPH. I may be able to get a time-lapse recording setup on my iPhone 5s.

During the test if the car stops at a light, the REx turns off. But once the car is above 20-25 mph, the engine never shut down. A Prius on the same loop at the same speed will frequently shut the engine off. The Prius engine rpm varies to keep it in the peak BSFC and minimum power when running is ~10 kW. Any excess energy is banked in the traction battery and used when the engine is off. In contrast to the Prius, the BMW REx does not appear to have significant banking of energy in the traction battery so the REx runs at fuel wasting idle.

This particular benchmark route has relatively shallow grades. There is another benchmark route with an 8% grade, 525 ft (160 m) hill. I need to replicate this test with this hill to determine if the engine continues to run descending this hill when in charge sustaining mode. I will also look at hill climb on REx metrics to determine how fast the car can ascend an 8% grade in charge sustaining mode.

This is not criticism of the BMW i3-REx as just trying to understand the vehicle operational parameters ... things not found from the usual suspects. I will also review the Argonne data to see if it provides more insights about REx transient operations.

Bob Wilson

 

[gt1]

The REX will shutdown at 6MPH/10KPH. It shouldn't replenish the battery, but would be interesting to see if extending driving at 15-20MPH will cause the REX to stop.