Determining glide eMPG

Apologies for the length of this post!

In the myth of pulse and glide thread, many have objected to the inclusion of an mpg figure for the glide phase of P&G (for hybrid cars) since the Prius and Ford Fusion Hybrid get "infinite" mpg when gliding. However, due to battery losses during the glide (due to A/C, electric motor current draw, and other factors) the glide uses battery charge which must be recharged later by the engine. To account for this we can assign an "equivalent MPG" (eMPG) amount to the glide. This is the amount of MPG used by the internal combustion engine (ICE) to recharge the battery due to the battery discharge during the glide.

The question becomes, what is the actual glide equivalent MPG for a hybrid? I've worked out an experimental protocol for determining the glide eMPG.

We need to establish values for all variables except glide eMPG. Then we can calculate glide eMPG from the other variables. The variables that we need measured values for are:

• Ratio of Glide distance to Pulse distance (eg 4 to 1)
• Total Distance
• Pulse MPG
• Total MPG

Once we have measured those values experimentally we can determine the glide eMPG for the experiment as:

Pulse Distance = Total Distance/(Ratio + 1)
Glide Distance = Total Distance - Pulse Distance
Pulse Gal = Pulse Distance/Pulse MPG
Glide Gal = Total Distance/Total MPG - Pulse Gal
Glide eMPG = Glide Distance/Glide Gal
​

So, how do we determine these values experimentally? I propose setting up an experiment on a long stretch of level roadway (as long as 5 miles if possible).

Phase 1: Establish baseline Glide to Pulse Ratio
Initially we run a pulse and glide test with a target range of, say, 30 - 45 MPH. The battery should have a high initial state of charge (SOC) so that the ICE does not need to run to recharge the battery. All electrical equipment should be off (A/C, lights, etc) so as not to drain the battery and force the ICE on. Its important to do a true glide, not a glide assisted by EV mode or reduced by regen, so we put the car in neutral during the glide. We measure the average length of the pulse and glide phases. We may determine that the pulse lasts 20 seconds and the glide lasts 80 seconds (4 to 1 ratio of glide to pulse).

Phase 2: P&G test with low battery SOC and electric equipment on
Next, we run the experiment. The battery SOC should be low, very near the point where the engine will turn on to recharge it. The reason is, we want the engine to turn on during the experiment to recharge the battery as necessary. If we started with a full battery, the test would not determine the glide eMPG because we would be running the battery down for a portion of the test.

Turn on any electrical equipment such as lights and A/C used in normal driving. These will be a primary cause of lower pulse eMPG, as will electrical draw from the drivetrain.

We start the experiment by accelerating to 30 MPH, then resetting the trip distance and trip MPG computers. Then we start the pulse and glide routine:

1. Pulse at 20 MPG to 45 MPH for however long it takes
2. Glide down to 30 MPH in neutral for however long it takes
3. If the engine stays on or turns on during the glide, ignore it. Keep the car in the glide until it gets to 30 MPH.
4. Repeat for the length of the course until the last glide is complete, then note Total MPG and Total Distance

Phase 3: Calculate glide eMPG
Once the experiment has been run, we can calculate the glide eMPG. We know Total MPG and Total Distance from the car's computer. We know the Pulse MPG because we will held that steady at 20 MPG during the experiment. We know the Ratio from the initial test. We can plug these values into the formula above and calculate glide eMPG.

Here's a sample calculation:

Total Distance = 10 miles
Total MPG = 50 MPG
Ratio = 4 to 1
Pulse Distance = 10 / (4 + 1) = 2 miles
Glide Distance = 10 - 2 = 8 miles
Pulse MPG = 20 mpg
Pulse Gal = 2 miles / 20 mpg = 0.1 gal
Glide Gal = 10 miles / 50 mpg - 0.1 gal = 0.1 gal
Glide eMPG = 8 miles / 0.1 gal = 80 mpg
​

Phase 4: Use pulse eMPG to predict Total MPG in other situations
Armed with glide eMPG for the given experimental conditions (eg A/C on or off, lights on or off, etc) we can predict Total MPG for varying pulse MPGs and glide to pulse ratios as follows:

Glide Gal = Ratio/Glide eMPG
Pulse Gal = 1/Pulse MPG
Total MPG = (Ratio + 1)/(Glide Gal + Pulse Gal)
​

For example, if your pulse MPG is 25 and glide to pulse ratio is 5:

Glide Gal = 5/80 (80 is eMPG from above example)
Pulse Gal = 1/25
Total MPG = (5 + 1)/(5/80 + 1/25) = 58.5 MPG
​

Be gentle! These are initial thoughts.

 

Hi donee, eMPG is a pretty well-established concept, see [ame="http://en.wikipedia.org/wiki/Miles_per_gallon_gasoline_equivalent"]Wikipedia entry[/ame]. For instance, the electric [ame="http://en.wikipedia.org/wiki/Tesla_Roadster"]Tesla roadster[/ame] is said to get 120 eMPG.

If you're open to a new way of looking at things, putting a new tool into your arsenal, take a look at the other paragraphs!

 

Yes, this would measure the advantage of P&G over cruise control, which is not in question and its not the subject of my post. :focus:

 

Hi Ken, can you explain how you got pulse ratio? It doesn't look correct to me. Ratio should be the length of glide divided by the length of pulse under high SOC conditions.

 

You seem to be trying to show that glide eMPG is infinite using some existing data with my formula - but your ratio is not calculated according to the experimental protocol. You can't calculate ratio as proportion of MPG contributed by the engine as you did here:

Your approach will always show infinite glide mpg because it has no way to differentiate what proportion of the pulse fuel usage is due to recharging the battery and what proportion is due to getting to the P&G top speed.

Ratio should be experimentally determined as follows:

 

Knowing eMPG gives us a predictive tool for determining Total MPG:

 

No argument from me but the predictive modeling is fun too.

 

For the experiment, which must only be run once to determine eMPG for given battery use conditions (eg lights on/off, AC on/off, etc), you need an open road.