Pulse and Glide Fuel Economy Calculator 4 valve / Cylinder
 

Attached is my updated fuel economy calculator for generic 4 valve EFI engines. I've tidied it up a bit, and automated it so that most people here should be able to figure out how it works - I've really dumbed it down this time, no looking up BSFC values, you don't even have to google an air density chart, all you need is temperature and altitude. I assume dry air, but I did the calculations to adjust density for humidity and decided not to bother. Even at 30 deg C, and 100 degrees C, the difference is only 1.6% in air density. At 25 degrees, it's only 1.1%.

Note that it is available either as an ODS file in a nod to open formats, or in reverse engineered xls (MS Excel format). Either should work. Created in Ubuntu using Openoffice. Note that EVERYONE can use this spreadsheet for free, whether they have Windows, Mac or Linux. I suggest trying either gnumeric or openoffice.

Figures you will need to know:
Average speed during pulse and glide (assumes constant acceleration)
Total drop in speed until the next pulse starts
rpm@100kph
Max Power of your car (just google it)
Drag Coefficient (google it, or do a coast down test)
Frontal Area
Coefficient of Rolling Resistance (use 0.06 for heavily pumped tyres)
Total Mass of Car (include driver etc)
Temperature
Altitude above sea level
Displacement of engine (or the idle fuel burn rate)

Note that you can unhide the rows to see my workings out and verify my equations, which I'd strongly encourage. Read my provisos as well.

No comments yet? Let me know if anyone desires a two valve per cylinder version. It's a bit of a pain because the BSFC is not linear along a line of best fit over the best BSFC/rpm curve. The 4 valve per cylinder model was a gift.

I just got a chance to play with it, very cool! Seems like gearing makes a large difference in my case (as I would expect).

Think about making a web version?

Are you sure it's the gearing? Gearing is basically rpm @100kph. Did you change it from the base 4200?

My car is insanely highly geared (the defaults are for my car, and me), and a best case gearing for my car would be financially impractical IMO, the best I could do would be to increase tire radius by 15%, which might net a 9% gain at 100kph, lessening as I go slower. Going the whole hog would net me about 15% from memory.

Easier and cheaper to just take 20% longer to get to my destination, and travel at 80-90kph, and 100kph when I can't help it. At that speed, everything is working for me. Gearing is better, drag is way down, coasts are nice and long. It feels like riding around on a bike!

I can't help but think that there ought to be dedicated slow lanes on highways, where people can travel 80kph and not be pestered. It would open things up to vehicles like the Honda Cub etc.

If businesses were granted a fixed number of allotments where people could come to work and leave during morning and evening rush hours, traffic would be vastly improved and more efficient highway speeds would not result in more congestion. I used to hate the nanny state, but in this day and age it makes sense. At the moment the general population is behaving like a bunch of idiots, having feasts at the beginning of winter with the seed grain and the vegetables in the root cellar.

I wouldn't mind, but I happen to be sharing the same house with those idiots.

Anyway, I was thinking that gearing losses at speed might be useful. It would just be Loss = 100*[BSFCcurrent - BSFCbase)/BSFCbase]
Not really, I like the open nature of ODF, and the fact that other people can double check my calculations (i.e. basic Open Source theory) so that other people can build on my work and everyone can benefit. Of course, someone else is free to do so. The equations are there.

Interesting observations indeed. Of course speed was a huge factor for my car (more so than acceleration), but I was surprised at how much difference playing with gearing at 100kmh while driving at 100kmh changed things around.

The only problem with dedicated slows lanes is that they would have to be cross by traffic to get in/off ramps and things, where the speed difference might make things unsafe, I think.

Um, yes please. Will try out the 4-valve version shortly...

Ben: you've got 3 valves per, don't you? :p

One thing I forgot to add, this assumes that we are accelerating using 62% of available power, whatever throttle that is at. Deviate too far either way and there will be FE penalties. See the BSFC graph. Pick an rpm, and vary the load on the engine. The BSFC is efficiency, lower = better.
I think this is done in Germany already. Might be better to just slow down everybody to about 50mph/80kph. I almost can't believe I'm writing this - I used to go a bit above the speed limit religiously. But that's a very good compromise speed - lions share of the benefit, and still a fast speed.

I prefer slowing down to 285 kmh, by train!

Anywho, Darin, I see that you're making a joke, I just don't get it, :D

Urg. That's a bit of work. If someone feels like printing out the 2 valve engine map in the spreadsheet, drawing a line between (2000, 102) and (5200, 125), marking every gradation from 0.40 (estimated) at (2000,102) and 0.565 (estimated) at (5200, 125), i.e. 0.40, 0.41, 0.42, ... 0.56 by interpolating between the lines, and measuring where they are in terms of rpm, I'd be more than happy to write a lookup function to lookup the correct value.

I might do it later sometime though.

Until then, a useful kludge would be to go into the hidden columns and add 0.05 to the BSFC formula, for rpm at actual speeds greater than 3000rpm

I'm OK with the kludge, too. Will report in later.

For "rpm at actual speed" of 3000 or less, adding 0.03 would probably work ok.

Here's a question: it looks like the calcs are based solely on top gear, correct?

According to the spreadsheet, with all my vehicle's data plugged in, I can theoretically get 132 mpg (US) / 1.78 L/100km at an average P&G speed of 40 km/h, with a total 30 km/h speed delta.

And you know what? That's almost bang on what I observed in those conditions. I did just that one day this summer in my car on an ideal route (a ring road) and after several loops, was averaging 129 mpg (US).

The major difference was that I was pulsing in 2nd and 3rd gears, not 5th.

Cool stuff.

Does it matter if the car has a automatic transmission for the worksheet?

Shouldn't think so provided that the rolling resistance is similar to a manual (i.e. a function of tires and wheel bearings only, and not the trans).

In devising the spreadsheet, I assume that you can hit BSFC(minimum) if you are below the speed at which you will hit BSFC(minimum) in top gear. You have 4 gears to do this with, so it's not a bad assumption. It'll be near enough.

Above that speed, the BSFC is the best you can do for that rpm in top gear.

As explained above, it should work at all reasonable speeds you'd pulse and glide with, assuming you accelerate at 62% of BMEP available at that rpm, that you choose the gear that will enable you to get closest to BSFC(minimum), and that the glide speed drop is not too large (it uses air resistance calculated at the average speed, so if you give it a pulse to take you up to a high speed, most of that energy is wasted in pushing wind). It also assumes that most cars don't deviate much from these maps.

You can't achieve peak FE without P&G, and current instantaneous FE meters will not teach you how to P&G properly. Instead, you learn to accelerate anemically in all circumstances.

That's where this spreadsheet comes in - you can fiddle with variables and see what is theoretically achievable with your car, before you spend money and time on building something, and also how you will have to drive to get those benefits. Then you go do it, and confirm it.
I thought so, just needed some people to play with it. It appears to be in the ballpark for my car, but I wanted some confirmation. Thanks for providing some! It's gratifying that it appears to be working so well. Provided I've got the equations right, it should work. Newtonian mechanics works just dandy at those speeds, and all we are doing is calculating fuel used in a pulse, fuel used in a glide, and the distances traveled in each to come up with a distance/fuel figure.

After that, we are relying on the particular engine maps (which were an average of several manufacturers' cars) being applicable to our cars, my assumptions as listed in the first paragraph, and that my line of best fit is good. I double checked things as I went.

I'd love to get ahold of all the coordinates of the original engine maps, then I could have it instantly calculate steady state FE for a comparison. One thing at a time.

Excellent system of algorithms. As a un-educated American, it takes a little longer to convert from darn English system. Enter Metric rant here -- we should have it as the everyday standard here. Now, to convert how many KW the 'Teg has...:confused:. I'll get it eventually...

Excellent work, however!

Cheers.

RH77

Thanks, I should really have added the conversions to the spreadsheets, considering my audience. I was just so glad to get it working and get others to share in the joy of seeing where the gains can be had.

One thing I have to wonder though is if I am forgetting accessories (alternator etc) in the equations.

I think it's outstanding also. I'm struggling with the conversions too. Dang American System. Rick try here. I think your 106KW.
What's a frontal area of 20 sq ft = to

Google does conversions. Just enter "N hp to kW" in the search box. (Or any other units.)

Good point - for the figures I quoted comparing the spreadsheet output vs. real life, the alternator was in fact disconnected at the time.

You know what... I suspect that the default on parasitic loads may not really matter that much, depending on how long your respective pulse and glide times are. The idle fuel burn rate incorporates those loads, so if your pulse time is short, you could effectively ignore calculating them during the pulse. But it would be simple to include an alternator load in there.

Obviously A/C makes a big difference and you can expect your FE to suck (technical term) with the use of such a device.

Another thing is if claims of companies like Synlube are to be believed, you can improve BSFC some small fraction, possibly dependent on rpm and perhaps load. It can also be added to wheel bearings etc, which would decrease Crr.

I made a mistake I think when I said automatics would have no issues, there are transmission losses to contend with. From what I remember, 8% is the figure generally given. So your BSFC would be reduced by 8% during the pulse. It would be helpful for someone more familiar with transmissions to comment here.

BTW I wrote the authors of that paper asking if they had the original data for those graphs. We'll see if I get a response.

featurecreepitis
 

I'm putting down a wishlist of features I'll include in version 1.1.

-US units - I can't count on people having either completely US units or metric units as a resource, since a lot of these figures will be straight out of google. So there will have to be options for each.

-parasitic loads included (e.g. alternator), maybe A/C (suggest others and likely power draw)

-transmission losses for autos

-constant velocity cruise in gear automatically calculated for comparison

-two valve per cylinder engine map (I believe that Variable Valve Timing and Lift (VVT&L) engines should be the same as a 4 valve/cylinder engine in terms BSFC(min) for a given rpm. Based on the graphs here.) Note that the vertical lines of BSFC from 2300 on are at identical rpms, and this is where we want our engine operating during the pulse.

-diesel engine map

-something saying that Engine Size is only useful for calculating idle fuel burn rate, so if you have a hybrid this should be zero. Or maybe just a check box for Hybrid/Engine Off Coast (versus idle).

-I'll include Synlube after effects have been independently verified and quantified.

-results in l/100km, mpg, km/l.

Let me know if I've forgotten anything.

The instructions page doens't seem to load correctly Drew. Also, welcome to the site.

Yes this works

I've fixed the instructions and am currently working an easier-to-use version for common American units - gallons, miles, and m.p.h.

The hard part is maintaining that elusive 62% at different gears/throttle positions and speeds.

This is the one figure I am tracking on the ScangaugeII while pulsing. Dramatic results! Am achieving sustained fuel efficiency close enough to BSFC(min) to make friends seriously envious

If only we could get some Audible alarm that buzzes a LOW tone below ~57% and a HIGH tone above 67% engine load and I would not have to look at the Gauges at all while driving!