Pulse and Glide Fuel Economy Calculator

[Mighty Mira]

Hi,

I created this spreadsheet the other day to enable me to fine tune my driving techniques and modifications for ultimate fuel economy, and also to compare with steady state, in gear cruising. It actually enables a person to do several things not necessarily related to P&G.

Calculate Pulse and Glide Fuel Economy
Calculate coast down time given drag coefficient (or vice versa, useful for determining Cd*A, and given A, Cd)
Calculate steady state, in gear cruising fuel economy


To compare engine on in neutral versus engine off, just adjust the idle fuel burn rate.

This will also give an idea of gains from gearing, rolling resistance, air resistance etc, and providing you have an accurate engine map, should give you a good idea of what the fuel savings will be at the speeds you are looking at.

The only thing this won't do is give an idea of how much fuel you will save (or more likely, won't save) by having the engine on and feathering the throttle to put you in the section of engine map where no fuel is being used. However, this is (IMO) a false economy because your engine is being turned at a higher rpm than neutral, and you will have to accelerate more to regain speed/distance after the same time of coasting. The only reason to coast with engine on (braking or feathering) is if you have an unavoidable stop ahead, or perceived safety reasons.

Note with the format, it's in the Open Document Format (ODF), in this particular case, Open Document Spreadsheet (ODS). You can use openoffice or gnumeric to open it, or any of the others listed here including MS Excel (with plugin). I use ODF format because it is guaranteed to be easily read and modified by anyone for free, indefinitely.

Please check the spreadsheet to make sure I haven't made any errors. The figures look right, but one can never be too sure.

[Mighty Mira]

For those too lazy to get the plugin, I've also uploaded the spreadsheet as an xls file for Excel.

As an enticer, I've calculated that my fuel savings are 30% over steady state driving at 95kph, and about 11% over the previous mild acceleration I was doing during the pulse.

From memory, I can do a glide lasting about 11 seconds from 100 to 90 seconds.

[Mighty Mira]

Ok, well, I've attempted to measure the drag coefficient of my car. The first step was to take a front on picture of my car, and estimate how many pixels there were in the frontal area. Then it was a simple matter of measuring the height of the car in pixels, comparing with known height (1.4 metres) to get a pixel/metre figure, taking the square root of the total pixels, multiplying that by the pixel/metre figure, then squaring that to get the frontal area in metres squared (1.79).

I then did several 100kph to 90kph coast downs in neutral to get the times. Unfortunately, I didn't have a completely flat section of road. Times varied from 7.82 going up to 10.59 going down. An average of those times is 9.21.

Temperature was 24.6 degrees and 50% relative humidity. Note that according to the formula here this brings the density of the air down to 1.174 kg/m^3 from 1.181, which has a small, almost negligible effect on the drag coefficient.

Drag coefficient for 9.21 seconds is 0.213. So that means with all my modifications so far, my car has a significantly better drag coefficient than the honda insight's 0.25, which is currently the lowest drag coefficient of any production car. Combined with my car's tiny frontal area, my drag area is 0.381, quite a bit smaller than that of the insight (0.47m^2). Even if I take the up hill drag coast times as what I should have got, that still gives me a drag coefficient as good as the insight.

Not bad, considering that a car with a very similar shape, the Renault Twingo has a drag coefficient of 0.37. (That's the best starting Cd seeing that the Cd of the Mira is too hard to find out). That would mean I've shaved 42% of the drag off, and removed a bit of the frontal area as well by removing the mirror. And I've yet to clean up the gaps under the bonnet, and put on front skirts.

(Consider that now that I know what I'm doing I could do the same modifications on another car for probably $200 in materials, and that I'm hardly inconvenienced by any of the modifications indicates how shockingly wasteful automobiles are.)

Thinking this should probably go in another thread, but oh well. I'm pretty stoked.

[Mighty Mira]

I just realized that I forgot to add my weight to the curb weight of the vehicle. So now my drag coefficient is 0.245, not 0.213. Which is still better than the insight.

[Snax]

I have a hard time believing your drag coefficient is that good. I'm not saying it's not, but it's truly noteworthy if it's that good.

Anyway, nice work on the spreadsheet Perhaps one day I will take the time to figure it out! :P

[Mighty Mira]

Snax, when I find an exactly flat road, I'll do some more tests.

I know at the very least, the drag coefficient is at most 0.29, because that corresponds to the coast down times I measured (twice) going up hill.

However, I'm not surprised by the results. I know the car is pretty darn slick, it will happily glide down a long, fairly mild grade hill at 80kph.

One thing I did forget was to weigh the additional aluminium, which will of course add to the curb weight (and increase coast times). However, there is not more than 10kg of additions to the car. You can do the math - the Al is 0.6mm, and the density is 2700 kg/m^3. An 8 by 4 sheet is 4.5kg.

To recap, look at a picture of the insight. Compare to my car. The boattail on the insight isn't any more than a 1/4 of the total roof height. If anything, mine is more extreme. Note the extremities on mine must separate except the lights and directly below, the angle is 180 degrees. On most of the back. On the insight, that angle is 90 degrees.

The insight grille is approximately 10-20 times larger than mine. Big difference. The grille on mine is not only blocked rather extremely, but also contours much of the bumper so that the curve continues rather than is broken up as the standard bumper is.

The insight rear wheel skirts cover maybe 3/8 of the wheel. My rear wheel skirts cover more than half the wheel.

My underbody is completely covered in smooth aluminium, and also goes beyond at the back so that the flow separates easily. I know this is more extreme than the insight.

My wheels are small, thin and are covered by completely smooth wheel covers. (No holes, or lines going to the center as the insight has).

I don't have a left hand mirror. The insight does.

The deflectors are as far down as I can go without scraping (done by trial and error). Again, they only cover the width of the tires and the air leaving shouldn't miss the tires by that much. On the insight, they extend a couple inches at most.

In summary, I would expect to have a better drag coefficient than the insight. I know the theory as to why my modifications should work, and on every count I've done it more gung ho than whoever designed the insight. There are a few inefficiencies left, but they are minor (otherwise I would have tackled them, e.g. door handles.) But then, I didn't have to please a market having access to the fuel prices of 1999.

[Mighty Mira]

One thing, I have to mention the difference having 4 valves per cylinder makes on a car, enabling a more efficient pulse at higher rpm (no difference with low load situations). This was mentioned further down the paper I grabbed the initial 2 valve engine map from, see here. The link compares a 4 valve engine map versus a 2 valve engine map.

This means that my engine is only 17% away from peak efficiency at 100kph, instead of 31% as calculated with the 2 valve engine map. It also drops soon, such that at 80kph I'm only losing 6% from peak efficiency.

Note also that the % of maximum power for best BSFC at a particular rpm also changes - it's lower, at about 62% instead of 70+%, and also less forgiving (i.e. going to full throttle will cost).

[Mighty Mira]

I've also been thinking about where the throttle position is in relation to BMEP as per the graph. BMEP is basically torque divided by engine displacement. Since all the values of BMEP are positive, I'd say that to figure out what 62% of BMEP is, first you have to give throttle to keep the vehicle at constant speed, then give it full throttle to determine what the maximum acceleration is, then adjust the throttle until you are at 62% of that, then memorize that throttle position.

[Greyg]

It was my understanding there would be no math.

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