Measurement of MPG vs Tire Pressure in Gen-3

An excellent point worth some discussion. It may be helpful to look at this via two idealized models. Also, I prefer to have the axle stationary and the road moving backwards (looking at the tire from the moving vehicle).

Expanding Circle Model: (the model I was using) The action can be approximated by a rotating circle whose circumference increases proportional to the height of the axis above the road. Here, the true distance covered must be corrected by the ratios of the circles' circumferences, since the length of road passing under the wheel in one rotation is equal to the circumference of the circle.

Constant Circumference with Flat Zone Model: (Fuzzy1's suggestion, if I understand him) The action can be approximated by a circle with a flat zone (in contact with the road) and constant circumference. As the pressure increases, the length of the flat zone decreases increasing the height of the axis but not the circumference. Here, the distance (length of road) covered in one rotation does not increase with pressure.

I believe the truest representation of a rolling, steel-belted radial tire must lie between these two models, the question is: which model is closest. The expanding circle model cannot be true since the contact length does change with pressure and the steel belts do resist circumference changes. Likewise, the constant circumference model can't be true since the tire does expand somewhat with pressure. Not to do that would require materials with infinite Young's Modulus.

So far I haven't found the answer to our question, but two (retrospective) observations in my own data (all in this thread) suggest that the constant circumference model is closer to the truth.

1) Althought my MPG vs PSI tests do not require the test runs to made over exactly the same distances, I have tried to make them close to the same distance. Using the results of my height measurements (which were assumed to equal the circle's radius), the highest pressure runs should have been measured by the MID (Trip gauge) as 3% shorter (i.e., 13.0 miles) than the lowest pressure runs (which were 13.4 mi), but they were actually measured as 1% longer (13.5 mi).

2) I think the height vs PSI plots should have been more linear than they were if the expanding circle model were correct. However, flat zone in the constant circumference model would change more at lower pressures as zone get longer and the tire begins to sag more, as was observed.

I will try to get some data tomorrow (weather and traffic premitting), so please stay tuned.

In the meantime, thanks to Fuzzy1 for his input on this!

This seems to be the 64 dollar question. Each driver must answer this for him/herself. The "official" word is not to exceed the sidewall maximum pressure. I can only say that the general belief is that burst pressures for uncompromised tires are about 400% higher than the sidewall maxima and that there are volumes of people out there who have rountinely run at pressures substantially higher than Pmax with no reported problems in blowouts or handling. They say the tread wear actually improves. Everyone seems to agree that the ride itself is harsher, although many people say they like this.

Thanks again to all.

- g

 

Well, folks, I spent 3 hours this afternoon driving 12 10-mile legs on the Nonconnah Parkway trying to resolve (or at least shed more light on) the MPG vs PSI and the effectivetire diameter vs PSI for the Gen-3.

MPG vs PSI - The total increase in MPG vs PSI (from 25 to 55 PSI) that I measured today was even smaller than last Sunday. It was about 0.4 MPG if you use all the data and about 1 MPG if you exclude the first 55 PSI round trip by arguing that the drive train was still not fully warmed up (after about 20 mi of highway warmup).

I think people in FLA or some other very flat area may do better. There are a lot of ups and downs on the road that are not helpful and the traffic is really not light enough. If I get back in the mood, I may try Arkansas at some future time.

Effective Tire Diameter - Here, at least, I was able to conclude something.

The average distances between two signs (that were about 10 miles apart) was measured using TRIP B was measured repeatedly for three different PSIs. The resulting average distances measured were:

10.05 mi (@ 25 PSI) - 4 trips
10.05 mi (@ 40 PSI) - 2 trips
10.00 mi (@ 55 PSI) - 4 trips

Within the measurement error, I would call this a null effect. If the tire had been expanding proportional to the rear axle height, there should have been an increase of about 0.3 mi in TRIP B at the low pressure and this would have been easily seen.

So, I am afraid I will have to take back that 1-2 MPG expanding-tire bonus for high PSI that I so glibly handed out yesterday!! arty:

Elevation Effects - If anyone is interested in how small a change in elevation the MPG gauge is sentitive to, I have some info on that, too. I've now made 7 round-trips over the same section of highway where I used my GPS (with averaging) to find the elevation difference. It is about 65 feet over 10 miles (about 1 foot per 1000 feet). In all 7 runs, the return (downhill) leg had higher MPG than the outbound (uphill) run.

The average trip MPGs are 60.0 (downhill) and 57.3 (uphill), and this section of road is far from flat - it has maybe a dozen rises and falls of about 30-50 feet that the MID has to "see through". Does that sensitivity seem possible???

Thanks again to Bob, Fuzzy1 and the rest of you for your help and encouragement.

- g

 

Well, continuing the saga of how to take MPG and exit ramp elevation data on limited -access highways without getting killed, I was back on the road again today. Previously, I made elevation measurement by eyeballing the GPS for five minutes and doing a "cerebral average". Today, I actually wrote down 25 readings at 15 second intervals to get means and standard errors (of the mean).

Math says the mean elevations I got at three points ("A", "B", and "C") have statistical uncertainties of about one foot, but I'd guess it was closer to 2-3 feet. Since I only want elevation differences, the systematic errors should mostly cancel out.

As you can see from the attachment, the value of

K = (MPG downhill - MPG uphill)/elevation difference

should be the same for my A to C runs and my B to C runs. I got

Kac = 0.046 and
Kbc = 0.039

I you assume for argument's sake that the true value is in the middle (it is probably closer to Kbc, which has more data), you get both numbers being within 8.7% of that value.

Note that the small elevation differences come out to be

AtoC = 75ft in 13.5 miles and BtoC = 58ft in 10.0 miles

BOTH slopes I drove across are almost exactly 1 ft in 1,000 ft! The Prius is sensitive to MINISCULE elevation changes. So, if somebody says I drove 100 miles from one place to another place and got 62 MPG, that is meaningless. You have to stick with round trips (where the elevation and wind cancels).

I think I am giving up my fuel economy by making all these data-gathering runs

- g

 

I am gradually learning what the important paramters are (or may be) in collecting solid data. It's not too hard to collect data - but very tough to collect solid data. I think my technique needs improvement. For example:

As Fuzzy1 mentions "adequate stretch of road", makes me wonder, what is adequate? For example, all my past runs have been on a limited-access road with a 65 mph speed limit. I think I need to slow down to avoid competition from air resistance. In addition, this road has multiple overpasses that rise then fall 30-40 feet. You can feel the engine pick up then back off. Maybe I need to avoid this, because even with the great regeneration of the Prius, you never get back all the energy you put out in traversing rolling hills.

Y'know checking for elevation effects in a slope of 1 ft per 1000 ft is a great way to demonstrate the sensitivity of the Prius and its gauges, but it's probably pure madness when trying measure elevation effects (the signal-to-noise ratio is too low!!!). I need to run out to Crowley's Ridge in ARK which has a ~400 ft rise in a few miles.

Roger on that. I keep forgetting that this data is not for me, but for others, who are not sitting in the car with me.

I know Bob has developed a fine technique over the years, something a new Prius owner (like me) is just beginning to understand.

For example, when taking data, I have been resetting the Trip B as soon as possible after getting on the highway. Usually I gun the engine to accelerate up the steep entrance ramps, get to speed, then hit cruise while resetting Trip B. This puts the engine in a somewhat unstable state, I'll bet. I probably should be accelerating onto the road less wildly, setting cruise, taking half a mile or so to make sure it is, say, 60 and not 61, and THEN reset Trip B at a convenient marker further down the road.

I think I will take off some time off from data taking and drive around the contryside a bit to check for nice flat county roads with no stops and little traffic. Places where I can drive at 40-50 mph without getting rear-ended.

I think I am beginning to understand the reasons for the wildly different results people are reporting regarding MPG. This is no easy business.

 

Please excuse double post, but I made a couple of fixes in my last spreadsheet. There was a mistake in the extra fuel required per 10,000' of climb (this is a projection - I actually climbed 75 and 59 ft). Now my results are much closer to Fuzzy1's results (of 1 gal extra/10,000').

Also, I removed one of the 25 PSI data (which was an outlier wrt the uphill vs downhill behavior shown by all other data) and the plots improved. The other 25 PSI data set is also a bit flaky, so I included a second spreadsheet (rev3A) just to show what the results would look like with that one out, as well. I also noticed that the 13.5 mi trips seemed to produce somewhat better results than the 10.0 mile trips. Not sure why.

Drove around Rossville TN area looking for ideal road conditions. So far, no luck. Will try southest of Marion AR next.

Any suggestions about any of this?

- g

 

FINAL RESULTS:

Well, folks, after logging over 350 miles taking data on TN and AR highways (Thanks, Bob Wilson for Google Earth & RT 64 tip!), I am finally ready to post my final results on the MPG vs PSI in the Gen-3 with AVID S33D 15" tires (and all the other factors in the attachment).

You get (2.5 +- 0.3) MPG more when you raise the pressure from 25 to 55 PSI. You can just look at the "TOTAL" graph and see where you are now and what you will get at the maximum PSI you are willing to use.

Why is there so much confusion in this area? It is extremely difficult to come up with an accurate answer. After many days of data logging, I can tell you that there is a huge difference between taking controlled data vs. saying "Last year I had 30 PSI in my Prius and this year I put in 60 PSI. Now, I'm getting 5 MPG more!!" Or, as we sometimes hear "I don't see any change at all." I'm not at all surprised to hear those comments. Also, it's important to remember that I only studied one type of tire. Other tires could behave differently.

At least the people with the OEM AVID 15" tires on their new Prius can now know what to expect when they start charging up those babies.

Cheers !!

- g