Stan,

First a typo. My number is 12.052 and not 12.025. I think the difference is because I have my snow tires on (Primacy Alpin PA3), and they are a little smaller in diameter (26.093 in), and also a little softer, so the static radius is smaller. Yes, I did measure it by using a cold tire distance per RPM over 10 revolutions under light traction using the technique described in the link in my last post. The static radius for the Energy S8s is slightly larger.

Incidently, you cannot go by the Michelin published specification for "Tire Rotations per Mile". It might actually be acheivable with a cold tire at 45 miles per hour under a light load, but my own research did not even come close to that on asphalt at my commute weight. 816 is typical for the S8, and the 836 number is what I am seeing on the snow tires.

RFB

 

Stan. The one thing missing to permit me to calculate what Toyota uses as a rolling radius was the redline RPM for MG2. The Oak Ridge report states that it is 14,000, so with a 121 miles per hour top speed, that makes the Toyota used rolling radius approximately 12.707 inches or about 32.3 cm.

Since that's the "official" version, I suggest we use that for any "standardized" discussion. This gives just under 794 axle rotations per mile, which is not very far from my original figure.

RFB

 

FastMover — Yes, I was about to mail you about the 14 000 rpm limit mentioned in the Oak Ridge report. I was pretty sure that I'd seen that number somewhere before (I don't know where), and now it's confirmed! The Manual states a top speed of 185 km/h (115 mph) on page AP-02 of the New Car Features Guide (attached). Both these numbers have presumably been rounded to "nice" numbers, so they should only be taken as approximate. Relating revs per mile and top speed to tire radius is a good idea, but I don't quite duplicate your numbers.

I calculate that the formula relating the Road Speed RS (in km/h) to MG2rpm and the tire rolling radius r1 (in meters) is:
r1 = 23.2888 RS / MG2rpm
So, if I use RS = 185 km/h, and MG2rpm = 14 000, I obtain r1 = 0.307745 m (~12.1159 inches). So we have the following possibilities, amongst others, for r1:

1. Michelin's unloaded radius of 13.1 inches = 0.33274 m
2. Michelin's stated 793 rev/mile at 45 mph => 12.7163 inches = 0.322995 m
3. FastMover's suggested 816 rev/mile => 12.3579 inches = 0.313891 m
4. Relating TCH's top speed to MG2's max rpm as above => 12.1159 inches = 0.307745 m
5. FastMover's relation of TCH's top speed to MG2's max rpm => 12.707 inches = 0.322758 m

The first is wrong, but which of the remainder should we use? Perhaps we'll have to await a measurement obtained using your tach counters! By integrating their output, you should be able to get a "real" rev/mile number (using the S8 tires please — so we'll have to wait for summer!). What do you think?

Stan

 

Somehere, (I will need to look) I saw a bit that stated that 121 miles per hour was equivalent to the MG2 redline. I don't remember where I saw it, but I do remember referencing it when I put that number into "Gears". This was before the Oak Ridge paper was released. the problem with that paper was that it did not state what the MG2 redline was in RPM.

I will look for it.

 

FastMover — I believe that 121 mph was someone's reported top-speed measurement using his car's speedometer. Bear in mind that the TCH's US speedometer is much more blazed toward over-reading the car's speed in mph than the metric version's speedometer is in km/h (see the attached file). My own comparisons between my metric speedometer's readings and my GPS show that my speedometer (and odmeter) are accurate to better than 2% up to 120 km/h (~75 mph), and within 1% over much of this range. (My tire pressures were nominally 220 kPa = ~32 psi.)

By the way, for interest the US version of the metric formula I gave in post #13 is as follows. The Road Speed RS (in mph) is related to MG2rpm and the tire rolling radius r1 (in inches) by:
r1 = 1475.58 RS / MG2rpm.

Stan

 

FastMover — Page 62 of the Oak Ridge National Lab. report (see the thread "Camry Hybrid Transaxle National Labs Report") gives us yet another set of numbers relating MG2rpm and top road speed RS. They give a ring gear speed Nr of 5500 rpm, corresponding to MG2rpm of 13 585 rpm, and RS of 113 miles per hour.

• ORNL's numbers => r1 = 12.2739 inches = 0.311756 m

This lies between the largest and smallest of the previous five numbers given in my post #13.

Stan

 

FastMover — After thinking about it a bit more, I like the idea of using the ORNL numbers (see post #16 above) in our formulas. The ORNL numbers (page 62) are pretty close to your 816 rev/mile numbers, by the way (point 3. in post #13). What do you think? We could revise them later in light of further experimentation.

So, if we accept that Nr = 5500 rpm (i.e., MG2rpm = 13 585 rpm) corresponds to RS = 113 mph, we can compute that

r1 = 12.2739 inches = 0.311756 m

and then we deduce that the wheels make 821.588 rev/mile. The formulas linking the shaft speeds then become:

• Ns = 3.60 Ne - 78.3716 RS [for RS in km/h]
• Ns = 3.60 Ne - 126.127 RS [for RS in m p h]

On a different matter (the transaxle lubrication issue with the ICE stationary), there appears to be a discrepancy between two of the report's statements:

• page 39: Differential speed (= wheel speed) > 900 rpm fills the oil wells. This implies a car speed of 65.7 mph according to my calculations (Nr = 3187.8 rpm => MG2rpm = 7899.4 rpm).
• page 59: Ring-gear speed Nr > 1000 rpm fills the oil wells. This implies a car speed of 20.6 mph according to my calculations (MG2rpm > 2478 rpm).

I'm inclined to disbelieve the former and believe the latter. What do you think?

Stan

 

The ORNL number are close enough for me to work with.

As far as lubrication -- it better be the latter, or my car would have had a problem long ago. I have a long evening commute level stretch without stops that works out right at the 40-42 miles per hour EV mode for over 5 miles. Most of the time I can make it most of the way without an ICE start, but it takes the battery right down to minimums. It's cool because right after that I have a long uphill stretch to get home.

 

Reading this thread, I can't help but think that the differences of a few percent on the rolling radius can easily be explained by tire pressure. Michelin and Toyota very likely used several different pressures for their various tests and calculations, and those pressures may not even be close to the pressures that any of use actually run. Trying to pin down the third significant digit when the experimental data is unknown is, very likely, an exercise in futility.

 

SteveHansen — As regards the third significant digit, you're quite correct; demanding that sort of accuracy wouldn't make sense. But the difference between the unloaded radius and a loaded radius (whichever one we finally choose) can be a substantial 8%. We're really just trying to make the best educated guess that we can with the currently available information. Yes, tire pressure, tire temperature (cold, warm, hot, ...), car speed, and passenger/luggage load, etc. all affect things. When FastMover has his instrumentation going, he should be able to get readings of revs/mile under various conditions, and deduce from the formulas the corresponding rolling radii r1. Until we have a more reliable number for r1 it seems reasonable to use the numbers computed from the figures given by ORNL.

Stan