mpg numbers are shown on website for 2016 Prius

Wouldn't the rolling resistance associated with flexing the tire walls and tread be a greater contribution to static drag coefficient than the wheel bearings?

 

One of the reasons we run 51 psi rated tires is to reduce tire rolling resistance losses. However, Google "low resistance wheel bearings."

• lower viscosity grease
• ceramic
• oil bath

Source: Rolling Resistance

Let me suggest taking some of the tire rolling resistance coefficients and calculate the contribution of tire rolling resistance to the static coefficient of friction from the roll-down numbers. If you use the spreadsheet, you can add a linear trend line and see the function:

• y = 0.0082x - 4.9786 # Slope is the in the upper range of tire drag coefficients

The nice thing about reducing wheel bearing drag is it becomes low or no maintenance. Tires have to be kept inflated.

Bob Wilson

 

Bush bearings are designed for high radial loads, but not axial. Esp those are not suitable for highly variable axial loads(Wheels in this case). That is why we find tapered roller bearings for axles commonly. In transmissions also when there are helical gears, they use tapered roller bearings. It is possible have a bush bearing in places like example Turbos, where axial play is acceptable and everything is oil cooled. But it is not tolerable to have axial movement in wheels.

I am looking at your spreadsheet, wondering how did you calculate Target Coef A (lbf), Target Coef B(lbf/mph), and HP at various speeds?(Been long time since I worked on road/load hp calculations during from Automobile Engineering!! )

Thanks

 

Actually I found in race car, parts suppliers potential sources for lower rolling resistance bearings as well as wheel assemblies. It isn't trivial but it looks like the folks on the track have already addressed my speculations.

There should be three coefficients (scroll the left pane):

• Target Coef A (lbf)
• Target Coef B (lbf/mph)
• Target Coef C (lbf/mph**2)

The formula I use is:

• HP = ( mph * ( (A) + (B * mph) + (C * mph**2) ) ) / 537 ## Found at Ecomodder.com

In effect, the velocity times the force gives the power and the 537 is scaling constant. Of course this is all SAE numbers meant to confuse those who use standard units. <grins>

Bob Wilson

 

I think first and easier step would be to adopt to ceramic bearings. Reduced friction and more tolerant to contamination and lubrication requirements. This would be a straight replacement. Ofcourse expensive compared to regular steel bearings, and how tangible benefits are going to be, needs evaluation. Road race bikes do use ceramic bearings.

 

I agree and asked the usual suspects who hang in the Gen I forum for the bearing specifications. Then comes the joy of which car to test:

• 2003 - heard what could be bearing but could also be tire 'growl' the last couple of months. MG2 is still cool, no problem with stator short.
• 2010 - could do with an MPG tweak if proven in the 2003. The best thing is this could be a popular retro-fit for all models.
• 2016 - Two Eco, hummmmm!!!

The reason I calculate the drag power is the coefficients play a big part. What I need to do is plot the drag power contribution by A, B, and C so folks can see how each plays a part and the speed range. Each coefficient is subject to individual optimizations. Understanding how they play together makes it easier to weight the price-performance benefits:


Bob Wilson

 

But some how I feel bearings at most contribute to 200 watt max(wild guess based on how much it saves in bikes). I think more can be gained by high pressure thinner tires (aka BMW i3) with lower rolling resistance than bearing replacement.

 

I've already got the highest pressure tires, 51 psi, for both cars. They have years of tread remaining so I don't see changing them anytime soon. But I agree I need some hub metrics.

I've got an IR thermometer and need to run some high-speed warm-ups and measure the hub temperature difference before and after. This will give a basis to estimate the potential.

Bob Wilson

 

I would caution against hub temp difference as a way to measure bearing efficacy. Even slight imperceptible brake drag would cause hub to become warm. Unless we explicitly take out brake caliper, there will always be some drag because of brakes(not because of bearing).

 

Brake caliper drag is also mentioned in the racing forums. Testing the effect is not trivial. But it isn't impossible either. Do you have some suggestions?

Bob Wilson

 

Sunday, I developed an approach that uses miniVCI to measure the engine BSFC in our 2010 Prius. My data matches the Toyota SAE paper results. The technical challenge is miniVCI polling, ~0.8 sec, too slow for the metrics needed:

• T[0], T[4] - timestamp
• T[1], T[5] - engine rpm
• T[2], T[6] - MAF flow g/s
• T[3], T[7]- engine torque Nm

Sampling is subject to a race condition where the engine power can change faster than the delay in any of the three data metrics. This leads to noise and impossible numbers. The timestamp just lets us know roughly when data elements were captured.

Since miniVCI is showing ~0.8 seconds between timestamps, we can assume there is between 0.8/3 or ~266 ms between each data item. Typically reading the system clock for the timestamp is measured in 10s of microseconds. Unfortunately, 266 ms is so slow that if the car is accelerating or decelerating, the two fields that calculate power, 'engine rpm' and 'engine torque Nm' can change enough to give a false value for the fuel flow . . . (i.e., engine efficiencies > 100%). There are various math tricks to 'normalize' the data and throw out the outliers.

In my benchmark, I used cruise control to minimize driver 'fretting'. But there were surprises in the data:

• maximum engine rpm > 4,400 rpm - the documented limit is 5,200 rpm but ascending an 8% grade hill at 75 mph on cruise control did not give 5,200 rpm. I could have floored the pedal and possibly gotten 5,200 rpm BUT this gets exciting when the police are looking for holiday party drivers.
• 3,200 rpm transitions to fuel enrichment - the maximum EGR setting happens at 3,200 rpm but thereafter, BSFC increases (more fuel per HP/kWhr.) This suggests fuel enrichment is going on to moderate the exhaust temperature.
• simple relationship between BSFC and thermodynamic efficiency - invert the BSFC and multiply by 85 gives the engine thermodynamic efficiency. There are variables including fuel energy (i.e., ethanol ratio and energy content of gasoline.) Regardless, it makes a simple calculation.

	Eff %	BSFC	Efficency % ~= 83.25 / BSFC (gm/kWhr) for gasoline engines as other fuels have a different constant
1	30%	278
2	31%	269
3	32%	260
4	33%	252
5	34%	245
6	35%	238
7	36%	231
8	37%	225
9	38%	219
10	39%	213
11	40%	208
12	41%	203
13	42%	198

Bob Wilson

 

It takes a very steep hill to get the engine up to 5000 RPM. We have one here, which I'd estimate is around 16%, on a secondary highway. It's not very long, maybe a kilometre, but both Pearl and Pearl S reached 5000 RPM with the cruise set at 100 km/hr. Oh, and both cars slowed slightly, due to cruise lack of anticipation (they didn't react until the speed had dropped, then had trouble increasing the speed).

 

I had to stop because every time I descended the hill for another run, even using "B", the traction battery warmed up. We have one 'switch back' hill, a former logging road, about 40 miles (64 km) over in Jackson County that is a little steeper. Sad to say, it is not a constant grade. I am curious, only to complete the chart.

Do you have miniVCI with TechStream 10?

All we need is to set the 'snap' depth to infinite and configure a custom data list of rpm, MAF, and engine Nm. The rest is just a spreadsheet to handle the sums.

Bob Wilson

 

You don't need constant speed, you need constant rpm, so you could just floor it from 0 rpm and measure that 5,200 rpm BSFC in 5s on the level road. Or is 5s not enough?

I had BSFC formula in the Torque app, the biggest question was fuel density, I used 0.750 kg/lit and the best I got was between 220-230 g/kWh in cold weather it rarely went under 240 g/kWh.

 

Here is my data from miniVCI both the raw and reduced:

1. Only positive power samples with rpm and Nm > 0.
2. Only samples where the previous and current MAF rates were withing 98% of each other.
3. Eliminated BSFC values > 1,000 or less than 200 gm/kWhr.

Bob Wilson