Hi,

We had a strong cold front come through the other day and overnight, the temperatures dropped to 25F (-4C). So at midnight, I plugged in my block and pan heaters at midnight. Eight hours later, the ICE started at 34C, MG1 at 31C and MG2 at 28C. That morning I got 53.4 MPG @32F (0C) after 8 hours of engine block and transaxle pan heat. This is my typical summer time MPG.

The following day with only 30C (-1C), I was able monitor the block heater warm-up performance and later, the complete warm-up and morning commute:

time ICE MG1 MG2 W
6:48 3 3 3 384
6:55 10 3 3 377
7:14 19 5 3 376
7:47 26 8 3 370
8:10 29 10 4 375
8:31 31 11 5 375
8:34 51 16 8 ICE
8:36 65 19 9 ICE
9:04 84 39 29 ICE

50.1 MPG w/o transaxle oil pan heater

I was able to refine a heat transfer formula to calculate the coolant temperature as a function of time:

%_temp = 1 - e**(-r(t**k)))

%_temp - percentage of temperature change, in my case 35C
e - natural log
r - constant derived from materials
k - constant derived from shape
t - time in days (aka., excel time format)

For those used to using excel, the formula looks like:

=(1-(EXP(-1*Q$1*POWER(L3,Q$2))))

Q$1 - r, 11.000 for my NHW11
L3 - t, in excel format, 1.0000 = 1 day
Q$2 - k, 0.725 for my NHW11

Using this formula derived from experimental data, we get the following warm-up table:

hh:mm - % - dTemp
0:30 - 49% - 17C
1:00 - 67% - 23C
2:00 - 84% - 29C
3:00 - 91% - 32C
. . .
8:00 - 99% - 35C

So what use is this table?

It lets us determine how long my NHW11 block heater should run before reaching the point where further heating has a diminishing effect. Off hand, one hour looks like a pretty good return on electric energy used. Even two hours is OK. But anything beyond two hours is going to use a lot of electricity for little rise in temperature.

Now if one had a chart that showed the effect of cold temperature on engine warm-up, one could then determine how much heat is really needed to achieve warmer temperature milage. Say a chart that shows how many miles it takes to achieve 70C coolant temperature as a function of outside temperature:


Near as I can tell, 40F (5C), is a threshold temperature. From 40F and above, my warm-up protocol of 25 mph with maximum use of "N" seems fairly effective. But once the temperature goes below 40F, the amount of block heater time needed to bring it up to 40F can be easily calculated.

What this means is if the morning temperature is 40F (5C) or above, I can just use my normal warm-up protocol. Since I'm usually up for at least an hour before leaving for work, if it 40F or below, it makes sense to slip on something and plug in my Prius.

One wild card is the effect of the transaxle heater. Unfortunately the untimely pan heater failure (my poor installation) will defer that until I can get it replaced. The replacement should be here the end of January with enough time to quantify the transaxle pan heater effect before the cold weather is gone.

Bob Wilson

 

Nice analysis Bob. Next step is to compare the money saved on gas vs the money spent on electricity. Perhaps some way to compare CO2 emissions plugged in and not plugged in as well. This is becoming the dominant factor.

 

Thanks! It has already paid a dividend. This morning with 45F, I didn't bother to plug in the block heater. It took 1.7 miles at 25.4 MPG to reach 70C but after resetting the display, the remaining 8.8 miles came in at 64 MPG. It would have been higher but I stopped for a bite of breakfast.

For now, I'm less worried about the CO(2) emissions as much as my expenses. My next objective is to quantify the transaxle heating effect by observation and analysis. Due to the substantially lower rate of warm-up, I suspect an oil pan heater will pay bigger dividends than the block heater and useful over a larger temperature range. The UT Battelle report on Prius transaxles gave me my first clues.

Eventually, I may have an NHW11 that 'plugs in' when I park and with a smarter block heater, transaxle pan heater and traction battery 'topping' be pretty efficient, year round. Then if I can recover more of the exhaust heat, heck, I may have to change my vanity plate from C-52MPG to C-53MPG or possibly higher. <grins>

One of the nice things I'm finding is many of these techniques apply to any of the Toyota/Ford hybrid systems. This potentially means the base performance of a substantial family of hybrids might be substantially improved.

Bob Wilson