Block heater analysis

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. 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 heating. 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 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 miles per hour with maximum use of "N" seems fairly effective. 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 is 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 December with enough time to quantify the transaxle pan heater effect before the cold weather is gone.

Bob Wilson

 

Hi Gary,

I have a North American, NHW11, and it is hobbled by a kludged, hydrocarbon capture system. This requires the ICE coolant in our units to reach 70C before full hybrid operation can begin. The Asian and European NHW11s and the NHW20s have a lower limit. Ken@Japan and I had collaborated on these studies but I don't have hard data on the transition temperature.

Because of our hobbled North American, NHW11s, I do the following until the coolant reaches 70C:

• speeds <= 25 mph - by cutting through my neighborhood, I can drive at slower speeds without other drivers stacking up behind me. In fact my speeds are in the range of 18-27 mph.
• "N" coast - it turns out that the engine fuel consumption at idle in "D" is about twice the consumption in "N". By shifting into "N" at every opportunity, I can get the MPG during the warm-up to 25-35 MPG when the coolant reaches 70C. This usually occurs in less than 2 miles.
• NOTE: the transfer of heat from the exhaust is a function of geometry, not the amount of fuel burned. The 600C exhaust temperature does not instantly permeate the block but is limited by the thermal conductivity of aluminum and coolant.

I would suggest getting some measurements of your configuration. In particular, if you can read out the engine block thermistor value and the heater power drain (the real drain including any extension cord.) Do a controlled test measuring the values at say minutes: 5, 10, 20, 30, 1 hr, 1.5 hr, 2 hr, 3 hr and 8 hr. With these values (see my earlier list,) we can then put the points in a spreadsheet and find the respective "r" and "k" values that will 'fit the curve.'

Bob Wilson

 

We have identical engines and heaters but I may have a longer, higher resistance extension cord. What this means is my numbers should be on the 'long side' or conservative on how long the block heater is needed. The power consumed really needs to be measured (if we're going to get accurate cost model for using a block heater.)

Understand that we may be talking only a couple of cents. My electricity rates are $.07/ kw-hr and my configuration is using ~375W. We're looking at about $.02/hr to run my heater. Also, I have a well defined, minimum fuel burn warm-up cycle, which is especially important when away from a power outlet.

To accurately answer these questions, we need to see some detailed warm-up studies of the North American NHW20 Prius to find out when they really can enter S4, the final warm-up stage. Then we need to see studies about driving strategies that minimize the fuel burn during this warm-up phase. The thermos tank in the North American Prius means Ken@Japan's data, excellent that it is, may not apply directly.

Bob Wilson