目次

## The result of previous tests

### Result 1

Temperature of inside of the car will be higher than outside by **3 degrees Celsius** until midnight with following items.

- Electric blankets or 1 person ( 120W heat generator)
- Fiberglass insulator (Installed inside of inner linings.)

### Result 2

If you add the items below, temperature of inside of the car will be higher than outside by **4 degrees Celsius **until midnight.

- Styrofoam window panels
- Curtains between the passenger cabin and cargo room

**Hereinafter, I shall omit “Celsius”.**

## Heat insulating items I brought to Hokkaido

Taking them into consideration, I went to Hokkaido with following items.

- Electric blankets
- Fiberglass insulator (Installed inside of inner linings.)
- Styrofoam window panels
- Curtains between the passenger cabin and cargo room
- Heat insulation mats

## Temperature graphs in Hokkaido

Typical 3 types of ** difference **variations are found.

### Feb/27 Very warm => Very cold

I arrived at Tomakomai, Hokkaido by ferry at 21:00 on Feb/27/2018. Then, drove to Shimukappu village, and reached there around 23:00. At that time, outside temperature was -10 degrees, and inside temperature was more than 15 degrees. So the * difference *was almost 30 degrees at first.

I stopped the engine, and started again around 5:10 next morning. While the car was parking, outside temperature fell rapidly and was below -20 degrees, and * difference *also fell rapidly as well, but still it was about 8 degrees 6 hours after engine stopped.

At 5:00 next morning, inside of the car temperature was -15 degrees, and it was very cold, but still * difference *was relatively high compared with

**previous tests**.

### Feb/28 Very warm => Cold

This graph is the next day’s temperature graph. After I left Shimukappu, drove around Furano city and Biei town. Then, arrived at **Minami** **Frano town Roadside Station**. (Roadside Station is public rest area along main roads.)

It was still 16:00 and outside was a bit warm, and inside was very warm. Then, engine stopped, and inside temperature fell, but outside temperature was not as cold as last night at Shimukappu.

### Mar/1 A bit warm => A bit cold

Again, this is the next day of above graph. Heavy snow was falling all day, and the roads to other cities were all closed. So I must stay in **Frano town Roadiside Station** all day. I drove the car several times to go for shopping or make space for snow removing machine. * Difference *never exceeded 10 degrees all day, and it reached almost zero at night.

## What is common among these graphs?

Since I have made these graphs, have been thinking there must be something common, and they must be part of a certain curve.

And a few days ago, I found what I was looking for.

The below graph is reproduced from Wikipedia. This is **exponential decay** graph.

This graph is described by below equation.

**dN/dt=-λN**

This means the reduction rate of **N** is in direct proportion to its value. So reduction rate becomes smaller when N decreases.

If you put a car in the cold weather, heat of the car is discharged by **heat conduction**, and the amount of heat to be discharged is proportional to the * difference *between inside and outside temperature. So I guess this equation can explain the

**variation of**.

*difference*I drew a graph of **exponential decay** with N=-90, λ=8.

N and λ are adjusted to fit for above temperature graphs.

## Is the assumption correct?

Are these temperature graphs are part of exponential decay graph?

I overlaid temperature graphs and exponential decay graph as below.

### Feb/27 Very warm => Very cold

I overlaid the graphs by Photoshop. I made exponential decay graph transparent and put on the temperature graph. You can see that the temperature graph is **left part** of exponential decay graph.

### Feb/28 Very warm => Cold

The temperature graph is **central part** of exponential decay graph.

### Mar/1 A bit warm => A bit cold

The temperature graph is **right part** of exponential decay graph.

## If insulation power changes, λ changes

As shown in above, if conditions such as heat generation inside of the car and heat insulation are same, * difference *graph follows the same curve. It is not affected by outside temperature, only by value of

*.*

**difference**If you add or remove insulation, **λ** changes.

As shown below, if λ increases, temperature falls rapidly, and it represents removing insulation.

**Graph 1** N=90, λ=8

**Graph 2** N=90, λ=14

## Conclusion

If you find N and λ of your car, you can predict value of * difference *(= inside temperature – outside temperature) after given time.

### Example

If you heat inside of the car up to 40 degrees warmer than outside, it will take

(0.33-0.12)= 0.21 day = **about 5 hours **until * difference *goes down to 10 degrees.

On the other hand, if you heat up to 20 degrees warmer, then it will take

(0.33-0.22)= 0.11 day= **about 2.6 hours** until * difference *goes down to 10 degrees.

Provided that radiant heat like sunlight does not come in.

Thank you for reading my article.

## Note

The original article was written and published on Mar/18/2018.