Non Linear Gauges and Exploding Jeeps

On Friday, November 13, I drove back home to San Jose from Las Vegas. The drive is a long one, and requires a lot of energy. In the last year, I have made it several times. It takes me just about nine hours and 20 gallons of gasoline to supply the motive force that compels my Jeep to travel the 515 miles from the middle of the Las Vegas strip to my house. The drive takes me through about 300 miles of the Mojave Desert and 140 miles of California’s Central Valley. See Figure 1.

Figure 1  Las Vegas to San Jose

Figure 1 Las Vegas to San Jose

In the last few months I have had a few problems (about 8K bucks worth) with my Jeep, so when I drive it now, I keep my ears open for sounds that might indicate approaching danger and my eyes on the Jeep’s instrument panel gauges for indications of imminent vehicle
failure and/or the end of the universe. See Figure 2.

Figure 2  Jeep gauge panel

Figure 2 Jeep gauge panel

Just this last August, 2009, I left the Flamingo Hotel in Las Vegas at 2:30 AM to make the drive back to San Jose. About 50 miles out and in the desert, I started getting a clanking sound at about 70 mph. I slowed down to 65 mph and the clanking stopped. But then it started again at 65 mph. I slowed to 60 and it stopped. Then it started again at 60 mph. This was not good, I thought. I am in the middle of desert at night and my car is going to break down and strand me. I will die a horrible death, my bones being picked clean by buzzards near Zyzzx Road. I don’t know much about scavenger type birds, but this is what I imagined. See Figure 3.

Figure 3  Zzyzx Road near Baker, CA

Figure 3 Zzyzx Road near Baker, CA

I get chills just thinking about it even now.

My Jeep did not break down and I was able to limp home without incident. It turns out the problem was in my transmission. I forget now what the part was called, but I do remember it cost me 22-hundred bucks to get it and install it.

Staring just this last July, 2009, the “check engine” light on my Jeep’s instrument panel began illuminating. It first illuminated when I was in Los Angeles putting gas in my car to start the 265 mile drive to Las Vegas. Just what anyone would want to see, the check engine light. What light could be worse? Of course the check engine light must be Jeep’s way of politely saying, “impending and inescapable engine explosion.” See Figure 4.

Figure 4  Denny's Jeep exploding

Figure 4 Denny's Jeep exploding

I drove to Vegas anyway. I was nervous the entire trip, but I still went. Then, with the light still on, I drove around Vegas for a few day, then drove the 520 mile back to San Jose.

My mechanic checked for the cause of the light. His diagnostic machine announced the cause of the problem as, let’s just call it Mistaken Cause 1. He fixed it. Three hundred miles later, the check engine light pops back on. The diagnostic machine states the cause of the problem as, let’s call it Mistaken Cause 2. To make a long story shorter, the cause was not found until after $1200 worth of Jeep parts. The Jeep dealer finally correctly determine the cause to be an 80¢ fuse.

Now I am always nervous about the ability of this car to operate in a way that will not leave me stranded in the middle of the Mojave Desert in the 150 degree summer heat or the biting winter cold.

When I drive my Jeep now, I am constantly aware of noises and smells and clunks and jerks. I keep a close eye on my instrument panel gauges.

So Friday on my drive back to San Jose from Las Vegas, I am on Highway 58 passing the Desert Sage apartments near Edward’s Air Force Base and the town of Mojave, and I check my water temperature gauge. I expect to see the needle in the standard operating zone just slightly to the left of 210. But its not! Oh no, it is just slightly to the right of 210. It is never there, it is always just to the left of 210. I am sure my engine is overheating and ready to explode. See Figures 5 and 6.

Figure 5  The bad zone and the good zone

Figure 5 The bad zone and the good zone

Figure 6  The Desert Sage Apartments near Mojave

Figure 6 The Desert Sage Apartments near Mojave

To delay engine explosion, I back off on my speed from 65 to 60. Ahh, the temperature gauge needle moves to the left back into the standard operating zone. All is well. I speed back up to 65. The needle moves back to the right in the engine explosion zone. Oh no, I am 300 miles from home and my car is about to ignite into flames.

But now I have another problem. I am having trouble reading and making sense out of the water temperature gauge. Check out the increments on both the fuel and oil gauges. See Figure 7.

Figure 7  Fuel and Oil and Water temp gauges

Figure 7 Fuel and Oil and Water temp gauges

I think they read as one would expect. Each increment is the same. That is, the scale is linear. In the case of the fuel gauge, each increment is 1/8 of a tank of gas. In the case of the oil gauge, each increment in 10 psi. Count them. The oil pressure starts at 0, then with markings at every 10 units, goes to 40 psi then to 80 psi. Forty psi is right in the middle between 0 and 80 psi, right where we would expect it to be. These scales are linear as they indicate constant change.

But look at the increments on the water temperature gauge. What the? The increment lines are evenly spaced, visually giving us the idea that the gauge is set up linearly. But look closely at the numbers. Visually 210 is halfway between 100 and 260.

If the scale is linear between 100 and 210, then each increment represents an increase of 27.5 degrees.

(210 – 100)/4 = 27.5

If the scale is linear between 210 and 260, then each increment represents an increase of 12.5 degrees.

(260 – 210)/4 = 12.5

So not each tick mark represent an integer value water temperature. The tick marks represent:

100
100 + 27.5 = 127.5
127.5 + 27.5 = 155
155 + 27.5 = 182.5
182.5 + 27.5 = 210
210 + 12.5 = 222.5
222.5 + 12.5 = 235
235 + 12.5 = 247.5
247.5 + 12.5 = 260

This looks like a crazy way to design a gauge to me. There must be some logic to this as I want to believe that Mr Jeep would not be joking around with me while I am in the middle of the desert.

Now I worried about high water temperatures and crazy gauges. I am in the middle of the desert and I am about to drive uphill into the Tehachapi mountains. I am sure my water temperature indicator needle will move even farther to the right, my car will overheat and my engine will explode, taking me out as well as all the cars around me.

It didn’t happen. I eased the Jeep up the mountain, the needle bounced back and forth between OK and Explode and I made it to the summit. Once there, I could drive without putting much of a load on the engine, keeping the water temperature in the safe zone. That went well.

When I got down the mountain and into Bakersfield, the needle stayed in the standard zone and all was well.

Driving north on Hwy 5, I tried to figure out why the needle moved to the right when I was in the desert. The outside air was cool and I was at a high elevation. Both these features I thought would keep the water temperature low. But if the Jeep really is running well and is not experiencing mechanical problems, there is something else going on. I am thinking about the gas laws and I will explore that this week.



3 Responses to “Non Linear Gauges and Exploding Jeeps”

  1. Jessica H Jessica H says:

    I’m glad to hear that your car didn’t come to an impending and inescapable engine explosion and I hope (aside from the near attack of flesh and bone picking penguins)you had a good time in vegas =]

  2. Denny Burzynski admin says:

    Hi Jessica, its nice to hear from you and know that you are reading the blog and still thinking about mathematics. Once you get interested in mathematics, you are hooked. My car seems to be running just fine right now, thanks. I asked my mechanic why the temp gauge climbed above the midpoint and he gave me the “moths-stuck-to-the-radiator” theory. He said it could have been too many moths collected on the Jeep’s radiator and that caused less air to pass through to cool the engine. I don’t think so. I still cannot explain it. I thought the gas laws might help, but then realized that the water in the radiator was still liquid and not steam. I just hope it doesn’t happen again. Too much stress in the middle of the desert. Since my trip to Vegas, I have been to LA a few times. I have not encountered any penguins at all along HWY 5. I imagine they don’t do well too far from Zzyzx Road. And yes, I did have a good time in LV. I lost only $50 in a small poker tournament and ate at all of the In-and-Outs in SW Vegas. I keep up with things at WVC. Are you there this semester? When do you move on from WVC? To where and what do still plan on studying. There are openings in mathematics departments.
    –Denny

  3. Jessica H Jessica H says:

    Hey Denny =]

    Vegas sounds fun! I’m waiting for Brandon to turn 21, so the me & him can go try our luck at gambling.

    I’m still at WV, but hopefully next semester will be my last one. I applied to UC Berkeley, Davis, Santa Cruz and LA; San Jose State as well.I’m a psych major, so I do use a lot of the stats you taught me.

    Brandon and I always see this guy that walks around WV and from far away kinda looks like you. We are very disapointed when we see that it isn’t you. I think you have an imposter lurking around and may want to inform the authorities about this. haha.

    Take Care,
    Jessica

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