How do you guys think the Nav's dead reckoning would cope with 245/40R18s? Any change in where it "thinks" it would place you? Is there a way to tell the computer what tire size you're running, or does it just assume you're always running a 225/45R18s?

 

will the new tire size change your speedometer readings? will your shift points change? I think the NAV receives a tach signal (I would have to look into that). If NAVI assumes 2K RPM=65MPH and the tires change the RPM, then it may not be as accurate. I would assume a small tire change will not affect NAVI.
The system uses three methods to calculate (GPS,internal gyro,and speed signal) in most cases your GPS will keep the system accurate.

 

The speedometer readings will change to read about 1% higher than what they should be with the new tires. The shift points should remain the same (I drive a manual), but if the nav makes the assumption that a certain RPM and gear equals a speed, then yes it would be off. My main concern would be that with my slightly sub-par gps signal, I wouldn't want to jack with the other main way the nav determines where I'm at. If I had the GPS signal strong, it's a no-brainer, 1% isn't much, but I have no idea how the nav determines position.

 

If memory serves, the navigation system adapts to new tire sizes by using a combination "perceived distance" through what it believes the wheel sensors are telling it and the "actual" distance travelled by the GPS receiver. There are basically three conditions that are going to cause the navigation's dead reckoning to get out of kilter. All of these assume an absence or serious degradation of the GPS reception AND one of the following.

The first, and probably most dramatic, is going to be moving the vehicle with the system turned off. This really only applies to folks that have to use a ferry or auto-train. Or a more common case would be getting towed.

The second is roadway realignment or new construction. There's plenty of construction around my house and the period that my GPS was misbehaving made this point obviously clear. In my case the roadway shifted to the left significantly for a new intersection and after turning right it eventually came back. Unfortunately when it came back it might be 50-100 feet off. The road matching would try to correct for it but sometimes it would just plain get lost.

The third condition is obviously tire diameter, which you've discovered. If you check the navigation system owners manual in the back of your normal manual on page 34 you should see a description of Automatic Distance Correction. It points out that tire pressure and wear can contribute to different correction coefficients. It also points out that using a spare tire (or different sized tires) can affect it as well.

In all of these cases the recommended solution is drive while the GPS is operating. In my case I had little to no reception and was constantly having to update the car's position and direction using the setup menu.

The accuracy of the dead reckoning is going to be based on the gyro readings and how far the car "thinks" it has travelled. In your case, the smaller tire size is going to affect that distance some. If your GPS problems were as bad as mine you may spend some time repositiong the car manually until the coefficent catches up.

 

I like Pavehawk's explanation, very well done
It sounds like you will need a strong GPS signal if you want to stay on course.