Breezeway Roof Geometry

This has been driving me crazy. Based on careful measurements of the weird triangles where the breezeway roof extends down to the garage fascia, the breezeway ridge should be a little higher than the garage ridge. And yet, we can see that it is actually slightly lower.

Note the taper on the right, indicating that the breezeway is steeper than the garage.

Clearly, the breezeway ridge joins the garage just a little lower than the garage ridge.

The other "evidence" that the breezeway ridge is higher is that the opening from the main house seems taller than the calculated elevation shows.

If the ridge is lower than the garage ridge, the height of this opening is about 24". If we let the breezeway ridge be where it calculates to be, the height is 31".

The solution may be that the breezeway ridge slopes down to the garage. Things are pretty loose--the roof is just 2x4s with a 1x6 ridge. We're only talking about 7".

What do you think? Is it possible the ridge to the right of the electrical mast drops as much as 7"?

Further investigation shows that the eave on the north is 26", but the eave on the south is 22", which means either that the ridge is not centered on the breezeway walls, or that the pitch is different front and back. My guess is that the ridge isn't centered, but it's very difficult to judge.

The breezeway as seen from the garage. Note the heretofore unknown 1/4" hardware cloth screen. The blue 1x6 is an insulation dam--there is blown rock wool on the other side. 

To keep things straight, I've been using elevations--260 for the garage floor, 263 for the main house--but I realize that I'm trusting the GeoDimensions survey. It's hard to confirm within a 1/4" that the floors are exactly 36" apart.

If the main house is 263, the finished floor in the breezeway is 262.9583. That puts the breezeway ceiling at 270.5416. The breezeway eaves align with the main house eaves at 269.8333. The 1x6 fascia has a 1/2" reveal below the eave, so the top of fascia is 5" above the eaves: 270.25. The ceiling in the main house is 92-1/2", so the plate is 270.75.

Clearly, the width of the eave determines the elevation of the eave relative to the plate line. Unfortunately, the main house eave is 2'6" at the north porch and along the east wall, 2'5" at the south and the west wall of the kitchen, and 2'5-1/2" at the west wall of BR2. It's close enough to avoid offending the eye, but hardly precise.

At the breezeway, the eave is 2'2" to the north and 1'10-1/2" to the south. (The 3-1/2" difference seems related to the 2" bump out for the electric panel.)

The miter where the west wall of BR2 meets the south breezeway eave is offset because the eaves are the same elevation, but different widths.

At the garage, we can measure the plate accurately due to the lack of a ceiling. The plate is 269.375. The garage is 20'3" wide outside face of stud to outside face of stud. Unfortunately, we can't just solve for a triangle 10.125' on one side with an angle of 4:12 (18.43°) because the top of the roof is a few inches above the plate. If we assume that it's 4" above the plate (see drawing, above), the garage ridge is the plate (269.375) + 4" (0.33) + the opposite side of the triangle (3.374) = 273.079.

The breezeway is 10' wide (ignoring the electric panel bump-out). With the north and south eaves, that means the roof is 12' 0-1/2" (12.04167), so the base of the triangle is 6.02083. Starting with the calculated top of fascia, 270.25, the breezeway ridge calculates to 272.25 at 4:12. We know it is steeper than the garage, however, due to the tapering valley shown in the first photo and here:

This triangle is a clue, but it is not definitive. (For example, the roof pitch is not as dramatically different between the garage and the breezeway as it appears here.)

The breezeway ridge should be 272.7587 if the pitch is 5:12. Hold that thought and let's consider the triangle in the photo above.

The height of the triangle is the distance between the top of the garage fascia (268.75) and the top of the breezeway fascia eave (270.25), or 18". The base is hard to measure, but it seems to be 35. That's an angle of 27.216, which is steeper than 6:12. This puts the ridge at 273.346.

Let's calculate it another way, based on the observation the breezeway roof seems to land at the north wall of the garage. The wall in question (the east wall of the garage) is 69" wide from the front of the garage to the north wall of the breezeway (ignoring the electric meter pop-out), or 43" from the front of the breezeway fascia. Bottom of breezeway fascia to bottom of garage fascia measures 17-1/2" (confirming previous calculations), which gives us a triangle with an angle of 22.714, very close to 5:12. This puts the ridge at 272.77.

So, the breezeway ridge ranges from 272.7587 (5:12) to 273.346. What's 7" among friends? Based on how the breezeway hits the main house as seen from the street and from inside the main attic, I'm inclined to take the higher number. From the first photo, it appears that the breezeway ridge connects at least 2" below the garage ridge (273.079, for a connection at 272.912333).

If we say that the breezeway ridge slopes about 3" before it connects with the garage, then the main breezeway ridge can be 273.16667, an inch higher than the garage ridge.

All this precision around a roof that was clearly eyeballed seems crazy, but it has to fit together like a puzzle.

Basement floor	256.08
Garage, BR3 floor	260.0
Breezeway floor	262.9583
Main floor	263.0
Breezeway ceiling	270.5416
Main ceiling	270.70833
Garage plate	269.375
Main plate	270.75
Top of garage fascia	268.791667
Top of main fascia	270.25
Garage eave	268.375
Main eave	269.833
Breezeway ridge	273.167
Garage ridge	273.08
Main ridge	277.16