Pitched Bay Roofs - What's the angle?

[barrie.sharp]

This is a question about compound angles. Normally do these using trial and error but want to be a bit more methodical using maths.

Please refer to the attached jpg. Given W, D and angles A and a, What are angles B and C. Any solutions will be gratefully recieved. :beer:

[mthurnauer]

In your example, it would appear that all of your roof surfaces would have the same pitch.

[barrie.sharp]

In your example, it would appear that all of your roof surfaces would have the same pitch.
It would appear that way but they are not. The difference can be anywhere from 1-4 degrees depending on the bay proportions. Sounds small but the difference can look substantial. Try to replicate the scenario to see what I mean. It's an equation I'm after.

[bvpe]

It appears that all of the roof planes meet at a common elevation at the low end of the roof. Call this the fascia point or fascia elevation. All of the roof planes would thus have the same rise or vertical height change from the fascia point to the ridge. You should determine by measurement the run or horizontal projection of each roof plane onto a horizontal plane that passes through or is positioned at the same elevation as the fascia point. This then would give you the rise and the run to use rise/run=pitch/12 and basic trig or put the pythagerum theorm to work to calculate the pitch angles of each roof plane. Alternatively, draw a line in the plane of the aforementioned horizontal plane that starts at the intersection of the hip lines with the ridge, the other end of the line would be perpendicular to the fascia line. This gives the run of the roof plane projected onto the horizontal plane.

[barrie.sharp]

It appears that all of the roof planes meet at a common elevation at the low end of the roof. Call this the fascia point or fascia elevation. All of the roof planes would thus have the same rise or vertical height change from the fascia point to the ridge. You should determine by measurement the run or horizontal projection of each roof plane onto a horizontal plane that passes through or is positioned at the same elevation as the fascia point. This then would give you the rise and the run to use rise/run=pitch/12 and basic trig or put the pythagerum theorm to work to calculate the pitch angles of each roof plane. Alternatively, draw a line in the plane of the aforementioned horizontal plane that starts at the intersection of the hip lines with the ridge, the other end of the line would be perpendicular to the fascia line. This gives the run of the roof plane projected onto the horizontal plane.
That's kind of what I'm after. This is easy for the side pitch using simple trig and will help me define the ridge location. Where I get stuck is with the angled corner planes. To make them meet, I have to use the side run and corner angle to calculate the projected run for the corner plane. If I used the corner angle for theta and the side run for the adjacent, would the opposite give me the corner planes run length?

[bvpe]

Say "W" is the out to out of the fascia line of the main roof span and "a" is the pitch angle of the this main roof. If "C" is the pitch angle of the hip end roof, the intersection of the hip end roof plane with the main roof plane defines the end of the roof ridge line. In plan view, draw a line from the end of this ridge line perpendicular to the fascia line of the roof plane on the angled wall. This is the run or projection of the angled roof plane onto a horizontal plane, which you already know the vertical distance from the fascia elevation to the ridge. Again, this gives you the run and rise of the roof plane associated with the angled bay wall.

[barrie.sharp]

It's still confusing me how to project an angle at an angle. Can you look at my family and advise what the formula is for 'Corner Pitch'. The rest was fairly straight forward but this one piece is eluding me. There is a ratio using Corner Angle to factor for the adjacent against a projected adjacent but I can't work it out.

This has now become a family based question if anyone can move it?

[barrie.sharp]

The ratio is a funtion of sine but can't quite shoe it in. I have updated the family

[barrie.sharp]

Bump. Anyone have any ideas?

[barathd]

Barrie:

This may not be what you want however here is what I do. I refuse to struggle with these roofs so I always resort to using perfect polygons and then all the slopes are the same. Very simple.

Good luck.

[barrie.sharp]

Barrie:

This may not be what you want however here is what I do. I refuse to struggle with these roofs so I always resort to using perfect polygons and then all the slopes are the same. Very simple.

Good luck.
I hear what you're saying but the family is almost there. It's also about learning the maths. I want to be able to create powerful families and let Revit do all the work, surely that's the point? I'm just missing something and hoped someone would understand the trig. :beer:

[DoTheBIM]

I had a brief look at your family. Usually the corner pitches are a result of the the side and front pitches, but you have front pitch as being a calculated value. Which seems confusing to me. How would you calculate the front pitch if you don't have the corner value? You don't know where the peak line is going to stop without having 3 known pitches.

I usually just do the math manually while creating the roof...This confuses many users as their math skills just aren't there to understand what's going on. Not a shot at them, just not their forte or patience for understanding it. I attempted to make it easier for them by showing them how to use slope arrows and not having to know the corner pitches but just a height measurement at the peak, but Revit barfs at me saying it can't create the roof. BOOOO! So now they rough the roof in, then take a section perpendicular to the corner, sketch a line from the eave to the peak, use the spot slope tool to get the pitch, then edit the roof to put the pitch in for the corner planes.

[barrie.sharp]

Usually the corner pitches are a result of the the side and front pitches, but you have front pitch as being a calculated value.
There is a relationship between the front and the corner determined by the sides. I have set the front pitch to be driven by the corner angle so that meets with corner angle's perpendicular line. This made it easier to rationlise the sine adjustment. This is a work in progress of course and I would like to add front pitch as a variable once I get my head around it. I think it would either require a formula for sine or I would have to drive the perperndicular instead of eq'ing it.

Meanwhile, good news!!! I have the formulas working :-D. It all meets at a peak. Have a look and see what you think. 10 points to whomever frees up the front pitch.

[DoTheBIM]

There is a relationship between the front and the corner determined by the sides. I have set the front pitch to be driven by the corner angle so that meets with corner angle's perpendicular line. This made it easier to rationlise the sine adjustment. This is a work in progress of course and I would like to add front pitch as a variable once I get my head around it. I think it would either require a formula for sine or I would have to drive the perperndicular instead of eq'ing it.

Meanwhile, good news!!! I have the formulas working :-D. It all meets at a peak. Have a look and see what you think. 10 points to whomever frees up the front pitch.
I think you've made the front pitch calculation more complicated than it needs to be. Technically you've calculated the front pitch to be the same as the side pitch. except that your angle dim is above the slope instead of below the slope (like the side pitch angle dim).

All of this -- atan((Corner Pitch Offset * tan(90° - Corner Angle) + (Bay Depth - Side Length) / 2) / Pitch Height) -- can be simplified to 90-Side Pitch.

And for that reason you can just leave the front pitch calculation empty and have a flexible front pitch and redo your corner offset calculation so that it accounts for the peak location moving as the front pitch varies from the side pitch.

[barrie.sharp]

I think you've made the front pitch calculation more complicated than it needs to be. Technically you've calculated the front pitch to be the same as the side pitch. except that your angle dim is above the slope instead of below the slope (like the side pitch angle dim).

All of this -- atan((Corner Pitch Offset * tan(90° - Corner Angle) + (Bay Depth - Side Length) / 2) / Pitch Height) -- can be simplified to 90-Side Pitch.

And for that reason you can just leave the front pitch calculation empty and have a flexible front pitch and redo your corner offset calculation so that it accounts for the peak location moving as the front pitch varies from the side pitch.
LOL.:Oops: Talk about being to close to the problem! I tried driving the front pitch from the base but it wouldn't take it so I had to drive the opposite angle. From that moment on, I didn't see the connection. I'll try to work out the corner offset calc, that's the tricky onebecause it travels the hypotenuse of the corner angle. :beer:

[barrie.sharp]

Just played around to get the front pitch dim on the right side. It worked when I added the dim and added a fresh parameter. I then just transfered the formula across. I noticed at that point that my thinking was correct, the front pitch is entirely unique. I have updated the family above. If you flex it, you'll see that the three pitches are different values. Still have no ideas for offsetting the perpendicular line.