Hi! OK, all you mathematical types out there, here's a challenge for you! Say you have a first roof, at some pitch. You want to put a second roof at a 90d angle, which may or may not have the same pitch (like a garage). How do you cut this second roof on a flat sheet of wood to match up with the roof ridge (top) of the first roof?
Tony! What are you trying to describe? The solution is really quite simple and will not require any special math skills. GM [ March 30, 2006, 05:50 PM: Message edited by: GM ]
The roof of the garage show here: Is not a rectangle, but the odd shape above in orange. I need to know the angle A, given the size of the roof and the pitch. [ March 30, 2006, 06:32 PM: Message edited by: Tony Burzio ]
Tony, Thats, what I thought you might be after. The solution is a variation on the slope problem for determining the grade on a railroad track. Slope1 = Rise1/Run1 Slope2 = Rise2/Run2 Since the rise in both equations is equal, we can restate as follows: Slope1* Run1 = Slope2 * Run 2 You just plug the numbers you know into three of the variables in the last equation and solve for the remaining. Once you know the run on the second slope. You have the short leg in the triangle you show in the photo. Just looking at the picture, I suspect that the pitch on both roofs is a 4/12 which was common to those ranchers. You can check this out better by climbing up on a ladder with a level and tape measure. If Run = 12 and Slope = 4, then you have a 4/12 pitch roof. When you measure the rise, anything other than a nice integer inch indicates poor technique in your measurements or a very special roof. GM
Don't think y'all answered his question. I gathered he wants to know how to layout the roof on a flat sheet. There is no rise and run on the flat sheet, but there is an angle between the line which defines the where the two roofs meet (when the flat sheet is folded at the ridge line) and the edge of the roof. That's the angle he seeks, if I understood correctly.
Ray, It's kinda confusing isn't it The angle in the horizontal plane is 45°. All the carpenters I have worked with could lay that out in a second. Trouble is the angle he seeks is not the 45° shown in the plan view. The angle Tony thinks he wants is something less than 45°. When the sheathing for these roofs is cut, the value of the angle is not even considered. Instead, the carpenter will measure the strike in the valley from two place 4' apart on the plane of the roof. The difference in those measurements is the short leg of the triangle tony superimposed on that photo. It is also the difference in the long side of his red figure and the short side. About the only people on the construction site that work with angles are the Surveyors. All the rest of the trades avoid them like the plague. GM
A diagram with a few equations, courtesy of our old friend Pythagoras... Does this help? Do you see where I'm getting the numbers? If not, let me know and I'll try to "unpack" it a bit.
Ok guys Lets look at what Tony actually asked. "Say you have a first roof, at some pitch. You want to put a second roof at a 90d angle, which may or may not have the same pitch (like a garage)." Then he compounded the question by moving from the subject of geometry to methods of cutting materials. This second part of the question deserves a topic all by itself. "How do you cut this second roof on a flat sheet of wood to match up with the roof ridge (top) of the first roof?" The answer is not a single angle but a set of angles that range from 0° to 90°. Given a range of slopes for the two roofs there are many values that will satisfy his question. What I am curious about is how you measure, scribe, and cut the material to a predefined shape. After the cut is finished, how do you further prepare the edge to match the slope of the roof. Finally, does it really matter if the roof fits properly. After all, it is just a toy. GM [ March 30, 2006, 09:04 PM: Message edited by: GM ]
I usually just start out with more material than I need and keep trimming and filing a little till it fits. That is how I did the roof on this house that I scratch built. http://www.railimages.com/albums/Modeling-stuff-and-train-room/adh.sized.jpg
Hi Russell, That is a beautiful model! You should be proud of your work. If you were to remove the balusters from the second floor, and dispose of the fancy tops on the chimneys, you would be looking at a model of the last Prototype house I built. GM
Or you could go here, enter your dimensions, and find the sheathing angle of the adjacent side: http://ca.geocities.com/web_sketches/hip_valley_dimensioning/framing_working_points.html
Sorry, you're just making this all so complicated.... If you build a 'ridge line' out of a piece of vertical styrene, or stripwood, less the thickness of the intended material sheathing, you can measure the actual dimensions between all parts, on the actual model. Focus on getting the height right, then just measure and lay out the parts. I frequently 'frame' the roof just so that I can measure the 'sheathing' accurately. All the roofing on La Posada is cut styrene Faller sheet (spanish tile), and every one had to line up precisely. So the 'ridge line' was determined for every pitch, and the parts measured off the actual model. I've tried to use math for this, but the thickness of the material will throw you off every time. Faller styrene roofing is thick stuff, also expensive, and I can't afford to screw up pieces because my assumed/calculated measurements are wrong. The only time in my life I EVER used actual geometry on a model was in trying to draw and lay out the roof for the Flagstaff. But if you flip it over, you'd see the entire roof was framed up inside. Some kind of framing is invaluable so that you have a good place to glue to as well. You really can't depend on the sheets themselves to keep the proper alignment and geometry; that's the job of the framing underneath. You don't have to frame the roof in detail, but the function is the same. [ March 31, 2006, 08:17 AM: Message edited by: randgust ]
Randy has the best approach, for N scale. As he notes, the thickness will throw off all geometrical calculations, unless you take it into consideration, or bevel edges. In real life, carpenters did this with a carpenter's square, sort of a crude slide rule. I can calculate a mathematical solution, which I often do as a starting point. But actually fitting the piece requires some adjustments. And these are best done by the good old human eye.
