Paper model question

Good morning (at least it is morning here...)

From time to time, there have been posts here about paper models, so I'm hoping that at least a few of you are experienced wnough with them to help me out with this one...

What is the math involved to lay out a "flat" piece for a roof that when cut & assembled, will have a certain amount of slope to it? If I laid the roof out flat for a 90° corner, then tried to put some slope to it, the angle that the two pieces formed would be something less than 90°. I'd like to know the math involved so that I can figure roof slope on ANY angle that I might encounter. This has to be pretty easy, but I'm stumped.

Anyone know?



------------------------------------------- Dan L. Merkel

Reply to
Dan Merkel
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A squared plus B squared = C squared-- A is the length of the flat part of the roof you are covering B is the amount of drop at one end for the slope C is the length of the piece you have to cut for the sloped roof.

Use a calculator to do the square root of "C squared" unless you have a clue on how to mathematically do square roots. Suggest you do the measuring of A and B in real-life measurements using a scale ruler, then convert the answer(square root of C) to whatever your scale requires to avoid complex squaring of lots of fractions. You will find that the answer "C" is just an itty-bit larger than "A", assuming the drainage slope is very modest.

Reply to
Carl Saggio

Like he said, A squared + B squared = C squared.

I'd assume you have the height of the roof peak (whether it's a center ridge or a sloping shed roof, you probably know that distance rather than know the angle of the roof slope), and the horizontal width a roof panel needs to cover. Call the peak height above the wall top A, call the width B (half the width if center ridge, all if shed). Calculate the square root of (A * A plus B * B) - in the classic 3-4-5 right triangle example if A = 4 and B = 3, then C = 5 ( 9 + 16 = 25, square root of 25 = 5 ). Add whatever eave overhang you need.

Of course, you could always just lay it out on paper or on a computer and measure the length of the hypotenuse.

I recall seeing somewhere - a reference here, or perhaps in an article in MR or RMC - a calculator for determining the shape of "pie wedge" panels for 6 or 8 sided roughly conical roofs such as on top of water tanks.

Reply to
Steve Caple

Good evening Dan;

Know any rough carpenters? They use rise/run - 4/12, 6/12, etc. A 4/12 ratio will give you 1' rise per 3' run, a 6/12 ratio will give you 1'-6" rise per 3' run.

Cheers, John

Reply to
John Fraser

Sounds like a carpenters question/issue... the only thing I can add is the "Carpenters Lament"... 'I cut it twice and it's still too short..'


John Fraser wrote:

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I am assuming you are having trouble with the compound angles of a hip roof, not an ordinary gable. The easiest way to lay this out is to copy the ancient Greeks and use plain old geometry:

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First draw the roof's end and side view. Measure the length of the ridge A, long eave B,and long-side slope E. Draw the ridge A on your roof material. Draw two parallel lines of length B, each a distance E from the ridge line, on opposite sides, with their midpoints lined up with the midpoint of A. Connect the ends of these eave lines to the ends of the ridge line. You now have your long sides.

Now set a compass to the length of short eave D on your end view. Place the compass point at the end of a long eave B, and draw an arc. Set the compass to the length of end slope C, place the point at the end of ridge line A, and draw an arc that intersects the arc just drawn. Draw lines from this intersection to the ends of lines B and A; the triangle formed is the shape of the roof end, joined to the long side.

This will work quite as well with styrene if you score and snap the parts apart; you can also use it to make a paper template for cutting your roof material.

Cordially yours: Gerard P.

Reply to

Ack, I screwed it up. You can use C, but not the way I mentioned.

[To use C, set the compass to length C and draw an arc centered at V1. Draw a straight line through V2 and tangent to this just-drawn arc, which will intersect the arc of radius D centered at V2 described above. From this intersection, draw a straight line to V1]
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Don't bother with math, just draw it. You're going to draw the parts of the card model anyhow, so you may as well make a couple of preliminary drawings first to get the measurements right.

You need a side view of the building with roof, and an end view. Make sure you draw the correct overhang at the eaves, too. And make sure it's to scale. If you're precise enough, you can draw it in the scale you're modelling. Otherwise, better to draw it to 1/2" scale or larger - a larger drawing will have a proportionally smaller measurement error. You'll get some error when you transfer the measurements to the card for cutting out, anyhow, so the smaller the error in the dimensions, the better.

Gable end: consists of two rectangles. The length is taken from the side view, it's the length of the eaves or ridge. The width from the end view

- it's the length of the eaves from peak to gutter.

Hip roof: consists of two trapezoids and two triangles. The trapezoids' two parallel sides are taken from the side view. Their height is taken from the end view: its the length of the eaves from peak to gutter. The triangles' height is seen on the side view: it's the distance from the ridge to the gutter at the end. The triangles' width is measured from the end view.

That's all there is to it.

Have fun!

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