half pyramid – any math whizzes out there

[Dwight Shackelford]

Here’s something I’m ponying up to try to make a half pyramid tent without seams on the roof edges.

I’m making some assumptions here that the back width of the tent will be twice the width of the fabric itself. This thing is not to scale though. The pentagram is automatically being dimensioned by my graphics program. I couldn’t tailor it like I wanted.

I tried trig, but I kept coming up with two unknown variables. Through some geometry inspection, it seems that the angle between the door line and the foot of the side wall needs to be 90 degrees.

I’ve been trying to find a formula that I could use to exactly place points for cutting, and my trig is too ancient to get far right now.

I know I could lay this thing out with a large compass, which is likely what I’ll do. I was just trying to calculate the x and the y of that 90 degree point (B) to do it in a Cartesian way so it would be easier to make a pattern that others could use.

If someone had a formula that someone could just plug in fabric width, apex height, and tent width, that would be wonnamous.

This thing is not proportioned right. I just eyeballed it to get the angle to approximately 90 degrees, and wasn’t totally successful. This is a depiction of the fabric flattened, not of a floor plan.

Though my geometry verified it should be 90 degrees, logically it seems like it should be 90 degrees also, because when you’re looking from the side of the erected tent, and the front of the tent is making a 90 degree angle with the ground, and the sidewall are squared to the whole floor plan, the front of the tent should make a 90 degree angle with the side wall floor line.

[Bill Fornshell]

Dwight, Check out the early part of

This Thread where I made a lot of card-stock models. The models were made to scale so the real measurements were easy to figure when I got something I liked the looks of.

Once the model is finished you can cut one seam open and lay it flat on a scale drawing of your fabric size and see if it will fit.

[Dwight Shackelford]

I’ll probably need to try that, at least to get the basic formulas worked out. After that, I like to load them into a spreadsheet and try out different heights, widths, etc, to quickly see what I get.

If I get the formulas worked out.

[Michael Martin]

Dwight-

You’re right, you get two equations with two unknowns as follows:

taking the center of the bottom edge as the cartesian origin, x and y are variables giving the coordinates of your point “B”, w = fabric width, h = height…

1) (w-y)^2 + x^2 = sqr(w^2 + h^2)

2) (x-w)^2 + y^2 = sqr(w^2 – h^2)

These two equations can be solved by hand substitution (have fun!), or with matrix or simulatious equation solvers in most scientific calculators. I’m not sure how to easily do this with a spreadsheet. Any Excel power users know how to handle simultaneous equations?

Looks like a fun project. Good Luck!

Cheers,

-Mike

PS – I haven’t checked these two equations… Always possible I botched the math. ;-)

[Anonymous]

Dwight,

Have you tried using a 3D Cad modeling program and build a virtual tent? As you change / modify your design it could tell you the amount of materials needed and overall weight making the design process a snap.

[Dwight Shackelford]

It seems to become easier to visualize once you start drawing it out within a circle, with the floor lines becoming arcs. Using geometry instead of trig and algebra. Then you can see some relationships that are like “doh, of course”.

That point out there will always be on a 90 degree angle, because its half of a equal sided triangle. I’m getting closer I think, but still got some work to do. Now I’m trying to figure out how to calculate compound angles. I’ll probably backtrack from that again.

It will be easy as hell to do with a large compass. No calcing at all, except the door line and the side wall line, and that’s just hypotenuse stuff.

[Dwight Shackelford]

Any free 3d cad programs about? Or really cheap?

Sorta fun though, dusting off the cobwebs of all that geometry and trig. I used to be pretty good at it.

Or maybe I could do some orthogonal projections. Dust off my old drafting training.

[Vick Hines]

Dwight,
Don’t go all technical on this. Just get a planning pad and a compass. It will all become clear.

[Dwight Shackelford]

Not get techie????? I’d have to change my whole personality.

Nah, when I get home I’m going to get the compass and pad out. It would take too long to learn the cad thing.

[David Olsen]

A string, thumbtack, pencil or sharpie and large table.

[Dwight Shackelford]

I took a cue from Bill and just started lining this out within a circle, and also paying attention to how the pyramid sides would hinge on each other as the lay within the circle.

I’ve found an interesting relationship that I kept running into when using trig and such, and I didn’t trust it because my fabric length was exactly twice my fabric width, and I thought it was a fallout from that.

Though its harder to be exact when just drawing it with straight-edges, I did use totally different ratios than when I was doing trig.

Anyway, here is what kept popping up, and it seems to be a slam dunk for getting the points, but I don’t mind being proved wrong.

I tried a small paper model, and it seems to be correct. I’d have to expand it to see. Again, this particular drawing is not exactly to scale, so I wouldn’t try measuring the drawing to see if it’s right. I just tried to tweak a shape my program draws automatically, for representation purposes.

Dwight

[Dwight Shackelford]

I just went back to my trig spreadsheet and plugged in the parameters for my hand drawn tent, and the lengths for those two dimensions are not exactly the same, though very close (73″ vs 74.65). Probably just a coincidence for the particular framework I’m working within.

[Dwight Shackelford]

Bill,

After I ponied my up, I went back and read your dimensions. Looks like we’re really close. I think I want to go deeper than 36, but the 48X90 matches what I came up with just by drawing lines where they didn’t touch a little box representing my comfort area.

Have you tried that tent in some wind?

[Sam Haraldson]

Google offers a free CAD-like program called Sketch-Up. I’m only mentioning this because I noticed a call for possible programs. I cant’ attest to it’s prowess in this particular application.

I know it allows users to draw 2-D shapes and then extrude them into 3-D shapes which is basically what we want to do here. It may however have limitations.

http://sketchup.google.com/

[Rich DeLuca]

Dwight,

I hope this helps with answering some of your angle questions. I have access to a pretty good CAD program and I decided to model a half pyramid tent. Take a look at the pictures below to see how a 90L x 48w x 48H tent unfolds. This isn’t a mathematically “perfect” representation as I was modeling the tent in Sheetmetal and then unbending it; the software uses bend allowances to make the flat pattern. Anyway…check out the pictures and the dimensions. If you want me to model the tent with different dimensions let me know.

Later that night….

I’ve been thinking about this and there seems to be something wrong with my flat pattern. I’ll leave the original post for now but I plan to double check the model tomorrow.

[Anonymous]

Dwight, Sam & Rich,

Although I work primarily in AutoCAD, I tried downloading Googles free Sketch-Up software. It may have some limitations but is very intuitive to use. This drawing took me less then 3 minutes to draw.

[Sam Haraldson]

Roger – I think we need to teach that model in your drawing about the use of backpacks. They look mighty uncomfortable carrying that odd-shaped box around.

And Rich, thanks for those great graphics of the “metal” tent. I couldn’t help but giggling, thinking about a rigid metal pyramid tent.

[Rich DeLuca]

While I can’t get to my CAD software right now, I can get to a spreadsheet. In my first read of your problem statement I glossed over the fact that you wanted to avoid seems in the tarp. Like you and Michael pointed out there are two equations but there are three unknowns (x,y, & h or depth depending on how you formulate the equations). I created a quick spreadsheet that plots the pattern taking fabric width and tent depth as inputs. You could use height instead of depth is that is more important to you…either way you will be making a tradeoff.

[Dwight Shackelford]

Is it possible to get a copy of that spreadsheet?

I’ve been fooling with SketchUp this evening, and could not get it to do a double truncation like the pyramid. I could make extruded triangles only.

How you do dat?

[Sam Haraldson]

Like I said, Dwight, SketchUp probably has it’s limitations. It’s primarily for shape-massing architectural layouts.

We can go places wit Rich’s software and spreadsheet though.

[Dwight Shackelford]

Looks like he made it do the tricks required to do what he wanted though. I don’t think it will then give you a flattened cut pattern, but at least you can test out dimensions.

[Dwight Shackelford]

From looking at the spreadsheet layout, it looks like my assumption that that angle at that point needing to be 90 degrees might be wrong.

But I’m still not sure of that. Since its the base of a side, cut in the middle up to the apex, seems like it should always be 90 degrees between the center line and the base line.

[Rich DeLuca]

Just give me an email address and I will send it to you.

-Rich

[Anonymous]

Sam

How dare you speak of the young lady in the CAD drawing as “That Model”…
Her real name is: 2D_Woman_Standing_Sandra.

I’m not sure how hurt she feels about that demeaning title but if she feels that offended I suppose I’ll have to go to the sampler library and replace her with some of the following possibilities: 2D_Women_Sweater, 2D_Man_Backpack, 3D_Man_Walking or maybe even a LDSCP_Shrub_2D.

[Dwight Shackelford]

zydeholic at yahoo.com

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