Forces created by fixed tarp in the wind

[Grinkle]

TL;DR Summary

If a fastened tarp has wind blown across it, what can one say about the lift it generates on the fasten points?

Consider a rectangular tarp with a grommet in each corner, and each grommet is tied to a pole in the ground with a short piece of rope, such that the grommets are basically fixed to the tops of the poles. The poles needn't be at equal heights and the tarp aspect ratio is not specific, in my questions.

Can one say anything in general about the shape a fixed tarp or sail ends up taking in a wind? Does it take a shape of max lift or min lift or something else when the shape is at equilibrium with the fastening points and the wind (ie when the tarp is no longer moving but is in some shape caused by the wind)?

The follow on question is the engineering one -

If one changes nothing in a given situation except the tarp is now tied to the fasten points at the ends of the poles by an elastic rope, so that the rope will stretch in the wind and allow the grommets of the tarp to come away from the ends of the pole for some distance, is the lift going to be any different at equilibrium? Will the forces on the poles be any different?

Wind is not steady, in general, and I think using elastic rope would introduce degrees of freedom that could resonate with the changing winds in some cases and not be a good idea (in plain English, the tarp would be likely to really whip around in changing winds). But anyway, while I was thinking about this I ended up being very curious about the questions above, and thought someone here might know. I haven't been able to reason it out on my own.

 

[Baluncore]

If the tarp is not tight, then it will flap in the wind until the corner grommets tear out, so I will assume the tarp is pulled tight to the top of the support poles.

You have not specified the height of the poles.

If the top of the poles are not co-planar, then the tarp will take a double curved shape like a saddle. That will probably be stable, and NOT flap in the wind. The lift will depend on the wind direction and the slope of the tarp surface in that direction. Elastic connections to the top of the poles will not change the stability of the tarp to flapping, but will allow more static deflection due to wind pressure in some situations.

If the top of the poles are co-planar, then the tarp, assuming zero mass, will rest flat. Depending on direction, the wind will cause the tarp to deflect either upwards with positive lift, or downwards with negative lift. It will probably switch between those two unstable positions, placing high loads on the grommets, and high side forces on the top of the support poles. Elastic connections at the top of the poles will quieten the banging sound of the tarp flapping between concave and convex, and will reduce the forces on the top of the poles.

You might define the support structure, or explain what you are trying to achieve.

 

[Grinkle]

Thanks very much for the response.

I thought a simplified scenario would be easier to describe and might give me enough understanding to apply my actual issue.

I have some triangular sun-sails (their function is to provide shade) attached at one point to the facia of my roof and on the opposite side of the triangle to a 2x4 that I have screwed into an existing brick wall. The triangle height of the sails are 8', and the distance from my roof facia to the wall is about 7', so the sails have some sag. There are three of them, they are alternating in orientation, so the first sail has one grommet on my facia and two on the brick wall, the second has two on my facia and one the wall and the third is like the first. They are not perfectly parallel to the ground, but I didn't put a deliberate tilt on them either, they are roughly flat, within the error bounds of an eye-ball only installation. The wind, of course, is not regular, so I don't know that it matters if I tilt the sails or not.

Sometimes there is significant wind blowing across these sails. The 2x4 attached to the brick wall has shown no issues. The facia on my house gets pulled away from the house frame over time. Its attached with framing nails and these get worked out of their holes after a few months of being pulled on by the sails.

So I wondered if I used elastic attachments instead of firm rope whether I should expect the load on the facia to be relatively lower or higher or not change.

What I am doing now, which I am not comfortable with but am living with it nonetheless, is to take a hammer and bang the facia back flush to the house every once in a while. I don't want to just screw the facia in, because I don't know if that will just transfer the problem to whatever I screw the facia into, back inside the frame of my house where things may pull apart and I won't even see it happening. I think I need to take the sails down unless I can figure out a way to not need to attach them to my house, but I haven't given up quite yet.

 

[Baluncore]

I think I need to take the sails down unless I can figure out a way to not need to attach them to my house, but I haven't given up quite yet.

Triangular sun shades will always flap in the wind, make noise, tear out the grommets, and damage the support structure. That is simply because a triangle is flat. It takes a doubly curved surface, with four corners and a stretchy fabric to be stable and not flap. A doubly-curved surface is formed when the four mounting points are not co-planar.

They make triangular shade sails because they look right, are easy to attach, so they seem to sell well, but they all flap in the wind. There are some rectangular shade sails available that do not stretch, so they also flap. The manufacturers do not care enough to get it right.

Make a rectangular shade from a knitted shade cloth that will stretch, (from the garden centre). Stitch a hem for a cord or a wire along each edge. Attach two corner points to the fascia at the same height, the other two corners attach to two points at two different heights on the wall. When it is tensioned, it will form the doubly curved surface that will not flap. Tension in the edge cords will pull the edges into a curve that will prevent flutter.

Now all you need is a sewing machine and the time to experiment.

 

[berkeman]

I have some triangular sun-sails (their function is to provide shade) attached at one point to the facia of my roof and on the opposite side of the triangle to a 2x4 that I have screwed into an existing brick wall.

Pics?

 

[Grinkle]

Here are the shades and a shot of what the facia looks like after a while. I mis-remebered the brick attachement, I guess I put the 2x4 on after the sails and to string the lights to - the sails are attached directly to the brick. That wall is actually the exterior wall of my house, this little open-air area is notched out of the floorplan in my home. I put the sails up to give some plants a shot at survival in the Dallas summer. When the sun hits that brick wall, anything close to the wall gets too hot to survive.

 

[Juanda]

Triangular sun shades will always flap in the wind, make noise, tear out the grommets, and damage the support structure. That is simply because a triangle is flat. It takes a doubly curved surface, with four corners and a stretchy fabric to be stable and not flap. A doubly-curved surface is formed when the four mounting points are not co-planar.

Can you share a link or source to read more about that? I'd like to better understand what you are pointing at.
Is it that the negative curvature of a saddle shape makes it stable against the wind? (By stable I guess we mean it does not flap)
Why does the fabric need to be stretchy? Is it to better create the saddle shape without wrinkles?

 

[Baluncore]

Can you share a link or source to read more about that? I'd like to better understand what you are pointing at.

There must be sources from 30 years ago, but my answer is accumulated wisdom of discussions at that time and experience fixing shade sails since then. I could not find a reference when I looked.
If anyone finds a reference, please post the link here.
It is time to educate the market.

Is it that the negative curvature of a saddle shape makes it stable against the wind? (By stable I guess we mean it does not flap)

Yes. The centre of a flat sheet can move with minimal restraint in the lightest winds. Double-curvature pre-loads the surface with tension from two directions, which raises the minimum wind speed (pressure) needed to significantly deflect the surface. The fabric life is greatly extended by double curvature because it eliminates fatigue due to flapping in the wind.

Why does the fabric need to be stretchy? Is it to better create the saddle shape without wrinkles?

When you pull a rectangle into a saddle, the area of the fabric must change, to be redistributed to cover the new surface. That is best done with a knitted shade cloth. Avoid woven cloth that can only be distorted to a rhomboid.

A wire, cord, or a tape stitched to the edge of the fabric, allows the edge of the elastic fabric to be pulled inwards to form a catenary curve. That prevents edge flutter, and corrugations (wrinkles) forming parallel with the edge.

As an example of a knitted fabric, look at a Spandex-Lycra one piece swimsuits, that stretch to follow the form of the body, try not to be distracted. Notice how corrugations form in parallel to the unsupported edges of the fabric. Examine the fine detail of a Spandex knit with an eyeglass. Then examine the knitted shade-cloth available on wide rolls from garden centres.

The Dacron used to make sails for boats is practically useless for shade sails. It is designed not to stretch, to be cut and stitched to maintain an accurate airfoil shape. For a shade sail, you want to pull on four corners, then tension four edges, to get an elegant smooth saddle, without needing to calculate and build the curvature into the surface before installation.

 

[Baluncore]

Textile Architecture. Membrane Geometry.
https://sollertia.ca/en/textile-architecture/membrane-geometry/

M. Van Craenenbroeck, S. Puystiens, L. De Laet and M. Mollaert.
Creating Temporary Doubly Curved Tensile Membrane Structures Without Cutting Patterns Using High Strain Fabrics. 2015.
https://core.ac.uk/reader/132529670

Xavier Tellier, Cyril Douthe, Laurent Hauswirth, Olivier Baverel.
Linear Weingarten membranes with funicular boundaries. Structural Concrete, 2020, ?10.1002/suco.202000030?. ?hal-02988774?
https://hal.science/hal-02988774/document

 

[Juanda]

That was just great. I'll admit I'll have to take some time to fully digest the papers but I think I got the overall idea clear.
The videos from the first link felt especially illustrative because they look more like a mass connected to springs which is a structure I can grasp more easily in terms of rigidity.
I don't know when I'll need this but now I know it forever. Thank you for the posts!

 

[berkeman]

View attachment 334667View attachment 334666

Here are the shades and a shot of what the facia looks like after a while. I mis-remebered the brick attachement, I guess I put the 2x4 on after the sails and to string the lights to - the sails are attached directly to the brick. That wall is actually the exterior wall of my house, this little open-air area is notched out of the floorplan in my home. I put the sails up to give some plants a shot at survival in the Dallas summer. When the sun hits that brick wall, anything close to the wall gets too hot to survive.

Do the shades need to be as opaque as that, or would some sort of netting triangles do the trick as well?

 

[Grinkle]

Do the shades need to be as opaque as that, or would some sort of netting triangles do the trick as well?

The brick wall gets direct sun for 5-6 hours per day in the summer, so the more blocking of the sun, the better. 'Good enough' is if the plants survive, hard to predict in advance. I think I get where you are headed, though. Maybe I can cut a couple slits in each of the triangles to reduce the flapping without sacrificing much shading functionality. I think they will eventually come apart if I do that, but if my alternative is to uninstall them anyway, I might give that a try.

 

[berkeman]