Tatterproof flag design needed

[anorlunda]

I'm a retired engineer who lives on a sail boat. I'm tired of frequent replacement of my flags that tatter rapidly as they flap in the wind. I would like to suggest this as a challenge to other engineers. How can we design a tatterproof, flexible and affordable flag?

I added the word flexible, because the obvious design of a rigid flag would have been used for millenia past if it satisfied flag customers. Therefore, I reject rigid flags as a solution.

Good engineering usually starts with good descriptions of the physics. They tatter when they flap but why do they flap? Wikipedia has a non-explanation here. Physics forums has a whole lot of non-explanations here. Physics.apps.org has a very interesting explnation here. It says, "Since gravity tends to collapse a flag along its diagonal, while wind tends to stretch it out, the wavelike motion of folds in a flag is at an oblique angle to its length." That's ingenious but I'm sure that flags flap and tatter when hung horizontally as well as hung vertically.

Then there is the related but separate topic of tattering as distinct from flapping. I can't find any scientific literature on that at all.

 

[SteamKing]

I predict a tatter-proof flag will follow soon after the development of a fabric which does not degrade or wear out under the action of wind, sunlight, friction, etc. See the film, "The Man in the White Suit" for what happens when such a fabric is developed.

 

[anorlunda]

Sorry SteamKing, the theme of "The Man in the White Suit" is simply that entrenched interests resist change. That's far too general and too cynical to count for much. There would be no Internet to have forums on if that principle ruled.

 

[SteamKing]

Well you could try making flags out of carbon fiber or kevlar, but they might be too expensive for general use. Maybe someone could make a flag out of carbon nanotubes.

 

[Q_Goest]

Hi anorlunda,

Good engineering usually starts with good descriptions of the physics. ... Physics.apps.org has a very interesting explnation here. It says, "Since gravity tends to collapse a flag along its diagonal, while wind tends to stretch it out, the wavelike motion of folds in a flag is at an oblique angle to its length." That's ingenious but I'm sure that flags flap and tatter when hung horizontally as well as hung vertically.

Then there is the related but separate topic of tattering as distinct from flapping. I can't find any scientific literature on that at all.

The force that wind can produce on anything is a function of the drag and shear forces. I'd have to believe it's pretty obvious that those forces alone are far too slight to cause stresses in the fabric from exceeding the value needed to damage them. To damage the threads in the fabric, the stresses in the fabric have to be enormous compared to the drag and shear forces. Wind simply doesn't have the energy to damage threads.

It seems to me the wind is not just imparting a force on the flag, it is imparting energy to the fabric. The interaction between the flag and the wind has to be concentrating or focusing energy in order to produce enough stress in the fabric to damage it. Any description of how the wind can produce stresses in a flag’s fabric sufficient to damage the fabric has to show how those forces can arise, and I’d suggest that the way to do that is to look at how energy gets transferred to the flag and how that energy gets focused.

The description of how gravity tends to collapse the flag along its diagonal with the wind unfolding it, producing waves is a good clue. Waves can focus energy fairly easily, so it must be part of the reason of how the wind can impart energy to the fabric. The fabric must accelerate such that the velocity at the tip of the material where it snaps is where the energy is finally focused and where the velocity of the fabric far exceeds the wind's velocity. Perhaps it's a bit like a whip which actually can focus the energy of someone's arm so as to accelerate the tip of the whip to sonic velocity. Note also that a whip gets more narrow toward the tip. So the mass per unit length along a whip decreases, and I believe that’s at least part of the reason why the energy can become focused. For the case of the flag, if there's a focusing of energy, it might at least partially be the shape of the flag that’s focusing the energy. That focusing of energy is always easier if mass gets smaller such that the energy is transferred to a smaller and smaller piece of the flag; say the corners. I suspect it's the corners where the energy gets focused from the vast majority of the flag's material picking up energy from the wind. And isn’t it the corners that always ends up beginning to fray?

Any solution then would need to look at ways to eliminate that focusing of energy. Methods of dampening the movement and dissipating the energy prior to it getting to the corner might work. Some nonlinear stiffness built into the flag might work. Eliminating the corner altogether might also help. But I think simply making the same flag out of stronger material, although it might work, is nothing but a brute force approach to the problem and not an elegant solution.

 

[anorlunda]

Thank you Q_Goest and Steamking.

If there is a solution, it may well be some kind of nonlinear tuning is the key, but what kind? Taper which direction? Stiffness? Mass distribution? Perhaps even permeable fabric.

Q_Goest's comparison with a whip may be close to the answer, with a whip being a 1D analogy of a 2D flag.

Tatters are horizontal rips in a vertically hung flag. They don't all happen at once,so presumably they happen one at a time if energy decided to focus on one spot. But new tatters appear so that means that an already tattered flag must continue to focus energy. One more clue, the horizontal tears seem to be all the same length, 10-20% of the length of the flag. Continued exposure causes new tears (up to a dozen or so), but it does not seem to lengthen the earlier tears. All that suggests that the important physics are not in the trailing edge, and that may be why trailing edge hems are so ineffective at preventing tattering.

However, I'm sure that material strength or stiffness alone can not be the solution. The main sail on a big sailboat is made from very heavy, stiff and strong Dacron. It also has a very thick hem on the trailing edge. Still, if the sail is carelessly allowed to flap in a 60+ knot wind (sailors call it flogging), it will self destruct in as little as 10 seconds; much faster than a light flag in the same wind would tatter.

There could be hard science analogies of the same problem. Light sails have been proposed for interstellar space ships. I read of one proposal for an aluminum light sail only 3 atoms thick. Obviously any kind of traveling ripple or flapping of that sail would be easily destructive.

 

[turbo]

Have you looked into materials such as Tyvek? That stuff is very strong and resistant to wind-damage. Plus, it is really cheap.

 

[AlephZero]

Q_Goest is probably right that the forces in the fibers are too small to break them in tension, but because of the "whip" action at the trailing edge you will get large amounts of bending. The threads will probably weaken because of UV light exposure (both direct and reflected from the water) and might become brittle through absorbing salt spray, etc.

Woven cloth has strange mechanical properties because it is very anisotropic. It's hard to stretch it along the directions of the threads, but very easy to shear it into a diagonal shape.

If the failures are always horizontal, if would be interesting to try a flag with the threads running diagonally rather than horizontal and vertical. You would need to cut this from a larger piece of cloth and hem all the edges to stop them fraying.

Even if it doesn't last long, you might learn something from the way it fails.

Kevlar might be work a try. Kevlar cloth is readily available in reasonable small pieces (say 1 meter square). It's not dirt cheap, but by comparison with the cost of most boat-related equipment it's not ridiculously expensive. But putting a design on a kevlar flag would be another problem to solve...

 

[CraigAllan]

Interesting post. Made me think.
I think the all answers are in the posts above. Just nobody has written them in sequence.

A flag flaps due to wind action. Some of that (hypothesis) is Bernoulli effect acting on the curved surface of folds in the flag. The suction on the raised fold or pressure on the hollowed fold opposite side would increase the amplitude of the fold as it traverses the flag horizontally. And more suction and presure will deform the ripple into a bigger ripple. At the end of the flag, all that energy has go nowhere to go so it produces a whipsnap and we know flags can crack loudly in strong winds.

The ripping (hypothesis) happens when two adjacent ripples of reverse polarity traverse the flag, both ending at the trailing edge at much the same time. The whipcrack for one ripple is in a +ve direction and the other ripple whipcrack is in the -ve direction. So a small piece of the trailing edge is trying to go +ve at high velocity, and another adjacent piece is trying to go -ve at high velocity. Somethings got to give. So the edge of the flag rips in the high stress area between the two whipcrack zones.

Ok, so how to fix it. One way is to do an impedance match. You don't want all the energy in the ripple reflecting from the bad match at the trailing edge and stressing the fabric. It must dissapate harmlessly. I'd suggest adding a strip of loose weave mesh to the edge. Mesh has high drag and as its permeable to air it has no Bernoulli effect. The ripples will be dampened and the fatal high energy reflection from the trailing edge will not happen.

This is why the flag rips don't propagate the full length of the flag - the ripped tatters dampen the high energy ripples and stop the cracking so energy levels don't rise to a level that can rip the fabric. Ripping is thus self limiting.

The professionally made ceremonial and national flags I know are made of hairy fabric and have a strangely loose weave. Until today I always wondered why, but without applying my mind to the problem. Since flag makers are not physicists this must have evolved in Darwinian fashion. Hairy means high drag, so the wind catches the flag and carries it open, and loose weave knowingly or not defeats the Bernoulli pressure differential on opposite sides of the flag ripples, saving it from thrashing itself to tatters.

 

[sophiecentaur]

An alternative way of increasing the damping on the trailing edge would be to make it more rigid by loading it with some plastic compound. Alternatively, the flag could be made with a 'frame' around it of some semi-rigid material (in a pocket, sewn into the periphery).
But I guess the flag still needs to look like a flag and the way it flaps in the wind is a major part of its appearance.
The standard fabric doesn't seem to stand up to many months of flapping before it starts to fray. It's standard practice to lower flags at dusk and raise them at dawn. I guess that could be another 'Darwinian' development to halve the rate of wear.

If it were designed like the one planted on the moon, perhaps people would say there was a conspiracy about reports of your trips on your sailboat.

 

[anorlunda]

The things CraigAllen said sound very promising. A loose weave makes the fabric permeable. That would change the dynamics considerably. "Hairy" threads to increase drag also sound good. I'd like to experiment modifying a standard flag. Perhaps sewing some gauze on the trailing edge might provide evidence.

I also notice that expensive flags are knitted while inexpensive ones are woven. Perhaps it is easier to make a loose permeable knit.

Sophiecentaur, In a post above I discussed sailboat sails. Mainsails have very heavy and stiff hems on the trailing edge, but they are more vulnerable than flags. Of course a hem increases mass at the trailing edge as well as stiffness. I'm pretty sure that the mass distribution of the flag plays a role.

 

[Danger]

Have you thought of just using a hologram of a flag?

Okay, what about using one of the aforementioned super fabrics, but perforating it? When I worked at the sign shop, we cut U-shaped relief all over outdoor banners. They looked perfectly normal, with no distortion of the graphics, but the flaps would pop open under strong winds to let the air through without ripping the material.
I didn't mean that to come across as being a rip-off of Craig's idea. It's just a modification.

 

[sophiecentaur]

The things CraigAllen said sound very promising. A loose weave makes the fabric permeable. That would change the dynamics considerably. "Hairy" threads to increase drag also sound good. I'd like to experiment modifying a standard flag. Perhaps sewing some gauze on the trailing edge might provide evidence.

I also notice that expensive flags are knitted while inexpensive ones are woven. Perhaps it is easier to make a loose permeable knit.

Sophiecentaur, In a post above I discussed sailboat sails. Mainsails have very heavy and stiff hems on the trailing edge, but they are more vulnerable than flags. Of course a hem increases mass at the trailing edge as well as stiffness. I'm pretty sure that the mass distribution of the flag plays a role.

I was thinking, rather, of a lossy material, like a loaded rubber impregnation. I was thinking of the process as the effect of terminating a wave as an alternative to the suggestion above, which uses the damping of the air rather than the damping within the material.The way sails behave at the leech will be due to the tension between foot and head, I think. Sails are, of course, set to extract a lot of energy. This could put more stress on the trailing edge. A flogging foresail will not last long, though. The trouble is that sails have to work in light winds as well as being strong enough to handle a Force 6,7,8.

 

[sophiecentaur]

Have you thought of just using a hologram of a flag?

Okay, what about using one of the aforementioned super fabrics, but perforating it? When I worked at the sign shop, we cut U-shaped relief all over outdoor banners. They looked perfectly normal, with no distortion of the graphics, but the flaps would pop open under strong winds to let the air through without ripping the material.
I didn't mean that to come across as being a rip-off of Craig's idea. It's just a modification.

Another good damping mechanism.