Tent poles - technical questions

[Orion]

Suppose you have a tent pole of length L and you constrain the ends (say with pole tips in grommets) a distance D apart.
How high is the of the arch of the pole?

H = f(L,D) --- what's the formula?

And what is the maximum radius of curvature (at the top of the arch)?


Furthermore, how much can you bend an aluminum tent pole? What is the minimum safe radius of curvature? Obviously that will depend on the specific pole, but are there general guidelines for aluminium poles?

[Moondog55]

Check the TPT website?
I think those questions are discussed and answered there { I just checked and they are not } I must have seen them some other place
Partly it depends on the diametre of the wand sections, smaller sections can be more flexible and bend through a greater radius. My limited experimental experience is that once you try and bend more than a certain amount the wand sections simply shatter at the most stressed place and in my case that was at the top of the arch and at a tighter radius than a semicircle
Quest are very low on stock of poles and the only links I found there are here
http://www.handymath.com/cgi-bin/rad2.cgi?submit=Entry

[Mark F]

In theory the poles when bent should form part of a circle but if you look at various tents with a single pole it appears the center parts of the pole tend to bend more than the ends leading to the height of the arch more than half the distance between the ends.
Examples - Nordisk Telemark 1 - width at pole ~1.4m, height 0.96m
Terra Nova Laser Competition 1 - width at pole ~1.45m, height 1.0m

In theory assuming that the pole forms half a circle then the heights should be around 0.7m. While it is hard to tell exactly neither tent appears to deliberately extend the poles below this half circle point. This would show as the poles would initially bow outward but in neither case (I own both) can I see this.

How tight a curve can you safely create? It depends on the pole but many tents achieve a diameter of around 1.4 metres (radius 0.7 metres). For tighter curves then you need to consider pre-bending some pole sections or using angled joints between pole sections.

As to a formula - no idea. I suggest getting a set of poles approximately the correct length for your design and then measuring.

[Moondog55]

Question
What have you got and what are you trying to do?
I have some spare wands here and I could do some non-destructive testing with the assemblies I have

[Franco]

This is Doug Johnson from Seattle ( used to do reviews for BPL) demonstrating how you can bend a carbon fiber pole

fibraplex-fibrapole-292-poles-review-3.jpg (107.95 KiB) Viewed 36141 times

the problem with that is that as it is that pole will shatter with very little pressure.
So it isn't about how much you can bend a pole but how much you should.
Short answer : as little as possible...
BTW, I like that shot because I have been on those stairs...

[Orion]

In theory the poles when bent should form part of a circle but if you look at various tents with a single pole it appears the center parts of the pole tend to bend more than the ends leading to the height of the arch more than half the distance between the ends.
Examples - Nordisk Telemark 1 - width at pole ~1.4m, height 0.96m
Terra Nova Laser Competition 1 - width at pole ~1.45m, height 1.0m

What theory are you referencing to predict that it will be an arc of a circle?

I have also noticed that height > width/2, at least in the few examples I've measured. And this is in addition to the fact that the poles rarely (if ever) contact the ground at a 90° angle. So if the circle theory were correct tents would actually have height < width/2.

How tight a curve can you safely create? It depends on the pole but many tents achieve a diameter of around 1.4 metres (radius 0.7 metres). For tighter curves then you need to consider pre-bending some pole sections or using angled joints between pole sections.

Do you know of a specific example of a tent with a width (at the pole) of 1.4m?

EDIT: Doh! You just gave me two examples.
Do you know what the pole lengths are? I'm going to guess about 2.5m

I notice their Starlite 1 tent has a width of only 1.0 meter, although that might be the inner dimension.

[Orion]

Question
What have you got and what are you trying to do?

Curiosity, mainly. I've made one tent in the past and decided on the pole length and spacing primarily by a combination of gut instinct and comparison with similar commercial designs.

I know that carbon fiber poles can be bent to a smaller radius of curvature but they are expensive and have an unpleasant failure mode. They are an interesting option however. The smiling man in Franco's photo thought CF poles were quite good, provided they weren't abused. Of course aluminium poles can also fail due to abuse.

I assumed that natural pole shape would be a well understood thing. Wouldn't a tent designer use it in constructing a computer model of a tent? And breaking force and how it relates to radius of curvature would be another important design parameter. I couldn't locate any specifications but surely Easton and DAC provide them to tent designers so that they can calculate a safe bending radius.

Short answer : as little as possible...

Or maybe not. Perhaps it's all just trial and error and tradition. I don't know.

[Orion]

I found a solution but the math looks difficult. I can't easily parse it.

Fortunately the author provided some graphs:




d = deflection (height) and h = spacing between the ends of the pole, the opposite of how I defined d and h above.

Measurements of the two poles in my Hilleberg Nallo 3 are in agreement with the second graph. It suggests that the longer (higher) pole is inclined at an angle of about 80° and the shorter rear pole is at about 70°.

[Mark F]

Pole lengths 283 tip to tip for the Terra Nova and 277 for the Nordisk. Both pole sets DAC.

Thanks for finding that explanation. I had often wondered about it but never enough to research the issue. My so called theory is more of a combination of brain fart and deluded thinking.

With cf poles the Easton ones which are usually the easiest to obtain and all arrow shafts are very rigid and only really work with prebent joiners. I remember Fibraplex stated a minimum radius of 750mm for theirs which are very bendy.

[Chezza]

There's a simpler approximation for slender rod curvature, but it still involves minimising a potential energy equation.

http://homepage.tudelft.nl/p3r3s/IASSpa ... enboom.pdf

The other option would be to do this in finite element software, but if you go that way you really should have a way of validating your results. It's pretty easy to put garbage in and end up with garbage out.

Even if you can calculate minimum radius of curvature for a given pole length and base width combination calculating the right amount of pre-stress isn't easy. You need to account for both wind and snow loads. There's a measure of educated guesswork there.

My suggestion would be to use an FEA package so that you can play with snow and wind loads as well. I know in ANSYS I can put the ends of the rod on sliding pivots and slide the pivots towards each other, then apply loads to that solution. I'm sure other packages have similar capability.

FEA will also allow you to model the section changes & ferrules at the joins, which is important because that's where poles usually fail.

[Orion]

Pole lengths 283 tip to tip for the Terra Nova and 277 for the Nordisk. Both pole sets DAC.

Thanks for the measurements. Those poles are not consistent with the graph I posted. The height is very roughly 8% lower than the graph predicts based on the horizontal spacing of the tips. That's for both of those poles.

I wonder if pre-bend is responsible for that deviation? Even the Nallo 3 poles have a small amount of pre-bend in them. How aggressively are the Terra Nova and Nordisk poles bent?

With cf poles the Easton ones which are usually the easiest to obtain and all arrow shafts are very rigid and only really work with prebent joiners. I remember Fibraplex stated a minimum radius of 750mm for theirs which are very bendy.

It was the Fibraplex poles that I was thinking of. I thought that flexibility was a property of CF poles in general. Apparently I was wrong.

[Orion]

Chezza, thanks for that. I'm not sure what I can do with it though.

I was really hoping for a more canned solution, particularly with respect to how much bend is "safe". Obviously that's going to depend on expected external loads which is a hard variable to pin down. But I was expecting/hoping some rule of thumb could be distilled, for a given type of pole.


The Terra Nova Starlite 1 looks like a 1-person version of the Hilleberg Anjan. I've always assumed there was no Anjan 1 (or Nallo 1) because of the limit of how far a pole can be bent and still be strong. That's what I'm curious about. Is the Terra Nova Starlite 1 a tent that will break in heavy winds? Or by pre-bending the pole or some other trickery have they pushed the limit safely? Maybe there are other reasons Hilleberg thinks a Nallo 1 or Anjan 1 isn't worth doing.

[Moondog55]

I know I have seen the information [ this in the "potted" form] somewhere but I cannot find it, I was sure it was at the TPT site.

[Orion]

What is the TPT site?


The only specifications I've been able to find are on an Easton brochure where they detail the dimensions, wall thickness, tensile strength, and also the limits for pre-bends:

[Moondog55]

http://tentpoletechnologies.com/

[Chezza]

Chezza, thanks for that. I'm not sure what I can do with it though.

I was really hoping for a more canned solution, particularly with respect to how much bend is "safe". Obviously that's going to depend on expected external loads which is a hard variable to pin down. But I was expecting/hoping some rule of thumb could be distilled, for a given type of pole.

There are easy calculations for beams undergoing small deflections, but the problem gets a lot harder if you've got large deflections, as you can see. I was just trying to show you that what you're trying to do isn't easy.

I imagine it wouldn't be too hard to write an app that calculates rod shape and maximum stress using the paper that I linked. I've written code for similar problems during my undergrad, but I'm quite rusty now.

I think the tent industry largely relies on experience and trial and error testing.

A hack way of picking the safety factor once you can calculate max stress given a shape would be to benchmark the safety factors being used by multiple commercial tent manufacturers and look at the spread.

[Orion]

There are easy calculations for beams undergoing small deflections, but the problem gets a lot harder if you've got large deflections, as you can see. I was just trying to show you that what you're trying to do isn't easy.

I had already figured out it isn't easy. I thought you were trying to show me that it was maybe a little bit easier.

I think the tent industry largely relies on experience and trial and error testing.

I'm okay with the empirical approach. I would just rather not repeat the work of others.

I was thinking that Roger Caffin could probably answer most, if not all, of my questions. But I can't just write his name three times here and, like Beetlejuice, expect him to post on this thread. So I did the next best thing. I went and re-read his webpage on tent design. It has been a while since I've read it and, as before, I found a lot of common sense and wisdom there.

He used tent pole elbows in his designs in order to achieve the average radii of curvature he desired. He manufactured his own elbows but I may be able to use the ones that are commercially available. That's assuming I ever make another tent.

[Moondog55]

I once asked DAC if they supplied tent poles to the DIY market. During the exchange of information [ NO They don't and won't] I was told they rely on tent makers to provide the details and they just supply the materials; so somebody in the manufacturing side of things must; at some point; do some calculations.
On the other hand some "Expedition" tents look so overbuilt I think that there is also a lot of trial and major error occurring

[Mark F]

I have played around with the preformed angled elbows. The bend can be adjusted to some extent. I just put the elbow in a vice and squeezed it a bit. Seems strong enough and no signs of cracking or other damage.

I have seen old sets of poles with some sections, especially in the centre of the pole, with a slight bend even though they were originally straight. A bit too much stress in use, but not enough to break.

[Moondog55]

I don't think I have ever owned a tent with Easton poles that haven't taken a "Set" and become permanently curved over time with the exception being the Minaret that came with pre-curved wand sections

[Franco]

The photo I posted of Doug bending that CF pole was to show that it can be done but it should not...
At Tarptent we have used CF poles although we typically discouraged people from buying them.
For some shelters, the Moment for example, the pole had to be a CF/al hybrid because CF by itself was not appropriate for the rather small radius.
Easton had the reccommended minimum radius but that page has disappeared.

Moment : tip to tip distance (diameter) 183cm, 104 cm high.

[Chezza]

I had already figured out it isn't easy. I thought you were trying to show me that it was maybe a little bit easier.

Well, I think the approach in the paper I linked IS easier to solve than the approach in the textbook you linked. You seem to have some mathematical training, so I wasn't sure what you were comfortable with. If you're looking for an accurate solution as you asked for in your first post, your choices are to sit down and write a bit of code involving solving or optimising differential equations, or use an FEA package. There is also Matlab/Simulink or Rhino3D/Grasshopper/Kangaroo either of which would allow you to approximate the solution by modelling the pole as a series of small linear/torsional spring elements.

I was thinking that Roger Caffin could probably answer most, if not all, of my questions. But I can't just write his name three times here and, like Beetlejuice, expect him to post on this thread. So I did the next best thing. I went and re-read his webpage on tent design. It has been a while since I've read it and, as before, I found a lot of common sense and wisdom there.

He used tent pole elbows in his designs in order to achieve the average radii of curvature he desired. He manufactured his own elbows but I may be able to use the ones that are commercially available. That's assuming I ever make another tent.

I have noticed that Roger's cross-sectional drawings show a slight bend in the CF poles, and always wondered what equations he used to calculate that curvature. The curvature is small, so those equations are probably not applicable to the case of a long flexible Al pole.

The Easton elbows are strong and light enough in .340". I have weights and CAD models of the .340" and .490" 145 degree arches. PM me if you ever want these.

[Chezza]

Okay, it appears others have already done the work with regard to a simple equation for the centre height, and a Rhino plugin that will plot the shape.

https://www.physicsforums.com/threads/b ... ht.735200/

It's still not clear to me how you'd extract the minimum radius of curvature from the shape.

If you can find the minimum bend radius then maximum bending stress (at the apex) with the tent setup and unloaded can be calculated fairly easily. Then, you need a kind of "safety factor", where safety factor = (yield stress) / (max equiv stress at apex). Yield stress of 7075-T6 should be a close enough approximation. I don't believe DAC or Easton release their exact yield stresses.

Benchmark a bunch of tents by reputable manufacturers, and calculate their safety factors as above, and use something in that range for your design. You'll find that, in practice, living space considerations constrain your choice of safety factor as well.

Lastly, remember that bending a pole as little as possible may not be optimal when snow loads are considered. There is a range of arches that handle both snow and wind loads well. So make sure the tents you benchmark are about the same width & height as what you want to design. It's pretty easy to eyeball the right shape. In the words of Bill Lear, if it looks right it will fly right.

[Orion]

I have played around with the preformed angled elbows. The bend can be adjusted to some extent. I just put the elbow in a vice and squeezed it a bit. Seems strong enough and no signs of cracking or other damage.

I have seen old sets of poles with some sections, especially in the centre of the pole, with a slight bend even though they were originally straight. A bit too much stress in use, but not enough to break.

That's good to know about the elbows.

The pole in my homemade tent has developed a curve in one of the sections, although not at the arch. It's about 1/3 up from one side, probably the result of the stress during pole installation/removal. My tent is designed in such a way that the pole goes in from the same side and always in the same direction.

[Orion]

Moment : tip to tip distance (diameter) 183cm, 104 cm high.

And the length? The tarptent websites says: "Pole length is just over 10 ft / 3 m". So maybe 10.1 feet / 308cm?

[Orion]

You seem to have some mathematical training, so I wasn't sure what you were comfortable with. If you're looking for an accurate solution as you asked for in your first post, your choices are to sit down and write a bit of code involving solving or optimising differential equations, or use an FEA package. There is also Matlab/Simulink or Rhino3D/Grasshopper/Kangaroo either of which would allow you to approximate the solution by modelling the pole as a series of small linear/torsional spring elements.

Some mathematical training, but perhaps not enough. And I have no experience with Matlab or any CAD software either. When I made my tent I did it the old fashioned way, with a mockup at first, and then doing the final fitting by eye and by hand. It was awkward but a simple enough design that I could get away with it.

Okay, it appears others have already done the work with regard to a simple equation for the centre height, and a Rhino plugin that will plot the shape.

https://www.physicsforums.com/threads/b ... ht.735200/

It's still not clear to me how you'd extract the minimum radius of curvature from the shape.

I had already found that discussion on PhysicsForums. But when I tried the "easiest way to solve for m" with WolframAlpha it didn't work. So I continued searching and never went back to it. Maybe it's worth looking at again.

The graph I posted above includes a trace for "-L/Rmin". I've been puzzling over what it means. I would expect the ratio of length to minimum radius to be 2 somewhere between 60 and 90°. So is there some typo? And what does the negative sign imply?

Benchmark a bunch of tents by reputable manufacturers, and calculate their safety factors as above, and use something in that range for your design. You'll find that, in practice, living space considerations constrain your choice of safety factor as well.

Lastly, remember that bending a pole as little as possible may not be optimal when snow loads are considered. There is a range of arches that handle both snow and wind loads well. So make sure the tents you benchmark are about the same width & height as what you want to design. It's pretty easy to eyeball the right shape. In the words of Bill Lear, if it looks right it will fly right.

It seems to circle back to comparing with existing designs coupled with trial and error.
It's probably a good thing I'm not thinking of building aircraft.

If I decide to make another tent I think I'll order a number of extra pole sections and do some bending and breaking.

[Chezza]

Did you see the simple formula half way down, that gives you h as a function of L and D, as you asked?

I have the same difficulty with the graph you posted.

Use x instead of m in Wolfram Alpha and everything should work.

<http://www.wolframalpha.com/input/?i=solve+for+x:+45.2%2F67.1%3D2*E(x)%2FK(x)-1>

I failed to notice the VB script for plotting x and y in Grasshopper in that discussion. The complete solution is in there. I wasn't sure how to solve for m, but it's actually very simple. Calculating the minimum radius of curvature is straightforward once you have a complete solution for x and y.

Try giving Rhino and Grasshopper a go with that plugin. The trial period is three months and the learning curve isn't too bad.

[Chezza]

I really like that little blue tent you built. I'm toying around with making a similar design.

After all this discussion, I failed to mention that these analytical approaches will not work in the case where there are pre-bent poles. FEA is your only real option there for a desktop solution. There are free FEA packages available but expect to spend several dozen hours learning at a minimum before you have some basic proficiency.

https://en.wikipedia.org/wiki/List_of_f ... e_packages

[Franco]

Moment : tip to tip distance (diameter) 183cm, 104 cm high.

And the length? The tarptent websites says: "Pole length is just over 10 ft / 3 m". So maybe 10.1 feet / 308cm?

Yes, we call it a 10' pole. The tips are extra.
don't stress over an inch or two....

[Orion]

Did you see the simple formula half way down, that gives you h as a function of L and D, as you asked?

Yes, I originally tried using that but it didn't match my measurements very well. The graph above is much closer.

I'll go back and see what I can do with that guy's solution. I can see many hours in my future spent learning new tools but having design tools would be very useful if I try to make a more complicated tent.

Thanks for all your help.