Newbie here: How can I figure out the point at which body tubes buckle?

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SpaceStudent

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Hi all!

The body of my rocket consists of a LOC 54 mm paper tube, and I'm planning on flying it on an H motor for my L1 certification. However, I'm not sure what kind of calculations (other than empirically testing the tube past the point of no return!) would help me determine if it's feasible to fly with a J motor. Any advice for a newbie? (I've used mid-power rocket motors before but this L1 launch will be my first HPR launch; any advice is greatly appreciated.)
 
If you're using LOC high power tubing, I don't think you'll have a problem with a J, so long as the rocket is built correctly. I haven't heard of any calculations you might do to predict buckling. But the thick walled tubing from LOC is good stuff.
 
Look up Euler Buckling calculations. Selecting the proper geometric constants for a tube is simple, but the challenge is obtaining reasonable material properties for the cardboard material.
Finding those properties has been my greatest speed bump when it comes to applying analytical methods to sport-rocketry.

Good luck
 
Cylinders are incredibly strong along the long axis.

The weak spot on a standard 3 or 4 fin rocket will be just above the motor mount centering rings or just above where the leading edge of the fin meets the body tube (whichever one extends higher). The motor mount supports the lower portion of the rocket internally, while the fins support the exterior of the rocket. Both of these things give the lower section extra rigidity. Where they end is where the body tube would most likely fail if it were to fail. I have several LOC rockets and they are very strong and I wouldn't expect a failure if flying on recommended motors and the rocket is built per the instructions.
 
Look up Euler Buckling calculations. Selecting the proper geometric constants for a tube is simple, but the challenge is obtaining reasonable material properties for the cardboard material.
Finding those properties has been my greatest speed bump when it comes to applying analytical methods to sport-rocketry.

Good luck

Cylinders are incredibly strong along the long axis.

The weak spot on a standard 3 or 4 fin rocket will be just above the motor mount centering rings or just above where the leading edge of the fin meets the body tube (whichever one extends higher). The motor mount supports the lower portion of the rocket internally, while the fins support the exterior of the rocket. Both of these things give the lower section extra rigidity. Where they end is where the body tube would most likely fail if it were to fail. I have several LOC rockets and they are very strong and I wouldn't expect a failure if flying on recommended motors and the rocket is built per the instructions.

I watched another thread where the flier installed carbon fiber rods adhered to the inside of the airframe to strengthen it. I did not understand what failure that builder was trying to prevent.

What is the expected cause of buckling? Is it the compressive stress along the axis of the airframe under thrust?
 
Again, if you build per the instructions and use recommended motors you probably won't see failures due to thrust.

Just throwing out ideas here, but I would think hard landings would be a problem. Rockets almost never land flat on their rear ends; they usually land on one or two fins and that does cause stress where I said it would. Do that a few times and do it hard enough and the airframe will be weakened.
 
Again, if you build per the instructions and use recommended motors you probably won't see failures due to thrust.

Just throwing out ideas here, but I would think hard landings would be a problem. Rockets almost never land flat on their rear ends; they usually land on one or two fins and that does cause stress where I said it would. Do that a few times and do it hard enough and the airframe will be weakened.

I think I've bent more body tubes in the trunk of the car than anywhere else.
 
Again, if you build per the instructions and use recommended motors you probably won't see failures due to thrust.

Just throwing out ideas here, but I would think hard landings would be a problem. Rockets almost never land flat on their rear ends; they usually land on one or two fins and that does cause stress where I said it would. Do that a few times and do it hard enough and the airframe will be weakened.

I tend to agree. I should probably say that I am asking the OP (and everybody else) what is the expected cause of failure?
 
I tend to agree. I should probably say that I am asking the OP (and everybody else) what is the expected cause of failure?

one type of failure i have seen is a rocket speed so great that the BT squeezed and popped the nose cone off. catastrophic zipper.
 
I think I've bent more body tubes in the trunk of the car than anywhere else.

A few days ago t snapped a fin off my Phoenix pulling it out of the car. In the past few months I have snapped the upper section off my Mister Victor Vector Force (a stretched Vector Force) at least twice putting it into the car. And I have also bent more body tubes putting rockets into or taking them out of cars than I care to count. HPR rockets are a bit tougher and you would have to drop something on it to bend a body tube or be seriously careless to bend an HPR tube pulling it out of the car.

I do have an HPR rocket that is showing body tube stress, but it is compression stress near the av bay. The rocket kit was made by K&S and when I unpacked the kit I could clearly see that the components were not as robust as the components LOC uses. This same rocket had the av bay bulkheads shatter during a deployment and the upper section separated from the booster and parachute. The section fell flat and the body tube got impaled on a corn stalk.

I8yH3QW.jpg


Bs0A8Lz.jpg
 
I do have an HPR rocket that is showing body tube stress, but it is compression stress near the av bay.

What does that look like?

I tested BT55 to destruction once. Doesn't account for off axis loads - so fly straight!

Good datum. <smile>

I wonder about loading rates. The maximum load under thrust is -- well its a calculus problem. A first order approximation might be the mass of everything forward of some separation in the tube, multiplied by the maximum acceleration of the rocket (plus whatever drag force acts on the forward section of the rocket at the moment of maximum accleration).

Does anybody know a reference for how laminated paper tube sets up under a dynamic load?

I'm not a materials scientist, but I'd also guess that the glue used adhere the lams of the tube and/or or the paper fibers, would be susceptible to fatigue with repeated stresses at less than the ultimate strength of the paper.

Without some more information about the OP's design, the rocket on which it will fly, and more information about the elastic properties of cardboard tubes than seems to be easily available, I don't think we can do more than speculate and offer anecdotal evidence of successful H and J flights with 54mm LOC tubing.
 
Isn’t the maximum load simply the thrust? Imagine the case where drag force = thrust. The rocket is not accelerating, and is under the load of the thrust. On the pad, there is no drag and all thrust. I think every thing in between is an exact trade off.

You can look at it from an acceleration viewpoint - but you are using the mass to and from force - and it’s the same mass, so I think it cancels out.
 
Isn&#8217;t the maximum load simply the thrust? Imagine the case where drag force = thrust. The rocket is not accelerating, and is under the load of the thrust. On the pad, there is no drag and all thrust. I think every thing in between is an exact trade off.

You can look at it from an acceleration viewpoint - but you are using the mass to and from force - and it&#8217;s the same mass, so I think it cancels out.

The axial force acting at any point on the airframe is the force required to accelerate the mass of the airframe forward of that point.

morephysicsbloviation2.png


Consider just the nosecone, The force that accelerates the nosecone is exerted at its contact surface with the airframe. There is a reaction force, exerted by the nose-cone on the airframe which is equal in magnitude to the force exerted by the airframe on the nosecone. This force is less than the thrust required to accelerate the entire rocket. This is -- neglecting the weight of the nosecone and any fluid forces acting on the system -- the force that compresses the airframe under thrust.

It is more complicated than this, of course. You can cut the airframe with a line perpendicular to its long axis at any point, and work out a force required to accelerate all of the stuff above that point. But, since the the nosecone is likely a different material from the airframe, this is probably a good place to start the analysis.
 
So the thrust is the worst case. Which still seems handy to me. It's the more conservative number and is easy to get.

If I understand you, the compression force at any point would be the force required to accelerate the mass above that point at the same rate the whole rocket is accelerating. That kind of finer analysis would require knowing the fraction of the mass as a function of position along the axis of the rocket.

For the case I did my buckle test for, a Nike Apache, wondering if the BT55 would take the thrust from a 6G Pro24 motor, most of the mass IS above the body tube - with all the electronics and dual deploy chute.

FYI - the tube held fine. The fins did not :) With only 2G Pro24 Blue Streak
 
What does that look like?

The booster and upper section are starting to compress where they meet the av bay tube. Since the body tube for the av bay has a coupler glued inside of it, it is much stronger than the top of the booster section and the bottom of the upper body tube. The cardboard at these locations is starting to wrinkle and bulge slightly. I still fly the rocket, but I avoid hard hitting motors.
 
Isn’t the maximum load simply the thrust? Imagine the case where drag force = thrust. The rocket is not accelerating, and is under the load of the thrust. On the pad, there is no drag and all thrust. I think every thing in between is an exact trade off.

You can look at it from an acceleration viewpoint - but you are using the mass to and from force - and it’s the same mass, so I think it cancels out.

Yes. You’re correct; that is the maximum load. From the mass of the rocket you can calculate the acceleration. If you convert that into Gee forces you can then multiply the gee force, which is a constant for all the parts of the rocket that are not moving in relationship to each other. The total mass above some point on the rocket (assuming it’s supported by that point) times that gee force will show how much force is acting on that point.
 
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So the thrust is the worst case. Which still seems handy to me. It's the more conservative number and is easy to get.

Using the peak thrust of the motor you are treating the case of the rocket being driven into a perfectly rigid barrier. If the rocket accelerates, that is to say if there are unbalanced forces, then the compressive force on the airframe will be less than the thrust delivered by the motor.

And the other side of the stress-strain relation is the strain, which is the fractional change in length of the body under stress. Moving the cross-section aft, means a shorter section of tube and a proportionally smaller deflection under the compression.

If you look at the Euler formula to which nytrunner directed us,

https://www.continuummechanics.org/columnbuckling.html

the critical load -- the stress under which the column fails -- goes as the reciprocal of the square of the length. The mass of the rocket above (and the force needed to accelerate it) would increase as the length of the forward segment. Which means, as you take cross-sections further down the rocket, the buckling strength of the aft section increases faster than does the load it must support.

A couple of months ago (or maybe longer) a related top came up on the mailing list of the club with which I fly. Somebody in that discussion posted this reference

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690013955.pdf

I tried to read it, without much success..

As nytrunner pointed out, its a deep dive to deal with this stuff.

If I understand you, the compression force at any point would be the force required to accelerate the mass above that point at the same rate the whole rocket is accelerating. That kind of finer analysis would require knowing the fraction of the mass as a function of position along the axis of the rocket.

Yeah, there is certainly way to make this into a differential equations problem. I think, though, that since the body tube is going to be homogenous and of uniform cross-section (piece-wise, anyway) that you could figure the compressive stress and buckling strength at each transition or discontinuity. It wouldn't be much fun, and I don't think it would be necessary. My guess -- based on the fact that rockets built with LOC paper tubes do fly successfully on J motors -- is that the tube will not buckle under stress. Some other part of the rocket is more likely to fail.

For the case I did my buckle test for, a Nike Apache, wondering if the BT55 would take the thrust from a 6G Pro24 motor, most of the mass IS above the body tube - with all the electronics and dual deploy chute.

FYI - the tube held fine. The fins did not :) With only 2G Pro24 Blue Streak

The booster and upper section are starting to compress where they meet the av bay tube. Since the body tube for the av bay has a coupler glued inside of it, it is much stronger than the top of the booster section and the bottom of the upper body tube. The cardboard at these locations is starting to wrinkle and bulge slightly. I still fly the rocket, but I avoid hard hitting motors.

Thanks. It does sound like fatigue, but I really don't know enough about this. The OP will have to comment on whether longevity is a concern.
 
Using the peak thrust of the motor you are treating the case of the rocket being driven into a perfectly rigid barrier. If the rocket accelerates, that is to say if there are unbalanced forces, then the compressive force on the airframe will be less than the thrust delivered by the motor.

And the other side of the stress-strain relation is the strain, which is the fractional change in length of the body under stress. Moving the cross-section aft, means a shorter section of tube and a proportionally smaller deflection under the compression.

If you look at the Euler formula to which nytrunner directed us,

https://www.continuummechanics.org/columnbuckling.html

the critical load -- the stress under which the column fails -- goes as the reciprocal of the square of the length. The mass of the rocket above (and the force needed to accelerate it) would increase as the length of the forward segment. Which means, as you take cross-sections further down the rocket, the buckling strength of the aft section increases faster than does the load it must support.

A couple of months ago (or maybe longer) a related top came up on the mailing list of the club with which I fly. Somebody in that discussion posted this reference

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690013955.pdf

I tried to read it, without much success..

As nytrunner pointed out, its a deep dive to deal with this stuff.



Yeah, there is certainly way to make this into a differential equations problem. I think, though, that since the body tube is going to be homogenous and of uniform cross-section (piece-wise, anyway) that you could figure the compressive stress and buckling strength at each transition or discontinuity. It wouldn't be much fun, and I don't think it would be necessary. My guess -- based on the fact that rockets built with LOC paper tubes do fly successfully on J motors -- is that the tube will not buckle under stress. Some other part of the rocket is more likely to fail.





Thanks. It does sound like fatigue, but I really don't know enough about this. The OP will have to comment on whether longevity is a concern.

Ah, the original poster. Almost forgot about that. Calculating from the material properties will be much harder. My method was ‘test to failure’, and I think that takes the need for calculus out. Especially with Openrocket handy.

I tested the same tube as the body of my Nike Apache until it failed under compressive load. I videoed the scale reading while slowly letting the weight settle into the to tube and used replay to find the peak. Let’s call 115 lbs-force 500N.

The payload bay with electronics and batteries weighs about .185kg

If I understand the discussion, what I want to watch is the combination of reactive force (the inertia of the payload against the top of the body tube) - and I’m going to add in the drag force. I know that not all the drag acts through the nose cone, but that would be a conservative simplification. If the rocket managed to accelerate all the way up to its ‘terminal velocity‘ (drag = thrust) then there would be no reactive force, but all the drag force (the case of pushing into a fixed surface above). In between, I’ll assume they simply sum.

So I set up a sim of my rocket for an I204 to G100 and export the data, including thrust, vertical acceleration and drag force. If I could get it by part, I would, but the sim outputs the total. I chase it through Excel to clean it up and add some columns to do unit conversion.

Then I drop it into JMP, because the graphing capability is so much better. Add a couple of formula columns to get my top end reaction and drag sum. Color code by stage.

IMG_0285.jpg

So the first stage has the most thrust. And drag force - but that includes the Nike. The payload bay reaction spikes with the Apache G100 skidmark. And you can see the dips that caused early drag separation on a real, though lower impulse, flight.
The sum of payload reactive weight and drag is the bottom curve. Interesting flat spot at the beginning as reaction and drag trade off during the regressive part of the burn.

But even during the I204 boost, the sum doesn’t go over 110N. Way under the 500N tested limit.

Does that look like a reasonable approach?
 
Come to think of it, with this method, I can find the peak load, convert it back to pounds and put that weight on top of the tube. 25 pounds in my case.

The OP might be able to use this approach- I’m guessing it’s well under the failure point of the 54mm tubing.
 
Ah, the original poster. Almost forgot about that. Calculating from the material properties will be much harder. My method was &#8216;test to failure&#8217;, and I think that takes the need for calculus out. Especially with Openrocket handy....

Does that look like a reasonable approach?

If you asking me, I have to say that I really don't know.

What you tested was the static loading of the tube. The load under thrust varies very rapidly, which is liable to have an effect on the buckling strength of the rocket.

The somewhat simple-minded way that my somewhat simple mind would model it: The mechanical pulse delivered at the forward end of the airframe will propagate (travel) downwards at some speed, determined by the density and elastic properties of the cardboard. If the rate of increase in the compressive stress is small to compared to the rate at which a pulse propagates, then the Euler formula -- with appropriate inputs -- will describe the buckling strength of the airframe. If the rate at which the load changes is greater than or equal to the rate at which that stress is transmitted along the airframe, then the airframe may behave differently (how it would be different, I will not hazard to guess).

I spent 30 fruitless minutes on Science Direct trying to find something useful about the dynamic loading properties of paper. I then spent too many useless minutes staring at my copy of Hartog's Strength of Materials (and some other book on the Mechanics of Materials, not in front of me now, which I must have gotten as an inspection copy sometime since 2007).

I really think that the OP can only rely upon the the experience of others in this regard.
 
I have the 1948 edition of Kent’s Mechanical Engineering Handbook on my desk but it includes nothing about phenolic tubes...

The actual answer here is going to be very complicated. Column buckling is well understood, but a typical analysis will assume no deflection at the ends and static axial loads only. That obviously isn’t the case with a rocket body that is experiencing all sorts of dynamic loads during flight - both axial and transverse and variable along the length. You might get in the ballpark, but be very cautious of any hard numbers. Those numbers will also only be as valid as the material properties you use - which as noted above may be impossible to come by unless somebody has spent some time and effort testing the specific tube you’re using.

I second the assessment above: this is a good case for the time tested approach: “Copy what has been working for the other guy and adjust according to the desired safety margin”
 
To the OP, J's are totally reasonable on a 54mm LOC tube. A J Vmax or Warp 9 might be pushing it, but I would love to see anecdotal data on that.

Complicating this whole problem is that the issue isn't really Euler buckling of the entire column. If the whole rocket folds in half, it's usually because of a coupler that's not very tight or doesn't have enough overlap. If it's a structural problem of the tube, it won't be Euler buckling where the whole column bows elastically (OK, except for super-rocs, but they're special). If the tube folds, it's a local buckling problem where one side collapses and dents in. The rocket can then fold around that.

Calculating local buckling is possible, but it's highly dependent on off-axis bending loads on the rocket. It's also made messy on cardboard tubes because the spiral winding isn't a uniform material. I'm pretty sure this is a place where to use theory, you'd have to make so many handwaves that the end result is not very useful. I'd go with experience and practical testing here.

If I were designing a potentially destructive test, I'd put a weight equal to max thrust on top of the same length of body tube I wanted to test, with a safety line to hold the weights if the tube buckles and a guide to keep the whole thing from tipping over. I'd then push with 2% of that force on the side of the tube in the middle. If it all comes apart, it fails. If not, it passes. The 2% number comes from my old college days in civil engineering. The profs said that you should design cross-bracing that prevents buckling to 2% of the load the column supports. Flying the rocket sounds like more fun, though.
 
Based on the experience of others, I’d say flutter will get the fins long before the body tube fails.

Doesn’t a mechanical force propagate at the speed of sound -in that material-?

I like the idea of putting a little side load and torsional load into the static test. I don’t think they would be very large -in a stable, low spin, straight flying- rocket. Otherwise it would flop about the sky.
 
Using the peak thrust of the motor you are treating the case of the rocket being driven into a perfectly rigid barrier. If the rocket accelerates, that is to say if there are unbalanced forces, then the compressive force on the airframe will be less than the thrust delivered by the motor.
Snip…

At the point on the airframe where the motor thrust is coupled to the rocket, the compressive force is the same, whether the rocket moves (accelerates) or not. An example of a single plane of compressive force being equal to the motor thrust is the recent trend toward “thrust plates”. (That’s also why I don’t like thrust plates. ) The compressive force is proportional to the acceleration (which is assumed constant throughout the rocket) times the supported mass for every point above.
 
Based on the experience of others, I’d say flutter will get the fins long before the body tube fails.

Doesn’t a mechanical force propagate at the speed of sound -in that material-?

I like the idea of putting a little side load and torsional load into the static test. I don’t think they would be very large -in a stable, low spin, straight flying- rocket. Otherwise it would flop about the sky.

I completely agree; fin flutter is far more likely to wreck a rocket than body tube compression although I have had a coupler snap when a body tube flexed coming out of thrust on a high thrust Vmax K motor.
In rigid material, mechanical force is carried much faster than the speed of sound in air. I don’t think that is referred to as propagation though; it’s just the strength of the material; the ability to withstand compression.
 
In rigid material, mechanical force is carried much faster than the speed of sound in air. I don&#8217;t think that is referred to as propagation though; it&#8217;s just the strength of the material; the ability to withstand compression.

Sorry -- propagation, in the sense of transport. The mechanical pulse takes time to move between points along the airframe. The rate of transmission is the speed of propagation.

Yes, this speed can be described as the speed of sound in the solid. "Sound", though, suggests a periodic vibration -- a train of pulses. Also, the phrase "speed of sound" in the context of this forum has a specific meaning different from the speed with which a mechanical force is transmitted through an elastic medium.

As others have mentioned, the analysis of a body under dynamic loading -- where there force which produces the compressive stress is changing rapidly -- is significantly more complicated than the the analysis of static loading.

And I was being honest when I described as "simple minded" my idea of the threshold for dynamic loading as the point where the strain rate (in our problem, the speed with which the free end of body tube is deflected by the compressive stress) approaches the speed with which mechanical forces travel through the material.

It is a topic which does not yield easily to this kind of simplifying assumption.
 
Sorry -- propagation, in the sense of transport. The mechanical pulse takes time to move between points along the airframe. The rate of transmission is the speed of propagation.

Yes, this speed can be described as the speed of sound in the solid. "Sound", though, suggests a periodic vibration -- a train of pulses. Also, the phrase "speed of sound" in the context of this forum has a specific meaning different from the speed with which a mechanical force is transmitted through an elastic medium.

As others have mentioned, the analysis of a body under dynamic loading -- where there force which produces the compressive stress is changing rapidly -- is significantly more complicated than the the analysis of static loading.

And I was being honest when I described as "simple minded" my idea of the threshold for dynamic loading as the point where the strain rate (in our problem, the speed with which the free end of body tube is deflected by the compressive stress) approaches the speed with which mechanical forces travel through the material.

It is a topic which does not yield easily to this kind of simplifying assumption.

You’re right; Force propagates ( I was wrong; that’s the word used) as longitudinal waves thru a medium at a rate calculated as the square root of (modulus of elasticity/density of material). Because sound really is a transmission of force through a medium, force will be transmitted through that medium at the speed of sound through that medium (and the greater the rigidity and lower the density the greater that speed will be).
 
If you're concerned about buckling, use blue tube, it will take just about anything you can throw at it.
 
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