How to calculate at what parameters the coupling between the 1st and 2nd stages will fail

[Jadon Walters]

Looking for some guidance on this problem. Would like to know what physics term this is that i'm looking for.

 

[Jadon Walters]

Just browsing around, Is what i'm looking for the Bending Moment?

 

[mikec]

Could you be more specific about what you're trying to understand?

 

[Jadon Walters]

Could you be more specific about what you're trying to understand?

Im trying to understand what forces would be required for the interstage coupling area to fail and how to calculate these forces. As in the forces required to rip a sustainer away from a booster.

 

[Alan15578]

Just browsing around, Is what i'm looking for the Bending Moment?

I guess that you are looking for structural design loads. the most important of which would be the bending moment.

 

[mikec]

I think it's really too complicated to easily say. It depends on what the interstage coupler is made out of, how it supports the second stage and over what length, and what kinds of forces it's subjected to, which depend on how the whole stack ends up oscillating in flight and bending as it does so. I'm sure one could make some simplified assumptions about all that, but even that would be pretty complex. All hobby rocket simulators assume the whole rocket is rigid, and a two-stage rocket is anything but.

 

[mikec]

But I guess I should mention that my last two-stage experience was my BALLS project, 3-inch MD first stage to 54mm MD second stage, that broke in half at the interstage coupler 3 seconds into the boost on a CTI M1590.

For rockets small enough, the interstage coupler need not be that complicated, but for a long, heavy, somewhat flexible supersonic rocket, it's a much bigger deal that it might seem.

 

[OverTheTop]

Bending moments are what causes them to fold in half. Thrust pushing up, air drag pushing down, and if your rocket is not stiff enough it bends. The largest bending moment is in the middle typically, so for a homogeneous tube (say a column, or a single rocket) that is where the maximum stress is:
https://en.wikipedia.org/wiki/Euler's_critical_load

Staging complicates things as it can lead to a weakness at the interstage coupler, and any slop in the joint shows up as more bending, just making matters go south really quickly. If done correctly there is almost no slop in the coupling and everything stays axial. If you are clever with your design the fit will exhibit minimal movement.

I flew this earlier in the year and there was less than 1/8" slop at the top of the stack when mated.

The sustainer motor protruded about 8" past the back end of the rocket, into the interstage coupler, to provide the stability of the stack.

Discussion on aeroelasticity will probably be interesting for you also.

 

[Nytrunner]

flew this earlier in the year and there was less than 1/8" slop at the top of the stack when mated.

Not following. In which direction is the slop

 

[jlabrasca]

Im trying to understand what forces would be required for the interstage coupling area to fail and how to calculate these forces. As in the forces required to rip a sustainer away from a booster.

What are you trying to do? What are afraid is going to happen?

Your profile says you are 18 y.o. How much physics have you had? How much math?

You are asking at least two different and really complicated engineering questions:

1) How do I calculate (predict) the stress at which the component that joins the booster to the sustainer will fail?

2) How do I calculate the force required to separate the booster from the sustainer?

The phrase "rip a sustainer away from a booster" is interesting. Are you worried about premature separation (the booster coming away before the sustainer fires) or are you worried that the booster won't separate?

 

[Chris_H]

But I guess I should mention that my last two-stage experience was my BALLS project, 3-inch MD first stage to 54mm MD second stage, that broke in half at the interstage coupler 3 seconds into the boost on a CTI M1590.

For rockets small enough, the interstage coupler need not be that complicated, but for a long, heavy, somewhat flexible supersonic rocket, it's a much bigger deal that it might seem.

Did your coupler fail? Or the airframe below the coupler? Construction? Would love to hear more details.

 

[mikec]

Did your coupler fail? Or the airframe below the coupler? Construction? Would love to hear more details.

The ISC was a machined piece of Delrin that held the bottom of the second stage airframe and the CTI tapered closure of the second stage motor and formed the top of a coupler/avbay in the first stage. (I'll post some pictures when I get a chance.) The Delrin broke from a side load -- I haven't decided if it simply wasn't up to the task (could have gotten some wind shear) or if the second stage wasn't properly seated in the ISC at the pad so the stack was a little off-axis at launch. I suspect the latter, though I am unlikely to use Delrin again in this fashion.

 

[Chris_H]

The ISC was a machined piece of Delrin that held the bottom of the second stage airframe and the CTI tapered closure of the second stage motor and formed the top of a coupler/avbay in the first stage. (I'll post some pictures when I get a chance.) The Delrin broke from a side load -- I haven't decided if it simply wasn't up to the task (could have gotten some wind shear) or if the second stage wasn't properly seated in the ISC at the pad so the stack was a little off-axis at launch. I suspect the latter, though I am unlikely to use Delrin again in this fashion.

Thanks for sharing.

 

[OverTheTop]

Not following. In which direction is the slop

Sideways, at the nosecone, with the booster fixed in position. So slight angular displacement of the two axes. Was less than 1/8", and probably more like 1/16".

FYI my Nike Apache used a non-locking taper (both surfaces aluminium) on the interface of the ISC. The sustainer motor was extended past the airframe for about 8" or so. There was another ring at the end location that was an accurate slip fit which kept everything in line.
https://forum.ausrocketry.com/viewtopic.php?f=6&t=5019&start=45

 

[Jadon Walters]

Bending moments are what causes them to fold in half. Thrust pushing up, air drag pushing down, and if your rocket is not stiff enough it bends. The largest bending moment is in the middle typically, so for a homogeneous tube (say a column, or a single rocket) that is where the maximum stress is:
https://en.wikipedia.org/wiki/Euler's_critical_load

Staging complicates things as it can lead to a weakness at the interstage coupler, and any slop in the joint shows up as more bending, just making matters go south really quickly. If done correctly there is almost no slop in the coupling and everything stays axial. If you are clever with your design the fit will exhibit minimal movement.

I flew this earlier in the year and there was less than 1/8" slop at the top of the stack when mated.
View attachment 395383
The sustainer motor protruded about 8" past the back end of the rocket, into the interstage coupler, to provide the stability of the stack.

Discussion on aeroelasticity will probably be interesting for you also.

I believe this is what I'm looking for, thank you for the guidance. Just starting to dive into the more math heavy bits of rocketry.

 

[mikec]

The ISC was a machined piece of Delrin that held the bottom of the second stage airframe and the CTI tapered closure of the second stage motor and formed the top of a coupler/avbay in the first stage.

Here's a picture. The white thing is the Delrin ISC. You could say that I didn't have enough depth of engagement into the ISC and you might be right, but I flew a test flight on a K1000 before the BALLS flight and it went fine. So I still suspect that the second stage wasn't seated correctly. If I do it again, I will probably make the ISC out of aluminum and increase its length all the way up to the second stage fins.

 

[OverTheTop]

Looks like brittle tension failure. Looks like the applied bending moment generated forces exceeding the tensile strength of the Delrin part. If you can get it a little further into lower tube then that part will take the forces in compression and the hoop strength of the lower airframe (is it fiberglass?) will help you out.

 

[Chad]

Here's a picture. The white thing is the Delrin ISC. You could say that I didn't have enough depth of engagement into the ISC and you might be right, but I flew a test flight on a K1000 before the BALLS flight and it went fine. So I still suspect that the second stage wasn't seated correctly. If I do it again, I will probably make the ISC out of aluminum and increase its length all the way up to the second stage fins.

View attachment 395449

for what it's worth, i setup my ISC to engage 1.5x body tube width in both directions. So, in your case, that would be 4.5" in the booster and ~3.25" in the sustainer. I haven't launched mine yet ( other priorities ) but i think 1.5x is in the ballpark.

this thread has some good discussion and pictures re: ISC thoughts/suggestions
https://www.rocketryforum.com/threads/2-stage-to-minimum-diameter.62175/#post-657458

 

[Nytrunner]

I will probably make the ISC out of aluminum and increase its length all the way up to the second stage fins.

Glad to hear you're moving away form delrin. It's a great material for many application, but I wouldn't pick it for an interstage from a structural standpoint

i setup my ISC to engage 1.5x body tube width in both directions

A whole new meaning to CHAD-staging