# Body Tube Pressurization

#### BigRiJoe

##### Well-Known Member
Any one got any empirical data on how many PSI a body tubes gets pressurized when a LPR motor ejection charge fires?

#### Handeman

##### Well-Known Member
TRF Supporter
Any one got any empirical data on how many PSI a body tubes gets pressurized when a LPR motor ejection charge fires?

There are formulas available to calculate the pressure. You need to know the size of the charge and the interior volume of the body tube. Without the BT volume, any number would be a WAG.

##### Well-Known Member
Can I ask why you want to know this?

The simple answer to the question is only as much as needed to push the wadding against the parachute against the base of the nosecone and then out of the rocket. That is probably not much. Think how easy it is to pull the nosecone off a rocket. Pressure builds up in the body tube only until the nosecone separates from the body tube, pressure decreases rapidly.

The pressure is the result of the rapidly expanding gases produced by the combustion of the ejection charge. The expanding gases push the gas (air) already in the body tube forward, ejecting the recovery system.

A better question maybe to determine the amount of pressure needed to rupture a body tube. Im sure something with a bicycle pump could be rigged up fairly easily.

Im not sure this can be modeled mathematically as there are so many variables from rocket to rocket.

#### BigRiJoe

##### Well-Known Member
Can I ask why you want to know this?

Sure. I'm thinking about an R&D project to establish information as to the ease in which various diameter chutes and various length/width streamer eject from a variety of body tubes . I'm also looking to see if baffles vs plugs vs a variety of recovery wadding make a difference. I 'd like to be able to use compressed air to simulate the ejection charge

#### hardinlw

##### Well-Known Member
You may find some interesting things. I am mentoring a TARC team. This year, the egg has to recover by streamer. Their design had the booster coming down on a parachute and I questioned whether they could blow both out without them getting tangled. We did some ground tests and over and over the payload section with the streamer would pop off while the parachute remained in the bottom of the booster tube. Ultimately, I concluded that it was not so much that the ejection charge blows the parachute out, thus pushing off the nose cone; rather, the ejection charge blows the nose cone off and the momentum of the nose cone yanks out the streamer/chute. In support of that, the instructions for a couple of Aerotech kits that use a separate chute for the forward and aft halves of the rocket tell you to pack the chute for the nose scection UNDER the one for the aft section. That apparently guarantees that the chute for the aft section gets pulled out. In our case, the solution was to install a piston that pushes everything out. Your research project may shed some light on what is really happening here.

#### Winston

##### Lorenzo von Matterhorn
Test data on the maximum burst strength of various paper LPR body tubes along with their ability to hold pressure might be useful, also, in the F-Superoc competition at the upcoming NARAM. Pressurization might be useful to get an airframe strengthening effect like that used in the Atlas ICBM. Pressurized plastic fluorescent light protectors might also be used since they come in eight foot lengths and the plastic tube, unlike a paper tube, would not be susceptible to air leakage due to anything other than an actual puncture.

#### Graham Orr

##### Well-Known Member
"Im not sure this can be modeled mathematically as there are so many variables from rocket to rocket."

This can ABSOLUTELY be modeled mathematically. In fact, almost everything can be modeled mathematically. Even turbulent flows are modeled used a statistical/stochastic approach (see K41 hypothesis and Perfect Isotropic Turbulence). Assumptions are the key to modeling something.

Now, the pressurization of a cylindrical tube with some restriction is very likely to have a nice closed-form solution. In fact, the model may have error less than 20% from actual.

Even though analytical solutions may exist, it doesn't mean that the hobbyist will be able to easily grasp them. They may require some engineering/physics/differentialEqs that most rocketeers are not exposed to.

I guess I'm just a little dismayed by the number of people who claim that mathematical modeling has limited power and use. There are such elegant methods out there... and I wish more saw the beauty of applied mathematics!

#### powderburner

##### Well-Known Member
" In fact, the model may have error less than 20% from actual.

I would expect a range of structural characteristics something like 20% (or more) for body tubes made from paper that is cheaply purchased, cheaply manufactured into tube form, and subjected to a wide range of storage and handling conditions. It's not going to be like aerospace-grade aluminums or anything.

More variables:
--local weather conditions, incl temperature & humidity, causing the BT to shrink or swell and changing the "grip" on the shoulder of the NC
--NC fit, incl manufacturing variation on diameter of the shoulder, surface roughness, intentionally molded surface protrusions (like those little ribs on some shoulders), unintended molded surface protrusions (mold flash), length of shoulder, and probably more
--age of BT and collective number of ejection events to which it has been subjected (abused?) already
--number, type, size/length, and spacing of external fins which may provide some degree of reinforcement

One of the bigger variables, over which we have no control or means to estimate, is the power/weight of the blackpowder ejection charge itself. Depending on exact components (carbon from one source does not behave the same way as carbon from another source), processing (were components powdered? to dust? were they mealed, corned, etc? how many times?), and a number of other factors (what color shirt was the chemist wearing?), blackpowder batches can have a tremendous degree of variation in thermodynamic performance, calorie content, energy release rate, and a few other things. Blackpowder manufacture today is still just as much about art as it is about science.

#### Graham Orr

##### Well-Known Member
"I would expect a range of structural characteristics something like 20% (or more) for body tubes made from paper that is cheaply purchased, cheaply manufactured into tube form, and subjected to a wide range of storage and handling conditions. It's not going to be like aerospace-grade aluminums or anything."

Remember, the question is not regarding the structural integrity of the tubes/structure but a pressurization model to eject the nose and parachute section.

"More variables:
--local weather conditions, incl temperature & humidity, causing the BT to shrink or swell and changing the "grip" on the shoulder of the NC"

Can be accounted for (1st order) as the difference of CTE's of the materials. More complicated models could include the tribology factors between the fibrous and polymer surfaces.

"--NC fit, incl manufacturing variation on diameter of the shoulder, surface roughness, intentionally molded surface protrusions (like those little ribs on some shoulders), unintended molded surface protrusions (mold flash), length of shoulder, and probably more"

Notches and small protrusions can have a Hertzian contact analysis done. "Random" imperfections can be handled as a probability distribution function or Monte Carlo simulation.

"--age of BT and collective number of ejection events to which it has been subjected (abused?) already"

This is probably the most challenging of the bunch. In aerospace, we basically will wear in moving parts to 10K+ cycles to understand their fatigue properties. This would probably be handled by a probability function or Monte Carlo if done at my company. It'd likely also have human factors studies attached to it to see the types of mishandling that are likely to occur.

"--number, type, size/length, and spacing of external fins which may provide some degree of reinforcement"

Again, if we're not concerned about structural failure this is not necessary. We are only concerned about "fit".

"One of the bigger variables, over which we have no control or means to estimate, is the power/weight of the blackpowder ejection charge itself. Depending on exact components (carbon from one source does not behave the same way as carbon from another source), processing (were components powdered? to dust? were they mealed, corned, etc? how many times?), and a number of other factors (what color shirt was the chemist wearing?), blackpowder batches can have a tremendous degree of variation in thermodynamic performance, calorie content, energy release rate, and a few other things. Blackpowder manufacture today is still just as much about art as it is about science."

All said and done, one could represent the nose ejection characteristics as a function of blackpowder weight and grain size. The deflagration of blackpowder in various forms/grades has been greatly studied and I do believe analytic models do exist for it. Other small factors like the color of the chemist's shirt and what he ate for breakfast are likely to come out in the wash.

Very important variables:
Parachute section volume
Amount of powder used

Important variables:
Cross-sectional area of nose cone (F=P*A)
Basic nose cone "friction" (including CTE)

Somewhat important variables:
Mass ratio of nose cone
Vent port size
BP grain size (less important in larger rockets)

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