Rocket Design Theroy

[Airdale]

Hello All,

I have some questions about compressive loading on phenolic tubing, and if it will survive without having to reinforce the phenolic tubing with either fiberglass or carbon fiber.

Known qualities are: phenolic tubes can withstand a compressive loading of 1000 psi based on this web sites research https://www.rocketmaterials.com/data/tubes/ before failing.

My rocket design has the following properties a 5.5-inch diameter Red Arrow hobbies phenolic airframe. The cross sectional area of a 5.5-inch tube is 23.75 inches. If I did my math right?

Maximum velocity of the proposed design is 2453.42 feet per second. Based on Greg Deputy Excel spreadsheet on compressive loading of airframes diameters. And selecting a 5.5-inch diameter airframe, and based on a flight of 2453.42 feet per second the spreadsheet indicated a compressive load of 1176.97 lbs. force at sea level. Which needs to be converted to psi to make all things equal (and not apples & oranges) right?

To do this I need to do take the frontal area of my rocket and divide by the force, that gives me psi (lbs force per square inch). Right?

So if I take the 1176.97 lbs and divide it by 23.75 inches in area. Force I should get 49.55 psi. Is this correct or did I mess it up completely?

 

[powderburner]

I don’t know how comprehensively you want to go through all the different aspects of design, but even a shallow pass through this stuff might get quite involved. If there is part of this you don’t follow, please don’t be afraid to ask questions, and we will try our best to keep on answering.

Yes, the cross-sectional area (and I am going to use the abbreviation X-sectn) of a 5.5 inch diam body is 23.75 sq in, but this is the X-sectn you would use for aerodynamic purposes. For internal loads (the forces, stresses and strains acting inside the structural components), the X-sectn area you are interested in is that of the airframe tube shell, because the empty space inside the shell is not going to support any structural loads.

If you have a body of 5.5 inch diam, the circumference is 17.28 inches (pi times the diam). If we assume a wall thickness of 0.10 inches, the X-sectn area of the airframe tube is 1.73 sq in (circumf times thickness). And if there are any holes or openings in the side walls of the airframe, they represent a weak point because of the structural cutout (loads are slightly concentrated around the edges of the hole) and for the reduced shell X-sectn in that area.

I am guessing that your spreadsheet represents an aerodynamic drag load acting on the front end of your rocket design? Yes, there will be aerodynamic loads, if your rocket ever gets going fast enough. Before that happens, however, you have some significant accelerations and loads that occur during motor burn. You have the thrust force of the motor (most severe during peak thrust) acting against the inertia load of all components of the rocket that are located ahead of the motor mount. The highest levels of internal loads caused by motor thrust will be found in the airframe shell in the zone at, and immediately ahead of, the motor mounts. As you move forward through your rocket design, past the weight of the lower airframe, past the ejection baffles, past the altimeter bay, etc, the weight (actually, mass) of components that are yet further forward is progressively reduced. The upper sections of airframe do not require the structural ‘beef’ that the lower portions do in order to withstand internal loads due to motor thrust. So if you feel you must reinforce the airframe with fiberglass or carbon fiber, you are wasting your time (and adding lots of dead weight) to add reinforcement to any of the front half (or even two thirds?) of the structure.

Now if you want to build a rocket that will withstand a free-fall from 5,000 feet (ejection failure) and come up out of the ground unscathed, go ahead and reinforce everything. You can even build the front end out of titanium or something.

This ignores the whole matter of the stability (in a structural sense) of the airframe tube, and whether to expect local crippling, column buckling, or other failure modes. Usually something else gets ya long before you approach the raw shear strength limits of the material. Hopefully the manufacturer has performed some realistic tests of his airframe product; you should look for qualifying statements such as ‘1,000 pound load on a 60-inch-long section’ or something to that effect. If you want to test this yourself you can perform a simple test in your garage by standing the tube on end (on a cleanly cut, perpendicular end face) and stacking sandbags (of a known weight) on top. The tricky part will be balancing the whole mess, and applying each additional bag GENTLY. Stand clear, don’t perform this trick within ‘reach’ of anything breakable, and don’t let the kids play underneath the sandbags. And of course, after you test the tube to failure, it won’t be any good to build with.

As far as aerodynamic loads are concerned, an axial load of 1177 pounds acting on 1.73 square inches will give you a stress level of 680 psi. Even if you apply a safety factor of 1.25 to cover the ‘unknown unknowns,’ the stresses would still only be 850 psi, well within the advertised limit of 1000 psi, without any added airframe reinforcement. If your airframe tube has a wall thickness less than 0.10 inches, you will obviously need to re-run these numbers.

I would bet that some of the experienced HPR guys (sorry, I can’t help here because I ain’t one of ‘em) could give you some rules-of-thumb on which you could base your design. I don’t know if the database is really complete enough to try to analyze these designs from an engineering standpoint. It seems you pretty much have to build-n-fly HPR, and adjust the next one to your personal preferences based on experience.

Oh, yeah, almost forgot . . . welcome to TRF!!

 

[Airdale]

Wow! powderburner that is a handfull of typing thanks for the feedback. I can see now that flying this design as a L3 will work!

However trying to fly it as I designed the project maybe another matter. If you have RockSim ver. 6.92 or higher you would be able to see why I am worried

After passing my L3 cert. I want to fly it as a two stage complex rocket. and the second stage when loaded with motor weighes in at 11.3 lbs. and is 3 inches in diameter. which could push the envelope and cause the airframe to fail.

 

[jflis]

This would make a great technical discussion at one of the national events (NARCON or a club convention)

or even a writeup (with more depth) for Sport Rocketry

 

[el chubbo]

One of the themes that I picked up in your reply to the original question was (and I'm paraphrasing here...)

- the overall stress imposed on a typical airframe is greatest at the foward point of connection between the motor mount and the airframe -

If I am correct in understanding your explaination (when they were passing out brains I must have been WAY behind you in line) this would almost negate glassing a rocket for reasons of (i'm making up a term here) "flight-induced stress loads" - e.g. the stress of acceleration, airflow etc....

If this is true then couldn't an internal structure that distributed this "connection point stress" more equally to the airframe be a viable substitute for glassing (assuming no cato of the recovery system)...

mmmmm.

 

[powderburner]

el chubbo,

You got the entire idea and applied it correctly. The highest levels of internal structural loads will be at the spot between where the motor is pushing and the airframe above (and contents) is pushing back.

Whether you need to glass that spot, I can't begin to say because I don't have any numbers to begin a 'real' analysis. I have only built a few mid-power rockets, and no high power birds, so I am certainly no expert as far as practical experience. There are undoubtedly some very good reasons for glassing the entire body tube, such as protecting the tube during rough landings. My comments were pretty much limited to the design condition during powered flight.

You are thinking in the right direction, though, as far as alternate ways to beef up the airframe. There could well be ways to construct internal reinforcements (laminate a second piece of BT to the inside?) but unless you are working with some really BIG airframe tubing, you will have a tough time getting your hands inside there to do any work.

As far as in-flight aerodynamic forces, these loads will probably reach a maximum at the moment of burnout (assuming your thrust curve ends fairly sharply and doesn't dribble off to some low level?) when the rocket is moving at maximum velocity. For that condition, you will need to estimate the drag force acting on the nose cone. Keep in mind that this is only one component of the vehicle drag (drag forces on the fins, base drag, skin friction drag are all acting elsewhere). The nose drag becomes the main force acting on the airframe during coasting flight, and the mass of the airframe is pushing against it (inertial loads). So during the beginning of coasting flight the front end of the body tube needs to be strong enough (or, another way, stress levels need to be low enough) to withstand these loads, and the load levels are reduced as you get near the tail of the airframe.

One of the bits of information that is key to this whole question is this: what exactly are the strength characteristics of the body tube, especially under compressive loading? I have not ever seen numerical data for anything, from BT-5 to ten-inch airframe stock. Until we understand how strong the basic body tube is, it will be pretty hard to estimate how much reinforcement is really needed.

 

[Airdale]

Hello All, This is another reply I received from a Mr. Bob Krech, I am posting it here to bring up just a different point of view. I appreciate all points of view expressed in these posts and have learned a lot from all contributors. Thank You very much!

P.S. I beleve I posted a web site link in my first post that gives Strength of different marterials used in rocket airframes, if you would like to use it as a base reference.

David

You messed it up a little but there's a much easier way to do the calculation.

Just try to remember your high school physics.

One of Newton's laws states that for every reaction there is an equal and opposite reaction. In a rocket the action is the thrust of the motor and the reaction is the resistance of the airframe to this thrust.

When you look at the problem this way, you don't have to worry about velocity or aerodynamic stresses since they are are a reaction soley due to the action (thrust) of the motor. If the thrust exceeds the aerodynamics forces the velocity increases, if they are equal the velocity is constant, and if the thrust is lower than the aerodynamic forces the rocket slows down, so ultimately the thrust of the motor is the determining factor of the loading of the airframe.

So to solve the problem you have to:

1.) determine the peak load,

2.) calculate the appropriate cross-section that must carry the load,

3.) determine the stress developed in the cross-section,

4.) experimentally determine the yield strength of the airframe,

5.) compare the measured yield strength to the actual stress to calculate the design factor and determine if the design is robust enough.

Here's how you do it.

In another part of the thread, it is stated that you plan to use a N4800 motor. The peak thrust from this motor is 1400 pounds, so

1.) The peak load is 1400 pounds.

This load must be carried by the airframe. The Red Arrow airframe is 5.375" i.d and has 0.080" thick wall. The cross-section that carries the load is simply the circumference time the wall thickenss or

2.) 5.375" x pi x 0.080" = 1.35 sq. in.

The maximum compressive stress induced in the airframe is simpley the peak load divide by the cross-sectional area or

3.) 1400 lb / 1.35 sq. in. = 1037 psi

The minimum yield stress for the 3" PML phenolic airframe is listed in your materials reference website as 4781 psi, so

4.) The yield strength of the material is 4781 psi

If we assume that both airframes use similar materials then you have a design factor (safety margin) of the measured material yield stess divide by the actual stress which is

5.) 4781 psi / 1037 psi = 4.6

Real rockets and airplanes use design factors typically between 1.5 to 2. I usually use 4 in most of my laboratory apparatus designs. ASTM boiler code typically calls for a design factor of 10. I would be comfortable with a 4.6 design factor on an airframe.

You should also be aware that in the real world the load may not be totally compressive. In a cross-wind there will be a bending moment in addition to the compressive loading, however since the design factor appears to be quite large, this should be a non-issue.

Also if you have point loading verses a distributed loading, the above calculations are not valid.

Hope this helps.

Bob Krech

 

[rstaff3]

Someone should summarize this in one write up and see if it can be archived here: https://www.rocketmaterials.com/

 

[bobkrech]

rdstaff3

I'm glad you found my analysis interesting. I first saw this thread on ROL and posted the reply there. Airdale must have liked it and reposted it here.

I do this type of analysis on every project I work on. All of the fancy finite element or finite difference design codes make it easy to solve complex coupled thermo-mechanical designs but the results are only as good as the data and boundary conditions that gets input to the code.

It's pretty easy for a good but inexperienced engineer to get into trouble quickly by obtaining what appears to be mathematically valid design that doesn't work because he didn't set the boundary conditions correctly because he didn't understand the basic physics and/or the materials properties got screwed up.

This simple 5 minute sanity check using basic physics prevents this kind of errors. If you use F=ma, v=at, d=1/2 a(t^2), and a few other simple equations, you can answer a lot of basic rocketry questions quickly.

Bob Krech