Barrowman method tutorial

[smstachwick]

Having had a copy of Stine’s Handbook for almost my entire rocket building career, I’ve always had a copy of the Barrowman equations at my disposal. I’ve wanted to learn how to do them for the longest time, but I started at an age when the math was beyond me and I still don’t believe my skills are up to doing it independently. I never completed any math class past Algebra 1 (8th grade in California at the time) and I think my mathematical know-how has deteriorated noticeably since then.

There are just so many placeholder variables, terms, constants, and operations that my brain just refuses to make any sense of them or figure out where to get started. I’ve been getting by through sticking with kit builds, making best guesses regarding modifications to those designs, and occasionally checking stability in OpenRocket, but I feel like I’m cheating myself by not gaining this deeper understanding.

What I’m looking for is a resource that can:

A.). Walk me through a few practice calculations with a simple rocket like an Estes Alpha or similar, just showing me where to get started and what steps to follow. The equations apparently support body tube transitions and multi-staging but I think that’s a bit ambitious for my first attempt.

B.). Explain in a simple way where the equations come from and how they account for a given rocket’s attributes, linking the abstract and mathematical with the concrete and physical. In my experience, the ability to plug and chug is distinct from actually understanding what I’m doing.

 

[WillMarchant]

Have you read the Centuri technical reports that Barrowman wrote? They’re attached to his, now complete, NARAM-8 report on the https://www.nar.org/members/rd-reports-in-chronological-order/ NAR site.

And he did his talk at vNARCON and that might be illuminating.

 

[Grog6]

If you are not good with math, get a copy of mathcad, and learn it. I use it for most hard stuff.

 

[dvdsnyd]

VNarcon 2021: Model Rocket Stability and Aerodynamic Equations, Presented by Jim Barrowman

 

[smstachwick]

Thank you for the suggestions. I will be sure to look at these and start calculations soon.

I’ll come back here either with questions or a successful result.

 

[Funkworks]

I've not had to use them myself (yet?) but this looks complete:

http://mae-nas.eng.usu.edu/MAE_5900_Web/5900/USLI_2010/Flight_Mechanics/Barrowman.html
Looks like it's about replacing each variable with a measurement, and then doing lots of algebra. Separating the calculation in many small problems would help.

I attach where the equations are from, but I haven't read it or tried to summarize it. It's almost certainly not a good starting point.

 

[samb]

Rocketmime has been my go to spot for math.
http://rocketmime.com/rockets/rckt_eqn.html
The Barrowman page has an example spreadsheet that is still usable AFAIK.
http://rocketmime.com/rockets/Barrowman.html

 

[Jeff Lassahn]

The equations aren't difficult, the big problem is that there's a lot of them so it's easy to get overwhelmed by the amount of stuff on the page.

The basic idea is that each component (nose, fin set, etc) has two numbers: An X value that gives the distance from the front of the rocket to the center of pressure for that component, and a Cn value that give the relative strength of the pressure force for that component.

To compute the whole thing, you go through each component and do one equation for X and one equation for Cn.

Then you do one final equation to combine all the Cn and X values into a final CP.

There's really only one mathematically difficult thing: the fin calculations need Lf, the length of the fin at mid-chord line. It's possible to compute this from the fin root chord, fin tip chord and fin semispan values, but there's no equation to tell you how. It's also possible to just estimate this by measuring a drawing. I can work out the details if anyone wants them.

Another resource that's helpful: OpenRocket has a Component Analysis page which shows the X value (which it calls CP) and the Cn value fore each component. You can use these to check your math for the intermediate steps. The bad thing (unless they fixed it recently) is that it seems to always report the X values in Meters no matter what you set the rocket units to, so if you're working in Inches the numbers are a lot less useful.

 

[smstachwick]

The equations aren't difficult, the big problem is that there's a lot of them so it's easy to get overwhelmed by the amount of stuff on the page.

The basic idea is that each component (nose, fin set, etc) has two numbers: An X value that gives the distance from the front of the rocket to the center of pressure for that component, and a Cn value that give the relative strength of the pressure force for that component.

To compute the whole thing, you go through each component and do one equation for X and one equation for Cn.

Then you do one final equation to combine all the Cn and X values into a final CP.

There's really only one mathematically difficult thing: the fin calculations need Lf, the length of the fin at mid-chord line. It's possible to compute this from the fin root chord, fin tip chord and fin semispan values, but there's no equation to tell you how. It's also possible to just estimate this by measuring a drawing. I can work out the details if anyone wants them.

Another resource that's helpful: OpenRocket has a Component Analysis page which shows the X value (which it calls CP) and the Cn value fore each component. You can use these to check your math for the intermediate steps. The bad thing (unless they fixed it recently) is that it seems to always report the X values in Meters no matter what you set the rocket units to, so if you're working in Inches the numbers are a lot less useful.

Thank you! That’s actually been pretty helpful.

Here’s what I’ve got so far with an Estes Alpha. I just pulled the numbers from an .ork file and started plugging them into the equation. Here’s my work on the main portion of the equation so far.


The crossed out portion is the terms for a conical transition. Obviously the Alpha does not have one so I’ve just ignored those and marked them as 0. Currently I’m working on calculating the Length of fin mid-chord line. (LF, I’ll figure out how to write the subscript later). My idea was to convert the supplied fins in the .ork file to freeform fins, pull the graph points from them, figure out the midpoints of the root and tip chords by figuring out the averages of the leading and trailing corners, and calculating the length of the line connecting the two midpoints with the Pythagorean Theorem. It’s still a work in progress, I just wanted to submit the idea and see if anyone with greater mathematical skill can tell me if it sounds valid or if I’d need something more advanced than that to figure it out.





(Also I’d be appreciative if somebody can double-check the math)

 

[Jeff Lassahn]

That all looks good so far. Your Lf calculation is basically how I would do it.

 

[smstachwick]

Excellent!

I was going to proceed with it tonight anyway but now I feel more confident with it.

 

[MJW]

If you are not good with math, get a copy of mathcad, and learn it. I use it for most hard stuff.

Wolfram Alpha is all online and nearly as useful as mathcad...

https://www.wolframalpha.com/
I'm pretty decent with math right up until you gotta start substituting numbers for all the variables. Just let the computers compute the numerical result avoid the part most likely to introduce silly errors.

 

[smstachwick]

Wolfram Alpha is all online and nearly as useful as mathcad...

https://www.wolframalpha.com/
I'm pretty decent with math right up until you gotta start substituting numbers for all the variables. Just let the computers compute the numerical result avoid the part most likely to introduce silly errors.

I feel like I’m generally ok with math if I have a solid grip on the concrete implications of the numbers, where they come from, and why they behave the way they do, but my education is full of holes and I never really advanced far enough to where I’d consider the Barrowman method doable without guidance. I had some behavioral issues during the time when one would normally learn the skills needed to do it, and those issues turned out to be more pressing.

I think revisiting this kind of work and learning how to do it can patch a few of those holes and maybe help me get my achievement/potential ratio closer to unity.

 

[Sandy H.]

I feel like I’m generally ok with math if I have a solid grip on the concrete implications of the numbers, where they come from, and why they behave the way they do, but my education is full of holes and I never really advanced far enough to where I’d consider the Barrowman method doable without guidance. I had some behavioral issues during the time when one would normally learn the skills needed to do it, and those issues turned out to be more pressing.

I think revisiting this kind of work and learning how to do it can patch a few of those holes and maybe help me get my achievement/potential ratio closer to unity.

I think your statement about understanding the implications of the underlying reason for doing the calculations (any calculations, honestly) is spot on. Once you understand the fundamentals or at least the reason different approximations or methods are used, you are much more likely to not only gain skill and general knowledge, but also make fewer silly mistakes. I highly respect this way of doing things.

I also highly respect your desire to revisit some things you missed out on to better yourself. It makes me believe you have the right attitude to successfully achieve your goals for Barrowman and beyond!

Sandy

 

[Grog6]

I love math, it's the only reality that doesn't lie, cheat or steal; it leaves that to physics.

 

[MJW]

I love math, it's the only reality that doesn't lie, cheat or steal; it leaves that to physics.

Formal logic is better than math... Any physicist can do math, but only a philosopher can prove an abstract thought.

 

[smstachwick]

Formal logic is better than math... Any physicist can do math, but only a philosopher can prove an abstract thought.

Begone, heathen!

 

[MJW]

Begone, heathen!

Just a lowly engineer here. But the best electives I took were in philosophy not math. To know truth one must seek the source after all.

 

[Grog6]

I speak boolean. Ive done electronics over 40 years, lol. My first computer repair was a PDP8, first software was z80 assembler.
I realized a few years ago that I can read both ascii hex and x86 assembly code from across the desk. (screens arent always where you want them to be, so you learn to deal. a vt100 console won't run in just any position. (we tested)
I still do pic assembler, and the occasional basic program.

 

[Alan15578]

I think your statement about understanding the implications of the underlying reason for doing the calculations (any calculations, honestly) is spot on. Once you understand the fundamentals or at least the reason different approximations or methods are used, you are much more likely to not only gain skill and general knowledge, but also make fewer silly mistakes. I highly respect this way of doing things.

I also highly respect your desire to revisit some things you missed out on to better yourself. It makes me believe you have the right attitude to successfully achieve your goals for Barrowman and beyond!

Sandy

Well said.

The genius of the Barroman equations is the simplification, using direct measurements, and eliminating details that can be covered by the one caliber stability margin.

The fin equations can be more easily understood by substituting in aspect ratio, area, taper ratio, and sweep, but then the equations appear more abstract to those not familiar with those terms. And yet one can find the fin CP accurately enough just by sketching in the quarter chord line and going out along it about 40 percent. As you do many hand calculations you will discover many other shortcuts. Slide rule accuracy is fine and a computer is not needed.

Alan

 

[Funkworks]

I love math, it's the only reality that doesn't lie, cheat or steal; it leaves that to physics.

To which a physicist would reply with:

I guess it takes a mathematician to believe there are many realities.

 

[smstachwick]

To which a physicist would reply with:

I guess it takes a mathematician to believe there are many realities.

(Laughs in quantum physics)

 

[smstachwick]

I’ve been working on the equations on and off, double-checking where I need to and only spending a few minutes at a time. I might have a final result tonight.

As a side question, does anybody happen to have \( X_N \) values for other nose shapes? A parabola for instance? Being restricted to cones and ogives doesn’t really seem that useful.

 

[rocket_troy]

As a side question, does anybody happen to have XNXN X_N values for other nose shapes? A parabola for instance? Being restricted to cones and ogives doesn’t really seem that useful.

Not really my area of specialty, but doesn't he provide an example for parabola in his Aero Paper for *Model Rockets* (p8) ie. not his complete paper, the one he did specially for model rockets?

TP

 

[smstachwick]

Not really my area of specialty, but doesn't he provide an example for parabola in his Aero Paper for *Model Rockets* (p8) ie. not his complete paper, the one he did specially for model rockets?

TP

I’ll look into that. I think I might have to recover my NAR login.

 

[rocket_troy]

Attached

 

[Ez2cDave]

As a side question, does anybody happen to have \( X_N \) values for other nose shapes? A parabola for instance? Being restricted to cones and ogives doesn’t really seem that useful.

 

[smstachwick]

View attachment 510947

Thanks to both of you, much appreciated!

 

[Citizen Baslim]

I love math, it's the only reality that doesn't lie, cheat or steal; it leaves that to physics.

Except when the math is statistics.

 

[Ez2cDave]

A little "math" never killed anyone . . . LOL !

Dave F.