# Using the Normal force coefficient CNa to predict stability of a rockets design.

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#### jahall4

##### Well-Known Member
Does anyone frequenting this forum have experience with using the Normal force coefficient CNa to predict stability of a rockets design? As I understand it CNa is a derivative of the Normal Force Fn or (N) that can be used to evaluate and compare the effectiveness of fin configurations (shape , size, etc). I have posted here because this tread will likely evolve towards RockSim since it is the source of my consternation.

Thanks to anyone who dares to venture into this topic.

Why consternation? Is there a particular design you are working on or is this more of a general question?

RockSim calculations for CNa seem to be amiss. :-(

Maybe. Can you define your terms a bit more?

Normal force with respect to which axis? (I assume radial/lateral for stabilizing moments).
Normal force on the rocket as a whole, or on a fin profile?
And which flow regimes of interest? (sub/trans/super....etc)

I do some rudimentary flow studies on my models that use resultant aero forces and the generated moments about a reference origin to calculate a theoretical CP which I compare to OpenRocket.

I've found OpenRocket to give conservative CP values (further forward than actual), and Rocksim to give a bit less conservative values sometimes. Usually the discrepancies show on odd geometry rockets.

Yep, in this case it is lateral. As far as definitions go I'm using RockSims. It appears my consternation centers around whether of not the CNa (Normal force coefficient derivative) would be a constant at subsonic (well under Mach) velocities. OR Is the constant a calculation a bug.

May be worth contacting Apogee and requesting information on how that term is developed.

Normal forces are a result of the pressure and sheer distributions on the solid in question, and those depend on the speed and angle of attack, so any 'Constant' value would be a gross assumption. Even taking the derivative of a corrective force shouldn't be constant over a flight (heck, over the boost phase alone)

Having said that, my gears have started spinning up......

In most of my flow studies, the resultant theoretical CP remains pretty much in the same place for a given model across a range of velocities. Hmmmm

I have already contacted Apogee, that's why I'm here

As I understand it AOA is assumed to be 0 for the purpose of calculating CP via Barrowman equations leaving just speed to calculate the Normal force and hence the corrective and damping forces to predict stability. An AOA greater than 10 or so and the CP changes to much to trust Barrowman.

I'm like you I was surprised to see a constant, but figured maybe that was what was intended, but then I stumbled into this... Turns out the CNa stops being a constant when the velocity exceeds ~460 ft/sec no matter what simulation is run! You'll also note that if CNa was a function of AOA it would "follow" that curve and oscillate, but it doesn't.

Having said that, my gears have started spinning up......

In most of my flow studies, the resultant theoretical CP remains pretty much in the same place for a given model across a range of velocities. Hmmmm

...which is a damn good thing

...which is a damn good thing

With the Caveat that All of my builds to date have been SUBSONIC and analyzed accordingly.

There is a confirmed forward shift of the CP at Transonic and beyond due to the flow shenanigans at the shock. I haven't gotten there yet, so I don't have any data to speak from.

With the Caveat that All of my builds to date have been SUBSONIC and analyzed accordingly.

There is a confirmed forward shift of the CP at Transonic and beyond due to the flow shenanigans at the shock. I haven't gotten there yet, so I don't have any data to speak from.

What's you thoughts on the chart?

Except for Nytrunner... "crickets"

Its a shame because I figured out what RockSim calls Fn (Normal Force)... "Pitch Force" and it follows the AOA like is should, but notice the kink in the line at exactly where CNa stops being a constant and it appears to always be ~473 ft/s no matter which simulation is run

I'm drawing a blank at the CNa still. Such a sharp step from 9.75 to 10.75 at a Very Specific velocity threshold.....doesn't look like a natural behavior.
Heh, the thing it reminds me of the most is when we were running matlab in college and the script would break at a certain point, so we'd introduce a forced bound to the data space where it'd be 1 or 0 or a constant etc....

The pitch force fits in better.

So the next question for you....... Have you heard about our lord and savior OpenRocket?

I found this value in its technical documentation.
Apparently the Normal Force coefficient is normalized using dynamic pressure and a reference area. This is all well ad good for FNC rockets, but I can see where Rocksim and OR start to get confused when transitions and pods and other odd elements get designed in.

OpenRocket? Certainly, but don't use it because it does not appear to handle tail cones correctly (e.g. V2) In fact I have been paid to redrawn OpenRocket designs in RockSim.

Correct. Its interpretation of the Barrowman assumptions does come with limitations.
I considered buying Rocksim until I started doing flow based stability calculations.

What I find amusing is that although Rocksim has a more refined stability algorithms (Tim Van Mil wrote about its development in a PoF some time ago), it has significantly poorer prediction capabilities in the transonic and beyond range when compared to OR and RasAeroII . The theory making its way around the block is that higher performance functionality is intentionally rudimentary to entice sale of the RockSim Pro suite.

Correct. Its interpretation of the Barrowman assumptions does come with limitations.
I considered buying Rocksim until I started doing flow based stability calculations.

What I find amusing is that although Rocksim has a more refined stability algorithms (Tim Van Mil wrote about its development in a PoF some time ago), it has significantly poorer prediction capabilities in the transonic and beyond range when compared to OR and RasAeroII . The theory making its way around the block is that higher performance functionality is intentionally rudimentary to entice sale of the RockSim Pro suite.

I not familiar with RasAeroII, but I'm not surprised as I never have considered RockSim a supersonic tool. This will interest you...

Caveat - To each their own

I just do not not apply that much thought to my toy rockets. Even the 6"dia 10' long ones. I do remember being at TARC when someone voiced "But Barrowman says" and Jim Barrowman turned around and said "I said no such thing". My understanding is that the Barrowman equations are an estimate based on a relatively narrow range of air-frame configurations.

I prefer to use the Abby-Normal coefficients on my oddrocs.

I prefer to use the Abby-Normal coefficients on my oddrocs.

Beware, I don't think silly oddroc mindsiming is going to fly in this quadrant of the forum. Only Vulcan Science Academy approved discourse based on pure logic, mathematics and science. If you can't sim it, don't fly it! You must do the math.

Caveat - To each their own

I just do not not apply that much thought to my toy rockets. Even the 6"dia 10' long ones. I do remember being at TARC when someone voiced "But Barrowman says" and Jim Barrowman turned around and said "I said no such thing". My understanding is that the Barrowman equations are an estimate based on a relatively narrow range of air-frame configurations.

Al, a lot of folks have never actually read Barrowman much less tried running the equations by hand.

His is a method to calculate Cp under certain restrictions. If you do not read the paper you do not know the limitations/assumptions.

Bits and pieces are dribbling out from Apogee... It appears that CNa and hence its curve is actually comprised if 3 or 4 different equations where the one used is dependent on the velocity of the rocket, which would explain why the curve is not smooth.

Does anyone frequenting this forum have experience with using the Normal force coefficient CNa to predict stability of a rockets design?

You cannot predict stability using CNa. That number lets you compute (if you also know angle of attack, air density, and velocity) the force applied at the center of pressure. It doesn't matter what CNa is if the CP is ahead of the CG as the rocket will be unstable.

It does others a disservice and dissuades participation to quote part of a post then argue it out of context.

It does others a disservice and dissuades participation to quote part of a post then argue it out of context.

Uh,it was humor...

What was?

Al and I have been around for quite some time- his humor was not lost on me.

Al and I have been around for quite some time- his humor was not lost on me.

Oh, Sorry Mark, didn't mean my comment to be attributed to Al.

Your last graph shows an upper velocity bound of CNa also now! Silly Rocksim.

Oh well. At the end of the day these are just hobby simulators. They can provide a rudimentary means of design for the average hobbyist and lead some on to pursue what's really happening with their rockets.

Or they can impart just enough knowledge to the "Make Tube Fly with Fire!" crowd to keep things safe.

Except for Nytrunner... "crickets"

Its a shame because I figured out what RockSim calls Fn (Normal Force)... "Pitch Force" and it follows the AOA like is should, but notice the kink in the line at exactly where CNa stops being a constant and it appears to always be ~473 ft/s no matter which simulation is run

View attachment 326572

I am not familiar with details of any of the popular sim tools. What this looks like, is some kind of compressibility correction applied to CN when the Mach number increases. At V=473 ft/sec you are around Mach 0.42, the Cn (and Cd-drag) compressibility corrections are applied gradually when you pass Mach 0.3, not just an on-off switch when you hit Mach 1. (The sim might be using the theoretical Prandtl-Glauert rule, perhaps?)

What is more concerning are the oscillations in the Pitch force (is really a moment or a torque that rotates the model about the c.g.) and wind angle of attack. If you get a wind angle of attack, you want the pitch force to restore you, and that is good static stability. But you don't want a pendulum effect where the pitch force and angle of attack continue to oscillate, you want dynamic stability. It appears that the oscillation does eventually damp out, but you might want to make some design changes to increase stability so that oscillation does not extend so far or the frequency of it slows down. That sim curve looks like the rocket is going over a washboard road. The sim curve is technically stable, but I would be curious as to the caliber measure of stability. Was there some wind event, or is the speed too slow off the rod that the rocket tilts? I don't know what you have going on in that particular sim to introduce those pitch oscillations.

I am not sure of the notation they are using, CNa might be the slope of the CN versus alpha curve, assuming a linear straight line near the low-alpha range. At zero-alpha, you have zero force, so CN would be zero at zero alpha, but the slope of the line from zero alpha to a small alpha < 10-deg would basically be constant.

Back to your original question, CN is used to help compute the location of the CP. The typical measure of stability for model rockets is the distance between the CG and the CP. When that distance is divided by the diameter of the rocket, this is called calibers. For a 1" dia rocket with 1-caliber stability, the CP is located 1" aft of the CG, for example. You want the Center of Gravity in front of the Center of Pressure. If you use the cardboard cutout method, then you are basically computing the CP location for an angle of attack of 90-deg, which is usually conservative. Barrowman equations compute CP location for a small alpha near zero degrees I think, right?

https://www.rocketmime.com/rockets/Barrowman.html

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