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

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#### jahall4

##### Well-Known Member
Your last graph shows an upper velocity bound of CNa also now!
It sure seems to, that's why I posted it.

#### Nytrunner

##### Pop lugs, not drugs
TRF Supporter
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.
Interesting thought about a gradually applied compressibility factor. I still find the discontinuous behavior unnatural though lol.

Do you really thing the oscillation is worrisome? After the initial 2deg deviation off the rail, its next highest peak is barely .2deg at 1 second and damps quickly.

#### jahall4

##### Well-Known Member
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?)
Yes! that was one of the "bits and pieces" that dribbled out of Apogee... that CNa = CNa / B where B is some type of compressibility factor based on Mach and the lower threshold was in fact 0.42 What was not explained was why CNa at velocities under 4.2 was a constant. Is that what you are explaining below? And yes CNa is the derivative of CN. Sometimes referred to as the "stability derivative".

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.
...and yep 10 deg. is the value I have seen referenced in other literature. "... The Barrowman equations are derived using the following assumptions: #1 The angle of attack of the rocket is low (&#945; < 10&#9702"

So what's you guess... Rocksim is NOT applying a compressibility correction below Mach 0.42? Subsequently CNa is intended to be a constant below 0.42? IOW it is not a bug but the expected result?

#### GlenP

##### Well-Known Member
Below Mach ~ 0.42 you don't really have significant effects of compressible flow, you are assuming, the flow is totally subsonic around all parts of the vehicle, so no theoretical corrections for compressibility are required there. Not a bug, just using mathematics that properly simulate the flow physics.

#### jahall4

##### Well-Known Member
Do you really thing the oscillation is worrisome? After the initial 2deg deviation off the rail, its next highest peak is barely .2deg at 1 second and damps quickly.
I don't :wink: Good observation. This is a sim of a proven kit that flies exceptionally well a, Madcow Tomach. I think what makes the AOA plot scary is the scale of the y axis and the fact that the wind on this particular sim was 20mph.

#### GlenP

##### Well-Known Member
Interesting thought about a gradually applied compressibility factor. I still find the discontinuous behavior unnatural though lol.

Do you really thing the oscillation is worrisome? After the initial 2deg deviation off the rail, its next highest peak is barely .2deg at 1 second and damps quickly.
I am not concerned about the low amplitude, but the high frequency. That is what we call "flutter" and that can potentially rip a rocket to shreds. But, since this is a proven design, it is probably just an exaggerated effect of the high winds used in the sim.

#### jahall4

##### Well-Known Member
Below Mach ~ 0.42 you don't really have significant effects of compressible flow, you are assuming, the flow is totally subsonic around all parts of the vehicle, so no theoretical corrections for compressibility are required there. Not a bug, just using mathematics that properly simulate the flow physics.
So you would expect to see CNa as a constant below Mach 0.42?

#### jahall4

##### Well-Known Member
I am not concerned about the low amplitude, but the high frequency. That is what we call "flutter" and that can potentially rip a rocket to shreds. But, since this is a proven design, it is probably just an exaggerated effect of the high winds used in the sim.
... but the frequency is only 2-3 cycles/sec. and then its gone.

#### GlenP

##### Well-Known Member
So you would expect to see CNa as a constant below Mach 0.42?
Yes, I think that is consistent with the typical theory for low-speed flows.

It may actually change with Reynolds Number, but that's another story! :wink:

#### GlenP

##### Well-Known Member
... but the frequency is only 2-3 cycles/sec. and then its gone.
The tendency to oscillate at that frequency is still there, if something disturbs it. Given that you were using such a high 20 mph wind disturbance, I don't think there is anything to be concerned about. (I did not know what kind of wind inputs you had specified when I voiced my initial concern of that sim response.) Which, you are correct, this is more of a low frequency flight disturbance, not really classical flutter which is typically considered a little higher frequency, but I was loosely using the term here to elicit a dramatic response, did it work?

Did the sim report the stability in calibers? I imagine it is between 1 to 2?

#### jahall4

##### Well-Known Member
Yes, I think that is consistent with the typical theory for low-speed flows.
Thanks! I just had to hear it. I have been struggling with this for the last few days. I'm not at all surprised by your explanation, but before, I could not trust my own conclusions w/o some validation.

#### jahall4

##### Well-Known Member
Did the sim report the stability in calibers? I imagine it is between 1 to 2?
1.72 I think it was.

#### GlenP

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

View attachment 326587
As there is the low end limit, there is an upper limit as well, probably like around Mach 0.9. The Prandtl Glauert factor is 1 at Mach zero, and goes to infinity at Mach 1, so most numerical codes put a practical limit in the factor between the range of Mach 0.9 to 1.1 or so. That is why you have the two different constant CNA portions of the curve in this example sim.

#### Nytrunner

##### Pop lugs, not drugs
TRF Supporter
As there is the low end limit, there is an upper limit as well, probably like around Mach 0.9. The Prandtl Glauert factor is 1 at Mach zero, and goes to infinity at Mach 1, so most numerical codes put a practical limit in the factor between the range of Mach 0.9 to 1.1 or so. That is why you have the two different constant CNA portions of the curve in this example sim.
Hah! I was right, it is a bound to keep the algorithm from losing its mind!

Now I'm why they provide CNa as a plottable value. Troubleshooting?

#### OverTheTop

##### Well-Known Member
TRF Supporter
The Prandtl Glauert factor is 1 at Mach zero, and goes to infinity at Mach 1, so most numerical codes put a practical limit in the factor between the range of Mach 0.9 to 1.1 or so.
Yep. The mathematical discontinuity at Mach 1 is usually pegged to a particular peak value, and is actually a very good representation of reality for most situations.

Oscilations
If the oscillation is damped relatively well and not excessive in frequency (a few Hz on the scale we work at would not worry me) then don't be too concerned. A little overshoot and slight ringing actually gets you back to zero AoA quicker than an overdamped response or an underdamped response. The quicker you get back to zero AoA the less dissipation of kinetic energy due to drag. The damped oscillations may offend some people, but they are the best response in most control system cases where you want to be within a given tolerance band as quick as possible.

BTW, I saw a disturbance of 20mph was used earlier. That is probably ok for lower flights, but if considering flying higher I would use a higher value for winds aloft calculations as there can be significant differences between the winds a different altitudes. If I were simming a flight to 20k' I would probably perturb it by about 40 knots to see the effect. That's the good thing about sims: you can push the numbers without re-kitting a real rocket.

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#### jahall4

##### Well-Known Member
As there is the low end limit, there is an upper limit as well, probably like around Mach 0.9. The Prandtl Glauert factor is 1 at Mach zero, and goes to infinity at Mach 1, so most numerical codes put a practical limit in the factor between the range of Mach 0.9 to 1.1 or so. That is why you have the two different constant CNA portions of the curve in this example sim.
Yep. I talked with the programmer of Rocksim yesterday for over an hour. He confirmed that Rocksim use a different algorithm to compute CNa between Mach 0.42 and 0.8 that takes into account compressibility, otherwise CNa is in fact a constant and the curve accurately reflects the calculations in the simulation.

He also confirmed that CNa is the best value to start with when comparing the effectiveness of the fins between different designs. In my case I'm designing a 3 fin version of a proven 4 fin rocket. Except for the fins the rest of the rocket is unchanged so if I match the CNa curves between the 4 and 3 fin version I should be well on my way to designing a 3 fin version that has nearly identical flight characteristics.

#### GlenP

##### Well-Known Member
I'm designing a 3 fin version of a proven 4 fin rocket.
As a starting point, I would scale the fins by 115%, that comes from the square root of 4/3, which is used as an area ratio of an individual fin. This would preserve the total fin area, the total fin area of the three fin version would match the total area of the four fin version.

#### jahall4

##### Well-Known Member
As a starting point, I would scale the fins by 115%, that comes from the square root of 4/3, which is used as an area ratio of an individual fin. This would preserve the total fin area, the total fin area of the three fin version would match the total area of the four fin version.
What's interesting is that simply removing the fin appears to make the rocket fly better. The 4th fin drove down the Damping Ratio down during coast to nearly .05, removing it brings it up to .06 so I'm tempted to do noting.

#### GlenP

##### Well-Known Member
Three fins will have a little less aft weight, and also less drag, compared to four fins. So you are moving the c.g. forwards a little along with the c.p. With 1.76 calibers you have some wiggle room to work with in how you want to deviate from the original and still have some margin.

#### jahall4

##### Well-Known Member
Three fins will have a little less aft weight, and also less drag, compared to four fins. So you are moving the c.g. forwards a little along with the c.p. With 1.76 calibers you have some wiggle room to work with in how you want to deviate from the original and still have some margin.
Actually, in the design that is being converted to 3 fins the margin is around 1.

#### boatgeek

##### Well-Known Member
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.
But... Engineering is the science of good enough. A professor told me that, so it must be true! I suppose everyone's level of good enough is different.

#### OverTheTop

##### Well-Known Member
TRF Supporter
But... Engineering is the science of good enough. A professor told me that, so it must be true! I suppose everyone's level of good enough is different.
Engineering is about being fit for purpose, not perfection. Think perfection with tolerance bands to keep it real. If you are CDO (that's OCD but spelt the correct way :wink the tolerance bands are probably more narrow.

#### Steve Shannon

##### Well-Known Member
TRF Supporter
Best is the enemy of good enough.

Steve Shannon