# back to the basics

#### Steve Shannon

##### Well-Known Member
TRF Supporter
thank you for the video. i will watch it asap. Im wanting to make sure that the stability number i picked for my rocket is actually good. I have been told 7 is too high, and i dont know why, and i have researched that 3 is good. is 7 "overstable" or "unstable"?
Unstable happens when Cp is even with or forward of Cg. That’s a negative value.
7 would be overstable but don’t forget that your stability margin must include the motor.

#### Lt72884

##### Well-Known Member
TRF Supporter
Unstable happens when Cp is even with or forward of Cg. That’s a negative value.
7 would be overstable but don’t forget that your stability margin must include the motor.
Ok, Cp with or ahead of Cg is unstable, while behind is stable and over stable . thanks for that.

like balancing a broom in my palm with the bristles up vs hanging it from the ceiling bristles down

#### Maxwelljets

##### Well-Known Member
Why would a fin that has a larger height cause more calibers of stability?
The others have pointed out that in your example, you've greatly increased the fin area. However, that's not the whole story.

One very important change that's also happening is you're increasing the aspect ratio of the fins. Aspect ratio is defined as b²/S, where b is the fin semi-span (the thing OR calls 'height') and S is the surface area of the fin. Higher aspect ratio fins are more aerodynamically efficient. For the same total surface area, at the same angle of attack, a higher aspect ratio fin will make more lift. This effect is independent of the effects others brought up such as the fin being "hidden" by the boundary layer. The lift curve slope as a function of aspect ratio can be found with the following equation:

where α is in radians.

If we graph this equation, we get the following:

Most rocket fins have aspect ratios around 1 or so, so as you can see the lift curve slope is very sensitive to aspect ratio in that region of the graph. A higher lift curve slope means that the same deflection will lead to a greater lift force, thus pulling the CP backward.

#### mtnmanak

##### ™

It will answer your current questions and the questions you don’t know you have yet.
View attachment 569203

There should be a pre-req that you have read Stine's book before being able to post on this site (only kind of joking...). At least some kind of banner that something like "Read Stine's book, then Post"

Stine's book isn't the end, but it is the beginning. Once you read it, it should launch your desire to dig deep and learn more.

#### Steve Shannon

##### Well-Known Member
TRF Supporter
Ok, Cp with or ahead of Cg is unstable, while behind is stable and over stable . thanks for that.

like balancing a broom in my palm with the bristles up vs hanging it from the ceiling bristles down
No, not at all.

The aerodynamic forces normal to the center of pressure steer a rocket around the CG. The greater the distance the greater the torque. If they are behind the center of gravity they’re pointing the rocket towards the direction thrust propels the rocket. That’s stability.

If the forces are ahead of the center of gravity they try to force the rocket to fly opposite the direction thrust propels it, which is impossible, so it switches direction over and over. That’s instability.

#### Lt72884

##### Well-Known Member
TRF Supporter
There should be a pre-req that you have read Stine's book before being able to post on this site (only kind of joking...). At least some kind of banner that something like "Read Stine's book, then Post"

Stine's book isn't the end, but it is the beginning. Once you read it, it should launch your desire to dig deep and learn more.
i own the book and have started reading it. Also some of barrowmans papers as well. im getting there

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#### Lt72884

##### Well-Known Member
TRF Supporter
No, not at all.

The aerodynamic forces normal to the center of pressure steer a rocket around the CG. The greater the distance the greater the torque. If they are behind the center of gravity they’re pointing the rocket towards the direction thrust propels the rocket. That’s stability.

If the forces are ahead of the center of gravity they try to force the rocket to fly opposite the direction thrust propels it, which is impossible, so it switches direction over and over. That’s instability.
In one of my earlier posts on here i was bringing up the moment arm with cp and cg. So the aerodynamic forces steer the rocket AROUND the cg! thats awesome. thank you very much for that. If that is in steins book, i have not read all of it yet. Im getting there.

i searched online about my broom analogy and what its supposed to be is a demonstration of negative and positive stability, not cp or cg.. my bad

#### Steve Shannon

##### Well-Known Member
TRF Supporter
In one of my earlier posts on here i was bringing up the moment arm with cp and cg. So the aerodynamic forces steer the rocket AROUND the cg! thats awesome. thank you very much for that. If that is in steins book, i have not read all of it yet. Im getting there.
Yes. That is the basis of aerodynamic stability. I thought I explained it in post 7, but maybe I wasn’t clear enough:

#### rharshberger

##### Well-Known Member
thank you for the video. i will watch it asap. Im wanting to make sure that the stability number i picked for my rocket is actually good. I have been told 7 is to high, and i dont know why, and i have researched that 3 is good. is 7 "overstable" or "unstable"?
How much a rockets margin of stability is will be dependent on the planned performance of the rocket, a rocket with a stability 1 would most likely be fine under transonic velocity, once mach shift sets in the stability margin needs to be higher as the CP shifts forward (if its only a 1 then a one caliber shift makes it unstable). Wind also has an effect on the stability...the higher the stability the more the rocket will weathercock (turn into the wind). A short fat rocket can be okay with a lower margin of stability of less than 1 due to base drag actually modifying the CP to improve its flight charactristics.

#### Lt72884

##### Well-Known Member
TRF Supporter
Yes. That is the basis of aerodynamic stability. I thought I explained it in post 7, but maybe I wasn’t clear enough:
i will go read post 7 again, maybe i read it to fast. it was late when i read some of these, like 3 am late after writing tech reports for fluids lab.. ill go re-read it.. thanks
EDIT: Ok, i went and re-read it. Both posts make sense, and i can see why larger fins cause over stability.

#### Lt72884

##### Well-Known Member
TRF Supporter
The others have pointed out that in your example, you've greatly increased the fin area. However, that's not the whole story.

One very important change that's also happening is you're increasing the aspect ratio of the fins. Aspect ratio is defined as b²/S, where b is the fin semi-span (the thing OR calls 'height') and S is the surface area of the fin. Higher aspect ratio fins are more aerodynamically efficient. For the same total surface area, at the same angle of attack, a higher aspect ratio fin will make more lift. This effect is independent of the effects others brought up such as the fin being "hidden" by the boundary layer. The lift curve slope as a function of aspect ratio can be found with the following equation:
View attachment 569413
where α is in radians.

If we graph this equation, we get the following:
View attachment 569415
Most rocket fins have aspect ratios around 1 or so, so as you can see the lift curve slope is very sensitive to aspect ratio in that region of the graph. A higher lift curve slope means that the same deflection will lead to a greater lift force, thus pulling the CP backward.
thank you for this graph and the math. Where did you find it? If its in steins book, i have not gotten that far yet.

#### Maxwelljets

##### Well-Known Member
thank you for this graph and the math. Where did you find it? If its in steins book, i have not gotten that far yet.
No, it's not from Stein. That book is a fantastic resource, but is more about the practical side of hobby rocketry rather than the theory of aerodynamics. I don't recall if it discusses the effects of aspect ratio or not. The equation is from an aerodynamics textbook, and the graph is something I made in Matlab.

The equation is algebraically equivalent to equation (3) in this NACA paper, which also discusses some more of the theory behind it as well as some caveats about applicability. The form of the equation I wrote is for α in radians, and the equation in this paper uses α in degrees, so you need to apply the conversion factor. They have also multiplied the whole fraction by AR/AR, so the equation looks slightly different. However, it is equivalent.

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#### Steve Shannon

##### Well-Known Member
TRF Supporter
i will go read post 7 again, maybe i read it to fast. it was late when i read some of these, like 3 am late after writing tech reports for fluids lab.. ill go re-read it.. thanks
EDIT: Ok, i went and re-read it. Both posts make sense, and i can see why larger fins cause over stability.
Great!
But, it’s really important to understand that over stability by itself is not a bad thing. Over stability simply makes a rocket more susceptible to weathercocking.

#### G_T

##### Well-Known Member

Though maxwell covered it. I grabbed the link before I saw his post. Overall, TL;DR - sorry; I don't have the time tonight!

But stability also affects the damping rate, and what form the damping takes.

More complex than this of course for a rocket since it is often spinning at some rate, and having an uneven number of fins adds more to the fun.

Gerald

#### Alan15578

##### Well-Known Member

Though maxwell covered it. I grabbed the link before I saw his post. Overall, TL;DR - sorry; I don't have the time tonight!

I am not buying that graph in the above URL.
But stability also affects the damping rate, and what form the damping takes.

Gerald

The older design rules for model rockets was 1 caliber static margin PLUS a damping ratio or factor of 0.05 to 0.3, or there about. In the interest of simplicity and laziness, we mostly ignore the damping and endlessly debate the static margin. Many rockets like dual-egglofters should have more than one caliber static stability margin just to get more damping. High q rockets like superrocs need more static stability just to maintain stability in the face of flexibility. The Estes Cineroc Omega had huge barn door fins to get the damping appropriate for a movie camera.

#### cjl

##### Well-Known Member
I am not buying that graph in the above URL.

Why not? It looks at least pretty close to reasonable to me.

EDIT: Actually, on second thought, no, I take that back. You're right that it has some problems. It's qualitatively at least sort of correct, but max Cl for the low aspect ratio should be below max Cl for the high aspect ratio, and I'd also expect much less difference from AR of 9 to 15, since 9 should already be getting you kind of close to infinite wing behavior. This is probably a more accurate representation.

High q rockets like superrocs need more static stability just to maintain stability in the face of flexibility.

That's not the main reason you need more stability for a long slender rocket. Long slender rockets will also tend to have more CP shift with angle of attack. We often assume that CP is a single location, but it actually isn't. The value calculated by openrocket or rocksim or similar is a pretty decent estimate of the CP at or very near to zero degrees angle of attack, but at higher angles of attack, it will nearly always shift forwards. On a long slender rocket, this forward shift can be quite significant, so you need to start with more margin to ensure stability even in case of a wind shear or perturbation in flight.

(That's also why I like to have a margin of 10% of rocket length rather than basing it on calibers - it's a bit more reasonable for rockets with unusual aspect ratios)

#### Alan15578

##### Well-Known Member
Why not? It looks at least pretty close to reasonable to me.

EDIT: Actually, on second thought, no, I take that back. You're right that it has some problems. It's qualitatively at least sort of correct, but max Cl for the low aspect ratio should be below max Cl for the high aspect ratio, and I'd also expect much less difference from AR of 9 to 15, since 9 should already be getting you kind of close to infinite wing behavior. This is probably a more accurate representation.

Much better.
That's not the main reason you need more stability for a long slender rocket. Long slender rockets will also tend to have more CP shift with angle of attack. We often assume that CP is a single location, but it actually isn't. The value calculated by openrocket or rocksim or similar is a pretty decent estimate of the CP at or very near to zero degrees angle of attack, but at higher angles of attack, it will nearly always shift forwards. On a long slender rocket, this forward shift can be quite significant, so you need to start with more margin to ensure stability even in case of a wind shear or perturbation in flight.

(That's also why I like to have a margin of 10% of rocket length rather than basing it on calibers - it's a bit more reasonable for rockets with unusual aspect ratios)
Once again, your argument is all about the static margin and ignoring damping and many other significant aspects.

#### cjl

##### Well-Known Member
Once again, your argument is all about the static margin and ignoring damping and many other significant aspects.
Yes, because the CP shift with alpha is the main reason you need more margin with long slender rockets.

(Also because damping behavior is somewhat more difficult to accurately estimate than static margin)

#### Alan15578

##### Well-Known Member
Yes, because the CP shift with alpha is the main reason you need more margin with long slender rockets.

Arguably, it is a reason, but not the main reason.
(Also because damping behavior is somewhat more difficult to accurately estimate than static margin)
Better, at least you are parenthetically addressing damping.

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