Rocket stability(center of mass)

I have read that the center of pressure must be below the center of mass but I guess there should also be a constraint about how high the center of mass is. I mean if it were too high, the rocket was likely to topple when in a vertical position. Please elaborate. Use of physics is appreciated.

Nope. No matter how high the center of mass is, there's no risk of toppling after liftoff.

(Of course, it could topple on the pad if the center of gravity were very high and the pad were very flimsy/poorly supported, but the solution to that is to use a sturdier pad)

As you raise your center of mass (Center of Gravity (CG)), you increase the stability margin. cjl is correct, there is no (theoretical) upper limit to how far the CG and CP (center of pressure) can be separated. There is no risk of this causing the rocket to topple during boost.

HOWEVER (there's *always* a however... LOL), the higher the stability margin the more prone the rocket is to the effects of the wind (weather cocking). By this I mean that with a very high stability margin the model will have a tendency to tip off of the launch rod sharply and turn into the wind if there is a stiff/steady breeze during launch. This can be most undesirable and it is often wise to launch such models in dead calm air.

Also, fwiw, the stability margin of a model is often referred to in calibers where 1 caliber is equal to the diameter of the fattest body tube. The rule of thumb for "good stability" is 1.5 to 2 calibers of stability (meaning a separation between CP and CG of 1.5 to 2 times the body diameter).

More than that and it can become "over stable", less it becomes "marginally stable" and at 0 (zero) it is "neutrally stable".

Hope this helps
jim

MaxPayne said:

I have read that the center of pressure must be below the center of mass but I guess there should also be a constraint about how high the center of mass is. I mean if it were too high, the rocket was likely to topple when in a vertical position. Please elaborate. Use of physics is appreciated.

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With sufficient air speed, the corrective forces on the fins keep the rocket from "tipping over". If the rod/rail isn't long enough for the particular rocket+motor combination, the initial velocity could be too low.

When the CG is too far forward from the CP it will affect the dynamic stability. This can happen with too much nose weight or fins that are too small. It also depends if the rocket is short&fat or long&skinny. The rocket may end up "tipping off" the rod/rail without recovering from the non-vertical arcing path. Or, it'll act like "balancing a broomstick by the end of the handle", with the backend wiggling around in response to disturbances or misalignments.

Probably the biggest problem with having the c.g. "too far" forward is that you would have to add an excessive amount of nose ballast to move the overall ("composite") c.g. The extra nose weight will make the rocket heavier and your overall performance (speed, altitude) will be reduced. The solution to that problem is to use a bigger motor, but those tend to be heavier (and located in the back end of the rocket), requiring even more nose ballast, and you can see where that design spiral is headed...

Unless you have an extremely unusual rocket configuration, the c.g. will typically be located where you can still get the center of pressure behind it (by an adequate stability margin) through the use of reasonably-sized fins. Even if you have to use a bit of nose weight, a small amount of ballast (placed well forward in the rocket) can achieve a significant shift of c.g. without killing the overall rocket design.

Do you have a specific design issue that you could post here? (or is your design a secret?)

powderburner said:

Probably the biggest problem with having the c.g. "too far" forward is that you would have to add an excessive amount of nose ballast to move the overall ("composite") c.g.

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I don't understand this. If the CG is already too far forward, why add more nose ballast?

I probably stated that poorly.

What I was trying to say is that if the overall c.g. is too far forward, that you probably installed excessive amounts of nose weight (or payload) to get it there. (Did that make any more sense?)

While we're at it, there is also a safety aspect to this situation: If you have some sort of failure during the flight a solid ballast installation (stack of washers, epoxied blob of lead weights, etc) has the potential to be quite dangerous. Worst case would be a separated NC with ballast fastened to it, free-falling to the ground.

A system is stable when its center of mass is in the lowest possible height. Suppose the com of a model rocket is located nearly at its nose cone. While in flight or at the apogee(before ejection of recovery device), will it not tip over?

cjl,
I'll agree to what you say, but I still don't understand this clearly.

MaxPayne said:

A system is stable when its center of mass is in the lowest possible height.

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That doesn't apply to flying objects. Low CG makes a stationary object "stable", if you're concerned about something tipping over while sitting on a table.

MaxPayne said:

Suppose the com of a model rocket is located nearly at its nose cone. While in flight or at the apogee(before ejection of recovery device), will it not tip over?

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If a rocket goes perfectly vertical, it will free-fall backwards until air resistance is enough to turn it around.

Objects on the ground "tip over" because they have an opposite force of the surface their sitting on pushing back against their weight, plus an uneven side force to get it started.

MaxPayne said:

A system is stable when its center of mass is in the lowest possible height. Suppose the com of a model rocket is located nearly at its nose cone. While in flight or at the apogee(before ejection of recovery device), will it not tip over?

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Not if the rocket is moving fast enough that its fins (or other stabilising surfaces) do their job. In that case, if gravity, wind or anything else tries to knock the rocket over, the fins will straighten it back again.

Think about a firework rocket. The centre of mass of this rocket is obviously very far forward since most of the rocket's length is the stick. It will certainly topple over if you try to stand it up, which is why it needs to be in a bottle before launch. Once the rocket is on its way, the stick acts like a rather inefficient fin and keeps it stable.

MaxPayne said:

A system is stable when its center of mass is in the lowest possible height. Suppose the com of a model rocket is located nearly at its nose cone. While in flight or at the apogee(before ejection of recovery device), will it not tip over?

cjl,
I'll agree to what you say, but I still don't understand this clearly.

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yes, launch a bowling ball.. Tipping over is what apogee is, since there is a trade off of aerodynamic stability, gravity, and vehicle energy loss.
the more vertical the sharper the "tipping would be"
The further aft the cg is, the less gravity can change the direction, since cp will be closer...
weather cocking of overstability, is only realative to the wind.

MaxPayne said:

Suppose the com of a model rocket is located nearly at its nose cone. While in flight or at the apogee(before ejection of recovery device), will it not tip over?

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To add to the other JD's comments...

Rockets tip over at apogee because of a moment created by the difference of aerodynamic drag ahead and behind the cg. Gravity by itself cannot generate a moment while the rocket is in free fall.

If you were able to fly a rocket non-perfectly-vertical outside the earths atmosphere the rocket would maintain its angular position with respect to the earths surface during its fall until it fell back into air resistance. This will be true regardless of how far forward the cg is.

ClayD said:

yes, launch a bowling ball.. Tipping over is what apogee is, since there is a trade off of aerodynamic stability, gravity, and vehicle energy loss.

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Gravity does not change the orientation of the rocket, regardless of where the CG is or how heavy the rocket is. Gravity acts equally on all portions of the rocket and does not cause it to rotate.

jsdemar said:

Gravity does not change the orientation of the rocket, regardless of where the CG is or how heavy the rocket is. Gravity acts equally on all portions of the rocket and does not cause it to rotate.

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Lets word that a little different. Gravity acts on the entire object, but it appears to act as if it was pulling directly on the single point which is the center of gravity (c.g.).

As noted, this gravitational force will not cause any torque or rotation. As the object moves in a vacuum, there is no rotational force. As the object moves in air or any other fluid, there will be a force created by the fluid passing over the surface. With our rockets, we have fins in the back to provide more surface area behind the c.g. than in front - so, just like the fat guy on the see-saw, the rocket will rotate around it's c.g. and keep the back end pointing backwards simply because therre is more area behind the c.g. than in front.

If the stable rocket flies straight up and there is no wind, it will slow down, stop and then fall backwards until it builds up enough speed for the wind passing over it to rotate the back end backwards.

And as for "over stable" - that is only a problem for an underpowered rocket - if it leave the launch rod at a fast speed relative to any cross wind, there will be little weathercocking. If it leaves the rod slow, it will experience severe weathercocking if it is overstable. Speed off the rod is good. Slow off the rod is bad.

And see the Classic Collection in the sticky post for more info.

shreadvector said:

Lets word that a little different. Gravity acts on the entire object, but it appears to act as if it was pulling directly on the single point which is the center of gravity (c.g.).

As noted, this gravitational force will not cause any torque or rotation. As the object moves in a vacuum, there is no rotational force. As the object moves in air or any other fluid, there will be a force created by the fluid passing over the surface. With our rockets, we have fins in the back to provide more surface area behind the c.g. than in front - so, just like the fat guy on the see-saw, the rocket will rotate around it's c.g. and keep the back end pointing backwards simply because therre is more area behind the c.g. than in front.

If the stable rocket flies straight up and there is no wind, it will slow down, stop and then fall backwards until it builds up enough speed for the wind passing over it to rotate the back end backwards.

And as for "over stable" - that is only a problem for an underpowered rocket - if it leave the launch rod at a fast speed relative to any cross wind, there will be little weathercocking. If it leaves the rod slow, it will experience severe weathercocking if it is overstable. Speed off the rod is good. Slow off the rod is bad.

And see the Classic Collection in the sticky post for more info.

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Splendid example !! "golf clap"

ClayD said:

Splendid example !! "golf clap"

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Clay learns more about gravity every day!

shreadvector said:

And as for "over stable" - that is only a problem for an underpowered rocket -

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Not true. An over stable rocket will have poor dynamic response to a disturbance. People generally use "static margin of stability" as rule of thumb and do not consider dynamic stability. It's a complex subject and not simple to analyze or simulate, so most people ignore it.

Overly stable rockets are more likely to "cone" if there's a fin misalignment or thrust misalignment.

Overly stable rockets are less likely to recover from a sudden wind gust. With a high polar moment of inertia, once deflected, the rocket keeps rotating while the fins attempt to correct the angle of attack. If it can correct in time, it will be stuck at a new path off vertical.

Another dynamics problem, consider two rockets could have the same mass and the same static margin of stability, but the mass is distributed differently. The one with the mass distributed more toward the ends (heavy nose weight and heavy motor) will have a higher moment of inertia, and will respond slower to disturbances (over damped). For the rocket with evenly distributed mass, the correcting moments from the fins will quickly respond to the delection, and possibly over correct if under-damped, bringing it back to its original vertical trajectory. Also, with heavy nose weight, the CG will shift forward more quickly as the motor burns out, creating an overly stable rocket (see above).

jsdemar said:

Clay learns more about gravity every day!

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i havent learned crap about gravity since mom dropped me...

jsdemar said:

Not true. An over stable rocket will have poor dynamic response to a disturbance. People generally use "static margin of stability" as rule of thumb and do not consider dynamic stability. It's a complex subject and not simple to analyze or simulate, so most people ignore it.

Overly stable rockets are more likely to "cone" if there's a fin misalignment or thrust misalignment.

Overly stable rockets are less likely to recover from a sudden wind gust. With a high polar moment of inertia, once deflected, the rocket keeps rotating while the fins attempt to correct the angle of attack. If it can correct in time, it will be stuck at a new path off vertical.

Another dynamics problem, consider two rockets could have the same mass and the same static margin of stability, but the mass is distributed differently. The one with the mass distributed more toward the ends (heavy nose weight and heavy motor) will have a higher moment of inertia, and will respond slower to disturbances (over damped). For the rocket with evenly distributed mass, the correcting moments from the fins will quickly respond to the delection, and possibly over correct if under-damped, bringing it back to its original vertical trajectory. Also, with heavy nose weight, the CG will shift forward more quickly as the motor burns out, creating an overly stable rocket (see above).

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Thanks John. That's interesting information.

Is the "coning" phenomena only caused by fin/thrust misalignment?

Greg

jsdemar said:

Overly stable rockets are less likely to recover from a sudden wind gust. With a high polar moment of inertia, once deflected, the rocket keeps rotating while the fins attempt to correct the angle of attack. If it can correct in time, it will be stuck at a new path off vertical.

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THis happens with any unguided aerodynamically stabilized rocket. regardless of margin of stability...once the direction of change occurs, you cant reverse it unless you had something to change its path.
you arent suggesting, that the rocket can sense the earths gravity to determine vertical - are you?
I think what you mean is that it will have angle of incident over the angle of attack on the flight path that will continue to worsen????
fins (non guided = fixed position ) cant fix angle of attack, only angle of incidence.

I was aware that I was responding to a question in the Beginners & Educational sub-forum, and not in an advanced sub-forum. Therefore, I responded as if we were talking about normal average model rockets.

Mis-aligned fins and off center thrust are bad in general, and if your speed off the rod is low, they will be a much bigger problem than if your speed off the rod is high.

Beginners need to remember that the reason for a launch rod (or rail, or tower) is to allow the rocket to build up speed. Slow is bad. Fast is good.

If anyone wants to see coning in action, build an egglofter with an egg in an agg capsule and a long slender body tube below. They launch it with a motor that has a long burn with not-too-perfect fin alignment. it will be stable, but it will "cone". And if it has a bad thrust to weight ratio, it will cone and turn at the same time as it weathercocks.

jsdemar said:

Not true. An over stable rocket will have poor dynamic response to a disturbance. People generally use "static margin of stability" as rule of thumb and do not consider dynamic stability. It's a complex subject and not simple to analyze or simulate, so most people ignore it.

Overly stable rockets are more likely to "cone" if there's a fin misalignment or thrust misalignment.

Overly stable rockets are less likely to recover from a sudden wind gust. With a high polar moment of inertia, once deflected, the rocket keeps rotating while the fins attempt to correct the angle of attack. If it can correct in time, it will be stuck at a new path off vertical.

Another dynamics problem, consider two rockets could have the same mass and the same static margin of stability, but the mass is distributed differently. The one with the mass distributed more toward the ends (heavy nose weight and heavy motor) will have a higher moment of inertia, and will respond slower to disturbances (over damped). For the rocket with evenly distributed mass, the correcting moments from the fins will quickly respond to the delection, and possibly over correct if under-damped, bringing it back to its original vertical trajectory. Also, with heavy nose weight, the CG will shift forward more quickly as the motor burns out, creating an overly stable rocket (see above).

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GregGleason said:

Thanks John. That's interesting information.

Is the "coning" phenomena only caused by fin/thrust misalignment?

Greg

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My decades of observation have shown me that misalignment is bad, but even if it's perfectly aligned, an egglofter with a huge egg capsule and tiny fins will be stable on "paper', but the tiny fins are lost in the turbulent boundary layer and do not produce a restoring force until the rocket swings wildly and presents the fins at a huge angle of attack and they are then sticking out into the airstream. My egglofters with the egg capsule at the front and a long slender body use fins that have a nice skinny aspect ratio so that they stick out well beyond the influence of the capsule 'wash' and therefore they are flying in clear air and there is no coning or wiggle. Laser straight boost and insanely over stable. And no weathercocking since the speed off the rod/tower/piston is WAY greater than any cross wind.

GregGleason said:

Thanks John. That's interesting information.

Is the "coning" phenomena only caused by fin/thrust misalignment?

Greg

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it is my understanding.. any irregularity that creates uneven deflection can create coning. I>E> nose cone deflecting inward.. if a plastic cone is used to break mach, it can heat (weaken) and deflect...
fin misalignment, generally creates roll, but yaw/pitch is also required to cone??wierd stuff around transonic flight.
coning is considered a phenominan.(however you spell that...)

angle of incidence, (fin alignment) can create coning, but thrust generally doesnt... (usually coning is experienced in coast phases comming out of mach.)

shreadvector said:

I was aware that I was responding to a question in the Beginners & Educational sub-forum, and not in an advanced sub-forum. Therefore, I responded as if we were talking about normal average model rockets.

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you absolutely are in a begginer forum.
you just stepped on "JS"'s sore spot...


thanks for clarifying the coning, I have only seen it as rockets come out of mach, i have never seen it on the way up... Thats cool...

ClayD said:

you absolutely are in a begginer forum.

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It's the beginners and EDUCATIONAL programs section of the forum. It's supposed to be used for stuff like outreach programs with schools, etc. No strict guidelines.

Some things can't be explained with simple answers. If someone does provide a simple answer, they shouldn't imply that it's the complete, absolute explanation. For example, Fred wrote: "And as for "over stable" - that is only a problem for an underpowered rocket". Stuff like that makes my keyboard light up like a Christmas tree! Especially when it comes from our preeminent pedantic poster.

The great thing about education (formal or otherwise) is that once you learn the fundamentals at one level, it opens the door to learn more. It can be interesting and motivating to the student to discover there's more depth to the subject than they first realized. In the courses I teach, I always include some examples that require a little more than they've learned, but shows a good application of the stuff covered so far. And... I always make a point to say "if you know this, you can make more money".

ClayD said:

THis happens with any unguided aerodynamically stabilized rocket. regardless of margin of stability...once the direction of change occurs, you cant reverse it unless you had something to change its path.
you arent suggesting, that the rocket can sense the earths gravity to determine vertical - are you?
I think what you mean is that it will have angle of incident over the angle of attack on the flight path that will continue to worsen????
fins (non guided = fixed position ) cant fix angle of attack, only angle of incidence.

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You are on the right track. The amount of change in the path is less if the rocket can quickly respond to the disturbance. For the over-stable, over-damped rocket, it will slowly correct and possibly only partially remove the angle of attack. It will continue to rotate from the induced moment caused by the initial disturbance plus the force of the fins and the angle of attack. With a smaller margin of stability and/or lower polar moment of inertia (more evenly distrubted mass), the rocket corrects quickly. Slightly understable (closer to unstable) can have advantages because it will over-correct a little. The pitch response will have small oscillation, heading to a final direction closer to vertical, and zero angle of attack. In summary, you want to spend as little time as possible responding to the disturbance so that the total accumulated error is less. (This applies to all types of control systems, not just guidance). But, if there's a continuous disturbance caused by something on the rocket, such as fin misalignment or off-balanced payload, or thrust misalignment, the rocket wastes lots of energy attempting to correct the problem.

Here's something more to think about. Professional rockets that are unguided are required to have some induced spin. You can't fly an unguided rocket on a professional range (White Sands, Wallops Island, Poker Flats, etc.) without it. By inducing a rotation (fin tabs, or fin canting), the amount of deflection is reduced by roll coupling. Without rotation, an uncorrected pitch error could accumulate until the rocket heads off the range area. Or, at an extreme angle of attack, the side loading causes the rocket to break up. With some rotation (5 to 10 rotations per second), the angle of attack is kept within a rotating cone and not in any specific direction.

MaxPayne

Even in this digital age of near instantaneous response, nothing beats a good book. Pick up a copy of the Model Rocketry Handbook by G Harry Stine. This book is a must read.

It will explain everything you are asking about in words, pictures and even things to try to get a better understanding of the relationship between CG/CP and model rocket stability. Even includes the math behind the physics. Not sure what edition they are up to - 7?, but any will do the trick in regards to CG/CP and model rockets.

jsdemar said:

With some rotation (5 to 10 rotations per second), the angle of attack is kept within a rotating cone and not in any specific direction.

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I really dont know about all that, but what I understood this rotation does this by increasing base drag, same on a bullet, which hardly has the aerodynamic cross section to be aero-stable. The shorter the bullet the more rotation required for stability... I believe the viper uses a spiral tower to instigate one heck of a roll rate...???

Yes, I understand the "lights up like a christmas tree..", you adressed dynamic stability in your first post. and as you stated its ignored in even HPR L3 rockets. We only use static stability tests in our rockets. When Fred made his post, i agree he and i both shot off un-wordy answers that could leave a question why? and exlcude the reason. most people would rather over-stable rockets be on the range. But lets just face the fact that you didnt help beginers or educators by your example either. Since it is so complex as previously put that its not worth going into.. Rod whip is the best example i see no one has addressed when an incident causes unstable flight.
weather cocking is an issue that may very well be complex, but doesnt need to be that way for all general use and intents, Unless your launching a commercial rocket at wsmr. Which would love to see a 6th grade science teacher go to that extent.

ClayD said:

I really dont know about all that, but what I understood this rotation does this by increasing base drag, same on a bullet, which hardly has the aerodynamic cross section to be aero-stable. The shorter the bullet the more rotation required for stability... I believe the viper uses a spiral tower to instigate one heck of a roll rate...???

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Rotation doesn't do anything to the base drag. The rocket still has the same shape, so the drag forces are relatively unaffected (other than from the angled fins). What it does is it adds an element of gyroscopic stability to the aerodynamic stability. In addition, as stated above, it ensures that any slight aerodynamic misalignment does not cause the rocket to angle off in a specific direction.

cjl said:

Rotation doesn't do anything to the base drag. The rocket still has the same shape, so the drag forces are relatively unaffected (other than from the angled fins). What it does is it adds an element of gyroscopic stability to the aerodynamic stability. In addition, as stated above, it ensures that any slight aerodynamic misalignment does not cause the rocket to angle off in a specific direction.

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It definately increases the drag. Realativly affecting is a load of BS....