Stability - percent rule original source?

[SolarYellow]

There are multiple in-depth discussions in recent weeks about stability of short/fat rockets. The conclusion that seems to be tentatively (OK, adamantly by some, and others open to it) accepted in them at this point is that a more appropriate denominator than airframe diameter is overall rocket length. Targeting somewhere in the range of 8 to 15 percent of overall rocket length works well. It is especially more useful and safer than "calibers" on both short/fat rockets and long/skinny rockets.

OK, I have sinned. Quoting stuff that's oft-repeated without knowing the original source.

I've been googling for much of the evening, reading old NACA/NASA/MIL papers about sounding rocket and projectile design and stability. Still haven't found the source for the 8 to 15 percent.

Does anyone know where it comes from, or even have a reference that cites it so I could start tracing down through their references?

 

[lr64]

Sounds like what you'd use for airplanes, relative to the average wing chord. Maybe someone borrowed it from that.

 

[SolarYellow]

The first time I remember reading it, it was specifically cited as being an old rule of thumb for sounding rockets.

 

[Buckeye]

Good question. The sounding rocket theory makes sense. Here is data from RASAero website with CP location measured as % body length.

 

[MClark]

A "Rule of Thumb" the original source is likely unknown.
The 10% of length is based off observations of what works in reality.
A typical looking rocket with a 1” tube and about 10” long the 1 caliber rule is the same as the 10% rule, all is well.
With a very short rocket the 1 caliber becomes unattainable without large nose weight and was found experimentally (launching the rocket) to be unnecessary.
Conversely a very long rocket with 1 caliber was found to be marginally stable, weight added and the magical 10% was good.
This has been around since the origins of model rockets.

 

[SolarYellow]

Well, so far, I've chased down the rule of thumb that says elliptical nose cones are the best for subsonic velocity and the rule of thumb that fillets should be 4-8 percent of chord length to what appear to be their origins, and found them both to be less than rigorous and/or complete. Along the way, I learned quite a bit and it was a fun and interesting process. I don't expect the percent of airframe length rule to turn out to be suspect, but I'm interested in the learning that will occur when I run it to ground.

 

[MClark]

Well, so far, I've chased down the rule of thumb that says elliptical nose cones are the best for subsonic velocity and the rule of thumb that fillets should be 4-8 percent of chord length to what appear to be their origins, and found them both to be less than rigorous and/or complete. Along the way, I learned quite a bit and it was a fun and interesting process. I don't expect the percent of airframe length rule to turn out to be suspect, but I'm interested in the learning that will occur when I run it to ground.

If pointy noses were less drag Boeing and Airbus would be using them.

 

[SolarYellow]

Note I didn't say what I think might be better than elliptical. I'm not aware of any jet airliner built in the last 50 years with an elliptical nose.

 

[Rschub]

Note I didn't say what I think might be better than elliptical. I'm not aware of any jet airliner built in the last 50 years with an elliptical nose.

Thats because the nose has constraints on it other than minimum aerodynamic drag. You will notice that the nose is pretty stubby looking though, since they are going for minimum wetted surface area.

 

[rharshberger]

Note I didn't say what I think might be better than elliptical. I'm not aware of any jet airliner built in the last 50 years with an elliptical nose.

They aren't pointy either, more of a parabolic shape similar to a Big Bertha nosecone.

 

[SolarYellow]

There are an infinite number of shapes that are neither elliptical nor pointy. I think a range of shapes in that space that is neither pointy nor elliptical will offer lower drag than elliptical of similar fineness ratio at subsonic speed. In fact, I think there's a good chance that the best approach is one that I have never seen discussed or written about in rocket-related literature. Most rocket people would look at it and call it elliptical, but it's not. Elliptical satisfies a very specific mathematical equation, and the nose cone design strategy I think is likely to perform better does not satisfy that equation. It's annoying that someone jumped to the conclusion that I meant pointy would be better, because it's obviously not if one has done any research at all. That's all I'm saying about that here.

Does anyone know what literature the stability ratio as a percent of overall length came from?

 

[Rschub]

"For aircraft and rockets, below Mach .8, the nose pressure drag is essentially zero for all shapes. The major significant factor is friction drag, which is largely dependent upon the wetted area, the surface smoothness of that area, and the presence of any discontinuities in the shape. For example, in strictly subsonic rockets a short, blunt, smooth elliptical shape is usually best."

From Wikipedia, no less. A more authoritative source I cannot imagine.

https://en.wikipedia.org/wiki/Nose_cone_design

As @lr64 above said, It most likely came from stability margin notation in airplanes, which predate rocketry by a few years.

 

[SolarYellow]

Using the mean chord makes sense, as it's a longitudinal characteristic of the main thing being controlled: the wing and its pitch angle. The aerodynamic lift forces generated by the wing dominate those generated by the fuselage. In that situation, the empennage is basically just there to trim the wing, or to apply correcting moments to ensure level flight, or control inputs. It doesn't normally do a significant amount of the lifting work in steady state.

In a rear-finned, aerodynamically stabilized, passively-controlled rocket, the closest analog is the overall rocket length, as the fins are generally small and the forces they generate can easily be dominated by those generated by a long airframe. So I see the argument for it being a parallel construction, but I'm still searching for the tracks back to an original (or any) source.

ETA: What we're doing with "calibers" in rockets is kind of like using the wing's airfoil thickness as the denominator in the stability calculation.

 

[Rschub]

A lot of this stuff was derived experimentally, for example this study comparing 2 different length rocket bodies.

 

[SolarYellow]

Dragging you guys into this thread by quoting. Hoping you have sources.

It's super-rocs and variable diameters that made me forego calibers in favor of the old sounding rocket stability margin of 8-15% of vehicle length. I aim for 12% and ignore diameters entirely.

From my readings, a separation between CP and CG 8-15% of the rocket's length should be a good design point for passive rocket stability (What we sport flyers use....Jim Jarvis and company excluded).

I haven't seen any evidence that the needed stability margin has any relationship to the diameter of the rocket.

 

[SolarYellow]

A lot of this stuff was derived experimentally, for example this study comparing 2 different length rocket bodies.

I read/scanned that paper last night. There's nothing in there that I saw about recommending a stability criteria, or referencing any accepted value. Rather, like most of the other papers I've seen, it in a very detailed way tracks the CP location and CP vs. AOA relationship as it varies against a multidimensional set of parameters.

ETA: There is another paper from about 1953 that provides a very complete method of analytically determining the CP of a slender body with multiple wing/fin sets including aspects of flow around the airframe. So not just experimental.

 

[SolarYellow]

One thing I will add is that a lot of the early literature seems to be coming from the artillery community. A lot of the discussion is in terms of everything being shot out of a tube. In that world, the caliber does kinda make sense as a denominator. At least kinda. But in a world where a Baby Bertha and a Mean Machine might be compared, using the identical denominator of airframe OD just seems silly. I mean, the stability margin for a Mean Machine might be longer than a Baby Bertha.

ETA: This thread is now coming up in my Google results for different search terms on the topic.

 

[rocketguy101]

I have never heard of a static margin ROT based on % length. I see mention of "center of pressure eccentricity" in "Exterior Ballistics of Rockets" by Davis, Follin, and Blitzer (1958) which is the ratio of CP to length of the rocket. They mention more as an observation than a rule of thumb to be "in normal fin-stabilized rockets it is usually about 0.2." (see attached).

Barrowman discusses short rockets in the Centuri report TIR-30

If you really want to get into the gory details of rocket flight, read "Fundamentals of Dynamic Stability" by Gordon K. Mandell. It was originally published as a 5 part article in Model Rocketry magazine. The NAR issued a single technical report TR-201 (not sure if it's still available from NARTS). It is also included in the OOP book "Topics in Advanced Model Rocketry".

The MRm magazines are available online
Part 1 - Oct 68 p 21-9
Part 2 - Nov 68 p 25-31
Part 3 - Jan 69 p 26-31
Part 4 - Feb 69 p 23-30
Part 5 - Mar 69 p 25-30
and then the all important Corrections - Apr 69 p28 -- this is handy even if you buy TR-201 as some of the errors carried over into that printing.

 

[bill_s]

Dragging you guys into this thread by quoting. Hoping you have sources.

One simple thing was just throwing a basic rocket model into Open Rocket and using Angle of Attack simulation to compare short and long versions of the rocket. The long rocket had much more shift of the CP forward at any angle of attack. This is because much of the mass being fins and motor, there is a tendency for both the CG and CP to be farther back with the long rocket, as a percentage of its length, and therefore the airframe has greater effect as AoA brings it into action. The short rocket needed almost no stability margin at all to deal with AoA.

As a simple margin of error, diameter does contribute to the size of the rocket. However, as an observed phenomenon, our method of calculating stability based on normal forces along the length of the rocket seems to have some error or omission of its own when that length is comparatively short compared to the diameter, in the favor of increased stability.

Interestingly in that TIR-30 report, Barrowman's example of a short fat rocket (P. 11) is awkwardly shaped, with a rear transition and almost no base drag, in the context of saying stability margin is something you don't want too much of also, before just throwing out there the one caliber rule of thumb. He seems most interested in having the rocketeer use a reasonably calculated CP to work with in the first place.