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Longitudinal stability analysis

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Longitudinal stability analysis

Old 10-13-2004, 02:45 PM
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Gizmo3D
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Default Longitudinal stability analysis

Hi,

I was just wondering how you would go about sizing a tailplane for positive longitudinal stability (particularly static stability).

Basically, as i understand it, longitudinal stability is all to do with the location of the CG relative to the neutral point (the aerodynamic centre of the whole aircraft). So long as the CG is forward of the NP then the aircaft should be stable in pitch. The distance between the CG and the NP is the staic margin.

Cambered wings generate a nose down pitching moment, and so the role of the tailplane is to produce anb equal and opposite nose up pitching moment to counter it. The tailplane also produces a restoring pitching moment should the angle of attack be changed by a gust for example.

Ok, thats what i know! What i'd like to know is how you decide on the surface area for a tailplane to achieve stability. Tailplane volume coefficient is an important factor, as is the moment arm of the tailpane etc.... so much to figure out!

I don't expect pages of equations(!) but i was wondering if anyone out there could shed any light on how to solve such a problem - i.e. i need first to calculate this, then go on to determine this and so on...! The methodology if you will.

Sorry for all the waffle! Any help is much apprieciated.

m
Old 10-13-2004, 08:42 PM
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Johng
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Default RE: Longitudinal stability analysis

It's a pretty involved question and various people have various methods that work for them. I calculate the stability based on the equations for stability I learned in college. I have calculated CG for various airplanes and various configs, and have never been surprised by the flight characteristics. Others use the tail volume coefficient and compare that to a table of standard values.

The first thing I recommend is that you do a search in the aerodynamics forum for 'stability' and find some of the threads where it's been discussed before. It's been discussed in depth. Read up, then come back here and we'll help on the stuff that might need explanation.
Old 10-13-2004, 08:46 PM
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khodges
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Default RE: Longitudinal stability analysis

Too bad Anthony Fokker is no longer with us. From what I,ve read about him, he just stood back and looked at the plane and said "Make the tail bigger (smaller) (longer) (shorter)". Even some models in the same production series varied because to him it just didn't look right. It sure worked for him, though. Sometimes empirical experimentation works better than the calculus.
Old 10-13-2004, 09:03 PM
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Johng
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Default RE: Longitudinal stability analysis

No calculus, just basic math. I don't see how you can get better than, right on the first try, every time. When the numbers don't work for people, it's usually user error.

TLAR is OK, especially for small models, or simple models that are very standard configuration. When I get to something that's a bit out of the ordinary, or maybe a more unique airplane as I tend to, I like to work out the details to get a feel for what to expect on that first flight.

For instance, I bought a plane called a privateer from a guy at a good deal. The privateer is a old-timer flying boat design with tail & wing ratios based on free-flight dimensions. The reason I got it at a good deal is that the thing would not fly off water. THe guy had put nearly 2 lbs in the nose to get it to balance at the 25% chord point, as noted on the plans.

Now I don't know where those plans came from, but I would guess they were modified by someone other than the designer, because stability analysis revealed that the plane would fly fine with the CG at 70% of the chord, which allowed all the lead to be removed. (The h-tail is 40% of the wing area) The tail incidence as-built also makes a lot more sense with the CG moved back. Lighter wing loading, better response. All found by a little calculation. TLAR didn't work well there.
Old 10-15-2004, 03:22 AM
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Default RE: Longitudinal stability analysis

There is a very good writeup on the effects of CG at the following site:

http://members.lycos.co.uk/A75Church/tips3.htm

I'll try and find a similar article that appeared on the EAA web soem time back.

Hope this helps,

Francois
Old 10-15-2004, 07:42 AM
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Gizmo3D
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Default RE: Longitudinal stability analysis

Hmm, quite an interesting site. Never heard of/seen those 'nomogram's' before. It'll come in handy when i arrive at an answer for my tail volume/surface area etc as i can use it to see if my values are in the right ball park.

thanks again.
Old 10-15-2004, 09:03 AM
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rmh
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Default RE: Longitudinal stability analysis

If the plane hits the ground tail first - it has the cg too far aft - If it hits nose first - too far forward
Basic math.
Old 10-15-2004, 10:01 AM
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Gizmo3D
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Default RE: Longitudinal stability analysis

I'll bear it in mind
Old 10-22-2004, 10:48 AM
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acropilot_ty
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Default RE: Longitudinal stability analysis

The neutral point is also the aerodynamic center. So you can calculate the location of the aerodynamic center, and the center of gravity without the tail first. Then size and place the tail to bring the aerodynamic center back to the desired location with respect to the center of gravity. Odds are you already have a fuselage length in mind so its just a matter of surface area. I actually prefer to start with a desired tail volume coeficient and calculate the aerodynamic center for the aircraft without the wing... then move the wing to the proper location... This way I can get the tail volume I want, and the exact static margin I want with fewer itterations. The mission of the airplane should determine the tail volume... then go about the design using the static margin and everything should work out.

Ty
Old 10-25-2004, 09:20 AM
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Gizmo3D
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Default RE: Longitudinal stability analysis

Yeah, defining a tailplane volume coefficient first and working from that is one way to do it. I didn't quite do it that way but what i did was to construct a spread sheet in Excel using all teh relevant equations. The beauty of this is that you can change one parameter, and then excel updates all the equations etc etc so that you can immediatly see the effect. Anyway you soon converge on a solution to the problem. Saves recalculating everything by hand when you change the moment arm for example!

m
Old 10-25-2004, 01:06 PM
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Default RE: Longitudinal stability analysis

There is a nice, empirical method you can use. Build a miniature solid balsa glider of the model. It turns out that stability stays pretty much the same despite gross changes in Reynolds number. The cg found by experiment with the miniature will be extremely close to the correct position for the final design.

Play with decalage (wing-tail angle differece) and cg location until you get a model that just pulls out of a dive slowly. If it porpoises, you have the cg too far forward and too much decalage. If it tucks under, go for more forward cg and more decalage.

Remember, angle of attack is measured from most forward point of the leading edge to the most aft point on the trailing edge. Second, the airfoil symmetry or lack thereof determines at what angle the airfoil generates no lift. For most non-symmetrical airfoils, you actually generate significant lift at 0 degree angle of attack. It is even worse with a "flat bottom" airfoil. Most people think the bottom is the determiner of the angle of attack, but it is actually several degrees below the datum line. And then you add the 0 angle lift, and you can easily end up with way too much decalage.

Check out the Lanier ST40 trainer. I put a semi symmetrical airfoil on it to control the "zoom" when you change power levels. It is an extremely easy plane to fly as a result. Very little downthrust was required as a result. Flat bottom airfoil trainers will climb drastically when you goose the power and drop like a stone when you cut it. The ST-40 is far better behaved.[8D]
Old 10-25-2004, 07:35 PM
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Default RE: Longitudinal stability analysis

Take a look at http://www.aalmps.com/freestuff.htm 2nd row from the bottom, 2nd across: "Tail Volume" It's a simple method to establish how effective the tail is at controlling that nasty 'ol wing and a starting point for the CG.

It's on a FF rubber model site but has worked well for me in the past on home-designed r/c (and FF) planes.
Old 10-25-2004, 08:02 PM
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Default RE: Longitudinal stability analysis

Actually, he who dies with the most good Cox engines is dead....
Old 10-25-2004, 08:32 PM
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Default RE: Longitudinal stability analysis

[sm=lol.gif]Yeah, yeah....last week you couldn't spell comedian and now you is one.
Old 11-06-2004, 09:07 AM
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joaoloureiro
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Default RE: Longitudinal stability analysis

hi people, I wanted to know what is the normal value of static margin for:

- trainer
-acobatic
Airplanes

Thanks
Old 11-09-2004, 10:14 PM
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Johng
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Default RE: Longitudinal stability analysis

ORIGINAL: joaoloureiro

hi people, I wanted to know what is the normal value of static margin for:

- trainer
-acobatic
Airplanes

Thanks
Trainer : 0.1 - 0.2

Acrobatic : 0.05 - 0.0, except first flights, then 0.1. 0.0 only when plane has sufficient pitch damping (tail volume) that divergence is not too quick.

I have flown a Stinger 120 that was balanced much behind the neutral point. The stab was well oversized and the plane was flyable enough to make a no-damage landing when 8 oz of lead that had been on the firewall broke loose and went all the way to the tail cone. This was with the plane essentially neutral SM=0 with the lead in the correct place. Once the lead broke free, it was a completely controllable airplane, it just kept wanting to climb from level flight.
Old 11-10-2004, 11:20 AM
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Bax
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Default RE: Longitudinal stability analysis

RC Modeler Magazine and Model Airplane News had articles on basic R/C model design in the early 70's. A look through back issues in your library's periodicals section should find them. For a very basic model that will fly successfully:

Start out with the wing. 500 sq. in. for a .40-.46 size model, 600 sq. in for a .61-size model. Pick a generic aifoil you know works. Settle on the wing's planform...constant-chord is the easiest for first attempts. An aspect ratio of about 6:1 or so works well. Ailerons should be about 10%-15% of the wing area

Now for the pitch stability factor....size the horizontal stabilizer/elevator to about 20% of the wing area, and give it an aspect ration of 5 or 6 to 1. Place the leading edge of the stabilizer at 4 to 5 wing chords' distance behind trailing edge of the wing. Sport type models should have the elevator at about 20%-25% of the area of the entire stabilizer/elevator surface.

Vertical fin/rudder area should be about 40%-50% of the horizontal stabilizer/elevator. Rudder can be 20%-40% of the vertical area.

The fuselage is just a way to join the surfaces together.

Balance the model at about 30% of mean chord to start.

These parameters won't give a model that's specialized in any way, but it will fly reasonably well. Many prolific designers start out with parameters such as these. All parameters can be adjusted to get more specialized handling...especially in the amounts of movable control surface to the fixed portion. A 3D model will have elevators that are 50%-75% of the total horizontal tail area, and the rudder sized accordingly. Ailerons would be as high as 30% of the area of the wing.

Examples of models built to these parameters can be found in the model magazines quite easily. One that really exemplifies the basic parameters, and also makes an easily-built, good flying model is the Scotch Lass by Chuck Cunningham. Designed in 1970, it a goodie. Small, but nice. I've build several over the years, and its parameters alter easily. You can just blow it up without problems to make larger models. I even used all the same surfaces and moments and made a low-wing model that was an excellent flier until my "helper" gave it 'up' during an inverted pass. No more model.

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