Problem with static margin and neutral point

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Scheny

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Hi!

I was already starting building my scale model (fortunately the wings where the design is already frozen), when I noticed I had one small error in my CoG calculation (CoG of fuselage estimated too much in the front, as front half has almost twice the carbon as the rear half). Now I did not want to take any risk and tried to verify the project three times more:
  1. I calculated the weight again with formulas from Raymer and guess what: 158,6kg (Raymer) vs. 160kg (my guess)
  2. I made a detailed analysis using VLM2 algorithm with a detailed fuselage panel model --> everything to my expectation
  3. I calculated everything with CFD and compared to VLM* data --> perfect match except for drag** (VLM)
Now I try to get the CoG right, but there is something which bothers me. According to literature:
  • the CoG should be located between 18-30% MAC
  • be in any case in front of the NP
  • static margin should be around 10% MAC
According to my simulations, the NP for the complete aircraft is located approximately at 84% MAC (26% for wing alone or 93% for wing+tail excl. fuselage).
This would mean that my static margin for CoG = 25% would be 59%!!! (SM=NP-XCg).

I checked this against other aircraft, but they look similar... CoG in the right spot at 25%, but the NP is way rear. I am now a little insecure about the static margin and hoped for some of your insights.
BR, Andreas

*VLM = vortex lattice method
**the viscous drag is not calculated by VLM, so it only adds a factor for it which is tuned for model aircraft
 

peter hudson

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Aircraft configuration, the size of the horizontal stabilizor, the fuselage shape etc all play into the neutral point. Fred Thomas' "Fundamentals of Sailplane Design" suggests defining your target CG range ...say 25 to 50% MAC then size the stabilizer to achieve 10% static margin at the aft CG. (so 60% MAC in that case)

A lot of indoor free-flight models have stab area limited to maybe 50% of the main wing, and long stick fuselages. Their neutral points and CGs wind up WAY aft of the main wing's 30% MAC. Canards, tandems etc all break the 18%-30% main wing MAC rule for CG location. That rule is sort of statistical for conventionally sized acft. The key is the neutral point of the complete configuration! I like using codes like OPENVSP, setting the CG where I want the neutral point, then dialing in the horizontal tail volume to get a flat CM/Alpha curve. Or, if your config is set, then moving the CG aft until the Cm/Alpha curve is flat. That is basically the neutral point.

Hot Wings is right though. A simple flat model will give an estimate of neutral too. I'd go one farther and say after you cut it out and locate the balance [neutral] point, ballast it to 10% forward of that, give it a little incidence or up elevator, and throw it when your done. Theory is all well and good but a simple model flying across the living room will really set your mind at ease!
 

wsimpso1

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I just looked at mine, Neutral Point is around 67.5% MAC. 84% MAC sounds a bit far aft.

Maybe review the calculation? Usual approximation on stick fixed

NP = (FSw*Sw*dCl/dalphaw + FSht*Sht*dCl/dalphaht)/(Sw*dCl/dalphaw + Sht*dCl/dalphaht)

where FS is fuselage station for the 1/4 chord point, S is area, dCl/dalpha is lift slope for the foil, usually a function of aspect ratio, but can also include sweep and Mach effects. Since tailplanes usually have smaller AR than most wings, dCl/dalpha is usually smaller for tailplanes than wings.

You get a static margin as big as you are talking, and you might have trouble lifting the nose for takeoff or flaring to land...

Billski
 

ragflyer

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What is your wing and tail area and AR and tail arm? If we know that it is easy enough to verify.
 

Scheny

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At first I want to thank you for your quick and really helpful replies!

Here a picture of the project in its current iteration and a short explanation for the MAC. Root chord is 1000mm and tip chord is ~600mm (winglet going down to almost zero), so MAC is ~850mm. This is why any percentage is quite big. 84% MAC means it is located at 75% root chord.

Beast.jpg

Tail volume = 0,7:
Wing area: ~4,7m²​
Span: ~5,9m​
Tail area: ~1,2m²​
Elev lever arm: 2,56m​

Geometric middle of the fuselage is roughly located at the trailing edge (slightly in front) --> should also contribute to aft NP.
 
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Scheny

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Cheap ease rough check for reasonableness:
Cut out a top view on card stock and find the longitudinal balance point. 84% MAC does sound a bit aft.
As stated above, fuselage center is slightly before trailing edge. So this roughly matches with NP.

The key is the neutral point of the complete configuration! I like using codes like OPENVSP, setting the CG where I want the neutral point, then dialing in the horizontal tail volume to get a flat CM/Alpha curve. Or, if your config is set, then moving the CG aft until the Cm/Alpha curve is flat. That is basically the neutral point.
This is how I reviewed the neutral point to be at 75% root chord, or 84% MAC.

I just looked at mine, Neutral Point is around 67.5% MAC. 84% MAC sounds a bit far aft.
I guess your aircraft hast a tail volume of ~0,5 so my 0,7 that is recommended for jet trainers sounds not that far off anymore.

You get a static margin as big as you are talking, and you might have trouble lifting the nose for takeoff or flaring to land...
This is exactly what I was afraid of 😁
 
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wsimpso1

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I urge you to revisit your specifics and algorithm. Here is why:

Your numbers say 4.7 and 1.2m^2 for wing and tail, or slightly less than 4:1 ratio on areas. Eyeball evaluation of the model sure looks like the ratio of wing to horizontal tail areas is 5:1 or greater. Are you perhaps listing total of vertical and horizontal tail areas?

Arm from near trailing edge of wing to quarter chord of tail sure looks like more than 2.56/0.85 = 3.01 MAC;

Arm to tail is usually cited as CG to 1/4 chord of tail surface, not to elevator.

Horizontal tail volume coefficient does not use span, but Vertical tail volume coefficient sure does. Using your numbers

HTVC = (Sh*Lh)/(Sw*MAC ) = 1.2*2.56/(4.7*.85) = .77 not 0.70.

Given these inconsistencies, I suspect the neutral point calculation also needs revisiting. You do not need to convince me, you do need to convince yourself and your partners…

Billski
 
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TFF

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Models, 10% of MAC behind the CG is pretty standard. CG 25% NP 35% of MAC of wing. A real plane has to be more flexible. How flexible depends on fuel location with pilot sizes. The tail has to suit that flexibility. It’s either big enough and far back enough or not. I have built some scale models that the tails were just too close to the wing. Enlarging the surface some helped but it needed to be much larger but would look cartoonish. This was a very conventional model similar to a big Cub. Scrap one model.

Free flight models use the aft CG as pitch, but has a built in turn, as the plane properly trimmed flies in a circle with fixed surfaces. It has to stay in the turn or they stall.
 

ragflyer

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I just looked at mine, Neutral Point is around 67.5% MAC. 84% MAC sounds a bit far aft.

Maybe review the calculation? Usual approximation on stick fixed

NP = (FSw*Sw*dCl/dalphaw + FSht*Sht*dCl/dalphaht)/(Sw*dCl/dalphaw + Sht*dCl/dalphaht)
Billski

Billski I think you missed a term. The above formula will give NP that are significantly aft. The usual formulation for NP includes effect of wing downwash change (1-de/da) as it has a significant effect on the NP. Typically it (1-de/da) is around (0.6 to 0.7).
 

wsimpso1

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Billski I think you missed a term. The above formula will give NP that are significantly aft. The usual formulation for NP includes effect of wing downwash change (1-de/da) as it has a significant effect on the NP. Typically it (1-de/da) is around (0.6 to 0.7).

Rather than give all the terms, I was concentrating on finding the source of the HUGE aft displacement (neutral point at 84% MAC is way aft) in the hopes of helping the OP figure out what might not be right. Yes, the effect of downwash is to reduce the stabilizing influence of the tail, usually by somewhere around 1/3, but this detail will not produce the large displacement seen by the OP.

Billski
 

ragflyer

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Rather than give all the terms, I was concentrating on finding the source of the HUGE aft displacement (neutral point at 84% MAC is way aft) in the hopes of helping the OP figure out what might not be right. Yes, the effect of downwash is to reduce the stabilizing influence of the tail, usually by somewhere around 1/3, but this detail will not produce the large displacement seen by the OP.

Billski

yeah I suspected that was your intent initally Billski but two things made me think otherwise: 1. the effect of the relative lift slopes of the tail and wing is also typically in the same ball park as the rate of change of downwash; but you included that term. 2. the formula was quoted as the usual approximation which it was not. I am sure it was just a slip no big deal.

In general when the error is this large it may be multiple factors but then again .......
 

ragflyer

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The NP approximation given earlier is very straightforward and is best to use. But for a quick rough approximation for typical conventional designs you can use:

NP = 0.25+ 0.5*Vh

With a Vh = 0.77 NP would be 63% of MAC.

Fuselage typically will move this forward by 3% to 5% and (tractor) power about 2% to 4% in addition.
 

Mad MAC

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Cheap ease rough check for reasonableness:

Cut out a top view on card stock and find the longitudinal balance point. 84% MAC does sound a bit aft.
I do this in AutoCAD, using the region function and mass proprieties.


This is a jet right, for most of us with propeller aircraft, the prop is destabilizing and also moves the longitudinal balance point forward if one is using the area method relative to a jet.

You might want to check Stinson, he covers small jets, so will likely to have a note regarding effect on longitudinal stability.
 

Scheny

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A quick update: I noticed that it makes a difference whether you calculate X_NP "without body influence" or when you turn the body off.
using the second method, the NP is calculated to be at 69% MAC.

Another thing I noticed: "mean geometric chord" is 814mm, but "mean aero chord" is 849mm. I assumed MAC to be the later, but it seems the first is rather true.
 
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