[1.x.x] On the particulars of Center of Lift and Center of Mass on winged craft

[Val]

Applies to KSP versions: 1.0.4 and newer.

TL/DR: Among other things, this post explains why your reentering Space Shuttle replica and other winged craft can be unstable even though you built it with Center of Lift (CoL) behind Center of Mass (CoM).

It also explains how you can improve general stability of any winged craft with Angle of Incidence (AoI), while at the same time making the craft very SAS friendly, and able to fly straight without SAS.

The difference between CoL and Aerodynamic Center
Longitudinal Stability, the ability of the aircraft to self stabilize, is attained by having the Aerodynamic Center⁺ behind CoM.

+) The wikipedia explanation for how to calculate the Aerodynamic Center for an aircraft is in the spoiler below.

Spoiler

The longitudinal static stability of an aircraft is significantly influenced by the distance (moment arm or lever arm) between the centre of gravity (c.g.) and the aerodynamic centre of the airplane. The c.g. is established by the design of the airplane and influenced by its loading, as by payload, passengers, etc. The aerodynamic centre (a.c.) of the airplane can be located approximately by taking the algebraic sum of the plan-view areas fore and aft of the c.g. multiplied by their blended moment arms and divided by their areas, in a manner analogous to the method of locating the c.g. itself. In conventional aircraft, this point is aft of, but close to, the one-quarter-chord point of the wing. In unconventional aircraft, e.g. the Quickie, it is between the two wings because the aft wing is so large. The pitching moment at the a.c. is typically negative and constant.

Source: Longitudinal Stability

I find it useful to imagine the Aerodynamic Center as an arrow that pulls backward in your craft, relative to it's movement, while the CoL pulls perpendicular to the direction of movement. Lift influences the Aerodynamic Center because, among other things, lift creates drag, but it is only a dominant part while the craft is pointed near prograde. When the craft points away from prograde other types of drag become dominant.

CoL actually has less effect on stability, than either Center of Drag and Aerodynamic Center. The CoL actually needs to move to be able to control the craft. To pitch down it needs to move behind CoM. To pitch up the CoL needs to be moved in front CoM. Left and right for roll. And that is exactly what control surfaces do*.

You can see this in action in the SPH.

• Create a simple aircraft mockup, with a handful of structural fuselage.
• Select the root part and Shift+S, to give it a little AoA, because that's needed for the wings to create lift.
• Add a couple of small wing panels with control surfaces in mirror symmetry as elevators, either at the front or back.
• Turn on CoM and CoL and add a couple of larger wing panels with control surfaces in 2x radial symmetry, and place them so CoL is on top of CoM.

Using the Rotate Gizmo you can now directly see what really happens to the CoL, when control surfaces move, by rotating them slightly up or down.

*) I'll ignore yaw for now. It doesn't contribute to CoL in the same way, because it's a vertical surface. In the SPH yaw is shown as a rotation of the CoL marker.

As long as the Aerodynamic Center stays behind CoM, designing your craft with CoL in front or behind of CoM doesn't change aircraft stability much, even in KSP, it just changes how much control input you need to apply, to fly straight. And keeping the Aerodynamic Center behind CoM is the hard part.

We can't see the Aerodynamic Center, and for many designs it is close enough to CoL, because large control authority can move the CoL to CoM, so that the CoL works OK as a stand-in for Aerodynamic Center, during design. But the closer then CoM is to the rear of the craft, the worse it gets. The Aerodynamic Center is now significatly in front of CoL. So even if CoL at design time is behind CoM, the Aerodynamic Center might be right on top of CoM or in front of it.

This is why most people believe CoL needs to be behind CoM. And with the available information it is the right thing to do. Except it's not always enough.

This is also one of the reasons why Shuttles in KSP are so hard to get stable, even when the CoL is far behind CoM. If the Shuttle isn't built to account for the invisible Aerodynamic Center, the mass and wings are often concentrated in the back, but that long fuselage, with lots of drag, pulls the Aerodynamic Center in front of CoM.

The result is a lawn darting shuttle, because of CoL too far back, which at the same time spins out of control, because of Aerodynamic Centre being in front of CoM.

This has led people to accuse the aerodynamics or the cargo bays of being bugged. Which is understandable given the information available at design time.

Angle of Incidence (AoI)

Most of us were taught how lift works with pictures like this.

Pictures showing lift from cambered wing profiles without Angle of Attack.

It's not completely wrong, but it's missing a big part. Most of the lift comes from Angle of Attack, not from the cambered shape.

But because of how we were taught, we all have a tendency to imagine wings mounted parallel to the fuselage. On top of that KSP defaults to wings mounted that way. When really we shouldn't. And to make things even worse, KSP does not model wings as cambered profiles.

Which means: Wings in KSP always need Angle of Attack to provide lift.

By giving the wings "built-in AoA", Angle of Incidence, the craft can be pointed prograde while still creating lift. That reduces fuselage drag greatly.

If you mount wings with no Angle of Incidence, then the fuselage has to point away from prograde (the direction of movement) in order to get the wings to create lift. This creates a lot of drag.

Even in real life, wings are mounted with incidence. For the same reason: Less drag from fuselage.

Quote

Wings are typically mounted at a small positive angle of incidence, to allow the fuselage to have a low angle with the airflow in cruising flight. Angles of incidence of about 6° are common on most general aviation designs.

Source:  Wikipedia 

There is no one AoI that works for everything and it isn't necessarily most optimal to have the fuselage pointed directly prograde, because the fuselage can also contribute to lift (not just Mk2). But in my experience it is always better to have at least 1° AoI than none.

Personally I use between 1-5° Angle of Incidence on my designs. I don't have any set rules, but fast craft and/or big wings, needs smaller AoI, and high altitude needs bigger AoI.

For SSTO spaceplanes, I've had good experiences with designs that can fly at 0° pitch, without losing or gaining altitude near sea level at 350-400 m/s. That also means the fuselage is close to 0° AoA at the critical phase just above supersonic where drag is highest and the engines haven't reached maximum performance yet.

My Solutions

Until KSP is able to show the Aerodynamic Center, I use the rule of thumb, that CoM of the craft needs to be as close as possible to midway between nose and tail, and never closer than 2/3 of the craft length towards the tail. Not a very accurate solution and doesn't work for all designs, but it has worked OK for me.

Additionally, I design my crafts so the forward most wing has more Angle of Incidence than those behind it. That works effectively as if the elevator has built in pitch, which you can use to move the CoL on top of CoM, without compromising stability.

Here are some examples.

A stable conventional design (craft file)	The conventional straight wing design with CoM forward of the middle. It's a breeze to get stable with CoL on top of CoM, because the Aerodynamic Center is most often behind CoL. Nonetheless, this design has 2° AoI on the main wing to reduce fuselage drag, and no AoI on the tail plane.
A stable canard design (craft file)	Canard designs, the most prevalent type in KSP, probably due to the way engines are massed in KSP for the LEGO™-modularity and gameplay balance. CoM is often way behind the midpoint, which means the Aerodynamic Center will most likely be in front of CoL. If the CoM isn't too far behind, you might get away with initially designing it with CoL a good bit behind CoM, using CoL as a stand-in for Aerodynamic Center. Once you've tested that it flies stable, you can then add a little more** AoI to the Canard than the main wing, to move CoL up to CoM. If the CoM is far behind the midpoint, see the Shuttle designs. It will now be possible to fly the craft without you or the SAS having to constantly apply pitch-up. It won't reduce drag, but it will make it easier for you or an autopilot to control the craft. The shown craft has a fixed canard with 4° AoI and the main wing has 2° AoI. **) Only very rarely will it be required to have more than 2° difference between main wings and tailplane/canards in KSP.
An unstable shuttle design A stable deltawing design (craft file)	Shuttles and other pure deltawing designs, are the hardest to balance and require great care taken during design to make sure the CoM doesn't fall too far back. If the CoM is far behind the midpoint, you may be forced to redesign it. It might not be possible to stabilize it without adding dummy weights near the cockpit. Moving the fuel tanks forward might help initially, but instability could re-emerge when the fuel is spent. If the CoM isn't too far behind, you might be able to do something similar as with a Canard designs, by initially designing it with CoL a good bit behind CoM, using CoL as a stand-in for Aerodynamic Center. Again, once you've tested that it flies stable, you can then use the Rotate Gizmo to prebake the elevons with some pitch up, to move CoL up to CoM, to get the craft to fly without you or the SAS having to constantly apply pitch-up. The deltawing jet shown here, has 2° AoI om the main wing and the elevons have been angled up 2° from their default attachment angle. Additionally, the big wing strake has also been angled up 1° more than the rest of the wing.

Test showing increased stability with AoI

Spoiler

Reused parts from a post later in this thread.

The test craft is a conventional main wing+tailplane craft, with 3 ore tanks as fuselage, where I can move the ore between the tanks to place CoM either, on top, in front or behind CoL. The craft is otherwise as well balanced as possible. The fuel tanks are exactly at CoM (when it's in the middle position right on top of CoL) and thrust is provide by 3 Juno's mounted in 3-way radial symmetry.

The test consists of:

• Taking off with the craft in neutral configuration, with CoM on top of CoL.
• CoL on top of CoM (sometimes skipped)
  1. Trim it to fly straight.
  2. Upset it with small pitch inputs and see if it's stabilizes or goes out of control.
• CoL behind CoM
  1. Transfer ore to forward tank and trim it to fly straight.
  2. Upset it with small pitch inputs and see if it's stabilizes or goes out of control.
• CoL in front of CoM
  1. Transfer ore to rear tank and trim it to fly straight.
  2. Upset it with small pitch inputs and see if it's stabilizes or goes out of control.

First test is an standard layout with no Angle of Incidence. Wings mounted parallel to the fuselage.

CoL inline with CoM. No Angle of incidence.

It stabilizes faster when CoL is behind CoM, just as you would expect.

Adding Angle of Incidence to the main wing. The first thing to note is that the main wing had to be moved backwards quite a bit, to align the CoL with CoM again. I'm certain it will help move the Aerodynamic Center backwards, too. I also had to move the engines forward to align CoM with the middle of the center ore tank, again.

If it had been a Canard design, I would add more AoI to the Canard than the main wing and it would also result in the main wing needing to move back to align the CoL with CoM again.

CoL inline CoM. Estimated 1-2° Angle of incidence.

That seemed to help a lot. It snapped back to the direction of movement rapidly. And there was much less difference between CoL forward or back.

What really happens is, I create a craft with CoL behind CoM, and just move the CoL forwards using AoI. It works because moving the CoL this way doesn't influence the Aerodynamic Center, the same way that moving a whole wing forward does.

Edit 2016-03-01: Fixed some grammar and clarified a few sentences.
Edit 2016-11-03: Added applicable KSP version.
Edit 2016-12-01: Added AoI image. (source)
Edit 2020-10-21: Format fixes as the new forum software made it apparant, that lots of old style formattings have been mixed over many, many edits.

Edited October 21, 2020 by Val
Updated title to 1.x.x and format fixes.

[katateochi]

This is very helpful and it explains why some craft I've had which looked like they should be stable (from where their COL and COM were), but didn't handle as expected. 
I have to confess that as most of what I know about aircraft design comes from playing KSP I didn't know about the aerodynamic center or it's significance.  Knowing this will change how I approach aircraft design. nice 1! 

[Evanitis]

Daaam, that's an eye opener... and a nice read. It needs some ingesting.

 

Cargobay myths busted. Thanks, nice job. I hate when such superstitions start to circulate honest, hard working parts. Want a Mythbuster badge?

Moral of the story seems to be that CoM-CoL balancing isn't enough, but one also needs to put that CoM to the middle. And when one fails because of the moar boosters on the back, it should be as close as possible. Guess that's the reason that the only Shuttle I built looks silly. Well, one of the reasons.

Though I don't get that Aerodynamic Center thing. It sounds interesting. So it's an elusive vector that remains hidden from us, independent of CoL. What makes the two deviate from each other? Is that the relative size of frontal and rear lifting area? The amount of control surfaces? Can't really visualize how that happens. Wish I knew a bored modder capable of creating an AC indicator to summon.

 

By the way... how that angle of incidence on wings work? I kinda' knew it would be better to add AoA, but somehow it didn't feel right... it reminds me of those old WW1 planes, so I always skipped that step on all my (post)modern looking planes. Does it work by reducing the drag by flying more... horizontal while still having lift? Guess I should have given it a try long ago.

EDIT: Ahh, text was hiding behind the pictures too.

Think I get it now. It's more comprehensive once one found the entirety of the text.
So I can push the CoL onto the CoM with AoI once I tested if the balance is right. Sounds cool.

Edited February 11, 2016 by Evanitis
And that's already small monitor friendlier? The CoM of that Shuttle is in my kitchen. xD

[Val]

I've added some extra pictures and links to the OP.

 

9 hours ago, Evanitis said:

but one also needs to put that CoM to the middle

Towards the middle, yes. It's just a rule of thumb to improve chances of creating a stable craft.

 

9 hours ago, Evanitis said:

Though I don't get that Aerodynamic Center thing. It sounds interesting. So it's an elusive vector that remains hidden from us, independent of CoL.

The Aerodynamic Center not independent of CoL. CoL is a part of it.

The Aerodynamic Center is the center of all aerodynamic forces, which essentially boils down to drag. But it includes lift because lift creates drag.

 

9 hours ago, Evanitis said:

Does it work by reducing the drag by flying more... horizontal prograde while still having lift?

Exactly. Wings don't create lift unless they have Angle of Attack. So if the wings are mounted parallel to the fuselage, then the fuselage has to point away from prograde (the direction of movement) in order to get the wings to create lift.

By giving the wings "built-in AoA", Angle of Incidence, the craft can be pointed prograde while still creating lift. That reduces fuselage drag greatly.

 

9 hours ago, Evanitis said:

So I can push the CoL onto the CoM with AoI once I tested if the balance is right.

Yes, that is correct.

Edited February 12, 2016 by Val
Clarified AoI

[Temstar]

I've seen the aerodynamic centre also referred to as "centre of pressure" from which derives the term "CGCP mismatch".

CG is centre of gravity, so essentially centre of mass in KSP while CP is centre of pressure, which is the aerodynamic centre you're talking about here. A CGCP mismatch is when CP is ahead of CG which as we can see in KSP causes flipping. This issue is one of the things that doomed HOTOL.


You can see when Reaction Engine people went back to the precooled air breathing engine concept with Skylon they changed the HOTOL design and put the engines in the middle:

This shifted the CG forward so its towards the middle of the craft slightly ahead of the CP.

Or if you look at another area of real life design that faces the same problem as KSP SSTO, that of winged flyback booster:

 

Notice something in common? They all have jet engines mounted in their nose. Flyback boosters need that jet engine because when it separate from the core stage it's going to be pretty far down range so needs powered flight to make it back to launch site. The easy way is to just put the jet engine in the back like the proposed production version of Buran shuttle. However like HOTOL and our KSP SSTOs flyback boosters suffer CGCP mismatch since they have that big hulking rocket engine on its tail, so by putting the jet engine in the nose (and so having to do all that complicated ducting) you shift CG forward to match with CP.

Edited February 12, 2016 by Temstar

[Val]

Thank you, @Temstar. Those are great real world examples/concepts that show design choices made to move CoM forward.

[Evanitis]

9 hours ago, Val said:

The Aerodynamic Center not independent of CoL. CoL is a part of it.

 

The Aerodynamic Center is the center of all aerodynamic forces, which essentially boils down to drag. But it includes lift because lift creates drag.

Thanks, that clarifies the matter a bit.

I was reading some more articles on the subject to wrap my head around it. It started to feel egg-shaped during the process.

As far as I understood, the position of AC is independent of the AoA of the plane and it's position - it's kinda' nailed to where it is. While CoL shifts along with the control surfaces (as your gif so clearly demonstrates) producing pitch when needed. Not sure if I'm totally right on that matter, but visualizing it this way helps my eyeball engineering. And it explains why can I push the CoL into the CoM with AoI for manuverability while retaining stability.

Now all that remains is field testing.

Edited February 12, 2016 by Evanitis

[Val]

6 minutes ago, Evanitis said:

Thanks, that clarifies the matter a bit.

You're very welcome 

I've updated the OP with a slightly expanded description of Aerodynamic Center and added a more detailed description of Angle of Incidence at the bottom of OP.

[Boris-Barboris]

10 hours ago, Val said:

The Aerodynamic Center is the center of all aerodynamic forces, which essentially boils down to drag.

If you would google definitions a little, you would not write that. Also, there's no such thing as "center of forces". And it has very little relation between drag and AC. Well, you can invent your own definition just for the purpose of this article, but then you would need to prove it's usefullness for stability eyeballing.

Stock CoL would perfectly be an aerodynamic center, if it would account for all parts, and SQUAD coder would stick to proper lift definition of  "force, perpendicular to airflow", not a force, prependicular to lifting surface symmetry axis. I had to write CorrectCoL to fix (mostly, again, with implications) that for me.

There's no point looking at CoL with moving control surfaces (other than for demonstration purpose, that indeed helps to demonstrate, what it truly shows), it's meaningful only for fixed airframe. Only when it's fixed, it has any relation to stability. Secondly, it's location after CoM means stability only if you look at it on equilibrium AoA, and only local stability. Basicly, you need to rotate your craft in SPH to find an angle, when CoL is behind CoM by the largest margin. If such angle exists, it will be equilibrium AoA, and your craft is locally pitch-stable around it. And there is a heavy-weight train of conditions to make previous statements true (one of them is that all forces, accounted in CoL calculations, are not only collinear, but parallel, only then weighted sum of vectors, wich is used is stock, can actually give true AC\CoL\whatever position). If anyone wants complete knowledge about it's craft static stability before actually flying, he needs tools like FAR static analysis, wich we don't possess. Torque and it's derivative are the only reliable judges, all other criterias will always be crap.

18 hours ago, Val said:

Designing your craft with CoL in front or behind of CoM doesn't change aircraft stability much

TRIGGERED  Excuse me? Well, i know what you wanted to say, but that particular sentence is very harsh.

On your wings incidence point, it needs carefull tuning for each plane, since it may result in negative AoA for level flight, or worse L\D ratios. It's not a very good alternative for trimming, but i will not argue, that it's SAS-friendly.

Shuttles are hard (not) to build because people are literally missing the point, that when they pitch up at 10 degrees, CoL is dangerously close to or ahead of CoM. People just need to tilt their head to the left a little sometimes.

[GoSlash27]

One caveat:

 The center of lift actually does directly contribute to/ detract from the longitudinal stability. As lift is increased, it creates a pitch moment about the CoG. Having the lift ahead of the CoG will result in an aircraft that is dynamically unstable with pitch; increasing AoA generates more lift, which creates a nose- up pitch moment, which creates more AoA.

 Having the lift behind the CoG has the opposite effect, creating dynamic stability. An excess of this stability is what causes lawn- darting. 

 For me, the key to stable and controllable aircraft isn't so much the longitudinal position of the CoG, but rather ensuring that it stays put as the fuel drains. This means fuel tanks directly at the CoG.

Best,
-Slashy

 

[Val]

50 minutes ago, Boris-Barboris said:

If you would google definitions a little, you would not write that. Also, there's no such thing as "center of forces". And it has very little relation between drag and AC. Well, you can invent your own definition just for the purpose of this article, but then you would need to prove it's usefullness for stability eyeballing.

I didn't invent. I used it, because it's what is used in the wiki article on Longitudinal Stability. 

Quote

The longitudinal static stability of an aircraft is significantly influenced by the distance (moment arm or lever arm) between the centre of gravity (c.g.) and the aerodynamic centre of the airplane. The c.g. is established by the design of the airplane and influenced by its loading, as by payload, passengers, etc. The aerodynamic centre (a.c.) of the airplane can be located approximately by taking the algebraic sum of the plan-view areas fore and aft of the c.g. multiplied by their blended moment arms and divided by their areas, in a manner analogous to the method of locating the c.g. itself.

Granted, I simplified it a lot, by reducing it to drag. But it made sense, as drag is a reasonably relatable term in KSP and stock aerodynamics context.

I will add to the OP that my most of explanations are specific to stock aerodynamics and not applicable to real world aerodynamics, even though I reference real world aerodynamics.

 

1 hour ago, Boris-Barboris said:

Excuse me? Well, i know what you wanted to say, but that particular sentence is very harsh.

Thanks for the feedback. I'll try to rephrase it.

 

1 hour ago, Boris-Barboris said:

On your wings incidence point, it needs carefull tuning for each plane, since it may result in negative AoA for level flight, or worse L\D ratios.

I can't back it up, but I'm pretty sure that is also true for real world aircraft.

At least that is what I take from the the sentence: "to allow the fuselage to have a low angle with the airflow in cruising flight". I understand that to mean a given Angle of Incidence is only optimal within a certain speed range depending on altitude. At low altitude the optimal speed is low, and at higher altitude the optimal speed is higher.

[Boris-Barboris]

28 minutes ago, Val said:

I didn't invent. I used it, because it's what is used in the wiki article on Longitudinal Stability. 

And that particular artical is containing a reference to it's definition, which quite differs from "center of all aerodynamic forces, which essentially boils down to drag".

28 minutes ago, Val said:

ranted, I simplified it a lot, by reducing it to drag. But it made sense, as drag is a reasonably relatable term in KSP and stock aerodynamics context.

That's quite bold, since lift torques and forces are much more important, and their magnitudes are much higher than drag ones, both stock and IRL. That's why CoA\CoL is a fine tool to analyze stability.

28 minutes ago, Val said:

I can't back it up, but I'm pretty sure that is also true for real world aircraft.

IRL good models of those aircrafts are availiable, angle of incidence is chosen accordingly to provide maximum expected fuel efficiency on most probable cruise speeds and altitudes. They can do it, we can't, so we'll be simply guessing. Fuselage is providing lift as well, it's bad to simply assume, that the plane will be optimal, if we keep fuselage at zero AoA.

Edited February 12, 2016 by Boris-Barboris

[Val]

56 minutes ago, GoSlash27 said:

The center of lift actually does directly contribute to/ detract from the longitudinal stability. As lift is increased, it creates a pitch moment about the CoG. Having the lift ahead of the CoG will result in an aircraft that is dynamically unstable with pitch; increasing AoA generates more lift, which creates a nose- up pitch moment, which creates more AoA.

 Having the lift behind the CoG has the opposite effect, creating dynamic stability. An excess of this stability is what causes lawn- darting. 

Having the CoL behind CoM is not what makes the craft dynamically stable, because as soon as you take-off with that craft, you'll have to use trim or SAS to get your control surfaces to pitch up, so the CoL moves up to CoM. If the craft is going to fly straight.

What makes it stable is that it's aerodynamic center is behind CoM. And yes that is certainly easier to achieve when designing the craft initially with CoL behind CoM, because CoL influence where the aerodynamic center ends up, especially if you have really large wings. But it is not a given that the craft will be stable just because you design it with CoL behind CoM.

That is what my post tries to explain.

 

[Val]

41 minutes ago, Boris-Barboris said:

That's quite bold, since lift torques and forces are much more important, and their magnitudes are much higher than drag ones, both stock and IRL. That's why CoA\CoL is a fine tool to analyze stability.

I will take this into consideration and work on rephrasing it to be more precise. But I'm also hesitant to be too technical, both because I'm no expert and to not scare away readers, before the get to the point I'm trying to make about the relationship between CoL and CoM.

 

41 minutes ago, Boris-Barboris said:

it's bad to simply assume, that the plane will be optimal, if we keep fuselage at zero AoA.

In my experience it has always been better with a little incidence, than none. But that doesn't make it optimal. I'll rephrase that.

[Boris-Barboris]

8 minutes ago, Val said:

because CoL influence where the aerodynamic center ends up

Origin of stock CoL is aerodynamic center, when all lifting surfaces are parallel to reference axis (root part, for example), and body lifts of other parts are negligible. Other craft configurations, unfortunately, break it, and i'm starting to understand, that you want to point out this particular fact, and i support you on this.

16 minutes ago, Val said:

What makes it stable is that it's aerodynamic center is behind CoM

Well, not only that, but good enough.

[Boris-Barboris]

3 minutes ago, Val said:

But I'm also hesitant to be too technical, both because I'm no expert and to not scare away readers, before the get to the point I'm trying to make about the relationship between CoL and CoM.

We are victims of our tools (CoL), as long as we use it, we'll have comprehension problems.

[Evanitis]

Meanwhile: Tested the above in practice with a smaller SSTO-plane. Got like ~100 m/s of extra dV on orbit, increased manuverability, no noticable loss of stability. Maybe it stalls a tiny bit sooner than I was used to, but it's kinda' negligible - even on water. Can't wait to see what it does with the big guy. I'm expecting more as it has a huge S that it keeps in the airflow with straight wings.

Believing you about AoI would have made the 1.0.2 days easier. But it feels better to understand have a vague concept about why this actually happens.

[Val]

I've updated the OP with some of the recommendations from @Boris-Barboris

Thank you, for the feedback.

[GoSlash27]

8 hours ago, Val said:

Having the CoL behind CoM is not what makes the craft dynamically stable, because as soon as you take-off with that craft, you'll have to use trim or SAS to get your control surfaces to pitch up, so the CoL moves up to CoM. If the craft is going to fly straight.

What makes it stable is that it's aerodynamic center is behind CoM. And yes that is certainly easier to achieve when designing the craft initially with CoL behind CoM, because CoL influence where the aerodynamic center ends up, especially if you have really large wings. But it is not a given that the craft will be stable just because you design it with CoL behind CoM.

That is what my post tries to explain.

Val,

 Yeah, I understood that from your OP, but I'm just correcting the oversight. All other things being equal, the location of the CoL relative the CoM *does* matter for dynamic stability, regardless of what the pressure center is doing.

 I need to differentiate between static stability and dynamic stability as I'm using the terms.

 Dynamic stability is the tendency to resist disturbances and actively seek a stable state. Static stability is the tendency to fly straight and level with no trim adjustments or control inputs.

 What you're talking about by my definition is static stability, and yes... the pressure center is what's important here. But for dynamic stability in pitch, you want the CoL behind the CoM. It doesn't have to be far behind it, but it does need to be behind it. Otherwise it will amplify disturbances in pitch rather than damping them.

Best,
-Slashy

 

 

[Val]

19 hours ago, GoSlash27 said:

But for dynamic stability in pitch, you want the CoL behind the CoM. It doesn't have to be far behind it, but it does need to be behind it. Otherwise it will amplify disturbances in pitch rather than damping them.

Well, you certainly put me to work with this one. I've spent the whole day coming up with tests and making test crafts. And here are my findings.

The test craft is a conventional main wing+tailplane craft, with 3 ore tanks as fuselage, where I can move the ore between the tanks to place CoM either, on top, in front or behind CoL. The craft is otherwise as well balanced as possible. The fuel tanks are exactly at CoM (when it's in the middle position right on top of CoL) and thrust is provide by 3 Juno's mounted in 3-way radial symmetry.

The test consists of:

• Taking off with the craft in neutral configuration, with CoM on top of CoL.
• CoL on top of CoM (sometimes skipped)
  1. Trim it to fly straight.
  2. Upset it with small pitch inputs and see if it's stabilizes or goes out of control.
• CoL behind CoM
  1. Transfer ore to forward tank and trim it to fly straight.
  2. Upset it with small pitch inputs and see if it's stabilizes or goes out of control.
• CoL in front of CoM
  1. Transfer ore to rear tank and trim it to fly straight.
  2. Upset it with small pitch inputs and see if it's stabilizes or goes out of control.

CoL inline with CoM. No Angle of incidence.

While it clearly wasn't need to have CoL behind CoM, it did seem to stabilize itself faster when that was the case.

So next I thought about what CoL really is. It is the center of LIFT. It is a force which pulls upwards. It lifts the craft. The craft is hanging from the sky in that point. (Well, at least when it's when it's flying horizontally.)

So what if I move the CoL above the CoM?

CoL above CoM. No Angle of incidence.

Meh. Some improvement maybe, but it's hard to tell. Might have helped...

For the next test I tried playing with Angle of Incidence on the main wing. The first thing to note is that the main wing had to be moved backwards quite a bit, to align the CoL with CoM again. I'm certain it will help move the Aerodynamic Center backwards, too. I also had to move the engines forward to align CoM with the middle of the center ore tank, again.

CoL inline CoM. Estimated 1-2° Angle of incidence.

That seemed to help a lot. It almost snapped back to its original position. And there was much less difference between CoL forward or back.

Now, you can argue, that what I really did was, create a craft with CoL behind CoM, and just cheated the CoL forwards using AoI. And there's some validity to that, because if you take that last craft and rotate it in SPH, then it will have CoL behind CoM as soon as it rotates away from horizontal.

Finally I decided to cheese the CoL completely and created this weird thing.

CoL above CoM (I think). No Angle of incidence.

Any thoughts? Did, I miss something?

 

Edited February 13, 2016 by Val
Minor typos and grammar

[GoSlash27]

9 hours ago, Val said:

Any thoughts? Did, I miss something?

Val,

 Actually, you hit on most of the major points, I think. Having the CoL above the CoM does aid in stability (both static and dynamic) and the CoL isn't necessarily where it appears to be in the SPH, which is demonstrated in your last pic.

 The important bit is this:

9 hours ago, Val said:

So next I thought about what CoL really is. It is the center of LIFT. It is a force which pulls upwards. It lifts the craft. The craft is hanging from the sky in that point. (Well, at least when it's when it's flying horizontally.)

  Adding to this, the CoM is the fulcrum; the point about which the aircraft rotates. Changes in lift will generate a torque about the CoM. That's why aircraft with the CoM ahead of the CoL are inherently stable, while the reverse is inherently unstable. This can be masked somewhat if you use a lot of control surface, but I'm notorious for using as little control authority as possible in my spaceplane designs.

Best,
-Slashy

Edited February 14, 2016 by GoSlash27

[Nich]

Very good article but I still disagree about Cargo bays being bugged.  I will have to get some re-entry pics but at angles as low as 15 degrees off prograde I had cargo bays generating twice the lift of big S wings.  I also find it interesting that body lift is normal to airflow but wing lift is normal to wing orientation.

 

I also think that COL does not take distance from the center of mass into consideration.

 

If I place a wing at the exact center of mass it produces lift exactly at the center of mass

Then if I place a lifting device at the very front the center of lift only moves forward a little. This is an incredibly unstable craft because the wing has no influence over stability but the control surface at the front has an enormous influence.  Moving the wing back so the COL is behind the COM does not make the craft stable because the arm for the CG on the control surface is so large

 

In order to get this craft stable I would have to do the math of lift x arm for the wing has to be greater then lift x arm for the control surface.  So the wings have 10 lift and the control surfaces have .5 lift.  The total length is the length of the wing from COM (x) plus the length of the control surfaces (y).  Then because we want to know where they are equal it would be 

10x = .5y and

x+y = L

Solving we get 

10x-.5(x-L) = 0

9.5x - .5L = 0

x > .0526L

y < .9474L

However this does not account for body lift and as you add engines to the back you get more body lift in front of the CG and less behind.  I suspect this is further complicated by the fact that body lift does not scale with AoA the same way wings do.  Please correct me if I am wrong but it looks like you get very little body lift < 10 degrees AoA but it grows very fast from 15-90

By eyeballing 6% and 94% the COL (wish I had a way to measure) the COL needs to be well behind the COM to achieve lifting surface stability neglecting body lift.

Edited February 24, 2016 by Nich

[Boris-Barboris]

2 hours ago, Nich said:

I also think that COL does not take distance from the center of mass into consideration.

It doesn't need to, it's CoL. It's builder's job to compare it's location to CoM. You have made errors while solving moment equation. And that sausage without engines would be stable with CoL right behind CoM,  because disregarded body lift is almost right on top of CoM (symmetrycal body).

Edited February 24, 2016 by Boris-Barboris

[Val]

I've rewritten parts of the OP. Changed the TL;DR, moved sections around, and incorporated parts my stability test post.

I might have garbled some parts. Any feedback would be appreciated.

 

7 hours ago, Nich said:

I will have to get some re-entry pics but at angles as low as 15 degrees off prograde I had cargo bays generating twice the lift of big S wings.  I also find it interesting that body lift is normal to airflow but wing lift is normal to wing orientation.

Unfortunately, the length of the cyan and blue forces in the aerodynamic overlay are not relative. My search fu is failing me, but it's been mentioned by mods that length of the arrows are bugged and the only useful information they provide is direction of force and whether the force on a particular part has increased or decreased.

7 hours ago, Nich said:

I suspect this is further complicated by the fact that body lift does not scale with AoA the same way wings do.

I might be smaller, but it's not insignificant. This craft has 5° AoI on the "wing" parts. Jump to 3:25 to see it fly.

 

Edited February 24, 2016 by Val
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[Nich]

Wow thanks for that last video.  I knew it was possible as the old expression with enough thrust you can make a barn door fly. I never imagined a weasley would be able too and that it would fly so well.