So, what exactly is the center of lift?

[T.C.]

I'm trying to understand center of lift, and I have several questions:

1) First, is center of lift an established scientific concept, or is it something invented for this game? Is it supposed to be the same as (or approximate) the aerodynamic center?

2) On the KSP wiki, center of lift is described as "...the point where the sum total of all lift generated by parts -- principally by wings, control surfaces, and aerodynamic fuselage parts -- balances out...". What does "balance out" mean in this context? Does it have something to do with a resultant force? If so, a resultant force identifies a line of application, not a point. How is the point defined?

3) Does the lift of a part depend on the craft's orientation? For example, does a wing provide a different lift when the nose is pointing prograde than it does when the nose is pointing radially? And if so, then how is KSP able to show you the center of lift while designing a plane in the hangar? Does it make an assumption about your craft's orientation relative to its velocity through the air? For instance, does it assume your craft will be moving in the direction defined as forward by the root part, and calculate the center of lift accordingly?

4) What is the difference between lift and drag? The wiki says "Lift is contrasted with drag, the force directly opposing an object's motion through the air." By this definition, lift vectors must always be perpendicular to the direction of motion, because any component of aerodynamic force parallel to the axis of motion is regarded as drag, right? But then why does the blue arrow in KSP's center of lift display sometimes tilt fore or aft? (When I trim a wing, for instance.)

5) Why make a distinction between lift and drag anyway? If I understand correctly, players use center of lift to understand the torque that will be caused by lift-inducing parts. But drag-inducing parts also cause torque when they aren't in-line with the center of mass, so wouldn't the center of lift + drag convey a more complete understanding of the torque than the center of lift alone?

-TC

-- CONCLUSIONS --

After receiving several replies, I think I understand center of lift now. I know future players may come here seeking answers, so I will summarize my conclusions in an edit. (Keep in mind that these conclusions still involve a fair amount of speculation on my part.)

• Conceptually, center of lift is the same as aerodynamic center. For a craft moving at a certain orientation and airspeed, find the resultant force of all aerodynamic forces. That defines a line. Then find the point on that line which remains unchanged after incremental perturbations in the craft's orientation. That point is the aerodynamic center and the center of lift.
  

• When KSP shows the center of lift in the hangar, it is showing an approximation which is inaccurate in two significant ways:
  

1) KSP's center of lift does not consider

all

aerodynamic forces; it considers only a special category of force which roughly corresponds to Bernoulli effects. As a result, the center of lift shown on the screen can be significantly off. For instance, the drag of parts on a front-loaded rocket should result in a center of lift in front of the center of mass, but you won't see that in KSP's center of lift display. Also, increasing the incidence of a wing increases lift both in real life and in KSP flight, but you won't see that increase reflected in the center of lift display.

2) KSP's center of lift does not take into account the orientation of lift-inducing parts relative to movement through the air. Thus, if you attach a lift-inducing part at anything other than the default orientation, you'll get an inaccurate center of lift. This particularly affects any craft with wings attached at an angle of incidence or trimmed control surfaces

The bottom line is that the center of lift display can be inaccurate for all but the simplest of designs. Whether the inaccuracy is significant enough to matter, I don't know -- I just know theory at this point.

• I believe KSP's center of lift is inaccurate in the ways described above because it is extremely difficult to calculate center of lift properly, and this approximation is the best Squad could do at the time. (No implied criticism here -- Squad's accomplishments are still A+ in my book.) During my research, I came across a comment from someone at Squad which said that to do lift properly, they would need to add a wind tunnel to the space center. So, it seems that the developers have already thought about this with an eye toward making it better.
  

I mention this because I saw comments which suggest that what I'm calling inaccuracies are actually intentional differences which make a valuable distinction between "lift" and "drag". I believe that is not the case. There is no need to make any such distinction, and a center of lift calculation without the inaccuracies described above would in all ways be better than the one we have now.

• We need to be careful not to let our understanding of drag and lift be defined by KSP's modeling of those concepts. Drag is any aerodynamic force acting parallel to the direction of motion, and lift is any aerodynamic force acting perpendicular to the direction of motion. KSP uses those terms slightly differently. It tends to use drag and lift to refer to different aerodynamic modeling techniques, where drag corresponds roughly to air resistance and lift corresponds roughly to Bernoulli effects. KSP's terminology isn't really kosher, so be aware that when KSP says "drag", it may be talking about a force that includes a component of lift, and when it says "lift" it may be talking about a force that includes a component of drag.
  

-TC

Edited August 18, 2015 by T.C.

[FancyMouse]

Any collection of forces on a rigid body is equivalent to a single force exerted to a certain point. Depending on the force, it may be different things. Gravity - CoM. Lift thus CoL. Thrust you'll have CoT.

And there's a distinction between lift and drag because of where they come from. Drag is just drag by pushing air in front of you move at your speed and you get the reaction force. Lift comes from the pressure difference between upper and lower surface (because of air speed difference produced by often wings or could be anything)

[Gaarst]

Short answers:

1) Yes, it is equivalent to aerodynamic center.

2) Yes, it is resultant force. It applies to a certain point on your ship, but you can see an arrow showing the direction of the force.

3) Yes, it does depend on a craft's orientation.

4) I think the blue arrow somehow describes a resultant force: lift is up, drag is back, so arrow is tilted.

5) According to my answer above, lift + drag are reprented. To be proven, though.

These are quick answers, I may post some more detailed tomorrow (I'm kinda tired right now) if needed.

[Kelderek]

This may not answer all of your questions, but it should be a useful read to start out:

Basic Aircraft Design Explained Simply With Pictures

3. If you attach parts normally in the SPH, then they will be oriented in a way the provides proper lift. If you try to rotate wing parts, then that can make them no longer provide lift. I think for wing parts they can be normal or rotated 180 degrees (backwards) and still function, but anything in between will provide less than optimal results. Scott Manley did a great video about this once illustrating the effects of rotating wing parts and how it affects your lift in the game. You could probably do similar tests to see these results.

[Xannari Ferrows]

Protip: You can use the center of lift as a good approximation for your center of drag, because really the two are the same thing, just spelled differently.

[T.C.]

Any collection of forces on a rigid body is equivalent to a single force exerted to a certain point. Depending on the force, it may be different things. Gravity - CoM. Lift thus CoL. Thrust you'll have CoT.

FancyMouse,

Thank you for the reply. You clearly know what you're talking about, but your post contained a technical mistake which my OCD requires me to correct:

It is not true that for any collection of forces on a rigid body there is an equivalent single force. Specifically, if the collection of forces results in a pure torque, there is no equivalent. Also, you said "exerted to a certain point". Technically, a resultant force can be exerted anywhere along a line. That is why in Question 2 I said "a resultant force identifies a line of application, not a point. How is the point defined?" I think I know the answer now. The center of lift is the point on the resultant force line which remains on the resultant force line after an incremental change in the angle of attack. This comes from the definition of the aerodynamic center, which Gaarst assures me is the same as the center of lift, and can also be inferred from your suggestion that the center of lift is similar to the center of mass. Thank you. I'm satisfied with my understanding of the definition of center of lift now, and will ask no more questions about that.

And there's a distinction between lift and drag because of where they come from. Drag is just drag by pushing air in front of you move at your speed and you get the reaction force. Lift comes from the pressure difference between upper and lower surface (because of air speed difference produced by often wings or could be anything)

Your second paragraph opens a whole new can of worms, however. You seem to be making a distinction between lift and drag which I don't think exists in the real world, but may exist in KSP's model of it. Are you implying that in KSP, "Center of Lift" considers only modeled Bernoulli effects, and no other aerodynamic forces? That would explain a lot, actually.

-TC

- - - Updated - - -

1) Yes, it is equivalent to aerodynamic center.

Gaarst,

Thank you for the concise answers. It was a big help just to hear that center of lift is equivalent to aerodynamic center. (To all: I recommend that someone add that to the wiki to help future novices up the learning curve.)

3) Yes, it does depend on a craft's orientation.

On the question of whether lift depends on orientation: I've been experimenting in the hangar, and I think maybe it doesn't. Rather, I think lift does depend on orientation during flight, but the center of lift calculation doesn't seem to take orientation into account, except for some broad assumptions about whether your airfoil is up or down. The bottom line is that the center of lift just seems wrong unless all lift-inducing parts are oriented the way KSP expects. Also, FancyMouse raised the possibility that center of lift doesn't refer to lift per se, but just a specially modelled type of lift. In other words, even though the KSP physics simulator would let you get your lift from a barn door attached to the fuselage with an angle of incidence, it might not consider that lift in the center of lift calculation. If true, that makes the center of lift in KSP a much more limited thing than I thought it was, and renders Questions 4 & 5 moot. (Also, who knows -- maybe the specially modeled lift that goes into the center of lift calculation doesn't depend on orientation even in flight, which would make the center of lift calculation correct for the limited thing it is trying to do.)

-TC

[FancyMouse]

Seems you do know more than I do.

Pure torque - fine degenerate case, and I completely agree with your details.

For the point or line - right I haven't thought too much about that when I first wrote them. Gravity can be seen as acting on a point because when you rotate it, you got a new line, but the new line still passes that point, or in other words, there is a point which is the intersection of all lines from all orientations, so we can define "center of gravity" for this point. CoL is trickier, since it varies by your orientation, so I actually doubt whether all these "lines" still converge at a single point. I don't know, and that may explain why I've heard people saying stock CoL in VAB is nonsense. It may, however, still be valuable when examining the case under small pitches.

For lift and drag - I agree the underlying mechanism is the same, but I feel it's the same thing as electric and magnetic field - they're different view angles of the same thing, but still they are different view angles. When we do computations at the angle when they do look different, they should be treated differently. That's how I look at lift and drag.

[_stilgar_]

Any collection of forces on a rigid body is equivalent to a single force exerted to a certain point.

Are you sure? If I have an object, and two vectors of force applied on opposite ends of this object, if the vectors have opposite signs, the body will not move, but rotate. How can you replace those two forces with just one?

[FancyMouse]

Are you sure? If I have an object, and two vectors of force applied on opposite ends of this object, if the vectors have opposite signs, the body will not move, but rotate. How can you replace those two forces with just one?

TC already mentioned and I already agree with him that I wasn't completely correct there. It's the degenerate case when the result is only torque. Technically you can say it's zero force applied at infinity thus producing only torque, but that just doesn't make common sense and I'm not going to insist on that.