%MAC and LEMAC: why?

[killbilly]

I first ran into the concept of CG calculated as a percentage of MAC when I was flipping through a Cirrus PoH some years ago, but didn't pay all that much attention to it. It didn't really come up on my commercial training, either. But when I was studying for the ATP written, quite a few of the w/b and CG/load shift questions looked for answers as a percentage of MAC and usually gave LEMAC as a constant.

My question is why?

Everything about loading calculations up to that point followed a pretty simple baseline of taking the weight, multiplying it by the arm or station, and there was your moment. Charts and graphs did some of the work for you, but it was still basic multiplication and division to arrive at a number. And since you can get fairly precise with the stations/centroids used in the charts, I just don't see WHY the CG needs to be expressed as a percentage of the MAC instead of as a fixed point referenced to the datum.

Is there some advantage to expressing it as a percentage? Does using MAC allow for an aerodynamic characteristic that I'm not making the connection on?

I learned to do all of the math for the test and I understand what's being calculated. I just don't know why it's done this way. Any insight?

 

[ahw01]

Mean Aerodynamic Chord (MAC) | SKYbrary Aviation Safety

Definition Mean Aerodynamic Chord is the average chord length of a tapered, swept wing. Description Chords on a swept wing

skybrary.aero

 

[killbilly]

Mean Aerodynamic Chord (MAC) | SKYbrary Aviation Safety

Definition Mean Aerodynamic Chord is the average chord length of a tapered, swept wing. Description Chords on a swept wing

skybrary.aero

I get this. I looked up these definitions.

But they don't answer the WHY. This is done on SOME light GA aircraft, and, it seems, on most large transport category aircraft. Why? What is the reasoning or school of thought on this?

 

[Roger Roger]

My best guess is that on large aircraft the actual numbers would get obnoxiously large and possibly subject to power of 10 errors.

 

[killbilly]

My best guess is that on large aircraft the actual numbers would get obnoxiously large and possibly subject to power of 10 errors.

Ok, I get that - makes sense - but hasn't every loading or w/b chart you've ever seen had a MOM/100 or MOM/1000 factor on it? That has been my very limited experience.

We asked this question of one of the instructors in my ATP/CTP class and he did not know. The first guy to bring it up was an ex-B1/B2/B52/C17 guy. (He had some terrific stories.)

 

[ppragman]

Temac, LEMAC, and MAC is all about pitching moments and controllability with non-rectangular shapes. The CG would be crazy hard to calculate if you were using traditional methods.

 

[killbilly]

Temac, LEMAC, and MAC is all about pitching moments and controllability with non-rectangular shapes. The CG would be crazy hard to calculate if you were using traditional methods.

So does that mean when a loading graph (or problem) has you convert the CG to a percentage (or, going the other way, converting a percentage to a specific station) it's just for the sake of the math, and the specific station (not the percentage) is meaningless? Or inaccurate?

 

[ppragman]

So does that mean when a loading graph (or problem) has you convert the CG to a percentage (or, going the other way, converting a percentage to a specific station) it's just for the sake of the math, and the specific station (not the percentage) is meaningless? Or inaccurate?

Well… I’m unsure about this exactly, but I’d suspect that fuel in a swept wing changes the CG non-linearly but changes %MAC linearly, but if you abstract the wing shape to a hypothetical square one?

Basically you convert a complex wing shape to a square one and in doing so you get a measurement that is similar across wing plan forms.

 

[killbilly]

Well… I’m unsure about this exactly, but I’d suspect that fuel in a swept wing changes the CG non-linearly but changes %MAC linearly, but if you abstract the wing shape to a hypothetical square one?

Basically you convert a complex wing shape to a square one and in doing so you get a measurement that is similar across wing plan forms.

This kind of makes sense...but I'm still not quite sure why, then, a fixed value (station) isn't okay but a percentage is, when you're looking at it from a practical/loading perspective.

 

[msmspilot]

This kind of makes sense...but I'm still not quite sure why, then, a fixed value (station) isn't okay but a percentage is, when you're looking at it from a practical/loading perspective.

If I understand correctly, the %MAC is a straight line on the wing, which angles back relative to the fuselage.

Using a fixed station would require you to determine a CG and a lifting moment, where expressing CG as a % of the chord allows you to calculate that the CG is within the window the wing can aerodynamically operate.

I feel like I’ve phrased this poorly, but maybe it’ll help

 

[killbilly]

Got a pretty workable explanation from another pilot I know that made sense. Here it is:

"It is important for longitudinal stability that the CG be located ahead of the center of lift of a wing. Since the center of lift is expressed as percent MAC, the location of the CG is expressed in the same terms."

This makes sense to me. @ppragman

 

[ppragman]

This kind of makes sense...but I'm still not quite sure why, then, a fixed value (station) isn't okay but a percentage is, when you're looking at it from a practical/loading perspective.

Because you don’t actually care about the cg - the cg is irrelevant to flying, what you care about is the stability you get at a particular CG. That’s the important part.

MAC is the tool to figure out if you’re in the range of permissible stabilities, which is easy if you have a relatively simple wing (you just use the CG) but really hard if you have a complicated wing.

For instance in a square winged machine (or a relatively square winged machine) the fuel burn makes a straight line if you draw it on a chart relative to cg.

But in your weird swept wing machine with weirdly shaped tanks etc it might make a curve during fuel burn. So if you’re plotting the CG, just because the cg starts in the envelope and ends in the envelope doesn’t mean it doesn’t exit the envelope during fuel burn.

So, convert the entire weird wing envelope to some weird morphadite envelope with a square wing shape and now you can calculate things with a ruler and a straight edge or a whizz wheel or something more human friendly. Either way, you don’t have to integrate the weight in the fuel tanks or refer to some crazy cg / fuel chart that’s hyper accurate with 1000 points.

This has the added advantage of ensuring that regardless of the aircraft forward and aft limits to MAC are about the same (relatively) if the airplane is to be controllable.

@inigo88 is probably the most knowledgeable person here about this sort of thing, am I on point or out to lunch? I’m just parroting what was explained to me many moons ago.

 

[msmspilot]

Got a pretty workable explanation from another pilot I know that made sense. Here it is:

"It is important for longitudinal stability that the CG be located ahead of the center of lift of a wing. Since the center of lift is expressed as percent MAC, the location of the CG is expressed in the same terms."

This makes sense to me. @ppragman

That’s what I was trying to say…

 

[Minuteman]

I may be late to the party, but I know LEMAC as a constant value for a given airframe. Specifically, the longitudinal distance from "the datum" back to the 0% point of the MAC.

Like, a 737-800 and a 737-900 have the same wing (mostly), so the chord length used to normalize the CG and CP locations (often, the quarter-span chord length) will be the same between them. Buuut the LEMAC value will be different since the -900 has a longer fuselage plug forward of the wing than the -800. But I think you already recognize that(?).

I suspect the "why" is because the correlation between "distance from the datum" and station numbers gets muddled the first time an aircraft gets stretched.

Different manufacturers use different conventions for the same concept. Ultimately, station numbers are just designators -- names for various places on the aircraft. On a clean-sheet design there will usually be a direct correlation between station numbers and the distance aft of the datum (e.g., "station 1234" is 12.34 meters aft of the datum). There is value always being able to say stuff like "the power distribution junction is attached to the bulkhead at station number 567"

Then you stretch the airframe and it gets complicated. That power junction is still in the same place relative to the surrounding structure, but it's now eight meters further back from the datum. You could address this one of several ways:

1. change all the station numbers aft of the plug so they still agree with the distance (this is not a popular solution)
2. subdivide the plug: say it starts at station 345, then theres "345+1," "345+2," "345+3" etc, and the plug ends at station "346"
3. create new numbers for the plugs; say the aft-most point of the unstretched airframe is station "846". The start of the first plug will be station "1000" (still inserted between stations "345" and "346"). That power junction is also still at station "567."

Now take that mess and translate it into a lookup table for pilats to compute the moment arm for the oddly-shaped fuel tanks whose CG at station "700" when full.

Usually when they stretch an airplane, they leave the wing box alone, which is convenient because the CG and CP are nearby. So instead of choosing a datum that will have totally different numbers for each stretch-variant, they choose a datum referenced to the LEMAC location, or computed a unitless "index" from a nominal 25% CG location. The moment arms will still be different for each stretch, but I guess it's nice when the sum of the static mass moments arms adds up to a small number.

 

[Roger Roger]

Got a pretty workable explanation from another pilot I know that made sense. Here it is:

"It is important for longitudinal stability that the CG be located ahead of the center of lift of a wing. Since the center of lift is expressed as percent MAC, the location of the CG is expressed in the same terms."

This makes sense to me. @ppragman

Yeah but….I don’t care about that as a pilot because I’m gonna look up on a graph and if it’s in the envelope good ape gets banana. I maintain that it’s just because the final numbers are easy to interpret and, for most aircraft, BECAUSE of said relationship between CP and CG, allowable CGs in MAC will generally be about the same. I guess it probably varies a bit when you get into airplanes with a lot of wing sweep but I bet almost every transport category airplane is gonna end up with a CG envelope at most operational weights between about 10-30%.

 

[mikecweb]

Yeah but….I don’t care about that as a pilot because I’m gonna look up on a graph and if it’s in the envelope good ape gets banana. I maintain that it’s just because the final numbers are easy to interpret and, for most aircraft, BECAUSE of said relationship between CP and CG, allowable CGs in MAC will generally be about the same. I guess it probably varies a bit when you get into airplanes with a lot of wing sweep but I bet almost every transport category airplane is gonna end up with a CG envelope at most operational weights between about 10-30%.

12-34% on the -11. Gather around and let me tell you about how much fun a 33 CG landing is.

 

[ahw01]

12-34% on the -11. Gather around and let me tell you about how much fun a 33 CG landing is.

Like a cat on stilts?

 

[mikecweb]

Like a cat on stilts?

And on a cat nip bender.

 

[ppragman]

And on a cat nip bender.

Like a cat on stilts?

I put this into Dalle-e:

 

[drunkenbeagle]

Is there some advantage to expressing it as a percentage? Does using MAC allow for an aerodynamic characteristic that I'm not making the connection on?

No idea why, but a whole bunch of gliders (swept wing ones mostly) do CG that way too.