Forward vs Aft CG and Cruise Speed/Efficiency

[nauga]

What is the "total moment" you're speaking of here? Same as "basic airplane moment" above? Or just the sum forces on the entire aircraft? (or both?)

The sum of the moments. Net non-zero moment causes pitch acceleration.

So, at a particular airspeed, a particular force on the yoke will cause a particular deflection and a particular change in down force.

At a particular dynamic pressure and local AOA (at the tail) a particular yoke *deflection* will cause a particular *elevator* deflection and a particular change in *force* (up or down) provided by the tail. You can basically substitute force for deflection if you prefer, but I tend to think of stability as defined by the deflection characteristics and handling qualities defined by force characteristics with some contribution by deflection.

(Lower airspeed, same yoke force will be higher deflection but same change in downforce, right?)

Close enough.

The change in downforce will create a torque around the CG of the airplane. As the CG moves aft, the arm decreases and thus the torque around the CG is lower. Is the reason for the change simply that the change in downforce is a higher proportion of the total downforce when we have an aft CG?

I'm going to throw the math card. Think of an airplane with the cg at location 0 and the center of lift at location X and the tail at location 10X. There's a base pitching moment, constant with angle of attack, of every airfoil, although it may be zero for some. Call it M0, call the wing lift LW and the tail force LT. The moment of the wing lift is LW * X and the moment of the tail lift is LT * 10X. If the CG moves closer to the center of lift by 10% the lift based moment will be LW * 0.9X, a 10% reduction in moment, but the moment at the tail will be LT * 9.9X, a 1% reduction in moment. Since the wing-lift induced moment moment is reduced by a significantly larger amount the tail becomes that much more effective as the CG moves aft. Not because the pure tail moment is increasing, but that the moment it's working against (or supplementing) is decreasing, even if the "downforce" is the same.

ETA: In this example since Wing lift moment decreases the tail lift (downforce) to compensate can decrease as well, meaning there is less induced drag produced by the tail - this is the basis for trim drag reduction.

Now, about that downforce. Look back at M0, the base pitching moment. If that is zero, then you've got the last situation I described. If it's zero or in the nose-down direction (which is positive by stability&control convention) then for any positive lift (up, like in level flight) the tail will always be providing a downforce for trim. It may produce 'upforce' when maneuvering nose-down, but that's a bit out of scope here - just consider that with nose-down M0 the tail will have a downforce.

However...

Adding camber or other clever shaping can tailor the base pitching moment, and it's fairly easy to get a mostly conventional airfoil with a nose *up* base pitching moment. What that means is that with the CG ahead of the center of lift the base pitching moment is counter to the lift-induced moment. It is possible to tailor the airfoil such that at some design condition the base nose-up moment is equal and opposite the nose-down lift-induced moment at, say, cruise condition, meaning there is zero force required at the tail to trim. The CG still has to be ahead of the center of lift to provide stability when you're off-condition or maneuvering, but you can minimize drag at the design condition with no induced drag at the tail and let a high-aspect wing generate *all* of the lift, not farming it out to a lower aspect ratio (less efficient) lifting tail or canard. If you miss your design condition and still have to deflect the elevator to trim, doing it with a long moment arm out the back results in less up- or downforce to trim, reducing induced drag. This is why almost all mass-produced airplanes where L/D is king (think gliders and commercial transports) have conventional layouts with long tails instead of canards.

Nauga,
who says, "It's all Geek to me."

 

[Dan Thomas]

Negative. Pitch attitude will be the same for any combination of *wing lift* and airspeed. More forward CG requires a higher AoA because you have to generate more lift with the wing to cancel out the increased tail down force.

That is true, but the difference would be small.

In flight, that R182 has an attitude like this:




How much more nose-up would it take to make those wheel wells start scooping air?

 

[Clip4]

What are you calling trim.....and trim drag?

It is well known that aircraft stall speed varies with CG. Is that a result of trim drag?

While there are some trim drag changes, changes to induced drag is the primary factor with increased efficiency with aft loadings.

If you don’t believe it, load an aircraft at 2 different weights and the same CG and see which is faster.

 

[Checkout_my_Six]

It is well known that aircraft stall speed varies with CG. Is that a result of trim drag?

While there are some trim drag changes, changes to induced drag is the primary factor with increased efficiency with aft loadings.

If you don’t believe it, load an aircraft at 2 different weights and the same CG and see which is faster.

Interesting....here I thought lift was a function of angle of attack?

 

[dmspilot]

Interesting....here I thought stall speed was a function of angle of attack?

Stall speed is a function of a lot of things.

But stall speed varies with angle of attack? Does that even make sense?

 

[Checkout_my_Six]

lift.....

 

[brcase]

Old wives' tale, though you can make some observations that would seem to support the theory.

As with most myths/Old wives tales there is an element of truth to it with airplanes with laminar airfoils (Mooney's, and others). Most have an area of l/d called the drag bucket (see example image below), is fairly obvious why they call it a drag bucket.

If you get into a situation where you don't have quite enough power to get into the drag bucket area, then a short climb followed by a descent can get you into the drag bucket area. But this only works if you have enough power to stay in the drag bucket and maintain the few extra knots of speed. So another way of saying it is the higher drag outside the bucket prevents you from getting into it, but once in it the lower drag can let you stay in the bucket.

The problem is this is a pretty specific scenerio and depends on the weight of the aircraft. If lighter the plane will just power itself into the bucket area anyway, if heavier you might be able to get into the bucket but won't have enough power to stay there. This is why some airplanes get significantly slower when you load them up.

Brian
CFIIG/ASEL

 

[Martin Pauly]

It is well known that aircraft stall speed varies with CG.

First of all, let's be careful with the word "stall speed" (some people suggest we should not even use the term). An airfoil stalls when the relative air is beyond the critical angle of attack, not below at a certain speed. Now, when we talk about 1g unaccelerated straight flight, at a given weight and configuration, there is a calibrated airspeed at which that critical angle of attack is reached. The slower we fly, the higher lift coefficient needs to be to still create the right amount of lift to offset the downward forces, and we can increase the lift coefficient by increasing the angle of attack - but only up to a point (i.e. the critical angle of attack).

If that's the speed we call "stall speed", then moving the CG to the rear does in fact decrease stall speed. The reason is that the downward forces from the tail decrease, so even though weight remains constant, the total downward force is reduced, and thus less lift is needed. That reduced amount of lift can be created by the wing (at the critical angle of attack) at a slower airspeed than larger amount of lift needed when flying with the forward CG, all else being equal.

- Martin

 

[Dan Thomas]

Interesting....here I thought lift was a function of angle of attack?

Plus airspeed. An airplane taxiing with its nose up isn't going to fly at 15 MPH.

 

[Checkout_my_Six]

Plus airspeed. An airplane taxiing with its nose up isn't going to fly at 15 MPH.

View attachment 135453

and ....there are other factors too.

 

[Brad Smith]

Waxing the airplane will probably result in more speed gain than loading to max aft cg.

Do Airplanes Fly Faster After Waxing Them? | AirplaneAcademy.com

A couple weekends ago I was preparing for a long cross country trip from Texas to Idaho to do some back country instruction in the…

airplaneacademy.com

 

[MauleSkinner]

Waxing the airplane will probably result in more speed gain than loading to max aft cg.

Do Airplanes Fly Faster After Waxing Them? | AirplaneAcademy.com

A couple weekends ago I was preparing for a long cross country trip from Texas to Idaho to do some back country instruction in the…

airplaneacademy.com

Cleaning the bugs off will do more yet.

 

[flyingcheesehead]

The sum of the moments. Net non-zero moment causes pitch acceleration.

So, moments around the CG. Got it.

At a particular dynamic pressure and local AOA (at the tail) a particular yoke *deflection* will cause a particular *elevator* deflection and a particular change in *force* (up or down) provided by the tail.

Yeah, that. Doh. <facepalm>

I'm going to throw the math card. Think of an airplane with the cg at location 0 and the center of lift at location X and the tail at location 10X. There's a base pitching moment, constant with angle of attack, of every airfoil, although it may be zero for some. Call it M0, call the wing lift LW and the tail force LT. The moment of the wing lift is LW * X and the moment of the tail lift is LT * 10X. If the CG moves closer to the center of lift by 10% the lift based moment will be LW * 0.9X, a 10% reduction in moment, but the moment at the tail will be LT * 9.9X, a 1% reduction in moment. Since the wing-lift induced moment moment is reduced by a significantly larger amount the tail becomes that much more effective as the CG moves aft. Not because the pure tail moment is increasing, but that the moment it's working against (or supplementing) is decreasing, even if the "downforce" is the same.

Now that you threw the math card, it makes perfect sense. Thanks!

 

[Rene]

Waxing the airplane will probably result in more speed gain than loading to max aft cg.

Do Airplanes Fly Faster After Waxing Them? | AirplaneAcademy.com

A couple weekends ago I was preparing for a long cross country trip from Texas to Idaho to do some back country instruction in the…

airplaneacademy.com

In WW2, the USAAF determined that a painted B-17 was slightly faster than an unpainted one and burned slightly less fuel - even though it was a couple hundred pounds heavier with paint - because it had smoother airflow due to a lower drag co-efficient.

 

[Clip4]

First of all, let's be careful with the word "stall speed" (some people suggest we should not even use the term). An airfoil stalls when the relative air is beyond the critical angle of attack, not below at a certain speed. Now, when we talk about 1g unaccelerated straight flight, at a given weight and configuration, there is a calibrated airspeed at which that critical angle of attack is reached. The slower we fly, the higher lift coefficient needs to be to still create the right amount of lift to offset the downward forces, and we can increase the lift coefficient by increasing the angle of attack - but only up to a point (i.e. the critical angle of attack).

If that's the speed we call "stall speed", then moving the CG to the rear does in fact decrease stall speed. The reason is that the downward forces from the tail decrease, so even though weight remains constant, the total downward force is reduced, and thus less lift is needed. That reduced amount of lift can be created by the wing (at the critical angle of attack) at a slower airspeed than larger amount of lift needed when flying with the forward CG, all else being equal.

- Martin

Who are these people who suggest we never use this term? It’s not the FAA and it’s not the airplane manufacturers.

The FAA wants pilots to understand what affects stall speed. That includes CG.

 

[dmspilot]

lift.....

Correct. Changing the CG changes the download on the horizontal stab, thus changing the amount of lift the wing has to produce. Moving the CG aft has the effect of reducing weight and vice versa. Since less lift is needed with aft CG, less induced drag is created, just as Clip said.

 

[MackMooney]

I am curious to know if there's any appreciable difference in cruise speeds and fuel efficiency if loading a small GA airplane (i.e. 182, Bonanza, Lance) near the aft limit vs the forward limit.

Does anyone here take this into account and load an aircraft one way or the other intentionally?

My Mooney is easily atleast 5kts faster with a reward cg. I now make it a habit to carry something in baggage and to slide the seat all the way back during long long periods of cruise.