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.