Ideal CG location

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gkaplan
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Ideal CG location

Post by gkaplan »

Hello,

After doing a lot of tinkering with W&B for a yet-to-be-received NG, I found myself wondering where the ideal location would be for the CG for level flight. My understanding is that if the plane has a forward CG, the elevator will have to work harder to keep the nose up, thus creating additional drag resulting in a lower airspeed. By adding weight in the baggage compartment, I can move the CG rearward to bring the nose up a bit and reduce the need for the extra elevator and thus reducing drag. Obviously, I could keep going until the plane becomes heavier in the rear requiring the elevator again to help get the nose level. My question - is there an ideal "target" location for T/O CG to minimize the need for the elevator to work?

Note - this is a general theoretical question - I realize the CG will shift in flight as fuel is burned, that there are limits to how much weight can be put in different places - I'm really just wondering where in the envelope is the best all-around "target" to minimize elevator drag.

For example, in the next two images, is the one where the locations are closer to the left going to require more elevator than the ones that are further towards the back?

Image 1: https://www.screencast.com/t/716C8w3Q
Image 2: https://www.screencast.com/t/7EIXnfvz

Thanks!
Gerry Kaplan
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Re: Ideal CG location

Post by Boatguy »

I'm not an aeronautical engineer so maybe there is some ideal CG. However I've flown about 500hrs in my 40NG. I've flown long distances (2-4hrs) with my wife and some luggage, with my wife and no luggage, and solo. I've never noticed any significant speed difference based on CG location.

I cruise at 85%, usually between 8,000' - 14,000' and see speeds from 145KTAS - 152KTAS.
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Rich
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Re: Ideal CG location

Post by Rich »

So I ran numbers. Adding weight to the plane toward the rear does in fact reduce the down-force load the tail must provide, but the additional weight must be carried by the wings with a much shorter lever arm. Therefore the net wing loading is increased. Because the wing load includes the total weight of the airplane + the reduced tail downforce, the full increase isn't felt by the wing, but nonetheless its induced drag does increase.

Moving weight to the rear while keeping the weight the same does give you the benefits of modestly reduced stall speed and higher cruise speed. But with the limited envelope on CG available in the DA40 - especially the NG, these effects are almost impossible to quantify.

The calculations are readily represented by a straightforward free-body diagram as constructed in High School Physics.

Both scenarios produce a somewhat less stable airplane with lighter stick forces.
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gkaplan
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Re: Ideal CG location

Post by gkaplan »

I'm curious about how you "ran the numbers". I took high school physics a long^3 time ago, so I wonder if you created a spreadsheet or used some engineering software. In any case, thanks much for your response.
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Re: Ideal CG location

Post by Soareyes »

As you already know, loading outside the allowable CG range is a bad idea.

Loading within and to the rear of the acceptable CG limit will give faster cruise speeds for the reasons you said; less down force from the tail, less drag. For a given weight I could gain 3-4 knots in my Lycoming DA40 moving the CG from the front to the back of the limit.

As a thought experiment that you should never try except maybe with a radio control model, one that you don't care about; the farther you load beyond the rear limit the plane will become more twitchy, more difficult to control in pitch. It will almost want to swap ends, pitching suddenly up or down with a slight control movement or a bit of turbulence. Maybe OK for an aerobatic plane. The nose could tuck under and the plane could tumble causing instant negative high G's, could even rip the wings off a normal GA aircraft. Respect the rear CG limit.

An overly forward CG is not quite as scary. It will stabilize the plane somewhat in cruise but could be a problem when it comes time to flare for landing.

The DA42 is potentially trickier. You've got heavy TKS fluid up front which in use moves the CG rearward in flight. Accessing the heavy fuel in the auxiliary tanks causes the CG to move forward in flight.
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Re: Ideal CG location

Post by gkaplan »

So just for the record, this was an exercise/analysis in finding the ideal CG within the envelope, absolutely not outside of it. I asked myself this question when looking at the envelope and wondering whether the ideal location would be smack-dab in the middle.

From what I see, I will need to put a little weight in the rear baggage compartment to accommodate when I fly with someone - I'm about 215, so if I put another 200lb person in the co-pilot, then the plane is outside the limit. If I put 20 to 40lbs in the rear compartment, it brings the CG back sufficiently. I will probably just leave it there and remove the ballast if I fly with 2 other people.
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Re: Ideal CG location

Post by DiamondMike »

As a general rule, an aft cg (within the envelope, of course) will provide a smaller tail down force, less drag, and higher cruise speed. However the airplane will be less stable in pitch.

So let’s say you are planning to fly solo with a 40 lb suitcase. Do you put the suitcase in the right front seat, the rear seat or the baggage compartment? For best speed and most economical operation, you put the suitcase in the baggage compartment.

Keep in mind that as you burn fuel the cg moves forward, so the benefit of the suitcase in the baggage compartment will be reduced as fuel is consumed.

Now these effects for such small airplanes cannot be measured in knots and lbs, but for transport category airplanes of high gross weight flying long distances the numbers are significant.
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Re: Ideal CG location

Post by Rich »

gkaplan wrote: Sat Jul 30, 2022 11:50 pm I'm curious about how you "ran the numbers". I took high school physics a long^3 time ago, so I wonder if you created a spreadsheet or used some engineering software. In any case, thanks much for your response.
Basically I drew the standard representation in a diagram to mentally focus and then set up the calculations in a spreadsheet to do the ready comparison. This ignores secondary effects such as pitch up/down moments of specific airfoils at variant AOA and Reynolds Numbers. In addition I estimated the location of the center of lift for wing and tail. But the qualitative representation is valid, though possibly slightly off quantitatively. Note that the "Total" column shown the load of both the wing and tail as both produce induced drag.
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Re: Ideal CG location

Post by Boatguy »

gkaplan wrote: Sun Jul 31, 2022 12:21 am So just for the record, this was an exercise/analysis in finding the ideal CG within the envelope, absolutely not outside of it. I asked myself this question when looking at the envelope and wondering whether the ideal location would be smack-dab in the middle.

From what I see, I will need to put a little weight in the rear baggage compartment to accommodate when I fly with someone - I'm about 215, so if I put another 200lb person in the co-pilot, then the plane is outside the limit. If I put 20 to 40lbs in the rear compartment, it brings the CG back sufficiently. I will probably just leave it there and remove the ballast if I fly with 2 other people.
I’m 190. When I fly with another big person up front, I have a couple of 20# dumbbells I put in the back.
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Re: Ideal CG location

Post by gkaplan »

Boatguy wrote: Sun Jul 31, 2022 3:32 pm I’m 190. When I fly with another big person up front, I have a couple of 20# dumbbells I put in the back.
That's exactly what I plan to do. But according to calculations, there is no harm to just leave them there when I fly alone.

Here's what the envelope looks like with me alone and 40lbs in the extended baggage compartment:
https://www.screencast.com/t/tRD7DzaN7

That puts me right in the middle of the envelope. If i'm going to fly with two other people, I will remove the weights.
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