# Two, CG in a not so unique design, questions

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#### Yankee Aviator in SC

##### Well-Known Member
My Single biggest concern:

Prior to deciding to build I had shopped the used homebuilt market extensively. I often found that many home built aircraft owner/operators knew within a few ounces what their airplane weighed, but had no idea what its empty weight CG was!!!! Nor did they have an understanding of CG limits, how to calculate loaded CG, nor how CG manipulation affected the performance of the plane.

I can’t accept a blind faith approach, so here’s question number one:

When in the construction process should a builder consider the implications of Weight and Balance?

Before you answer the above question, please consider my assumptions below. Help me to insure and perhaps refine my logic for asking. If it is flawed, let’s first correct my understanding! All of the below assumptions are for my situation of a tractor configuration, with conventional empennage controls, in this case a rag and tube taildragger.

1) Operational Center of Gravity (CG) must fall between the allowable CG limits as defined by the wing shape and aerodynamic factors. These limits are known as Max Forward CG and Max Aft CG. Attempting to operate the airplane outside of these limits will at the least result in decreased controllability and in the worst case prove fatal. The limits and the CG are most often expressed in either inches relative to a datum, or Percentage of Mean Aerodynamic Chord (MAC).

In very loose terms: A forward CG limit, is mostly determined by the aerodynamic ability of the tail to generate enough tail down force needed to keep the nose up. Aft CG limit is usually arbitrarily chosen, forward of a point where CG moves aft of the Center of Pressure (CP). If this is allowed, basic stability is traded for instability, something us average skill pilot guys, without the aid of sophisticated fly by wire computer systems and hydraulic controls, don’t have the skills to handle.

Airplanes are more fuel efficient when operated with aft CG, because tail down force needed and ultimately the load carried by the wing is less. Airplanes are most maneuverable as CG nears CP, a point to be strived for in an aerobatic design and avoided if the end result is intended to be a solid instrument platform.

2) With point one above in mind, using a tandem seat airplane as an example, the EMPTY weight CG, could theoretically be outside (or forward of) the forward CG limit, so long as when the pilot (plus passengers fuel and bags) sits in the plane, (Operational CG) the CG falls within the CG limits.

I’ve never owned one, but I think this is the reason a J-3 Cub is soloed from the rear seat. The average pilot weight wouldn’t have enough moment in the front seat to move the CG far enough aft and into the allowable range? I know its also why airliners sometimes carry sand bags or unusable ballast fuel.

3) In a proven plans built airplane, a guy should be able to plunder along with wings and fuselage without much care about CG. In my tube and rag case, the covering and paint will probably have a minimal effect on CG. Reason being that the materials are light and the entire airframe is covered almost equally forward and aft of the CG.

The real work that affects CG location has much more to do with things like the length and weight (or Moment) of the engine and accessories mounted to the airframe.

4) If my above assumptions are correct, here’s my theory towards a building plan….

A) Get the wings and fuselage built and on the gear, then conduct a weight and balance.

B) From that point of construction on, calculate (Weight X Arm = Moment) every installation and give consideration to typical load of occupants, fuel and bags, to arrive at a configuration that gives the safest range of CG for the planned use of the plane.

C) Along the way, and certainly after construction is finished, conduct additional weighings and refigure balance calculations to insure that empty CG is not determined by calculations alone but verified by actual weighing.

5) Engine mount length (the distance between the firewall bolt points and the engine block bolt points) will be the single biggest control over the ultimate empty weight CG.

My plans show a Z-bar style engine mount for a 65 hp engine. Feedback from most Christavia builders show that even 100HP can be a little underpowered. Since I am trying to achieve SuperCub like performance, a larger engine will be the only choice.

Question number two: Is it wisest to plan a preconstructed engine mount (assuming they come in custom or varying lengths), or is the best solution to purchase a dynofocal ring and weld the exact Engine mount length, to best locate CG, once most of the other data is available and/or know?

#### bobfitzgerald123

##### New Member
Todd: Thanks for asking the question about the CG considerations for a homebuilt.
I'm considering the purchase of a bi-plane, and so far, the indication is that it has a "tail heavy potential."
From what I understand so far, both the pilot and the passenger (front seat passenger) are seated aft of the CG. Depending on the weight of the pilot (back seat) the bi-plane may go out of CG range. (I have been told by the owner that if over 180 lbs. - (for the back seat pilot) then he won't sell the plane because it would be too tail heavy.
I'm going to watch your post to try to get some insight on the weight and balance matter.
If you might know of a book on this subject, please advise. (Also, I'm at 315 789-6618 Geneva, N.Y.) Good luck on your project.
Bob FitzGerald

#### Yankee Aviator in SC

##### Well-Known Member
Bob;

This one’s easy! Calculating the CG of an existing airframe is by no means guesswork. Have your favorite FBO, or a shop at the field where you’re buying the plane, actually weigh the plane. It shouldn’t be a big cost item, when compared to the peace of mind it will buy you. This is done using three accurate, calibrated scales. A scale is placed under each tire, while the longitudinal axis and the wings are perfectly leveled. The mechanic records all three scale readings. The shop will print out a Total weight and Total moment card. The card will have two figures on it for our concern, weight and moment. It may also be designated by (OEW=Operational Empty Weight) and should be the same two numbers. The intent is for you to keep the data in the aircraft logbook and use it every time you fly. In reality, familiarity with W&B is likely to be satisfactory for most light airplanes most of the time. On certified planes, the weight and balance (from the shop or manufacturer) is required by FAA to be in the POH (Pilot Operating Handbook). A new one should be done anytime any component (like a radio) is added or removed too.

Empty weight is the empty airplane, plus fluids and unusable fuel, fairly self-explanatory.

The Empty moment is a figure derived mathematically (at the shop), by the relationship of the weight on each tire relative to a datum (an arbitrarily chosen mathematical plane). If we take the empty moment and divide it by the empty weight, we get the empty ARM. When measured from the datum, THIS IS THE EMPTY CG.

Airplanes don’t fly empty, so lets talk about going flying!

The total weight should be self-explanatory, too, but as a recap; it’s the empty weight plus everything that you take with you flying, that isn’t included in the empty weight. All said and done, this total figure should always be less than all your operational limitations like:
Max Gross ramp weight,
Max taxi weight,
Max Allowable Take Off weight,
Max landing weight, or any other limitations that the particular airplane may be designed around. Fortunately again, most general aviation planes are far less complex and concerned with only one figure - Max Gross Weight, which is the same figure for all the above.

The total moment, is derived by taking each weight item, (things we take flying with us, ie. fuel, ourselves, golf clubs, bags, books, etc…), multiplying it by its arm, (distance from the datum), to get moment (effect on the CG). Next we add the moment number(s) for everything we take that we've calculated, to the empty moment figure the shop gave us. It doesn’t matter if we use inches, millimeters, kilos or pounds, so long as the same units are used for all weights in the plane and the same unit the shop used. The new CG, or operational CG (the one we count on for airborne safety), is derived by dividing the total moment by the total weight to come up with total ARM. THIS FIGURE IS OUR OPPERATING CG, expressed in inches or millimeters from the datum. If you know where the datum we’ve used is, you can again physically measure out the CG and look where it falls on the wing. The same can be done with the CG limits (measured our for illustration). Here’s the simple formula that makes it easy to calculate

W x A = M or M/W = A You’ve probably heard “weight times arm equals moment”.

Where W is weight (how much something weighs),
A is arm (how far something is from the datum)
and M is moment (How much effect the weighted item has on the CG!)

Lets say that in this case our datum is the firewall (a common practice, as is using the tip of the spinner). It doesn’t really matter where the datum is, as the result is the same. In this case all of the weight that gets put in the plane aft of the firewall, should have a positive moment number (remember Weight times Arm = Moment) and everything that gets put in front of the datum (like a new standby electric vacuum pump in the engine cowling) should have a negative number. Remember too that both items add total weigh so, add positive numbers to the empty weight figure in all cases. We simply measure the distance of the item from the datum and multiply the distance times what the object, person, or fuel weighs. That gives us that items’ moment. Then add the moment figure(s) (subtract negative numbers) to the empty moment that the shop gave us. Add the weights of the items to the total empty weight the shop gave us and divide the two numbers (M/W) to figure the new CG.

The only thing left to do is compare the calculated CG number to the CG limits. We want to be sure that the calculated number falls between the fore and aft CG limit numbers or “inside the envelope”! Make sure too, if you are counting on fuel that you take off with, to keep you in CG, depending on the moment (location of) of the tank, it may be possible to “burn out of CG” in some airplanes. Yet another good reason to locate fuel tanks between the spars, that way performance changes little with fuel burn off. Be sure to look at the figures both ways (takeoff weight/CG and landing weight/CG) BEFORE you blast off!

With respect to your Biplane sellers concerns, if you want the airplane, do the simple math. You may need to find the original design blueprints, to figure out what the Fore and Aft CG limits are located, in the event he doesn’t have them available. If it’s a Starduster Too by chance, I have the figures at home from the prints. Just because it doesn’t work now is no reason to give up entirely! Don’t forget that, components can be moved to make this teeter-tauter work safely. It could be that the builder was a light guy who planned on flying solo most of the time and put the battery behind the pilot seat for performance reasons. Moving it forward to the firewall, would be a huge change in the battery’s moment and may be all that’s needed to keep things in CG with a heavier pilot.

I know this much…its tough to fit a 200 plus pound pilot into a lot of short coupled homebuilt Biplanes, especially with a normal sized front passenger. No matter how far forward everything is mounted the pilot just moves the CG too far aft (has too much aft moment). Best of luck with your calculations, but most importantly fly safe - under gross and in CG.

#### Jman

##### Site Developer
Yankee,

According to the plans how much room do you have between the firewall and the recommended engine? Do you have quite a bit of room to play with?

I'm really only asking for my own understanding of your predicament because I don't really have an answer to your questions. I'll have to leave the answer part to someone more experienced than I.

Jake

#### Yankee Aviator in SC

##### Well-Known Member
It's funny how persistence pays off in life. I recently picked up a copy of Tony Bingelis's books "Sportplane builder" and "Firewall Forward". Both have sections on the design of CG. The books address things like how to buy an airplane and install a different engine of a different weight and do so without moving the CG. Pretty straight forward Weight X Arm = Moment stuff. It all has to do with the exact question of what does the engine weigh and how far is it to be mounted from the datum. The tricky part is going to be the engine mount welding. The math was easy. For those of you that offered help, thanks.

Todd

#### orion

##### R.I.P.
Great answer for calculating the weight and the procedures to do so.
But to make this discussion a bit more complete, let me add one or two thoughts.

You are correct in your statement that the airplane has two fixed points between which the airplane should balance. That point however is not a function of the CP, mainly because the CP (center of pressure) point varies with the angle of attack. When calcualting the limits, one generally wants to deal with the wing's aerodynamic center, which by definition is the point of the wing where the pitching moment is fixed, regardless of the wing's angle of attack and/or lift coefficient.

The forward CG limit is the point on the MAC (Mean Aerodynamic Chord) where the horizontal tail looses its ability to bring the airplane to full stall, with full flaps down and in ground effect. The last part is extremely important or the pilot could be in for a nasty surprise during landing.

In ground effect you loose the downwash that is created by the wing. This downward flow off the wing adds to the effectiveness (or power) of the horizontal tail. The presense of the ground plane effectively reduces or even eliminates the downwash therefore the tail must be able to bring the airplane to full stall without its aid. Notice that if you study the history of kit airplanes, virtually every kit manufacturer has, at one time or another, had to increase the size of the horizontal, some by as much as 35%.

The aft CG limit is set by the "Neutral Point" of the airplane. The stability of an airplane in flight is a function of the relationship of pitching moment and lift coefficient, or more precisely, the change in pitching moment versus the change in lift coefficent. For a stable airplane, this relationship must be negative so as the lift coeficient increases (airplane pitches nose up - positive number), there must exist an increasing countering pitching moment to try to lower the nose (nose down moment - negative number).

There are two conditions for this, one is stick fixed, the other stick free. The latter tends to be the design point to measure off since it is the more conservative (the stick free point is the most forward of the two on the MAC). The actual position varies from one airplane to another, depending on a number of aircraft design details but generally it can be located anywhere from about 35% MAC to just a hair more than 40% MAC (stick fixed).

As the center of gravity moves aft, its shift can overcome the negative moment capability of the airplane so that the ratio of the change in pitching moment versus the change in lift coefficient becomes zero. This is called the neutral point, and realistically you don't want to fly anywhere near here.

Thus, for most aircraft, the aft CG limit is placed several percent (5 to 10) forward of this point thus assuring that the airplane never flies where the average pilot could not control it.

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#### Holden

##### Banned
When you consider stability you must also include the vertical position of the C.G. In some cases, a large pendulum can eliminate a lot of the "trim" drag. The weight swings back when the negative pitching moment is strong (CP moves aft) in the cruise, and during the stall the weight moves forward as the CP moves toward the 1/4 chord.

One should model the forces on a spreadsheet (MS excel for example) and take the moments about the C.G.. Then plot the Cl vs Cm curve.

Traditional Cm is plotted with more negative Cm moving to the right with Cl on the Y axis moving positive up. The line or curve should not lean to the left. By modeling the forces you can easily simulate any loading condition and see the effect of placement of cargo, fuel, passengers or wings.

Holden

#### wsimpso1

##### Super Moderator
Staff member
Log Member
Yankee Aviator,

Your question indicated the basic knowledge is already present. Orion's response is nicely done, dispensing with CP and getting on to the more important issue of where the neutral point is. In doing so, he was talking like a friend of mine who was educated by Ed Lesher. For those of you who do not understand the comment, it is a compliment.

Practical issues seemed to be what you were looking for. Let's try:

My approach has been to do as good a job of estimating weights and positions as I can, and keep updating the spreadsheet;

Allow extra for finish and paint and remember that most of the surface area of the airplane of most airplanes is aft of the CG, so this extra weight for finish can lead you towards aft CG;

Plan some extra space in between the engine and the firewall. You can adjust the engine mount to accomodate various engine/propeller weights. I was originally planning on the Powersport rotary which is rather light, but also planning on getting into a IO-360 with a constant speed prop, so I used both extremes and some intermediate ones in my planning;

The battery location is also flexible. You can do quite a bit by going from forward of the firewall to aft of the firewall, to the back end of the bird.

Build a spreadsheet and keep it up to date. Atleast the surprises come in smaller chunks.