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Center of Gravity Basics

Center of Gravity Basics

After checking your engine performance and the radio operation, always make sure that your model is properly balanced before your first flight. It happens too often, unfortunately: Someone with a brand new airplane shows up at the field and has everything working perfectly. The radio checks out, and all the controls move in the correct directions; the engine runs reliably and provides plenty of power. The model taxis out and runs down the field and becomes airborne. Right away, it starts to rock its wings; the nose points up sharply; and after several frightening seconds, it hits the ground—hard! The pilot did everything right except that he forgot to check the model’s balance.

To successfully test-fly a new model, be absolutely certain that the model is balanced at the correct center of gravity (CG). Nothing can spoil your day more than trying to sort out a tail-heavy model after it has left the ground. It is a fair bet that improper CG location is responsible for more broken airplanes than engine and radio issues combined. Let’s look at some methods for determining the CG.

Better than using your fingers, a precise balancing device, such as the Great Planes CG Machine, will help you get the balance point correct.

Please note that these techniques are good for close estimations and will get your model balanced in the ballpark well within the proper CG range so that it is safe to test-fly. We’re not taking into account unusual configurations or lifting tail surfaces. If you want to see the math and more precise, detailed aerodynamic principles, check out Andy Lennon’s book Basics of R/C Model Aircraft Design, available from AirAgeStore.com.

BALANCING ACT

While balancing a monoplane, use the location indicated in your model’s instructions or plans measured back from the leading edge. If you don’t have this information, it isn’t hard to figure it out yourself. For most models, the balance point falls between 25 and 30 percent of the mean aerodynamic chord (MAC); 27 to 28 percent seems to be the average. With a constant chord wing, like on a Piper Cub, the MAC line is the wing’s chord line, or the distance from the leading edge to the trailing edge, and it can be measured anywhere along the wing’s span (Figure 1). With a tapered or swept wing, you have to determine the precise location of the MAC line (Figures 2 and 3).

FIGURE 1 CONSTANT CHORD WING

With a constant chord wing, the MAC can be measured anywhere along the span. You can balance the plane anywhere along the measurement line.

FIGURE 2 TAPERED WING

For a tapered wing, after you lay out the root and tip extension lines, connect their ends with projection lines to form the X pattern. Where these lines intersect is the location of the MAC, which is parallel to the root chord line.

FIGURE 3 SWEPT WING

Finding the MAC for a swept wing is exactly the same as with a tapered wing. Note, however, that the measurement lines for the 25 and 30 percent MAC positions are farther back along the root chord.

Using the wing’s top view, the chord length of the tip rib is added to either side of the root rib, and the root chord length is added to either side of the tip rib. The ends of these extension lines are then connected with projected lines forming an X. Where these two lines intersect is the location for the MAC line. The MAC line is parallel to the root chord. The MAC line is then divided by four to get the 25 percent MAC location and by three to find the 33 percent MAC location. These two points provide the wing’s CG range. You can then extend measure lines from the two MAC locations, which are 90 degrees to the root chord, and you can then balance your model anywhere along these lines.

Figure 4 shows Andy Lennon’s variation for finding the MAC line of a tapered wing panel where the MAC location is at the intersection of a single diagonal projected line and a line connecting the midpoints of the root and tip rib chords. The outcome for the two techniques is extremely close and well within the overall CG range.

FIGURE 4 ANDY LENNON METHOD

Andy Lennon recommends a less involved way to find the MAC. Instead of using the X pattern, he simply connects the midpoints of the root and tip chords and then uses a single diagonal line to connect the ends of the extension lines. Where it and the ½ chord line intersect is the MAC.

BIPLANES

When it comes to biplanes, the technique is very similar. Figure 5 shows a side view of a biplane with two straight constant chord wings. The MAC is estimated as the horizontal distance from the top wing’s leading edge to the bottom wing’s trailing edge. You then divide the MAC line to find the CG balance range. There are other ways to find a biplane’s CG location, but this is the simplest. If, however, your biplane has a swept top wing and a straight bottom wing, like with a Pitts Special, you use the same technique as for a tapered wing shown in Figure 6. The distance from the top wing’s root leading edge to the bottom wing’s root trailing edge becomes the root chord line, and the distance from the top tip’s leading edge to the bottom tip’s trailing edge becomes the tip chord line.

After determining the position of the MAC and finding the 25 percent and 33 percent MAC locations, add nose weight or shift the onboard equipment around so that the model’s balance point falls somewhere within the CG range. Use a sturdy balancing stand that’s sized according to your model, then make sure that your ballast weight is properly secured so that it can’t move or fall out of the airplane. I like to start in the middle of the range because the only way to truly figure out whether the model is slightly nose- or tail-heavy is to test-fly it.

FIGURE 5 MAC FOR BIPLANES

It is easy to find the MAC for a biplane with two constant chord wings. It is simply the horizontal distance from the top wing’s leading edge to the bottom wing’s trailing edge.

FIGURE 6 MAC FOR BIPLANE WITH SWEPT TOP WING

With a biplane that has a swept top wing, simply treat the planform as a tapered wing. Then use the extension lines and the projected X lines to find the MAC.

THE DIVE TEST

FIGURE 7 DIVE TEST

An excellent way to check your model’s CG is to use the dive test method (Figure 7). We learned this technique from Keith Shaw, an expert electric-airplane designer and a MAN contributor, and although it might seem backward, the test works very well. According to Keith, “An incorrect center of gravity, usually too nose-heavy, also increases unwanted drag. A nose-heavy plane has to carry up-elevator trim to maintain longitudinal stability. This means that the stabilizer is ‘lifting’ downward, and that creates some induced trim drag. It also means that the wing must now develop even more lift to maintain level flight, producing even more drag!

“Fly your plane at half throttle, and adjust the elevator trim until it can maintain hands-off level flight. Check this by making several passes without changing the throttle setting. You should be flying at an altitude of 100 to 150 feet. When the plane is nearing center stage, gently push it into a 30-degree dive, and hold it until the air speed has increased noticeably. At this point, take your hand off the stick and observe what happens. If the plane pulls up sharply, it’s very nose-heavy. If it continues in the dive or pulls up slightly, its CG is just right. If it tries to tuck under, it’s tail-heavy. This happens because the increase in speed amplifies the trim corrections. If the model was carrying some up-trim to correct a nose-heavy condition, the increased dive speed makes the model pull up and vice versa.

“A bunch of extra advantages comes with having a correct CG location.

The amount of elevator throw necessary for any maneuver will decrease, and that will mean less control drag. There will be virtually no need for down thrust, which is an inept attempt to ‘fix’ the tendency of an overstabilized aircraft to nose up as power is increased.”

LET’S GO FLYING!

With the model’s CG is in the safe balance range, you can take off and sort things out on the first flight. Fly the model at about ½ to ¾ throttle, and set the trims for straight and level flight. After landing and checking the trim-lever locations, adjust the clevises so that the radio’s trim levers can be set back to neutral. Make another flight, retrim, and see how the model performs. If it flies normally—not climbing or diving with minor power changes—this is a good CG indicator and you are very close. If there is still a lot of up- or down-trim, then the CG still needs to be adjusted. A lot of up-trim tells you that the CG is too far forward (nose-heavy); a lot of down-trim indicates an aft CG (tail-heavy).

BOTTOM LINE

The best insurance policy for any model airplane is to have it balanced as close as possible to its correct CG before flying. Feeling what the model tells you when test-flown will help you fine-tune its balance. Tail heaviness increases maneuverability, while nose-heaviness increases stability. A nose-heavy airplane, however, tends to land at a faster speed, while extremely tail-heavy airplanes can become uncontrollable. Some basic calculations before that first flight will help keep your model whole. Get the balance right.

Updated: July 26, 2017 — 9:59 AM
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7 Comments

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  1. How do you balance a delta? I’m building a Dyke Delta. CG is on the plans, but how do I double check?

  2. One issue that has created some confusion with respect to the MAC is weather or not the ailerons are included in the chord length for calculating purposes. Can you clarify this for us. Thanks

  3. This article covers all the basics of achieving correct longitudinal balance, but doesn’t cover lateral balance.

    The book mentioned, written by Andy Lennon, is valuable to those trying to get a better understanding model airplane aerodynamics and design. It’s heavy reading/deep stuff, but worth the effort. This book has helped me find and correct “hidden” design and building flaws in both BIY and ARF models. Models that crashed on takeoff or were unstable in flight became easy flyers.

  4. Excellent discussion on what many modelers (and full scale pilots) view as black magic and voodoo thus have aircraft that don’t perform as well as they could. At one time, I flew a Falcon business jet for a chief pilot who insisted a tail heavy aircraft was preferred since ‘all the old air race pilots’ did it that way to increase speed. I don’t know if that’s true or not but it seems a ‘lifting’ tailplane causes additional drag, I would have thought a perfectly balanced aircraft would be most efficient. As usual, no simple answers. For example, many of the bizjets I’ve flown have a 2-3 degree nose up attitude in steady, level flight. Does this equate to an increased angle of attack with an increase in drag? In this case, would a lifting tail reduce the AoA with an overall reduction in drag? Most acro models fly with a positive AoA due to symmetrical airfoils and I wonder again if the perfectly balanced aircraft is the answer.

  5. Does it matter if the plane is right side up or upside down when using a balancer as shown in the picture.

  6. I agree with the comment on downthrust as regards to an aerobatic plane platform. However, high wing aircraft, especially one with a flat bottom airfoil will need downthrust to counter pitchup when power is added.

  7. Wow! What a comprehensive article. Detailed and complete, yet easy to follow. Love the diagrams. Helpful in setting up completed completed flying model and great for scratch-building.

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