Moments: How to Do a Barrel Roll

What is moment?

Moment is the result of a force being applied to a point some distance away from that point and can be calculated as Moment = Force x Radius. One of the clearest examples of a moment is the see-saw. When you sit on one end of a see-saw you exert a force (your weight) on the bench, causing the see-saw to rotate towards you. this is because you are sitting at the end of the bench but the balancing point is in the middle. Had you sat on the middle of the see-saw, the bench would not rotate.

The center of gravity

The center of gravity (CG) is the point on the plane where you can effectively say all of the aircraft’s weight is located. This point is crucial in aircraft design as it plays a significant role in aircraft stability. The location of the center of gravity can be found with the following equation:

center of gravity = sum of (individual component’s weight x location of that component) / total weight of the aircraft

The center of gravity is designed to be at the quarter chord (c/4) of the wing. Having the CG before c/4 could result in a moment that would cause the plane to flip over or dive towards the ground. History has also shown that have the CG too far back can be catastrophic. During WWII, Germany tried to manufacture planes with its CG located at c/2, but the planes were unsuccessful due to the wings shearing off.

The aerodynamic center

The aerodynamic center is the point on the airplane where moment is no longer dependent on the angle of attack of the plane. This point is located at the quarter chord for symmetric airfoils. For cambered airfoils, the aerodynamic center of that particular airfoil is dependent on the moment coefficient curve and the lift coefficient graph put together by experimental data.

Why are moments important?

  • Moments control the stability of the plane.
  • Moments allow us to maneuver the plane.

How to maneuver an aircraft

By altering the the forces acting on the plane with control surfaces, we can make the aircraft rotate in 3 ways: roll, yaw, pitch.

Photo from Introduction to Flight by John D. Anderson, Jr.

By deflecting the control surfaces (i.e, the flaps or rudder) of the aircraft, the amount of lift being produced at that portion of the plane will be changed. More pressure will be applied in a certain direction causing a moment to occur. For example, if you put the flaps of the tail down, more lift will be generated at the end of the aircraft, which would make the tail go up and the front of the plane dive down. You will then perform a loop-de-loop by completing a full circle in such a fashion.

Doing a barrel roll applies the same concepts. A barrel roll is performed by creating an imbalance in lift to tilt the plane. The aileron on one side of the wing is raised up as the aileron on the opposite side is deflected downward. More lift will be generated on the side of the wing with its aileron deflected downward while pressure will push the other side down. This causes the plane to flip on its side. To complete a barrel roll, simply complete this flip in a full rotation!

Moments are something you can experiment with on the rubberband propelled plane listed in the projects page. It will help you visualize the effects of changing the CG or how an airplane maneuvers. Experiment with changing the weight of different components or the location of the wing. You can even try trimming some of the weight off or add some weight in different areas.

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