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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Lift: How Does a Plane Stay in the Air?

Why is it that a 650,000 pound Lockheed C-5 Galaxy is capable of staying in the air when everyday objects, like our sofa, would just fall to the ground? An aircraft can stay in the air by generating enough lift (upward force) to balance out its weight (downward force).

Lift is created by manipulating the air around the plane, particularly the wing. Air flows in paths that we call streamlines, and a certain amount of air passes between two streamlines with a specific speed. As air flows over the wing  the distance between the streamlines above the airfoil (which is the cross sectional shape of the wing) is decreased. However, the mass flowing through these squished streamlines must remain the same by conservation of mass (density of the fluid x Area x velocity = constant). This results in the air above the airfoil moving faster similar to how water comes out of a gardening hose much quicker than if you were pour the water out of a cup since the gardening hose has a smaller opening for the water to exit out of.

In 1738, a mathematician by the name of Daniel Bernoulli told us that the pressure from the non-moving surrounding air (static pressure) plus the pressure resulting from fluid motion (dynamic pressure) must remain constant. When the air began moving faster above the airfoil, the dynamic pressure on top was increased. By Bernoulli’s principle the static pressure above the wing must decrease. The dynamic pressure remains unchanged below the airfoil so the static pressure is also unchanged. The end result is a greater static pressure below the wing, creating a net upward pressure.

Summing up the pressure all along the surface area of the wing gives us a net upward force. If the upward force is equal to the downward force the plane will stay in the air. If the upward force is greater than the weight of the plane, the aircraft will begin to rise higher into the air. In the case of our sofa, the shape of the couch does not allow for the previously described phenomenon, which means the sofa cannot generate enough lift to balance its weight. As a result, the sofa falls to the ground and stays there.