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Camber vs. Angle of Attack

(posted by Tibor on Aug 14, 2007, on the former B AGGRESSiVE website)

(comment by Lorenz, Oct 26, 2018: the expression *exponentially* below should be replaced by *with the square of the forward velocity*)

The other article from Hard Knox:

There are two parameters which govern the lift produced by an airfoil: Camber, and Angle of Attack. These effects are easily predictable within certain limits. Drag is much more difficult to predict so we will focus on Lift.

Angle of Attack is measured in degrees from the flow direction to the chord line. Angle of Attack changes the Lift Coefficient (CL) by 0.125 per degree.
(CL = .125 x AOA).

Camber is measured from the chord line to the median curve. Camber is usually given as a percentage of the wing chord (%Camber = 100%*Camber/Chord). Camber changes CL by 0.1 per %Camber.
(CL = .1 x %Camber) Note: These formulae are only true for small angles and cambers.

Either parameter will produce lift. But, they can act differently on a boomerang.
Camber will produce positive lift even if the flow is in reverse. A positive AOA will produce positive lift if the flow is forward, and negative lift if the flow is reverse.

Consider the following graphs. The two lines represent two identical segments on two identical boomerangs. Boomerang A uses only AOA on its test segment to produce lift while Boomerang B uses only Camber to produce an equivalent amount of lift. Both boomerangs spin at the same rate. The flow over the segments due to the spin is the Spin Velocity.

The Spin Velocity produces lift even when there is no forward velocity. As the forward velocity increases from zero the Lift increases exponentially for both, until the Spin Velocity equals the Forward Velocity. At this point the flow across the segment is both forward and reverse. Some may remember from the previous topic, that the segment lies on the wheel circle at this speed. As the forward velocity increases further, the reversing flow causes the AOA segment to increase lift at a linear rate while the cambered segment continues to increase lift at an exponential rate. (The exponential rate is because Lift is a function of Velocity squared.)

The turning moment is similar. As expected, both booms have zero turning moment when the forward velocity is zero. Both have a linear increase in turning moment as forward velocity increases, until the Spin Velocity equals the Forward Velocity. Beyond this point the reversing flow causes the AOA segment to increase at an exponential rate while the cambered segment continues to increase the turning moment at a linear rate.

Now comes the interesting part. If we choose two more segments on each boom we will see a trend. The one additional segment on the graphs below is half the distance between the original segment and the CG. The other is 1.5 times the original distance from the CG. So we see out near the tip there is little difference between AOA and Camber, but close to the CG there is a big difference.

At higher forward velocities Camber produces higher lift and less turning moment especially near the CG. It is clear that the foils out near the tips produce larger forces and may have an overpowering affect on the flight. However, the foils near the CG may be much more useful for shaping the flight path.

It is possible to set the foils such that it has a slight negative turn moment at high forward velocities, then flies dead straight at mid-range velocities, and then turns hard when it reaches slower velocities.

Much emphasis has been placed on thin, low camber shapes to decrease lift and thereby increase distance. This is only partially true. Decreasing lift at the tips will reduce the turning moment, which allow the boom to continue out further before turning back. However, if the tips are producing very little or even negative lift, then the rest of the boom must be able to efficiently produce enough lift to keep the boom aloft.

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