|Bulk Angle of Attack
(Based on a posting on April 19, 2007, by Tibor on the former B AGGRESSiVE website)
Hard Knox sent me two more articles that I am going to publish over the near future. The next
article, bound to appear in middle of June or so, will be quite extended and talks about airfoil
choices. But first he is covering his understanding of angle of attack. Feel free to comment.
The foil shapes for current long distance boomerangs have very little Chamber and Angle of
Attack. As such they produce very little lift. The booms would in fact fall out of the air if they
flew perpendicular to the spin axis. If the flight path is lined up parallel to the boomerang base
plane, then these foils would not produce enough lift to keep the boom aloft. But, in reality
booms fly at an angle to the base plane. The angle between the flight path and the base plane
we will call the Bulk Angle of Attack. This is not to be confused with the Section Angle of Attack,
which is the fixed angle carved on any segment of the boom relative to the base plane. The Bulk
Angle of Attack is variable and changes throughout the flight.
How does this happen? There are two ways. First, if the boomerang is not producing enough lift
then it will begin to fall. This means the flight path will turn downward. But, the base plane will
stay facing the same direction since nothing has been done to make it tilt in this case. As the
flight path falls and the base plane stays the same the angle between the two (Bulk AOA)
increases. The increased angle of attack causes the foils to produce more lift. The Bulk AOA
increases until the lift matches the weight and the boom stops falling.
Second, the lift force produced by the wings is stronger on one side than the other because the
spin and forward motion combine so the velocity on one side is greater. This difference in lift
causes a turning moment that causes the spinning boom to precess. This is basic boomerang
physics we should already understand. But, that is not the end of the story. The boomerang
axis has tilted but the boomerang is still going in the same direction. This time the boomerang
base plane is tilted away from the flight path instead of the flight path away from the base plane
as in the first case. But, that does not matter. The result is the same, the Bulk AOA increases,
and again, the lift increases. But, this time the increased lift produces more turning moment.
This is how a boomerang "bites" into a turn.
These two ways of producing Bulk AOA (falling and precessing) are not really separate, but they
act at the same time. For example, a boom flying straight slows down. The slower boom
produces less lift and begins to fall. The fall increases Bulk AOA. The increase in AOA and Lift
can produce more turning moment, which increases AOA and lift and turning moment and so on.
So you see a boomerang can slow down and fall into a turn.
This is significant because LD boomerangs need to be able to fly straight and turn. A
boomerang that can fly straight with enough lift to support itself will have two halves: outer, and
inner. The inner sections of the boomerang produce extra lift and positive turning moment, while
the wing tips at the outer sections produce enough negative lift and negative turning moment to
prevent the boom from turning. When the boom slows and falls into the turn the Bulk AOA
causes the wing tips to produce positive lift as well.
(Answer by Manuel Schütz on April 20, 2007:)
Very nice explanations!
I agree that there is an "induced angle of attack" which you call "Bulk angle of attack". I have a
little different view of the things and divide the boomerang flight in two regimes
1. Air velocity at the wingtips bigger than the speed of the boomerang (no torques). In this
situation the boomerang with a negative lift airfoil will begin to fall as any other boomerang
(Example: hovering MTA or even a hovering Voyager!). The speed downwards will increase until
gravity equals drag/ up wards lift force. Here it is the classical angle of attack which plays its key
2. Air velocity at wingtips much smaller than speed of the boomerang (LD-boom right after the
Observing the boomerang as a right handed thrower from the throwers position: The boomerang
with negative lift airfoil will produce more negative lift at the right side of the boomerang. The
resulting torque will act 90 degrees later -> at the "back" part of the boomerang. Consequence:
There will be a "Bulk angle of attack" preventing the boomerang from falling down.
(Answer by Lorenz on April 20, 2007:)
Hard Knox goes deep into the matter. My feeling for a long time has been that the aerodynamics
of LD booms and standard ones are VERY different. The fact that the LD boom goes straight
out, then turns on a relatively narrow hairpin and flies back straight again indicates, as has been
mentioned, that there are these two flight regimes. The determining parameter is the forward
velocity of the boom, or, to be more precise, the "advance ratio" u, which is the ratio between
angular (rotation) and forward speed. u > 1 means that the receding wing tip is in reverse flow.
As to the two phenomena leading to an increase in the bulk angle of attack. The comment I
would like to add is: if the asymmetric lift distribution causes a moment that increases the bulk
AOA, which will then increase the magnitude of this moment (positive feedback), then we will
most likely end up with a "left" flightpattern. To avoid this, I presume, we have to make sure that
on the way out, the moments acting on the boomerang disk should be as small as possible, just
enough lift to keep the boom in the air..
(Answer by Hard Knox on April 25, 2007:)
The advance ratio Lorenz refers to, u, is related to the wheel radius in the previous topic. The
advance ratio u = 1 at the wheel radius. Outside the wheel circle u < 1, and the flow is non-
reversing. Inside the wheel circle u > 1 and the flow is reversing. High speed throws can often
have high u values meaning the wheel circle is larger than the boomerang disc and the entire
receding wing is in reverse flow. As the boomerang slows, the wheel circle begins to close and
the wing tips extend outside the wheel circle, no longer in reversing flow. The transition from
reversing to non-reversing flow may be useful for shaping the flight path. But, advance ratio is
quite different from Bulk AOA, which governs how much lift is generated by the wings, and thus
how much turning moment.
Manuel s second flight regime leads me to believe there are actually three flight regimes.
The first and second regimes are mentioned by Lorenz: the standard turn, and cruising straight.
The third is the negative turn at launch caused by negative lift at the wing tips. This negative
turn is responsible for the "Dive" flight pattern mentioned in the book "LD".
LD Boomerangs have negative lift at the wing tips to counteract the turning moment of the rest of
the wing. If the forward velocity is high enough the total lift may exceed the boom weight. In this
case the boom will rise instead of fall. The rising flight path produces a negative Bulk AOA and
thus a negative turning moment. The boom must be launched at a steeper angle, since the
negative turn would cause the boom to turn downward. As the boom climbs after launch, the
negative turn rotates the boom more level to the ground. Also, some of the kinetic energy is
transformed to potential energy (altitude) causing the boom to slow down and the Bulk AOA to
Kinetic energy is quickly dissipated by drag (drag and kinetic energy are both proportional to
velocity squared). So, storing some throw energy as potential energy is beneficial.
As for the "Left" flight pattern, Layover moment is the governing factor. Layover moment
has three possible regimes as well: Positive, Neutral, and Negative. Forward velocity and Bulk
AOA are the controlling factors for Layover moment. However, depending on the boomerang
shape, the positive layover moment may happen during the positive turn regime OR during the
negative turn regime. The Voyager shape has negative layover moment coinciding with positive
turn moment. Traditional booms tend to have positive layover moment coinciding with positive
turn moment. I have not yet decided which is more desirable.
(Answer by David on June 1, 2007:)
I too find this phenomena fascinating. In my throwing and study what you call BAOA I find more
useful to term as planar momentum because AOA etc relate more to fixed parameters of the
boom that cause particular actions. Whereas rotational, angular and planar momentums are
evolving forces that are experienced by the boom in flight caused by external forces acting on
the boom rather than generated by the boom structure itself. I wrote several long posts on the
Yahoo LD group a couple years back exploring my observations in this regard, particularly
because I had not seen any literature regarding this process and field observations suggested to
me it was a large part of what was happening in flight. Whatever you call it, I do not think this
phenomenon has been explored enough. And your article is great food for thought.
(Answer by ld_238 on July 2, 2007:)
Just realised that you can forget my last post about the BAOA. There is a mistake in my
Who can tell me what error it is
(Answer by Carl Morris on July 23, 2007:)
For a while I have been thinking that Felix Hess, or rather his thesis, has something to offer on
He explains how throw sticks can fly mostly horizontal over long distance when thrown side-
armed. The normal lift distribution for a throw stick would be shifted towards the leading arm
side because more lift is generated on that side, and normally that would show up 90 degrees
later as a force that tries to lift the front. Clearly, this does not happen, so what is the trick?
The trick is that the throw stick is carved or turned such that negative lift is generated at the tip.
The negative lift is further from the center, so it has more "leverage" than the rest of the arm. It
can shift the center of lift back towards the center while the overall lift remains positive, keeping
the throw stick aloft.
His simulations show a flight path that remains more or less level, but climbs near the end. I do
not recall the cause of the rise at the end being discussed, but it seems likely that the negative
lift at the tip becomes less effective as the throw stick slows.
Contemporary LD booms seem like they have a lot in common with throw sticks. If the tune is a
little off and you do not aim high enough you can get a similar flight path, right? Maybe what
Hess describes for throw sticks applies to LD booms as well.
In this view the plane of rotation of the boom could be the same as the plane of translation.
There is no need to tilt the front upwards to generate lift. The boom stays aloft because the
airfoils generate enough lift to counteract gravity.
Perhaps the normal case is that the front of the boom is trying to rise, and the boom is trying to
precess all the time, but during the high speed portion of the outbound and return flight path
forces at the tips hold these tendencies in check. We need something that accounts for the
different behavior when the boom is "cruising" versus "turning", this seems like a good candidate
to me. In this view the function of the upwards launch angle is not to keep the boom aloft, it is to
slow the boom so it will turn.
-- Carl Morris