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When I hear "angle of attack" or AoA, I think of an airplane. Usually, both the airfoil and the plane itself have a clearly defined 'top' and 'bottom'. In this case, the concept of angle of attack is applied in cartesian coordinates, and has a well defined sign convention.

Wikipedia thinks of an airplane also.

enter image description here

For a nominally cylindrically symmetric rocket, this graphic found at https://spaceflightsystems.grc.nasa.gov/education/rocket/rktstab.html uses "displacement angle", which if I understand correctly is applied in spherical coordinates and is therefore generally meant to be positive.

See also Figure 3.15 in Introduction to Rocket Science and Engineering, Travis S. Taylor

A rocket which is flying horizontally for example could have a displacement angle up, down, left, or right, and it would be pretty much identical aerodynamically. Not so for an airplane.

Are these two terms therefore not really interchangeable?

note: my question applies to 'rocket-shaped' rockets only, not car-shaped or plane-shaped rockets or spacecraft.

NASA Rocket Forces

enter image description here

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uhoh
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    A matter of definition. – Organic Marble Jul 12 '16 at 11:14
  • @OrganicMarble I'm not trying to be cute, or picky or anything like that. I just want to make sure I use the right terms. There is an amazing amount of stuff on the internet, but it doesn't always clearly delineate best practices and usages. So I asked here, where common sense and wisdom prevail. Are there generally agreed-upon definitions of AoA and Displacement angle? Do they differ from each other? The former has a clear distinction between the meaning of positive and negative values, while for the latter, should it always be positive? – uhoh Jul 12 '16 at 14:34
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    Rockets, even cylindrical ones, have a well defined coordinate system with a top and a bottom; they roll, pitch, and yaw like a plane does. Therefore while in atmosphere they have a well defined AoA with sign. I don't think I've encountered the term "displacement angle" as often; your references suggest that it's an absolute value and combines both pitch/AoA and yaw angles. – Russell Borogove Jul 12 '16 at 16:03
  • @RussellBorogove OK I see. So if a rocket 'flying straight' suddenly pitches up by 1 degree, that would be an AoA of +1 degree, and if it were down by 1 degree instead, that might be an AoA of -1 degree. And if it 'yaws left' by 1 degree, would that be an AoA of -1 degree?, If it tilted up and left by 0.7 degree in each direction, then would that be +1 or -1 degree AoA? Is AoA really defined for a rocket? Can it really be negative? For a plane, AoA only applies to pitch, not yaw, so it can have a sign convention. But for cylindrical symmetry, you have to treat pitch and yaw together. – uhoh Jul 12 '16 at 16:16
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    If it yaws left without rolling, I'd say it's AoA is still zero, but it's displacement angle is 1 degree. It still has 'lift' but the lift force is sideways instead of vertical. Pitching 0.7 degree and yawing 0.7 degree is 1 degree displacement angle but 0.7 degrees AoA. Historically, early guidance systems treated ascent as a 2D problem, so they ignored yaw (or dealt with heading independently of ascent) - pitch angle was the primary concern, so AoA was the angle that mattered. All the conventions came from aeronautics. – Russell Borogove Jul 12 '16 at 16:37
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    The angle perpendicular to angle of attack is referred to as the sideslip angle. Often alpha and beta. – Organic Marble Jul 12 '16 at 17:25
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    @OrganicMarble Aha! I remember seeing those mentioned in a comment yesterday, but I can find it right now. And is displacement angle commonly used as it's shown in the figures - roughy speaking $\sqrt{\alpha^2 + \beta^2}$? – uhoh Jul 12 '16 at 17:52
  • I am not familiar with "displacement angle". It was not a term used on any program I worked on. But none of those vehicles were "rocket shaped rockets". – Organic Marble Jul 12 '16 at 17:56
  • Here's an example of a rocket shaped rocket which uses alpha http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080048217.pdf As @RussellBorogove mentioned, this is all about the vehicle's coordinate systems and how they are defined (hence my comment). Any aerospace vehicles with normally defined x-y-z axes has pitch / yaw / roll angles and most likely alpha-beta angles. That is just the toolset aerospace engineers are used to working with. Another example http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19750010226.pdf – Organic Marble Jul 12 '16 at 18:11
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    The Pythagorean formulation doesn't hold up for large angles because it's in spherical instead of flat space (90 degree pitch then 90 degree yaw = 90 degree yaw then 90 degree roll, e.g.), but it's approximately right for the small angles you usually deal with. – Russell Borogove Jul 12 '16 at 19:04

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Summarizing:

NASA's introductory material defines "angular displacement" as

a vector quantity, which means that angular displacement has a size and a direction associated with it.

It goes on to say that the direction is specified by an axis with right-hand rule, so 1 degree of pitch-up would be defined as 1 degree angular displacement around the horizontal axis left-to-right (conventionally this is the +y axis).

For one degree of pitch-down, these three representations would be equivalent:

  • -1 degree around +y axis (minimum magnitude, always positive axis)
  • +1 degree around -y axis (positive displacement)
  • +359 degree around +y axis (positive displacement and axis)

So presumably the displacement angle is the magnitude part of an angular displacement value, and whether it can be negative is a matter of convention.

Angle of attack is in particular the angle between local airflow and the axis of discussion, generally in a particular plane. For a rocket that will generally be the longitudinal axis (often labeled +x) and the pitch plane.

(For a craft with substantial aerodynamic surfaces the angle of attack is usually given with the chord line of the wing as the reference rather than the longitudinal axis of the craft -- they aren't always the same!)

Rotation around the vertical axis is yaw, and the angle between the longitudinal axis and local airflow in that direction is the sideslip angle. Angle of attack and sideslip angle are sometimes abbreviated α and β respectively.

Russell Borogove
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