# Angle of attack, or displacement angle?

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.

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.

• A matter of definition. – Organic Marble Jul 12 '16 at 11:14
• 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
• 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
• 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
• 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

Summarizing:

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.

• aha! so that's what the α and β you mentioned are. Thanks for digging into this one - it's not really a fun question, but this 3D flight stuff is all new to me. I really appreciate it! – uhoh Jul 13 '16 at 14:52
• For some strange reason I didn't remember to click accept. Cosmic rays must be. Thanks! – uhoh Jul 18 '16 at 3:10