# What is the direction convention for Roll angle?

A positive rolling motion lifts the left wing and lowers the right wing.

Which means that if an aircraft has a roll of +20 degrees, it would bank towards the right. And for a roll of -20 degrees, it would roll to the left.

But when I used this flight indicators library, for a roll of +20 degrees the attitude indicator showed that the aircraft was banking left and vice versa.

Are there any conventions for the roll angle/attitude indicator?

• As someone who has actually worked on certifiable AHRS software, a positive roll is to the right. (Right wing down) – selectstriker2 May 29 '18 at 3:45
• @selectstriker2, is it defined that way somewhere? I'm just curious where the convention comes from. – Xpleria May 29 '18 at 5:52
• As someone who has actually worked with all sorts of simulation software, I say the sign convention in many libraries, particularly [those started as] amateur ones, can be anything. I've seen horrors like angles and angular rates having opposite sign convention. Of the popular ones, FSX/P3D has left roll positive. So a certain library is no authority, but expect anything. How it should be is written in Peter's answer; I'll just add that another common choice is forward-up-right (XYZ): it has convenient 'up' direction but yaw 'against' the compass. Either way, the system must be right-handed. – Zeus May 29 '18 at 5:54
• What I also noticed was, with the z-axis down convention, a positive roll increases the heading angle and vice versa. This way I don't have to change the sign for heading calculation. – Xpleria May 29 '18 at 5:58
• @NeilPatrao RTCA DO-334 MOPS for Strapdown AHRS defines Roll as - The angle of rotation about the longitudinal axis of the aircraft. Roll is defined as 0° when the aircraft is upright and the lateral axis is in the level plane. It is defined as positive for the right wing of the aircraft below the left wing. – selectstriker2 May 29 '18 at 13:41

## 2 Answers

That depends on the coordinate system, and the Wikipedia answer uses the most common convention. Flight mechanics uses a coordinate system with X in flight direction, Y sideways to the right and Z downwards positive. If you now apply the right-hand-rule for the positive direction of rotation around each axis, you will get a positive roll angle around X when the right wing moves down.

Right-hand-rule for rotation: Point the thumb in positive axis direction, then the other fingers will point into the positive direction of rotation.

If, however, X points backwards, then a positive roll angle would be as used in the linked library. Such a coordinate system is sometimes used to have Z point up, but is rather unusual for flight mechanics.

• I was going to answer the same, but then I noticed that OP is asking about the indicator. I cannot find anything specific about it and I doubt that any would deviate from the norm, but is it written anywhere? – Federico May 28 '18 at 16:52
• Curiously, the circular arrow in the diagram is visually ambiguous. It can be “seen” as either direction. – Jim Garrison May 28 '18 at 20:31
• @JimGarrison: Well, the hand gives you a perspective from which the arrow should be viewed, and the finger direction is obvious. There is always a problem to represent 3D in two dimensions, but to misread the arrow takes some effort. – Peter Kämpf May 28 '18 at 21:54
• In that case, I'm gonna modify the library. Thanks for the explanation. – Xpleria May 29 '18 at 5:46
• @Neil, be careful to change all rotations in a consistent manner! They are fully determined by the coordinate system, and if you use forward-right-down, not only positive roll will be right, but positive pitch - up, positive yaw - right. Nothing is worse than an inconsistent arbitrary choice of conventions. – Zeus May 29 '18 at 6:00

RTCA DO-334 Minimum Operational Performance Standards for Strapdown AHRS defines pitch, roll, and heading as the following:

Pitch The angle between local level and the longitudinal axis of the aircraft. It is defined as positive for the nose of the aircraft pointing above local level.

Roll
The angle of rotation about the longitudinal axis of the aircraft. Roll is defined as 0° when the aircraft is upright and the lateral axis is in the level plane. It is defined as positive for the right wing of the aircraft below the left wing.

Heading The relative angle between the projection of the longitudinal axis of the aircraft onto the local level frame and some definition of North, for example either True North or Magnetic North. Heading is positive for angles clockwise from (east of) North.

This corresponds to using the right hand rule with the positive axes forward, right, and down.