2 related questions: may a turn rate indicator be calibrated to be accurate at all airspeeds, or only for one? Likewise for a turn "coordinator".
The meaning of "accurate" intended in this question is this: -- if the instrument is labelled "2 minute turn" and we fly for 2 minutes with the needle at the calibrated index, we accomplish 360 degrees of heading change, not more or less.
Some added context: note that if the bank angle is very steep, a turn involves mostly pitch rotation, not yaw rotation. Consider the related question What is the formula for the bank angle required for a turn in line-abreast formation? -- several answers indicate that an aircraft flying at a higher airspeed and larger turn radius needs more bank angle to complete a turn in the same time than an aircraft flying at a lower airspeed and smaller turn radius. Therefore the faster aircraft will be turning with more pitch rotation and less yaw rotation, and a given turn rate indicator could not read exactly the same in both aircraft, IF the instrument only measured yaw rotation.
So the essence of this question is-- can a turn rate indicator accurately measure the rotation component of a turn that involves pitch rotation rather than yaw rotation? Is this true at all airspeeds, or only in a limited range? Is any shortcoming in this regard significant in actual instrument flying? Is the same true of a turn coordinator, or will it tend to be accurate only in a narrower range of airspeeds than a turn rate indicator?