Two Instruments Disagree
Cruise: 6,500 feet, 110 knots indicated, vertical speed 0, altimeter steady, turn-coordinator miniature aircraft wings level, ball centered. Over 30 seconds the heading indicator drifts from 090 to 095. The attitude indicator shows a steady 20 degrees of right bank. A placard in the aircraft gives the turn relationship: rate of turn in degrees per second = 1091 x tan(bank) / true airspeed in knots. At this altitude and temperature, true airspeed is within 2 knots of indicated. Cloud tops are 1,000 feet above, and the route ahead has no horizon. The pilot must decide which instrument to distrust and whether to continue.
1. What rate of turn does the attitude indicator imply, and what would the heading indicator have shown if that were true?
Read the worked answer
Use the placard with 110 kt true airspeed and 20 degrees of bank. tan(20 degrees) = 0.364.
Rate = 1091 x 0.364 / 110 = 397 / 110 = about 3.6 degrees per second.
Over 30 seconds that is 3.6 x 30 = about 108 degrees of heading change. The aircraft would have rolled through roughly from 090 to 198.
Observed change: 090 to 095, i.e. 5 degrees in 30 seconds, or 0.17 degrees per second - about one-twentieth of the claimed rate, and consistent with a slow instrument precession rather than a turn.
The disagreement is not marginal. It is a factor of twenty, far beyond any reading error.
2. Which instrument do you distrust, and what is the safe action?
Read the worked answer
Distrust the attitude indicator.
Four independent sources agree with each other and against it:
- Altimeter steady and VSI at 0 - no climb or descent, consistent with near-level flight.
- Airspeed steady at 110 kt - a 20-degree bank without back pressure would bleed airspeed; holding it would require a pull that changes pitch and vertical speed.
- Turn coordinator wings level, ball centered - no turn and no slip.
- Heading indicator essentially static - corroborates the coordinator.
A gyro that reads a steady 20-degree bank while the aircraft flies straight and level is the failing unit; a failed heading gyro would have produced a turn indication, not a phantom bank on a different instrument.
Action: cover the attitude indicator, transition to partial-panel scan, verify with the turn coordinator and altimeter, and do not enter the cloud layer on the strength of one instrument. Continue only if you are current and comfortable on partial panel; otherwise turn back. The cloud tops at 1,000 feet above remove the option of waiting for a horizon.
3. What bank would give a standard rate turn at this speed, and why is that figure useful here?
Read the worked answer
Standard rate is 3 degrees per second. Rearrange the placard:
tan(bank) = 3 x 110 / 1091 = 330 / 1091 = 0.3025
bank = arctan(0.3025) = about 17 degrees.
That number is a useful cross-check for two reasons. First, it shows how close 20 degrees is to a normal, unremarkable turn - which is exactly why the failed instrument's reading looks plausible and why pilots accept it. Second, it converts the placard into a working expectation: at this speed, anything near 17 degrees of bank should produce a heading change of about 3 degrees per second, or 90 degrees in half a minute. A bank indication with no matching heading change is the tell.
The judgment lesson: a bad instrument rarely reads something absurd. It reads something ordinary at the wrong time, and only a cross-check against an independent instrument catches it.