Crabwise · Library
How should an impossible wind-triangle solution be reported?
A 100 kt wind square to the course defeats a 90 kt airspeed, and a 70 kt headwind against 60 kt leaves no progress; Crabwise reports both as unsolvable.
The two refusal conditions
The wind triangle needs the correction angle WCA = asin(XW ÷ TAS). If the crosswind on the course is larger than the true airspeed, the ratio exceeds 1 and no angle exists. If an angle exists but the ground speed TAS × cos WCA − WS × cos θ is zero or negative, the aircraft would make no progress along the course. In both cases Crabwise stops and shows the message that the wind is too strong for this airspeed and the course cannot be held.
No heading is invented for these inputs; the result simply does not exist for them.
Check an unavailable result
- Confirm the wind direction is where the wind comes FROM, in true degrees.
- Confirm that TAS and wind speed are both in knots.
- Compute the crosswind on the course, WS × sin θ, and compare it with TAS.
- If the inputs are right, treat the course as not flyable at that airspeed.
One solvable case and two refusals
TAS 90 kt on course 000° with wind from 060° at 70 kt: the crosswind is 70 × sin 60° ≈ 60.621778 kt, below 90, so a solution exists with a correction of about 42.343613° and a ground speed of only about 31.520673 kt. With wind from 090° at 100 kt the crosswind is 100 kt, more than the 90 kt TAS, so no angle exists. With TAS 60 kt into a 70 kt wind from 000°, the angle is 0° but the ground speed would be 60 − 70 = −10 kt, and the app refuses again.
- Crosswind, wind from 060° at 70 kt (kt)
- 60.621778
- Correction angle in the solvable case (°)
- 42.343613
- Ground speed in the solvable case (kt)
- 31.520673
- Ground speed with a 70 kt headwind at 60 kt TAS (kt)
- −10
Common mistakes
- Entering wind speed in km/h next to TAS in knots, which inflates the crosswind.
- Swapping wind FROM and TO, which turns a tailwind into a headwind.
- Treating a very low but positive ground speed as a usable plan.
Scope
The refusal is a statement about the vectors you entered. The FAA navigation chapter below explains the wind triangle.
Educational calculation only. Check current aircraft limits, weather, performance and reserve requirements with approved information.