On this page
- Tests
- DGCA CPL and ATPL Air Navigation
- Core skill
- Resolving TAS, wind velocity and track vectors
- Tools allowed
- CRP-1 flight computer, scale rule, protractor, calculator
- Typical weight
- Several questions per paper
Every DGCA Air Navigation paper leans hard on one idea: an aeroplane moving through moving air ends up going somewhere other than where its nose points. The wind triangle is just the bookkeeping for that fact. Get comfortable with the triangle and a large chunk of the paper, drift questions, groundspeed questions, heading-to-steer questions, closing angle questions, stops being separate topics and becomes one recurring calculation done with different inputs.
What the wind triangle actually is
Draw three vectors nose to tail and they close into a triangle. The three sides are the true airspeed vector (length equals TAS, direction equals true heading), the wind velocity vector (length equals wind speed, direction equals the direction the wind is blowing to, which is the reciprocal of the direction it is reported from), and the resultant track and groundspeed vector (length equals groundspeed, direction equals track made good over the ground).
Five quantities describe the triangle: TAS, heading, wind speed, wind direction, track, groundspeed and drift angle. Drift angle is simply the angular difference between heading and track. Any exam question gives you enough of these to fix the triangle and asks for one or two of the rest. There are three standard question shapes:
- Departure planning: you know TAS, the track you want to make good, and the forecast wind velocity. Find heading to steer and expected groundspeed.
- Drift check: you know TAS, heading flown, and wind velocity. Find drift angle, resulting track, and groundspeed.
- In-flight replan: you observe an actual track and groundspeed different from flight planned, back-calculate the actual wind, then re-solve for a new heading.
When DGCA tests it
Wind triangle questions sit inside the DGCA Air Navigation paper under general navigation and dead reckoning. They are computational, so unlike Air Regulations or Meteorology theory questions, partial understanding does not help. You either set the triangle up correctly or the numbers do not close. The upside is that once the method is drilled, these are some of the fastest marks in the paper because there is no ambiguity in a well posed numerical question.
Two ways to solve it: whiz wheel and trig
DGCA permits a CRP-1 or similar circular slide rule flight computer in the exam, and most ground schools teach the wind side of the CRP-1 as the primary method. It is genuinely fast once practised: you mark the wind on the sliding grid against the TAS-to-heading relationship, rotate the compass rose to the heading, and read drift and groundspeed off the grid directly. Its only real weakness is precision, since you are reading a physical scale, and shaky wheel technique costs marks on tightly worded exam questions.
The trig method solves the exact same triangle with a scientific calculator and is what every worked example in this guide uses, because it shows the working transparently and generalises to any numbers without needing the physical tool in front of you. The core relationships are the sine rule and cosine rule applied to the triangle formed by TAS, wind velocity and groundspeed. For small to moderate drift angles, DGCA level problems tolerate a simpler approximation built on the crosswind and headwind components of the wind relative to your heading or track, which is fast enough to do by hand and accurate enough for exam tolerances.
Formula sheet
| Quantity | Relationship |
|---|---|
| Wind angle | WA = wind direction minus heading (or track), taken as the acute difference |
| Crosswind component | Xwc = wind speed × sin(WA) |
| Headwind or tailwind component | Hwc = wind speed × cos(WA), headwind if the wind angle is measured from ahead, tailwind if from behind |
| Drift angle (approximation) | Drift (deg) ≈ 60 × Xwc / TAS, valid to about a degree for drift under 20 degrees |
| Drift angle (exact, sine rule) | sin(Drift) = (wind speed × sin(WA)) / TAS |
| Groundspeed (approximation) | GS ≈ TAS − Hwc (headwind) or TAS + Hwc (tailwind) |
| Groundspeed (exact, cosine rule) | GS = TAS × cos(Drift) − Hwc, using the sign convention above |
| Track | Track = Heading + Drift, with drift signed left (subtract) or right (add) of heading |
| Heading to make good a track | Heading = Track − Drift, solved by first finding drift from the same sine rule using track's wind angle |
Example 1: drift and groundspeed from heading and wind
An aircraft flies heading 090°T at a TAS of 150 kt. Forecast wind velocity is 340/40 (from 340°T at 40 kt). Step 1: Wind angle Wind is blowing FROM 340, so it blows TOWARDS 160. Angle between heading (090) and wind-from direction (340): 340 - 090 = 250, or measured the short way, 360 - 250 = 110 So the wind angle relative to the nose is 110° (wind from left, slightly behind the beam... check: 090 to 340 going anticlockwise is 110°, meaning the wind is from the left rear quarter). Step 2: Crosswind and head/tail component Xwc = 40 x sin(110°) = 40 x 0.9397 = 37.6 kt (from the left, so drift will be to the right) Hwc = 40 x cos(110°) = 40 x (-0.342) = -13.7 kt, negative cosine means it is a TAILWIND component of 13.7 kt (wind from behind the beam pushes the aircraft along track) Step 3: Drift angle (sine rule) sin(Drift) = Xwc / TAS = 37.6 / 150 = 0.2507 Drift = arcsin(0.2507) = 14.5°, to the right (since wind is from the left) Step 4: Track Track = Heading + Drift = 090 + 14.5 = 104.5°T Step 5: Groundspeed (cosine rule) GS = TAS x cos(Drift) + tailwind component = 150 x cos(14.5°) + 13.7 = 150 x 0.9681 + 13.7 = 145.2 + 13.7 = 158.9 kt
Answer: drift is about 14.5° right, track made good is about 105°T, and groundspeed is about 159 kt.
Example 2: heading to steer to make good a required track
Required track is 270°T. TAS is 120 kt. Forecast wind velocity is 210/25 (from 210°T at 25 kt). Here the wind angle must be measured relative to the TRACK first, because we are solving for heading, not checking a heading we already have. Step 1: Wind angle relative to required track 210 to 270 = 60°, so the wind is 60° off the required track, from the left front quarter. Step 2: Crosswind component relative to track Xwc = 25 x sin(60°) = 25 x 0.8660 = 21.7 kt, from the left Step 3: Drift angle needed to counter it sin(Drift) = Xwc / TAS = 21.7 / 120 = 0.1806 Drift = arcsin(0.1806) = 10.4° Since the wind is from the left, it would push the nose right of track, so to make good 270 we must point the nose LEFT of track, i.e. heading = track - drift. Step 4: Heading to steer Heading = 270 - 10.4 = 259.6°T, round to 260°T Step 5: Resulting groundspeed Head/tail component relative to track: Hwc = 25 x cos(60°) = 25 x 0.5 = 12.5 kt, headwind GS = TAS x cos(Drift) - Hwc = 120 x cos(10.4°) - 12.5 = 120 x 0.9836 - 12.5 = 118.0 - 12.5 = 105.5 kt
Answer: steer heading 260°T for a groundspeed of about 106 kt to make good track 270°T.
Example 3: two-leg flight plan with different winds
Leg 1: track 045°T, distance 180 nm, TAS 140 kt, wind 000/30 Leg 2: track 135°T, distance 150 nm, TAS 140 kt, wind 000/30 (same wind, new track) LEG 1 Wind angle from track: 045 - 000 = 45°, wind from the left front quarter Xwc = 30 x sin(45°) = 30 x 0.7071 = 21.2 kt Drift: sin(Drift) = 21.2 / 140 = 0.1514, Drift = 8.7°, heading = track - drift = 045 - 8.7 = 036.3°T Hwc = 30 x cos(45°) = 21.2 kt headwind GS = 140 x cos(8.7°) - 21.2 = 140 x 0.9885 - 21.2 = 138.4 - 21.2 = 117.2 kt Time for leg 1 = 180 / 117.2 x 60 = 92.2 minutes LEG 2 Wind angle from track: 135 - 000 = 135°, wind from behind the left quarter Xwc = 30 x sin(135°) = 30 x 0.7071 = 21.2 kt Drift: sin(Drift) = 21.2 / 140 = 0.1514, Drift = 8.7°, heading = track - drift = 135 - 8.7 = 126.3°T Hwc = 30 x cos(135°) = 30 x (-0.7071) = -21.2, i.e. a TAILWIND of 21.2 kt GS = 140 x cos(8.7°) + 21.2 = 138.4 + 21.2 = 159.6 kt Time for leg 2 = 150 / 159.6 x 60 = 56.4 minutes
Answer: leg 1 needs heading 036°T at 117 kt groundspeed (92 minutes), leg 2 needs heading 126°T at about 160 kt groundspeed (56 minutes). Notice the same wind gives very different drift signs and groundspeeds purely because the track changed relative to it, which is exactly the kind of trap DGCA papers set.
Example 4: correcting after an in-flight wind change
Flight plan: heading 200°T, TAS 130 kt, planned track 205°T at groundspeed 140 kt
(i.e. planned drift was 5° right).
After 30 minutes flying heading 200°T, a fix shows the aircraft has actually made good
track 212°T and covered 60 nm in that time.
Step 1: Actual groundspeed
GS(actual) = 60 nm / 0.5 hr = 120 kt
Step 2: Actual drift
Drift(actual) = actual track - heading flown = 212 - 200 = 12° right
(more than double the planned 5°, so the wind has strengthened or backed)
Step 3: Back-calculate the wind causing this
This needs the wind triangle solved in reverse. With TAS 130, heading 200, drift 12° right,
groundspeed 120:
Track vector: 212°T at 120 kt
Heading vector: 200°T at 130 kt
Wind vector = Track vector - Heading vector (vector subtraction)
Doing this on a CRP-1 or by resolving into North/East components:
Heading vector: N = 130cos(200) = -122.2, E = 130sin(200) = -44.5
Track vector: N = 120cos(212) = -101.7, E = 120sin(212) = -63.2
Wind vector = Track - Heading: N = -101.7 - (-122.2) = 20.5, E = -63.2 - (-44.5) = -18.7
Wind speed = sqrt(20.5^2 + 18.7^2) = sqrt(420 + 350) = sqrt(770) = 27.7 kt
Wind direction (blowing towards) = atan2(-18.7, 20.5) measured from North =
bearing of about 318°T, so wind is blowing TOWARDS 318, meaning FROM 138°T
Revised wind velocity: 138/28 approximately
Step 4: New heading for the remaining track of 205°T (back on the flight-planned track)
Wind angle from track 205: 138 - 205 = -67, or 67° off, wind from the left
Xwc = 28 x sin(67°) = 28 x 0.9205 = 25.8 kt
Drift: sin(Drift) = 25.8 / 130 = 0.1985, Drift = 11.4°
New heading = track - drift = 205 - 11.4 = 193.6°T, round to 194°T
Answer: the actual wind is roughly 138/28, much stronger and from a different direction than forecast. To regain the planned track of 205°T from here, the new heading to steer is about 194°T.
FAQ
What is the wind triangle in DGCA Navigation?
The wind triangle is a vector diagram relating true airspeed and heading, wind velocity, and track and groundspeed. Any two of these three vectors fix the third, which is why DGCA Air Navigation questions almost always give you two vectors and ask you to find the rest.
Do I need a CRP-1 computer for the exam?
You are allowed to bring a flight computer such as the CRP-1 into the DGCA exam and it is the fastest way to solve wind triangle questions under time pressure. It is not compulsory. The trig and 1 in 60 shortcuts in this guide will get you the same answer with a scientific calculator, just a little slower.
What's the quickest way to estimate drift without a whiz wheel?
Use drift in degrees is approximately 60 times the crosswind component divided by the true airspeed. It is accurate to within a degree or two for drift angles under about 20 degrees, which covers almost every DGCA exam scenario.
How many wind-triangle questions come up in the DGCA paper?
Wind triangle and related drift, heading and groundspeed calculations are one of the most heavily tested topics in DGCA Air Navigation, typically appearing across several questions in every paper rather than as a single isolated topic.
Is the 1 in 60 rule the same as the wind triangle?
No. The wind triangle solves for drift, heading and groundspeed before you fly using true airspeed and forecast wind. The 1 in 60 rule is used in flight to correct track errors you have actually observed, and it is covered in detail in the companion guide on CP, PNR and the 1 in 60 rule.
We build the DGCA question banks these guides link to. Corrections welcome and credited.
Sources & references
- Oxford ATPL Navigation series, general navigation and dead reckoning chapters
- DGCA CPL and ATPL Air Navigation syllabus
- ICAO Annex 2, Rules of the Air, for direction and bearing conventions
Formulas and worked examples reviewed for the current DGCA syllabus. Spotted something out of date? Tell us and we will fix it.