A skill that gives a huge advantage to the instrument pilot, is the ability to mentally estimate, in flight, the wind correction angle (WCA) also known as crab angle. The following section will show you how to do this.
The wind correction angle (WCA) is the angle between the course (CRS) and the heading (HDG) that is required for the aircraft to track that course when there is wind (see figure 1). The WCA is basically added (when the wind is to the right) or subtracted (when the wind is to the left) to the course. The result of this addition or subtraction is the heading which the pilot must fly to maintain that course. On figure 1, note the following: - The wind correction angle (WCA) is always on the same side of the CRS line as the wind direction (WD).
- The heading (HDG) to track the course (CRS) will always lie somewhere between the CRS and the wind direction (WD).
where WS is the wind speed, and TAS is the aircraft's true airspeed. Make sure your calculator is in DEG (degrees) mode. In this example the WS is 10 knots and the TAS is 110 knots. Therefore we will have: which means that in the worst case scenario when the wind is 90
- If the wind speed doubles, triples, etc., your wind correction angle (WCA) will be approximately double, triple, etc. respectively. This works for wind speeds up to 50% of true airspeed (TAS).
- If the wind speed decreases in half, a third, etc., your correction angle (WCA) will be approximately half, one third, etc. respectively.
- If your aircraft's true airspeed (TAS) doubles, triples, etc. the wind correction will be approximately half, one third, etc. respectively of what it was.
- if your aircraft's true airspeed (TAS) is halved, is one third, etc., the wind correction will be approximately double, triple, etc. respectively of what it was.
The reason we used 10 knots for wind speed (WS) when we calculated WCA
There are two tables above, the first one (left) is more complete and more precise. We will use the less precise table on the right for our examples. You will see that even with this more simplified table we will get a pretty good estimate. To figure out your wind correction angle (WCA) just multiply the maximum wind correction angle by the appropriate factor. If wind speed is the same** as the one used to calculate WCA
You can compare your estimated wind correction angle (WCA) with the formula below (this formula is exact) to determine how far you are off. Remember that your goal using the technique above is just to get a rough idea of what the wind correction angle is, it does not have to be exact.
If your typical cruising true airspeed is 130 kts for your aircraft. Estimate the wind correction angle (WCA) for the following conditions: a) WS = 10 knots; AWA = 40
a) WS = 10 knots; AWA = 40
c) WS = 5 knots; AWA = 40
g) WS = 27 knots; AWA = 63
h) WS = 3 knots; AWA = 45
j) WS = 48 knots; AWA = 70
k) WS = 63 knots; AWA = 25
a) WS = 10 knots; AWA = 40 Substituting the values in the equation: The WCA calculated by the formula is 3
The WCA calculated by the formula is 6
Substituting the values in the equation: The WCA calculated by the formula is 1
Substituting the values in the equation: The WCA calculated by the formula is 4
Substituting the values in the equation: The WCA calculated by the formula is 13
Substituting the values in the equation: The WCA calculated by the formula is 0
Substituting the values in the equation: The WCA calculated by the formula is 11
Substituting the values in the equation: The WCA calculated by the formula is 1
Substituting the values in the equation: The WCA calculated by the formula is 2
Substituting the values in the equation: The WCA calculated by the formula is 20
Substituting the values in the equation: The WCA calculated by the formula is 12 Notice how close our estimates were, even using the simpler table on the right for the AWA correction!
During flight the pilot will need to visualize where the wind is in relation to the aircraft's heading and course. The following are a few suggestions on how to do this and figure out what the AWA is.
If the heading bug (figure 3) is not being used by the autopilot, or for other reasons, the heading bug can be set to remind the pilot where the wind is.
Figure 4 illustrates how a heading bug can be used on a heading indicator to remind the pilot where the wind is coming from. In this case the wind direction (WD) is from 090. If the course (CRS) that is going to be navigated is 040, for example, the pilot can visualize the 040 mark on the heading indicator to be that course. In this case wind is coming from the front (headwind), therefore the angle between the course (CRS) and the wind (WD) will be the acute wind angle (AWA). If the wind were a tail wind the AWA would be the angle between the reciprocal of the course (CRS+180) and the wind direction (WD). Knowing the AWA allows you to calculate, using the techniques described in the previous paragraphs, the wind correction angle (WCA). Once the pilot has intercepted the course (CRS), the WCA can be added or subtracted from the CRS to determine the heading (HDG) that is required to maintain that course and compensate for the wind. In this particular example since the CRS is 040 and WD is 090, the AWA is 90-40 = 50
Figure 5 shows how to visualize the above scenario's AWA on an analog and digital HSI. If for some reason the heading bug is being used for something else the pilot can make a mental note of where the wind is instead. Having a general idea of the wind is crucial to smooth and accurate navigation. If the wind speed (WS) in this example is 40 knots and the aircraft's true airspeed (TAS) is at 110 knots. Calculate the wind correction angle (WCA). First let's summarize the information we have and don't have: CRS = 040 To use our method of mentally calculating the wind correction angle (WCA) we have to first calculate and memorize the maximum wind correction (WCA The maximum wind correction angle is given by: where WS is the wind speed, and TAS is the aircraft's true airspeed. Make sure your calculator is in DEG (degrees) mode. In the case even though the actual WS is 40 knots, we will use 10 knots to calculate our base (WCA This means that in the worst case scenario for a 10 knot wind when the wind direction is 90 Lets now calculate WCA given: WS = 40 knots; AWA = 50
The VOR instrument needle is centered once on course (figure 6). If at this point the aircraft is on the correct heading to maintain course (keep the needle centered), the difference between the course and this heading will be the wind correction angle (WCA). In practice, the pilot that has mentally calculated the wind correction angle will be able to estimate what this heading is by adding or subtracting the WCA to the CRS. In this case the wind is to the right of the course so the WCA will be added to CRS to get the heading (HDG). Specifically in the example above, the CRS is 040 and the mentally calculated WCA is 15 Previously when intercepting the 040 course the pilot will maneuver in such a way that the aircraft will be at the 055 heading when the needle of the VOR instrument is centered. Once on course the pilot may have to make minor adjustments to the aircraft's heading in order to keep the needle centered. This is to correct for the actual wind which may be different than the forecast wind, or for an error in the mental calculation of the WCA. In this example, the exact WCA turns out to be 16
Figure 7 shows how to visualize the above scenario's WCA and AWA on an analog and digital HSI.
Below are a few other examples of how to visualize wind correction angle (WCA) and acute wind angle to course line (AWA), for winds that are coming from other directions. The examples deliberately have the same AWA of 50
In figures 8 and 9 we have the following configuration: CRS = 040
In figures 10 and 11 we have the following configuration: CRS = 040
In figures 12 and 13 we have the following configuration: CRS = 040
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