Is there an easy way to calculate the headwind and crosswind component while in the airplane? What about confirming the planned winds (you did do a flight plan right?) Is it possible to come close to get this information correct in the airplane?
Absolutely, there is a way to quickly get these numbers using simple math. For this method, it is important to memorize a couple numbers associated with the 0°, 30°, 45°, 60° and 90° angles. The other angles can be converted to the closest values. This will typically yield a very small error for wind speeds below 20 knots or so. I also remember the power of 60 rule. This rule states that for every 60 knots of airspeed, the wind speed decreases by 1/2, then 1/3, 1/4, 1/5 etc. For example, if your true airspeed is 60 knots, there is a direct one to one relationship between the crosswind angle and the crosswind speed. As the airplane accelerates to 120 knots, there is a one to 1/2 relationship and for every 2 knots of crosswind there is a one degree of crosswind correction. At 180 knots, a one to 1/3 relationship and so on. This also works for speeds less than 60 knots but the crosswind correction is opposite. For a 30 knots true airspeed, there is a one-to-two relationship and at 15 knots (can we fly this slow?) a one-to-three relationship.
A little example, let’s say you are traveling on a 090° true heading with a true airspeed of 120 knots. There is a wind coming from 120° at 20 knots. What is our headwind and crosswind components and crosswind correction? The headwind component from the chart up there is .9 * 20 or ~18 knot headwind making the groundspeed around 102 knots. The crosswind component is .5 * 20 or 10 knots. According to power of 60 rule will will divide the speed by two to get a 5 degree correction to the right. Thus the true course is 095° cruising at 102 knots.
Notice, it isn’t quite exact but it is definitely close enough for calculations in the cockpit. One more example, you are cruising at 14,000 feet at 180 knots on a 210° true heading. There is a wind outside at 150° at 24 knots. The same kind of analysis of what the headwind, crosswind and crosswind correction is. The wind is at 60° off the left side so we can see that the headwind is 12 knots making the groundspeed 168 knots. The crosswind component is .9 * 24 ~ 21 knots. If we take power of 60 rule we will divide that 21 by three and get a 9° crosswind correction. Thus our groundspeed is 168 knots and our true course is 201°. Again, it is not perfect but it will definitely get in into the ballpark.
What if want to work the numbers a little bit differently and get the wind speed and direction from the other four values. All we need to do is to work the numbers backwards. Let’s say your planned course is 310° with a planned TAS of 90 knots. We are currently flying a heading of 300° with an actual groundspeed of 80 knots. What is the wind speed and direction?
Start off by determining the crab angle. In this case it is 10°. Applying the power of sixty rule we can see that 90 knots is half way between 60 and 120 so the ratio is 1 to 1.5. Multiply 10° by 1.5 to get 15 knots of wind. At this point, find a ratio between 10 knots and 15 knots for the wind angle. In this case it is around 50°. Since the heading is lower than the course the wind must be coming from the left so we will subtract 50° from our course of 310° to get a wind of 260° at 15 knots.
Again, the formula isn’t perfect but it is much fairly accurate to confirm whether or not a wind shift has occurred. We all know that a wind shift indicates that we passed a front so knowledge of wind shifts provide other really important information.
OK, so why don’t we try some examples: My answers I got using the formulas are below as well as the mathematically correct answer.
|My Answer||Mathematically Correct Answer|
|1. TH = 50° and GS = 109 knots||TH = 50° and GS = 109 knots|
|2. TH = 124° and GS = 202 knots (Tailwind)||TH = 127° and GS = 191 knots|
|3. TH = 130° and GS = 100 knots (direct Tailwind)||TH = 130° and GS = 100 knots|
|4. TH = 148° and GS = 134 knots||TH = 148° and GS = 135 knots|
|5. WD = 060° and WS = 10 knots||WD = 050° and WS = 18 knots|
|6. WD = 310° and WS = 5 knots||WD = 302° and WS = 7 knots|
Like I said, it’s not perfect but it gets us in the ball park and that is what is important. For a more accurate method pull out the E-6B and do the calculation. Remember, aircraft control is #1 though.