Vectors: Drift Angle and New Heading (Airplane vs Wind)

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Jakotheshadows

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An airplane is flying at 150km/h at a heading of 70 degrees, and there is a 25km/h wind coming FROM 340 degrees. What is the airplane's new heading?

Since the wind is coming FROM 340 degrees, I made a vector of magnitude 25km/h acting on the airplane at an angle 160 degrees from north. (340-180=160) there is a 90 degree difference between the airplane's vector of 70 degrees and the wind's vector of 160 degrees.

SO I know that the vectors meet at a right angle, so I used Pythagorean theorem to determine the magnitude of the airplane's new vector, which is approximately 152 degrees. Then, I determined that the drift angle is about 9.5 degrees, which would make the airplane's new heading approx 79.5 degrees. However, in the answer list in the back of the book the airplane's new heading is 60 degrees, but that seems off since the wind is coming FROM 340 degrees making a vector of magnitude 25km/h in the direction of 160 degrees, thus the new heading should be between 70 degrees and 160 degrees.
 
Jakotheshadows said:
An airplane is flying at 150km/h at a heading of 70 degrees, and there is a 25km/h wind coming FROM 340 degrees. What is the airplane's new heading?

Since the wind is coming FROM 340 degrees, I made a vector of magnitude 25km/h acting on the airplane at an angle 160 degrees from north. (340-180=160) there is a 90 degree difference between the airplane's vector of 70 degrees and the wind's vector of 160 degrees.

SO I know that the vectors meet at a right angle, so I used Pythagorean theorem to determine the magnitude of the airplane's new vector, which is approximately 152 degrees. Then, I determined that the drift angle is about 9.5 degrees, which would make the airplane's new heading approx 79.5 degrees. However, in the answer list in the back of the book the airplane's new heading is 60 degrees, but that seems off since the wind is coming FROM 340 degrees making a vector of magnitude 25km/h in the direction of 160 degrees, thus the new heading should be between 70 degrees and 160 degrees.
Click to expand...
My understanding:

Heading 70° - Making 70° angle to y-axis (N_S) away from origin - counter clock-wise - in second quadrant (N-W)

Wind from 340°degrees - Making 340° angle to y-axis (N_S) toward the origin - counter clock-wise- in first quadrant (N-E)

So it looks like your calculations are correct.

I think book added the wind direction in the opposite direction - making the "ground heading" angle less. In my opinion - they misinterpreted the statement - "from". However, my interpretation in these problems are little shaky - becuse of the "avionic" definitions are not my forte.
 
Ok. No, I see no reason for you to doubt that I'm right :)
Thanks for looking at it though. From what I'm told the authors don't actually find the solutions in the back of the book, so whoever had that job could have misinterpreted the problem and gave an incorrect answer.
 
Jako,

I can state with some confidence that, with the plane headed E-N-E, with a breeze from the pilot's left shoulder, that the plane would drift more nearly EAST, just like you said. Some grad student goofed up on the answers, or the problem was mis-stated.

Regards,
Bill
 
An airplane is flying at 150km/h at a heading of 70 degrees, and there is a 25km/h wind coming FROM 340 degrees. What is the airplane's new heading?
Click to expand...

the question is asking (rather poorly) for a new heading to maintain a course of 070, not to find the course the plane makes good over the ground maintaining its present heading of 070.

\(\displaystyle \arcsin\left(\frac{25}{150}\right) \approx 10^{\circ}\)

the airplane should turn left to a new heading of 060 to make good a course of 070.
 
Ahah! Another pilot. I agree that would be the practical interpretation of the ambiguously stated problem.
 
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