Navigating Wind: Flying East in a Light Airplane

In summary, the direction of the wind as reported by the station's weather person is 10.35 degrees east of north, based on the given information and calculations using the law of cosines and the tangent function.
  • #1
mybrohshi5
365
0

Homework Statement


You are flying in a light airplane spotting traffic for a radio station. Your flight carries you due east above a highway. Landmarks below tell you that your speed is 52.0 m/s relative to the ground and your air speed indicator also reads 52.0 m/s. However, the nose of your airplane is pointed somewhat south of east and the station's weather person tells you that the wind is blowing with speed 19.0 m/s.

Homework Equations



N/A

The Attempt at a Solution



i tried drawing a diagram 52 being directly on the east line then another line going southwest from the end of the east line and that was my 19 then the resulting line was also a 52.

i found the angle between the two 52 lines to be 21.1 degrees but this is incorrect so i thought maybe it was 68.9 degrees since its the angle east of north but that is also wrong :(

any suggestions? any pictures would also be very helpful if possible.

thank you
 
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  • #2
Hi mybrohshi5! :wink:

You haven't told us how the question asks for the answer to be written … is it just a heading (< 360º)? or is it a compass thing, like 20º south of east?

Anyway, yes, your diagram is correct, but I don't quite make it 21.1º …

what formula did you use? :smile:
 
  • #3
Sorry i thought i had it in there.

It wants What direction is the wind blowing (in degrees east of north)

I used the law of cosines to come up with the angles i got but neither of the answers are correct.
 
  • #4
mybrohshi5 said:
Sorry i thought i had it in there.

It wants What direction is the wind blowing (in degrees east of north)

I used the law of cosines to come up with the angles i got but neither of the answers are correct.

Hi mybrohshi5! :smile:

ah, "East of North" would be 90º plus that angle (because East is 90º East of North :wink:).

(and yes, the law of cosines is fine, but in this case since two sides are the same, I'd have saved time by using tan-1 9.5/52, and then doubling it :smile:)
 
  • #5
i just tried the answer 111 and that is incorrect. i did the tan^-1(9.5/52) = 20.7 + 90 = 110.7 so i rounded to 111 cause I am sure it only wants 3 sig figs like always cause its mastering physics but it said it was wrong?

any suggestions? thank you
 
Last edited:
  • #6
D'oh! :rolleyes:

I've been making the same mistake as you, I've been finding the heading of the airplane.

(i thought that was the question originally, and i didn't notice when it was changed :redface:)

The heading of the wind is 90º minus the other angle of the triangle. :smile:
 
  • #7
it is also not 69.3 (90-20.7) or 79.7 (90-10.35) :( i have one try left and would like to get it right.

any other suggestions?
 
  • #8
so is the answer 100.35?

90+10.35 = 100.3533
 
  • #9
mybrohshi5 said:
so is the answer 100.35?

90+10.35 = 100.3533

Slow down …

The top-left angle of the triangle is (roughly) 2 x 10º.

So the top-right angle is (roughly) 80º.

So the wind is (roughly) 80º North of East.

So that's … East of North? :smile:
 
  • #10
80 degrees north of east would be 20 degrees east of north correct? i tried that though. well i tried 21.1 degrees east of north and that was wrong?
 
  • #11
mybrohshi5 said:
80 degrees north of east would be 20 degrees east of north correct?

Noooo :cry: …

10º :redface:​
 
  • #12
haha 10.35 was correct. i can't even subtract right anymore. this problem killed me LOL.

Thanks for all your help
 

Related to Navigating Wind: Flying East in a Light Airplane

1. How does wind affect flying in a light airplane?

Wind can greatly impact the flight of a light airplane. Headwinds can slow down the aircraft and increase fuel consumption, while tailwinds can increase speed and reduce fuel consumption. Crosswinds can also make it difficult to maintain a straight course and can affect the landing approach. Pilots must constantly monitor wind speed and direction to make necessary adjustments during the flight.

2. Is flying east more challenging than flying west in a light airplane?

Flying east in a light airplane can be more challenging due to the effects of the Earth's rotation. The rotation causes winds to move from west to east, so when flying east, the headwinds can be stronger and the tailwinds weaker. This means the aircraft must work harder to maintain airspeed and may require more fuel. Pilots must also consider the effects of prevailing winds on their flight path and plan accordingly.

3. How do pilots navigate wind when flying east in a light airplane?

Pilots use a combination of techniques to navigate wind when flying east in a light airplane. This may include adjusting the aircraft's heading to compensate for crosswinds, using the aircraft's instruments to measure wind speed and direction, and making adjustments to the aircraft's airspeed and altitude to maintain a desired flight path. Pilots also rely on weather forecasts and in-flight updates to stay aware of changing wind conditions.

4. Can wind conditions change during a flight?

Yes, wind conditions can change during a flight, and pilots must be prepared to adapt accordingly. Wind speed and direction can be affected by various factors such as changes in altitude, terrain, and weather systems. Pilots must constantly monitor wind conditions and make adjustments to their flight path and speed to maintain a safe and efficient flight.

5. How does flying in a light airplane differ from flying in a commercial airliner when it comes to navigating wind?

Flying in a light airplane differs from flying in a commercial airliner in terms of navigating wind due to the size and capabilities of the aircraft. Light airplanes are more susceptible to wind gusts and turbulence, so pilots must be more proactive in adjusting their flight path and speed to compensate for wind conditions. Commercial airliners, on the other hand, are larger and more stable, allowing for a smoother flight even in windy conditions. Pilots of commercial airliners also have access to advanced weather forecasting and navigation technology, making it easier to navigate wind.

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