This article covers the steps involved in finding the wind and jet vector.
Following are the concepts covered and features of this article
- How to interpret the bearing angles?
- Steps to take the positive angle for the velocity vector
- Finding the velocity vector of wind and jet plane.
- Calculating the true sped of the jet plane
- Finding the resultant direction of the jet plane.
- Summary steps to find the true velocity of a jet plane.
Problem: A jet is flying through a wind that is blowing with a speed of 40mph in the direction N10E. The jet has a speed of 625mph relative to the air, and the pilot heads the jet in the direction N20W.
- Express the velocity of the wind as a vector in component form.
- Express the velocity of the jet relative to the air in component
- Find the true velocity of the jet as a vector.
- Find the true speed and direction of the Jet palne
Finding the velocity vector component form of wind:
Given that the wind is blowing with a speed (S1)=40mph and the direction is N 10 E.
So this representation conveys that, starting from the north direction, move the angle towards the East direction by 10 degrees(Shortest part is taken).
Therefore the terminal side of the angle makes 10 degrees with the north direction as shown in the picture.
Now we take the Positive angle in degrees (anticlockwise direction), starting from the East direction. Till the terminal side of the angle. Form the above picture, it is evident that the positive angle is X=90-10 = 80 degrees.
Since we have the angle in degrees, we can find the Vector component form of wind using the formula
V1= S1 cos(X)*i+S1 sin(X)*j.
Hence the vector component of wind is
V1= 40* cos(80)i+40* sin(80)j.
V1= (6.94592 )i+(39.39231)j
Therefore ,the V1= <6.94592,39.39231>
Finding the velocity vector component of the JET Plane:
Given that the Jet is flying with a speed (S2)=625mph and the direction is N 20 W.
Starting from the north direction, the angle is moved towards the west direction by 20 degrees.
As shown in the picture below the red angle in the clockwise direction is 20 degrees.
The picture below explains it.
Therefore Positive angle in degrees, starting from the East direction. Till the terminal side of the angle, Y is 90+20=110 degrees.
Hence the vector component of the jet is
V2= 625* cos(110)i+ 625* sin(1100)j.
V2= <-213.7625 ,587.30788>
Calculating the TRUE velocity vector components of the Jet Plane
The effective velocity (V)of the Jetplane is given by V1 +V2
= <6.94592-213.7625 , 39.39231+587.30788>
Calculating the TRUE speed of the Jet Plane from TRUE Velocity Vector.
Speed is a scalar quantity. True speed is also called as ground speed.
Once we have the TRUE velocity vector, we can find the magnitude of the velocity vector.
Finding the direction of the Jet Plane:
The direction of the jetplane needs more attention and the concept of vectors play a key role.
Theta == -71.7366.
Let us ignore the negative angle that we get using the formula
So this angle is 71.7336° and this is the angle from the “x” axis.
The green angle will be 90-71.7336=18.2664°.
Therefore the angle is 18.3° rounded to one decimal place.
The direction in which the jet flies are N 18.3° W
18.3° (West of North).
Steps to find the true jet velocity :
Finding the vector component form of wind and the JET Plane.
- Find the positive angle x in degrees(taken in anticlockwise direction from 0 degrees ) to the terminal side of the wind direction.
- Similarly, Find the positive angle Y in degrees to the terminal side of the jet plane.
- Find the velocity vector of the wind “W” with the given speed of the wind and the angle X calculated.
- Similarly, find the velocity vector of the JET “W” with the given speed of the JET and the angle Y calculated.
Finding the TRUE velocity vector of the Jet Plane
- Add the wind and jet velocity vectors to get the resultant True velocity
Finding the TRUE speed and direction of the Jet Plane.
- Find the magnitude of the TRUE velocity vector and the direction using the arctan formula.