The pilot of an aircraft wishes to head directly east, but is faced with a wind speed of 40 milh

step 1 So we know that there is a wind coming out of the northwest. So it's coming out of the northwest

The pilot of an aircraft wishes to head directly east, but...

Key Concepts

Relative Velocity

The concept of relative velocity involves viewing the aircraft's motion in conjunction with the wind's motion. By considering these as relative vectors, one can determine the true motion of the aircraft over the ground, which is vital for both navigation and safety.

Trigonometric Methods in Navigation

Trigonometry is essential in navigation problems as it provides the tools needed to relate the angles and magnitudes of vectors. By applying trigonometric relationships, a pilot can calculate the precise headings and speeds needed to counteract wind effects and achieve the desired course.

Vector Addition

In navigation, vector addition is used to combine the aircraft's velocity vector with the wind's velocity vector to determine the resulting ground velocity. This principle allows the pilot to calculate the necessary heading adjustment so that the desired course is maintained despite the wind's influence.

Resolving Vectors into Components

To effectively use vector addition, each vector is broken down into its horizontal and vertical components. This breakdown simplifies the process of combining the vectors by allowing calculations to be performed separately in each direction, facilitating the determination of the needed adjustments.

Wind Correction Angle

The wind correction angle is the angle by which an aircraft must adjust its heading to counteract the wind and maintain its desired ground track. This concept is crucial in navigation as it directly relates to compensating for drift caused by wind, ensuring the aircraft follows the intended course.

Transcript

00:01 So we know that there is a wind coming out of the northwest.

00:05 So it's coming out of the northwest.

00:07 So it's coming down this way from the northwest.

00:11 And so it's coming down like this.

00:13 This angle would be 45 degrees.

00:16 And let's say its magnitude is 40 miles per hour.

00:22 And we know that the plane, i'll make the plane in red, is going to be flying along at 250 miles per hour.

00:30 And i don't have these proportion that i should make.

00:32 Longer, but that's okay.

00:34 This is moving along at 250 miles per hour.

00:38 And we want the resultant factor, which i'll do in blue, to end up being that the plane is going due east.

00:46 So that's what we want the result to be.

00:48 And we need to find what is the bearing? what is what is the bearing that this plane needs to make in order for this to happen? and then we want to figure out what that actual flight speed is moving to the east.

01:02 So let's look at what we'll look at what we're going to we have.

01:04 We have a triangle here and we know a side and an angle and we would like to find this angle, but we can actually find this one.

01:14 And i'll call this angle theta right there.

01:17 So we can use law of signs.

01:19 And we can say that the sign of theta is to its side opposite, which is that 40 miles per hour as the sign of 45 degrees, which we know is square of 2 over 2, is to 250 miles per hour.

01:36 So we can use law of sign since we have this side angle pair.

01:40 We know this is an acute angle.

01:42 This is going to be an obtuse angle.

01:44 It looks like it is going to be an obtuse angle.

01:46 So we're going to take 40, quit out of that, take 40 times a sign of 45 degrees, which again we know is square bit of 2 over 2, and then divide it by 250 and that's going to give me my sign of my angle.

02:00 So the sign of my angle is equal to 0 .11317.

02:06 And we're going to take inverse sign or i tell my students that the inverse function is an angle finder...

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