Charting a Course A helicopter pilot needs to travel to a...

Charting a Course A helicopter pilot needs to travel to a regional airport 25 miles away. She flies at an actual heading of $\mathrm{N} 16.26^{\circ} \mathrm{E}$ with an airspeed of $120 \mathrm{mph}$, and there is a wind blowing directly east at $20 \mathrm{mph}$. (a) Determine the compass heading that the pilot needs to reach her destination. (b) How long will it take her to reach her destination? Round to the nearest minute.

Charting a Course A helicopter pilot needs to travel to a regional airport 25 miles away. She flies at an actual heading of $\mathrm{N} 16.26^{\circ} \mathrm{E}$ with an airspeed of $120 \mathrm{mph}$, and there is a wind blowing directly east at $20 \mathrm{mph}$.
(a) Determine the compass heading that the pilot needs to reach her destination.
(b) How long will it take her to reach her destination? Round to the nearest minute.

Key Concepts

Vector Addition

Vector addition involves combining two or more vectors to determine a resultant vector that encapsulates the overall effect. In the context of navigation, this technique is used to account for different velocity components, such as the aircraft's intended airspeed and the wind's speed, to accurately determine the effective ground track and speed.

Relative Velocity

Relative velocity is a concept that compares the velocity of an object with respect to another moving object or medium. In aviation, it helps in determining how the wind affects the aircraft’s motion relative to the ground, which is essential for adjusting the flight path and calculating actual travel time.

Wind Correction

Wind correction refers to the adjustments made to an aircraft's heading to counteract the influence of wind. By adjusting the heading, the pilot ensures that the resultant path aligns with the desired track. This concept is critical for maintaining the correct course towards the destination despite crosswinds.

Trigonometry in Navigation

Trigonometric principles are used to break down and resolve vectors into their components, which is fundamental in navigation. Trigonometry helps calculate the correct angles for heading adjustments and the magnitude of the effects of wind on the aircraft's travel, thereby enabling accurate course plotting.

Distance, Speed, and Time Relationship

The fundamental relationship between distance, speed, and time is crucial in determining travel time. Once the effective ground speed (resultant speed after accounting for wind) is known, this relationship allows for the direct computation of the time needed to cover a certain distance, an essential aspect of flight planning.

Transcript

00:01 So we have some information given to us.

00:02 We know that this person wants to fly 25 miles.

00:07 However, there's a wind.

00:09 And we were given the vector for the actual plane velocity, 120 miles per hour.

00:18 And the angle was 20, excuse me, north, 16 .26 degrees east.

00:27 And we also know that we have a wind.

00:31 And the wind is blowing east at 20 miles per hour.

00:36 East, 20 miles per hour.

00:39 So let's draw a picture of our problem.

00:41 So i'm not going to make this be to scale, but here's our north and here's our east.

00:49 And we know that that first vector, i'll do it in green, that that angle is supposed to be, this angle in here is supposed to be 16 .26 degrees.

01:02 So north and then this many degrees east.

01:06 And we know that the magnitude of that vector is 120 miles per hour.

01:12 And then we have out of the east, we have this wind.

01:17 And it's not supposed to be a very long vector.

01:19 And again, this would be the north -south line.

01:23 So we know this angle is 90 degrees.

01:26 The magnitude of this vector is 20 miles per hour.

01:30 And we know how big this angle is.

01:32 Want to find the resultant vector.

01:34 And let's see if i'm coordinated enough to have that drawn up to there.

01:38 Not too bad.

01:39 So we need to find out what this angle is and what the magnitude is.