At 0020 UTC an aircraft is crossing the 310° radial at 40 NM of a VOR/DME station. At 0035 UTC the radial is 040° and DME distance is 40 NM. Magnetic variation is zero. The true track and ground speed are:
A) 088° - 232 kt.
B) 080° - 226 kt.
C) 090° - 232 kt.
D) 085° - 226 kt.
Draw a vertical line to represent the 360/000 radial
At the bottom of this line draw a cross to represent the VOR
From the VOR draw a straight line upwards and to the left to represent the 310 radial. The angle between this line and the 360/000 line will be 360 - 310 = 50 degrees.
From the VOR draw a straight line upwards and to the right to represent the 040 radial. The angle between this and the 360/000 line will be 000 + 040 = 40 degrees.
On the 310 radial line draw a cross to represent the initial position 40 nm from the VOR.
On the 040 radial line draw a cross to represent the second position 40 nm from the VOR.
Draw a straight line joining the two crosses.
You now have a triangle with corners at the VOR, position 1 and position 2.
The internal angle at the VOR is 50 + 40 = 90 degrees.
The side from the VOR to position 1 and the side from the VOR to position 2 are each 40 nm long. So the internal angles at positions 1 and 2 are equal.
To calculate the size of these angles subtract 90 degrees (the internal angle at the VOR) from 180 degrees (the total internal angle in a triangle) then divide by 2. This gives an angle of 45 degrees.
We now have a triangle with internal angles of 90, 45 and 45, and two side of 40 nmn length.
Using pythag the distance from position 1 to position 2 is the square root of ( 40 nm squared + 40 nm squared), which is 56.5685 nm. This distance is flown in 15 minutes (between 0020 and 0035). 15 minutes is 1/4 hour so multiplying this distance by 4 gives a ground speed of 226.74 knots.
At position 1 the internal angle is 45 degrees so the external angle between the 310 radial and the track is 180 – 45 = 135 degrees.
Adding this to the 310 radial give 135 + 310 = 445 degrees true track. This is greater than 360 so subtract 360 to give the true track of 85 degrees.
So the true track is 085 degrees and the ground speed is 226 knots.
Now try this one so see if you have learned anything.
At 0020 UTC an aircraft is crossing the 300° radial at 50 NM of a VOR/DME station. At 0040 UTC the radial is 050° and DME distance is 50 NM. Magnetic variation is zero. The true track and ground speed are: