1. The Triangle of Velocities
AIR NAVIGATION
Part 3
The Triangle of Velocities

2. Distance, Speed, Time We know that an aircraft travelling
a distance of 600 nm at 300 kts,
will take 2 hours to complete the journey.
This is calculated using the
Distance - Speed - Time
formulae
Distance
D S T
Speed
Time

3. Velocity and Vectors Having discussed the basics of
Speed, Time and Distance in flying,
it is now necessary to consider the Wind,
which is simply air that is moving.
But the wind can have effects on aircraft,
it can blow them miles of course,
and it can also cause the aircraft
to speed up or slow down.

4. Velocity and Vectors VELOCITY Having discussed the basics of
Speed, Time and Distance in flying,
it is now necessary to consider the Wind,
which is simply air that is moving.
When we talk about aircraft or wind movement,
we must always give both
the direction and speed of the movement.
Direction and speed together are called a
VELOCITY

5. Velocity and Vectors A velocity can be represented on paper
by a line called a VECTOR.
The bearing of the line represents
the direction of the movement,
and the length of the line represents the speed.
True
North
True
North
Track of 015°
Speed 140 kts
(015/140)
Track of 90°
Speed 200 kts
(090/200)

6. The Vector Triangle Imagine two children, on either side of a river,
with a toy boat driven by an electric motor.
The boat has a rudder,
to keep it on a straight course,
and has a speed of 2 knots. B A

7. The Vector Triangle Child A points the boat at her friend.
If the river is not flowing
the boat will cross the river at right angles
and reach child B on the other side. B A

8. The Vector Triangle However, rivers flow downstream to the sea,
so let’s look at a river
where the speed of the current is 2 knots.
Child B puts the boat back in the river,
and points it at his friend.
and the boat ends up at ‘C’. B A C

9. The Vector Triangle The boat velocity is shown
by a line with a single arrow.
The water velocity is shown
by a line with 3 arrowheads.
These two lines are the same length
as they both represent a speed of 2 knots. B A C

10. The Vector Triangle The third side represents
the actual movement of the boat
as it crabs across the river,
and is called the Resultant.
By use of Pythagoras’s theorem,
it can be shown that the speed of the boat
across the river is 2.83 knots. B A C

11. The Vector Triangle The same basic triangle can be used to show
the motion of an aircraft through the air,
the air itself, also moving.
There are two differences:
As aircraft speed is more than wind speed,
the triangle will be much longer and thinner.
and the triangle is labelled with different names.
Heading & True Air Speed (HDG/TAS)
Wind Speed
& Direction
Track & Ground Speed (TRK/GS)

12. The Air Triangle Wind represents 2 more components The wind Speed and
True
Air Speed
Heading
Drift
Wind represents
2 more components
The wind Speed
and
the Direction from which it is blowing.
(northerly in this diagram).
Track
Wind
Velocity
Ground
Speed
Heading & True Air Speed (HDG/TAS)
Wind Speed
& Direction
There are 6 components of the air triangle
Track & Ground Speed (TRK/GS)

13. A2 + B2 = C2 C = 5 Pythagoras's Theorum (A x A) + (B x B) = C x C C A
(3 x 3) + (4 x 4) = C x C
(9) (16) = C x C
= C x C
eg A = 3, B= 4
= C2
The Square Root of 25 = C
C = 5

14. Real World Scenario There are three likely scenarios
when we have to solve the triangle of Velocities.
The first is at the planning stage of a flight,
to calculate how long the flight will take.
The second scenario is in the air,
to calculate the Wind Velocity.
The final scenario occurs when you are over
a featureless area such as the sea.
You can calculate a
Deduced Reckoning position (DR)

15. Real World Scenario In the planning stage of a flight,
given 4 of the 6 elements of
the Triangle of Velocities
True Air Speed, Track,
Wind Speed and Direction
it is now possible to solve the other two,
Ground Speed
and Heading
and then use the DST formula
to calculate how long the flight will take.

16. Real World Scenario When the aircraft is in the air,
we know the True Air Speed and Heading,
and we can measure out our Track
and Ground Speed
by watching our position over the ground.
From these 4 elements,
we can calculate the Wind Velocity.
(Speed and Direction)

17. Real World Scenario When you know the Heading and True Air Speed,
and have a reliable Wind Velocity.
From these 4 elements you can calculate
your Track and Ground Speed
to produce a Deduced Reckoning position (DR)
by applying the time from your last known position
to the Ground Speed
to give a distance along your Track.

18. what is a vector representative of?
Check Understanding
On paper,
what is a vector representative of?
Velocity
Direction
Time
Speed

19. Check Understanding Time and Distance Direction and Speed
What is meant by the term
Velocity?
Time and Distance
Direction and Speed
Speed and Time
Distance and Direction

20. Check Understanding Drift Velocity Ground Speed Wind direction
In the air triangle of velocities,
What is the angle between the heading
and the track vector known as?
Drift
Velocity
Ground Speed
Wind direction

21. Check Understanding Heading and TAS Track and Ground Speed
In the air triangle below,
name the components of the 3rd side,
shown by a dotted line.
Heading and TAS
Track and Ground Speed
Wind Speed and Direction
Velocity

22. Check Understanding Hearing and Drift Heading and Ground Speed
In the air triangle of velocities,
the heading vector has 2 components.
What are they?
Hearing and Drift
Heading and Ground Speed
Heading and True Air Speed
Heading and Direction

23. Check Understanding Heading and TAS Track and Ground Speed
In the air triangle below,
name the components of the 3rd side,
shown by a dotted line.
Heading and TAS
Track and Ground Speed
Wind Speed and Direction
Drift and Ground Speed

24. Check Understanding 2 3 4 5 In the air triangle of velocities,
there are 6 components.
How many are needed
to calculate the missing ones? 2 3 4 5

25. AIR NAVIGATION
End of Presentation