AIR NAVIGATION

Part 3

The Triangle of Velocities

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

Speed Time

Distance

D S T

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.

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.

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

Velocity and VectorsA 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.

Track of 015°Speed 140 kts

(015/140)

Track of 90°Speed 200 kts

(090/200)

True North

True North

The Vector TriangleImagine two children, on either side of a river,

with a toy boat driven by an electric motor.

A

B

The boat has a rudder,to keep it on a straight course,

and has a speed of 2 knots.

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.

The Vector Triangle

A

B

The Vector TriangleHowever, rivers flow downstream to the sea,

so let’s look at a river where the speed of the current is 2 knots.

A

B

and the boat ends up at ‘C’.

Child B puts the boat back in the river,and points it at his friend.

C

The Vector Triangle

A

B

The boat velocity is shownby a line with a single arrow.

The water velocity is shownby a line with 3 arrowheads.

These two lines are the same length as they both represent a speed of 2 knots.

C

The Vector Triangle

A

B

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.

C

The Vector TriangleThe 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.

Wind Speed& Direction

Heading & True Air Speed (HDG/TAS)

Track & Ground Speed (TRK/GS)

The Air Triangle

There are 6 components of the air triangle

Heading & True Air Speed (HDG/TAS)

Track & Ground Speed (TRK/GS)

Wind Speed& Direction

HeadingTrue

Air Speed

TrackGroundSpeed

WindVelocity

Drift

Wind represents 2 more components

The wind Speed and the Direction from which it is blowing. (northerly in this diagram).

Pythagoras's Theorum

A

B

C

A2 + B2 = C2

(A x A) + (B x B) = C x C

eg A = 3, B= 4

(3 x 3) + (4 x 4) = C x C

(9) + (16) = C x C

25 = C x C

25 = C2

The Square Root of 25 = C

C = 5

Real World ScenarioThere 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 overa featureless area such as the sea.

You can calculate a Deduced Reckoning position (DR)

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 formulato calculate how long the flight will take.

Real World Scenario

When the aircraft is in the air,we know the True Air Speed and Heading,

and we can measure out our Trackand Ground Speed

by watching our position over the ground.

From these 4 elements, we can calculate the Wind Velocity.

(Speed and Direction)

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 positionto the Ground Speed

to give a distance along your Track.

Check UnderstandingOn paper,

what is a vector representative of?

Speed

Direction

Time

Velocity

Check UnderstandingWhat is meant by the term

Velocity?

Distance and Direction

Direction and Speed

Speed and Time

Time and Distance

Check UnderstandingIn the air triangle of velocities,

What is the angle between the headingand the track vector known as?

Wind direction

Velocity

Ground Speed

Drift

Check UnderstandingIn the air triangle below,

name the components of the 3rd side,shown by a dotted line.

Velocity

Track and Ground Speed

Wind Speed and Direction

Heading and TAS

Check UnderstandingIn the air triangle of velocities,

the heading vector has 2 components.What are they?

Heading and Direction

Heading and Ground Speed

Heading and True Air Speed

Hearing and Drift

Check UnderstandingIn the air triangle below,

name the components of the 3rd side,shown by a dotted line.

Drift and Ground Speed

Track and Ground Speed

Wind Speed and Direction

Heading and TAS

Check Understanding

5

3

4

2

In the air triangle of velocities,there are 6 components. How many are needed

to calculate the missing ones?

AIR NAVIGATION

End of Presentation