air navigation part 3 the triangle of velocities
TRANSCRIPT
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 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?