The Triangle of Velocities 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 Distance D S T Speed Time

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 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

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)

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

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

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

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

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

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)

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)

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 25 = C x C eg A = 3, B= 4 25 = C2 The Square Root of 25 = C C = 5

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)

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.

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)

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.

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

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

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

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

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

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

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

AIR NAVIGATION End of Presentation