2. Whiteboardmaths.com © 2009 All rights reserved 5 7 2 1

3. Guidance Notes for Teachers Some indication of content and range at level 1 and 2 is shown on the next slide. Relevant slides show all the diagrams/questions/answers that are required. End slides have student question sheets and a teacher question/answer sheet. End slides have printable worksheets for students. Calculator symbols are suggestions only and could be removed depending on the group. The vast majority of questions in this presentation are designed to be non- calculator. The aim of this presentation is to give students a brief taste of what it might be like to be an Air Traffic Controller. It is essential that the teacher becomes confident with the detail before attempting to deliver it to a class (particularly so with the KEYS on slides 24-29). The presentation starts by explaining the relationship: Visual Controller  Radar Controller  Centre Controller on slide 4 and this needs to be introduced to the students. (The main ATC Centre in the UK is at Swanwick. See http://www.nats.co.uk/text/80/london_area_control_centre.html http://www.nats.co.uk/text/80/london_area_control_centre.html for further information). It has been necessary to make certain simplifications throughout, otherwise the whole thing would become overly complicated. For example with regard to separation between aircraft there are times when 3 miles or 500 ft is acceptable (rather than the 5 miles and 1000 ft mentioned), the primary radar return is often not displayed on the radar screen (a secondary, computer generated return is often used) and the labels given are not exact. However, the presentation fulfils the key objective of getting across the essential key elements of an Air Traffic Controllers role and responsibility. Namely that of aircraft sequencing, separation and safety. MC (Guild of Air Traffic Control Officers) Generic Advice: The preparation below is advisable in the majority of presentations (But probably not this one which is different from many of the others). Print off the teacher question and answer sheets/worksheets Print off the student question sheets/worksheets Run through the presentation yourself answering the questions Decide how you are going to deliver the presentation. (a) Are you going to go through it from start to finish with the class, perhaps using it as an example/demonstration of functional maths and focusing on the development of the processing skills involved at each stage? (b) Are you going to use only part of the presentation? (c) Are you simply going to use the presentation to introduce the activity and let the class work on their own through the question sheets but refer to some of the elements/answers within the presentation when needed? Remember the slides are editable so if you wish to introduce an open question/small investigation of your own then simply choose the relevant slide add/delete your own text (using a text box if needed).

4. Content and Skills Coverage and range: Level 1 Understand and use whole numbers and recognise negative numbers in practical contexts Add, subtract, multiply and divide using a range of mental methods Multiply and divide whole numbers by 10 and 100 using mental arithmetic Understand and use equivalences between common fractions, decimals and percentages Add and subtract decimal up to two decimal places Solve simple problems involving ratio, where one number is a multiple of the other Use simple formulae expressed in words for one- or two-step operations Solve problems requiring calculation with common measures including money, time, length, weight, capacity and temperature Convert units of measure in the same system Work out areas, perimeters and volumes in practical situations Construct models and draw shapes, measuring and drawing angles and identifying line symmetry Extract and interpret information from tables, diagrams, charts and graphs Collect and record discrete data and organise and represent information in different ways Find mean and range Use probability to show that some events are more likely to occur than others Understand outcomes, check calculations and explain results Understand and use positive and negative numbers of any size in practical contexts Carry out calculations with numbers of any size in practical contexts Understand, use and calculate ratio and proportion, including problems involving scale Understand and use equivalences between fractions, decimals and percentages Add and subtract fractions; add, subtract, multiply and divide decimals to a given number of decimal places Understand and use simple equations and simple formulae involving one- or two-step operations Recognise and use 2D representations of 3D objects. Find area, perimeter and volume of common shapes Use, convert and calculate using metric and, where appropriate, imperial measures Collect and represent discrete and continuous data, using ICT where appropriate Use and interpret statistical measures, tables and diagrams, for discrete and continuous data using ICT where appropriate Use statistical methods to investigate situations Use a numerical scale from 0 to 1 to express and compare probabilities Title: Air Traffic Controller Content and skills covered Coverage and range: Level 2 At least 1 from each area

5. Intro What mathematics might be involved with Air Traffic Control?

6. Air Traffic Controller Air Traffic Controllers have a complex job and have many functions to fulfil but primarily they are responsible for the sequencing and safe separation of aircraft during the take-off and landing phase of a flight as well as ensuring the safe and expeditious transit of aircraft en-route to their destination airfield/airport. The Visual Controllers work and co-ordinate very closely with the Radar Controllers who normally operate from a radar room below them. Take-off and landing clearances will be requested and issued as appropriate. The Radar Controllers are responsible for directing inbound and outbound traffic to/from the airport/airfield. If a departing aircraft has a long way to go to its destination then it will want to fly at high altitude (saves fuel) and the Radar Controller will transfer control of the aircraft to an Air Traffic Control Centre. Once with the centre the aircraft may wish to join an airway (corridor in the sky). This protected airspace ensures that flights can be closely monitored in a safe environment. Aircraft that have very long distances to fly will be handed over from one Air Traffic Control Centre to the next as they continue their flight to the destination. As they approach their destination the Centre will transfer control to the Radar Controller in the Airport Tower who will co-ordinate clearance for landing with the Visual Controller.

7. Visual Circuit Pattern A Visual Circuit Pattern The controllers in the Visual Control Room are in communication with all aircraft that are taxiing for take-off and those that have recently landed. They also control any aircraft that are operating in the visual circuit pattern. These are usually the smaller- type light aircraft, that may wish to practise approaches to the runway or multiple landings and take-off’s. The controller will ensure that they are kept safely sequenced and separated from any inbound traffic that the Radar Controller may have. 23 05 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Diagram showing aircraft positions in a visual circuit pattern. This is a left-hand pattern for runway 23 with a downwind height of 1500 feet. Not to Scale

8. A Visual Circuit Pattern The runway numbers give the bearing that the aircraft will be flying on when landing or taking off. This is abbreviated from 3 digits to 2 digits by removal of the end zero. So in the case below, runway 23 is pointing in the direction of 230 o and the opposite runway is pointing in the direction 050 o. (The bearing of all runways end in a 0) 23 05 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Not to Scale Diagram showing aircraft positions in a visual pattern. This is a left-hand pattern for runway 23 with a downwind height of 1500 feet.

9. A Visual Circuit Pattern 31 13 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Q1. What are the bearing numbers for the runway shown? 310 o and 130 o Not to Scale

10. A Visual Circuit Pattern 28 10 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Q2. What are the bearing numbers for this runway? 280 o and 100 o Not to Scale

11. A Visual Circuit Pattern 28 10 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Q3. What is the relationship between the bearings at each end of any runway? They differ by 180 o Not to Scale

12. A Visual Circuit Pattern 22 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Q4. What is the missing runway number below? 04 Not to Scale

13. Q5. On what bearing is an aircraft flying when taking off on this runway? 320 o Q6. What bearing is this aircraft flying on as it lands on this runway? 270 o Q7. Five minutes after landing on the runway in Q6 another aircraft takes off from the other end of the runway. What are the numbers on that end runway? 09 Q8. This aircraft will shortly be landing on a bearing of NORTH. What are both runway numbers in this case? 36/18

14. A Visual Circuit Pattern 23 05 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Q9. What will the bearing be after take-off, of an aircraft making a 45 o departure from runway 23 below? 185 o Q10. Generally speaking aircraft like to take-off into wind. Why do you think this is? Gives them lift Not to Scale

15. A Visual Circuit Pattern 23 05 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet The names of some of the positions in the pattern are related to wind direction. The direction and speed of the wind changes constantly and it does not often blow straight down the runway. Not to Scale

16. A Visual Circuit Pattern 23 05 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Runway 23 would still be a suitable runway to use if the wind was blowing in any of the directions shown. Not to Scale

17. A Visual Circuit Pattern 23 05 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Here the wind is blowing more-or-less straight across the runway (cross wind) so the situation is marginal as to which runway to use. Not to Scale

18. A Visual Circuit Pattern 23 05 Downwind Base Leg Finals Crosswind Upwind Straight-ahead Departure 45 o Departure 45 o Join 1500 feet A situation like the one shown would mean that runway 05 would be used for take-off and landings and the circuit pattern direction would have to change to right-hand. Not to Scale

19. A Visual Circuit Pattern As shown below. 23 05 Downwind Base Leg Crosswind Finals Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Upwind Diagram showing aircraft positions in a visual pattern. This is a right-hand pattern for runway 05 with a downwind height of 1500 feet. Not to Scale The aviation world still uses imperial measures in many instances. For example lengths/distances as well as aircraft heights are still given in feet.

20. A Visual Circuit Pattern 23 05 Downwind Base Leg Crosswind Finals Straight-ahead Departure 45 o Departure 45 o Join 1500 feet Upwind Not to Scale Q11. Calculate the height of the downwind leg in yards. 500 yards Q12. Calculate this height in metres. 0.9 x 500 = 450m * Diagram showing aircraft positions in a visual pattern. This is a right-hand pattern for runway 05 with a downwind height of 1500 feet.

21. Runway Dimensions A Visual Circuit Pattern Not to Scale The dimensions of a typical runway at a medium sized airport are shown below. 1 : 50 8000ft 160 ft Q13. Calculate the width to length ratio of the runway. 23 05 1½ miles Q14. 1 mile = 1760 yards. Calculate the length of the runway in miles. Do not use a calculator and give your answer to the nearest half mile. Q15. Calculate: (a) The perimeter of the runway (b) The area of the runway 16 320 ft 1 280 000ft 2 *

22. Inbound Outbound Call Sign InboundOutbound From/ToFuel Required ETAETD 1KL 3810:00Aberdeenyes 2ATS 67510:12Humberside 3LV 1210:15Leedsyes 4GBV 5310:20Norwich 5RAF 23410:23Luton 6MNE 4210:29Birminghamyes 7OBI 110:45Newcastle 8CC 67510:48Leeds 9VTF 8710:55Norwich 10LST 17811:00Norwich Q16. Air Traffic Controllers on duty at a small regional airport have information displayed on expected arrivals and departures over a 1 hour period as shown in the table below. What is the estimated time of arrival of CC 675 from Leeds? 10:48 Q17. What fraction of the aircraft movements are departures? 2/5 *

23. Call Sign InboundOutbound From/ToFuel Required ETAETD 1KL 3810:00Aberdeenyes 2ATS 67510:12Humberside 3LV 1210:15Leedsyes 4GBV 5310:20Norwich 5RAF 23410:23Luton 6MNE 4210:29Birminghamyes 7OBI 110:45Newcastle 8CC 67510:48Leeds 9VTF 8710:55Norwich 10LST 17811:00Norwich Q18. What fraction of the aircraft movements are arrivals? Give your answer as (a) A fraction (b) A decimal (c) A percentage 3/50.660% Q19. What percentage of the arrivals require fuel? 50% *

24. Call Sign Outbound ToAltitude Climbing  ETD 1ATS 67510:12HumbersideFL 85 2GBV 5310:20NorwichFL 130 3OBI 110:45NewcastleFL 200 4LST 17811:00NorwichFL 150 5KLM 2311:05AmsterdamFL 230 (Join Airway) 6MON 5411:15CyprusFL 350 Another display (as in the table shown) gives the controllers some information on the heights that departing aircraft wish to climb to after take-off. Q20. What altitude will ATS 675 be climbing to in feet? 8500 ft Q21. What altitude will MON 54 be climbing to in feet? 35 000 ft Above 3000 ft and only at intervals of 500 ft, a Flight Level (FL) is given. This is based on a cockpit altimeter setting and is called an altitude. A Flight Level of 45 (FL45) means an altitude of 4500 ft. Similarly FL 130 means an altitude of 13 000 ft. You simply need to add two zeros.

25. Radar Controller CE 345 FL80  315 o LS 52 FL90 085 o TR 84 FL120  048 o Meanwhile, downstairs, the Radar Controller is controlling several aircraft as can be seen from her radar screen. The ones without labels are not being controlled by her and so are unknown traffic. Use the KEY to answer some of the questions about the aircraft. KEY: LR 22: Aircraft Call sign 075 o Bearing flying on  Climbing to FL  Descending from FL  Level at FL Range Rings: 5 mile radius Airport at centre of screen RAF 847 FL45 180 o LR345 FL95  358 o AW 147 FL230  075 o In most situations Air Traffic Controllers will maintain a minimum of 5 miles lateral separation or 1000ft vertical separation between aircraft. © bigstockphoto.com Aircraft primary radar return. Trail shows direction of travel. FL 85

26. CE 345 FL80  315 o LS 52 FL90 085 o TR 84 FL120  048 o RAF 847 FL45 180 o LR345 FL95  358 o AW 147 FL230  075 o Q22. Which aircraft is 10 miles NW of the Airport? CE 345 Q24. What bearing is AW 147 flying on? 075 o Q25. Which aircraft is climbing to FL 95? LR 345 KEY: LR 22: Aircraft Call sign 075 o Bearing flying on  Climbing to FL  Descending from FL  Level at FL Range Rings: 5 mile radius Airport at centre of screen © bigstockphoto.com Q23. How far is TR 84 from the Airport? 15 Miles Aircraft primary radar return. Trail shows direction of travel. In most situations Air Traffic Controllers will maintain a minimum of 5 miles lateral separation or 1000ft vertical separation between aircraft. FL 85

27. CE 345 FL80  315 o LS 52 FL90 085 o TR 84 FL120  048 o RAF 847 FL45 180 o LR345 FL95  358 o AW 147 FL230  075 o Q26. CE 345 has conflicting traffic, 10 miles at his 12 O’ clock position, height unknown. What avoiding action could the controller offer the pilot to keep the aircraft safe. Turn him left onto something like 260 o KEY: LR 22: Aircraft Call sign 075 o Bearing flying on  Climbing to FL  Descending from FL  Level at FL Range Rings: 5 mile radius Airport at centre of screen © bigstockphoto.com Aircraft primary radar return. Trail shows direction of travel. In most situations Air Traffic Controllers will maintain a minimum of 5 miles lateral separation or 1000ft vertical separation between aircraft. FL 85

28. CE 345 FL80  315 o LS 52 FL90 085 o TR 84 FL120  048 o RAF 847 FL45 180 o LR345 FL95  358 o AW 147 FL230  075 o Q27. LS 52 is transit traffic and will over-fly the airport at the indicated level. GBV 53 is about to take-off and fly due west climbing to FL 130. What might the Radar Controller ask the Visual Controller to instruct the pilot to do before take-off. Stop your climb at FL 80 initially KEY: LR 22: Aircraft Call sign 075 o Bearing flying on  Climbing to FL  Descending from FL  Level at FL Range Rings: 5 mile radius Airport at centre of screen © bigstockphoto.com Aircraft primary radar return. Trail shows direction of travel. In most situations Air Traffic Controllers will maintain a minimum of 5 miles lateral separation or 1000ft vertical separation between aircraft. FL 85

29. NAV Chart All Aircrew need comprehensive maps of the airspace that they fly within like this one shown. When they are flying along upper air routes or in airways they often fly along fixed tracks from beacon to beacon like those indicated here. These beacons transmit on certain known frequencies enabling the aircraft to home-in on them. This is the phase of the flights that the controllers at the Air Traffic Control Centres are involved in. © bigstockphoto.com

30. ATC Centre    24 FL 245 FL 75 B1B2 B3 21 090 270 226 046 Air Traffic Control Centre Q28. How far has the aircraft arriving at Beacon B3, inside the airway, got to fly to reach beacon B1? 45 miles Q29. Can an aircraft join this airway at FL 65? No, base level is FL 75 Q30. On what bearing will the aircraft arriving at beacon B3 fly on in order to reach B2? 046 o © bigstockphoto.com In most situations Air Traffic Controllers must maintain a minimum of 5 miles lateral separation or 1000ft vertical separation between aircraft. KEY:   Airway Beacon (Bn) FL  Airway from and to levels 195  Bearing to next beacon 20  Gives miles between beacons Airways are 10 miles wide

31.    24 FL 245 FL 75 21 090 270 226 046 Air Traffic Control Centre Q31. KLM 23 has just taken off and hopes to join the airway at beacon B2 at FL 230 then turn left and fly along the airway to B3. Do you think the Centre Controller will give clearance for this? By instructing KLM 23 to join at FL220 KLM 23 FL230  340 o AT 48 FL230 046 o Q32. How might the controller resolve this problem? No because AT48 is converging with him at the same level. 226 o Q33. What bearing will KLM 23 fly on after joining the airway at B2? B1B2 B3 © bigstockphoto.com In most situations Air Traffic Controllers must maintain a minimum of 5 miles lateral separation or 1000ft vertical separation between aircraft. KEY:   Airway Beacon (Bn) FL  Airway from and to levels 195  Bearing to next beacon 20  Gives miles between beacons Airways are 10 miles wide

32. Teacher Q & A (1) Q1. What are the bearing numbers for the runway shown? 310 o and 130 o Q2. What are the bearing numbers for this runway? 280 o and 100 o Q3. What is the relationship between the bearings at each end of any runway? They differ by 180 o Q4. What is the missing runway number below? 04 Q5. On what bearing is an aircraft flying when taking off on this runway 320 o Q6. What bearing is this aircraft flying on as it lands on this runway? 270 o Q7. Five minutes after landing another aircraft takes off from the other end of the runway. What are the numbers on that end runway? 09 Q8. This aircraft will shortly be landing on a bearing of NORTH. What are the runway numbers in this case. 36/18 Q9. What will the bearing be, after take-off, of an aircraft making a 45 o departure from runway 23 below? 185 o Q10. Generally speaking aircraft like to take-off into wind. Why do you think this is? Gives them lift Q11. Calculate the height of the downwind leg in yards. 500 yards Q12. Calculate this height in metres. 0.9 x 500 = 450m 1 : 50 Q13. Calculate the width to length ratio of the runway. 1½ miles Q14. 1 mile = 1760 yards. Calculate the length of the runway in miles. Do not use a calculator and give your answer to the nearest half mile. Q15. Calculate the: (a) Perimeter of the runway (b) Area of the runway 16 320 ft1 280 000ft 2 Q16. Air Traffic Controllers on duty at a small regional airport have information displayed on expected arrivals and departures over a 1 hour period as shown in the table below. What is the estimated time of arrival of CC 675 from Leeds? 10:48 Q17. What fraction of the aircraft movements are departures. 2/5 Q18. What fraction of the aircraft movements are arrivals. Give your answer as (a) A fraction (b) A percentage (c) A decimal 3/50.660% Q19. What percentage of the arrivals require fuel. 50% Teacher Q&A (1)

33. Teacher Q & A (2) Q20. What altitude will ATS 675 be climbing to in feet? 8500 ft Q21. What altitude will MON 54 be climbing to in feet? 35 000 ft Q22. Which aircraft is 10 miles NW of the Airport? CE 345 Q24. What bearing is AW 147 flying on? 075 o Q25. Which aircraft is climbing to FL 95? LR 345 Q26. CE 345 has conflicting traffic, 10 miles at his 12 O’ clock position, height unknown. What avoiding action could the controller offer the pilot to keep the aircraft safe. Turn him left onto something like 260 o Q27. LS 52 is transit traffic and will over-fly the airport at the indicated level. GBV 53 is about to take-off and fly due west climbing to FL 130. What might the Radar Controller ask the Visual Controller to instruct the pilot to do before take-off. Stop your climb at FL 80 initially Q28. How far has the aircraft arriving at Beacon B3, inside the airway, got to fly to reach beacon B1? 45 miles Q29. Can an aircraft join this airway at FL 65? No, base level is FL 75 Q30. On what bearing will the aircraft arriving at beacon B3 fly on in order to reach B2? 046 o Q31. KLM 23 has just taken off and hopes to join the airway at beacon B2 at FL 230 then turn left and fly along the airway to B3. Do you think the Centre Controller will give clearance for this? By instructing KLM 23 to join at FL220 Q32. How might the controller resolve this problem? No because AT48 is converging with him at the same level. 226 o Q33. What bearing will KLM 23 fly on after joining the airway at B2? Teacher Q&A (2) Q23. How far is TR 84 from the Airport? 15 Miles

34. Student Questions (1) Q1. What are the bearing numbers for the runway shown? Q2. What are the bearing numbers for this runway? Q3. What is the relationship between the bearings at each end of any runway? Q4. What is the missing runway number below? Q5. On what bearing is an aircraft flying when taking off on this runway Q6. What bearing is this aircraft flying on as it lands on this runway? Q7. Five minutes after landing another aircraft takes off from the other end of the runway. What are the numbers on that end runway? Q8. This aircraft will shortly be landing on a bearing of NORTH. What are the runway numbers in this case. Q9. What will the bearing be, after take-off, of an aircraft making a 45 o departure from runway 23 below? Q10. Generally speaking aircraft like to take-off into wind. Why do you think this is? Q11. Calculate the height of the downwind leg in yards. Q12. Calculate this height in metres. Q13. Calculate the width to length ratio of the runway. Q14. 1 mile = 1760 yards. Calculate the length of the runway in miles. Do not use a calculator and give your answer to the nearest half mile. Q15. Calculate the: (a) Perimeter of the runway (b) Area of the runway Q16. Air Traffic Controllers on duty at a small regional airport have information displayed on expected arrivals and departures over a 1 hour period as shown in the table below. What is the estimated time of arrival of CC 675 from Leeds? Q17. What fraction of the aircraft movements are departures. Q18. What fraction of the aircraft movements are arrivals. Give your answer as (a) A fraction (b) A percentage (c) A decimal Q19. What percentage of the arrivals require fuel. Student Questions (1)

35. Student Questions (2) Q20. What altitude will ATS 675 be climbing to in feet? Q21. What altitude will MON 54 be climbing to in feet? Q22. Which aircraft is 10 miles NW of the Airport? Q24. What bearing is AW 147 flying on? Q25. Which aircraft is climbing to FL 95? Q26. CE 345 has conflicting traffic, 10 miles at his 12 O’ clock position, height unknown. What avoiding action could the controller offer the pilot to keep the aircraft safe. Q27. LS 52 is transit traffic and will over-fly the airport at the indicated level. GBV 53 is about to take-off and fly due west climbing to FL 130. What might the Radar Controller ask the Visual Controller to instruct the pilot to do before take-off. Q28. How far has the aircraft arriving at Beacon B3, inside the airway, got to fly to reach beacon B1? Q29. Can an aircraft join this airway at FL 65? Q30. On what bearing will the aircraft arriving at beacon B3 fly on in order to reach B2? Q31. KLM 23 has just taken off and hopes to join the airway at beacon B2 at FL 230 then turn left and fly along the airway to B3. Do you think the Centre Controller will give clearance for this? Q32. How might the controller resolve this problem? Q33. What bearing will KLM 23 fly on after joining the airway at B2? Q23. How far is TR 84 from the Airport?

36. Worksheet 1

37. Worksheet 2 Call Sign InboundOutbound From/ToFuel Required ETAETD 1KL 3810:00Aberdeenyes 2ATS 67510:12Humberside 3LV 1210:15Leedsyes 4GBV 5310:20Norwich 5RAF 23410:23Luton 6MNE 4210:29Birminghamyes 7OBI 110:45Newcastle 8CC 67510:48Leeds 9VTF 8710:55Norwich 10LST 17811:00Norwich For use with Q 16 - 19 Call Sign Outbound ToAltitude Climbing  ETD 1ATS 67510:12HumbersideFL 85 2GBV 5310:20NorwichFL 130 3OBI 110:45NewcastleFL 200 4LST 17811:00NorwichFL 150 5KLM 2311:05AmsterdamFL 230 (Join Airway) 6MON 5411:15CyprusFL 350 For use with Q 20/21 Worksheet 2