Airworthiness Chapter 566 Appendix C - Part 2 Curriculum and Topic Guides Small and Large Aircraft Maintenance Training Standard - Canadian Aviation Regulations (CARs)

(amended 1999/12/01)

1.0 General

Identify:

1. The different classes of fires and suitable extinguishers.

Explain:

2. The legal and moral responsibilities of maintenance technicians and AMEs.

3. Human factors in maintenance.

Perform:

4. Tasks utilizing health and safety practices, including handling of chemicals, metals, pyrotechnics and hazardous materials, environmental considerations, workplace hazardous materials information system or equivalent.

5. Tasks extracting information from technical drawings including ATA system. 

2.0 Hand Tools/Precision Instruments

Perform:

1. Tasks utilizing the proper selection and use of hand and power tools.

3.0 Metallurgy

Identify:

1. The types of corrosion.

Explain:

2. The hardness testing process.

3. Relevant manufacturing treatment processes of aircraft metals.

4. The fundamentals of NDT processes including, visual inspection, liquid penetrant inspection, ultrasonic inspection, eddy current inspection, magnetic particle inspection, radiography etc.

5. The methods of corrosion treatment and prevention.

6. The inspection processes for welds.

7. The inspection process for bonds.

Perform:

8. Tasks identifying the types, properties and coding of aircraft metals.

9. Visual inspection and liquid penetrant inspection.

4.0 Aircraft Servicing

Explain:

1. Servicing of aircraft systems such as water, waste, oxygen, etc.

2. The classifications, functions principles and properties of lubricants including: engine oil, grease and hydraulic fluids.

3. Aircraft deicing procedures.

4. Operating procedures and safety precautions of ground support equipment required to service the aircraft.

5. Aircraft grooming procedures and precautions.

6. Aircraft storage procedures.

Perform:

7. A fuel contamination check.

8. Tire servicing and inflation.

9. Servicing of aircraft main batteries.

10. Servicing of lubrication, fuel, oil and hydraulic systems.

11. Standard ground handling practices.

12. Jacking of an aircraft.

5.0 Approved Parts

Identify:

1. Aircraft hardware using AN, MS, NAS parts systems.

Explain:

2. The application of metric and British Unified Systems to aircraft hardware.

3. The needs and rationale for aircraft specifications such as MIL, NAS.

4. The inventory control system including traceability, requisitioning, quarantine and bonded stores.

Perform:

5. Installation and securing of standard hardware and connectors.

6.0 Aerodynamics

6.1 Fixed Wing Aircraft

Explain:

1. The theory of flight, relative motion, dynamic stability, standard atmosphere, fluid dynamics, lift, drag, thrust and weight, forces and balance, stalling/landing speeds, speed of sound, aerodynamic loads, and high speed flight

2. The purpose of flight controls including primary, secondary, and auxiliary controls, lift and anti-lift devices.

6.2 Rotary Wing Aircraft

Explain:

1. Theory of flight applicable to rotary wing including:

6.3 Fixed Wing Controls and Rigging

Identify:

1. Types of flight controls and explain features and functions of flight control systems.

Explain:

2. Mechanical flight control system and components.

3. Servo powered flight control system and components.

4. Cables, fittings and repair of associated rigging hardware.

5. Incidence, symmetry checks and adjustments.

6. The purpose and principles of flight control artificial feel/feedback systems.

7. The systems which modify flight control travel due to altitude, velocity or other factors e.g. rudder travel limitation, aileron lockout, lift dump.

Perform:

8. Inspection of cable and control rod type flight control system.

9. Rigging of cable operated primary flight control system.

10. A cable repair.

6.4 Rotary Wing Controls and Rigging

Explain:

1. Elements of the drive train including:

2. The various fundamentals of flight control systems including:

3. The various fundamentals of flight control rigging including:

4. The fundamentals and effects of vibration.

5. Vibration types and causes including:

6. Vibration canceling devices including:

• dampers
• bifilar

7. Landing gear types and systems including:

8. Rotor tracking and balancing requirements, analysis and rectification.

9. Autorotational RPM adjustments.

10. Inspection requirements including:

11. Operational safety practices including approaching and exiting a running helicopter.

12. Ground crew responsibilities and precautions applicable to slinging external loads.

Perform:

13. Alignment and static balance procedures for a semi-rigid rotor head.

14. Tracking and dynamic balance of a main and tail rotor system using a simulator

15. The testing, troubleshooting, repair, adjustment, removal and replacement of dynamic components

7.0 Sheet Metal

Explain:

1. The difference between a structural and non-structural repair.

2. The application and installation/removal of special fasteners.

3. The requirements for scratch inspection.

4. The purpose and use of sealant.

Perform:

5. Installation, inspection and removal of solid rivets.

6. Installation, and removal of standard fasteners.

7. Sheet metal repairs including cutting, bending, forming and fabricating.

8.0 Aircraft Structures

Identify:

1. Structural members and stress involved in floats, hulls, skis, stabilizers, wings, engine mounts, cowlings and fuselages.

Explain:

2. Types of primary aircraft structures.

3. The fabric surfaces and wood components including inspection, materials, process, fabric repairs, wood types, uses, and repair.

9.0 Plastics and composites

Explain:

1. Reinforcement fibers, matrix materials, core materials, manufacturing techniques composite safety, methods of curing, pre-pregs, temperature and pressure applications.

2. Inspection, damage assessment and repair procedures.

Perform:

3. A repair using the following procedures:

• wet lay-up
• core repair.

10.0 Windows and lenses

Explain:

1. The construction of windows and lenses.

2. Inspection, repair, servicing and installation of windows and lenses.

3. Damage assessment of windows and lenses.

4. Handling and storage of windows and lenses.

11.0 Piston Engines

11.1 Basics

Explain:

1. The calculation of energy, work and horsepower.

2. The two stroke cycle and the Otto cycle.

3. Piston engine classification terminology (e.g. TSIO-520, R985).

11.2 Cooling and Lubrication of Engines

Explain:

1. The purpose and methods of engine cooling.

2. The functions, principles and properties of lubricating oil.

3. Lubrication systems including oil dilution and cold weather operations.

Perform:

4. The selection of the appropriate lubricants.

11.3 Component Parts of a Reciprocating Engine Assembly

Explain:

1. The purpose of parts including the following:

2. The procedure for lapping valves and seats, replacing bushings, removing nicks, burrs, scratches, scores, and replacing damaged studs.

Perform:

3. Disassembly, cleaning, inspection, measuring and reassembly of the engine.

11.4 Carburetion Principles

Describe:

1. Characteristics of fuel and fuel/air metering systems

2. Carburetion principles and components as they apply to float type and pressure injection carburetors, single and multi-point fuel injection systems.

3. Induction system principles and components as they apply to normally aspirated, supercharged and turbocharged engines.

4. The operation of turbocharger control systems.

11.5 Ignition Systems

Explain:

1. The principles of operation and identify the components of reciprocating engine ignition systems.

Perform:

2. The timing and installation of a magneto and ignition harness.

3. The inspection, servicing and testing of magneto ignition system components.

11.6 Installing, Testing, Troubleshooting Engines

Explain:

1. Run-in procedures including testing and troubleshooting.

2. The purpose and procedure for engine inhibiting.

Perform:

3. Engine removal and installation including installation of accessories and component systems.

4. Reciprocating engine run-up.

12.0 Turbine Engines

12.1 Basics

Explain:

1. Development, fundamentals and principles of operation of turbine engines.

2. Engine design and construction pertaining to:

3. Factors affecting thrust/torque.

4. The mathematics and physics relating to thrust production including the Brayton cycle and thrust calculations.

5. The purpose and advantages of modular construction.

6. Common designs of turbine engines including:

• torque producing engines
• turboshaft and turboprop
• thrust producing engines
• turbojet and turbofan

7. The principles of noise suppression techniques.

8. Turbine engine systems including fuel, lubrication, ignition, air, exhaust.

Define:

9. Common turbine engine terminology and acronyms

12.2 Fuel and Control

Explain:

1. Explain fuel systems including:

Perform:

2. Fuel nozzle inspection, servicing, testing and safety precautions.

12.3 Ignition

Explain:

1. Types and operation of turbine engine ignition systems and their components including:

• low tension (glow plugs)
• high tension (capacitive discharge)
• auto re-light

2. Turbine engine ignition system safety precautions.

Perform:

3. Ignition systems servicing and inspection procedures.

12.4 Starting

Explain:

1. Design and components of starting systems.

2. The operation of various turbine engine starters including air turbine starters, electrical starters, (motor and starter-generator).

3. Inspection and servicing procedures for starting systems.

4. The operation of an auto-start system.

Perform:

5. The inspection and servicing of an electrical turbine engine starter.

12.5 Engine Controls

Explain:

1. Rigging requirements for gas turbine controls and systems.

2. Adjustments of fuel controls including:

3. Mechanical, electronic interface, Full Authority Digital Engine Control (FADEC) systems.

12.6 Lubrication

Explain:

1. Types and requirements of turbine oil.

2. Engine lubrication system principles and component operation including:

3. Contamination monitoring system operation principles including:

• chip detectors
• filters
• spectrometric oil analysis program (SOAP)

12.7 Exhaust

Explain:

1. Types, operation and control of thrust reverse systems including hot and cold stream.

2. Principles of thrust vectoring systems.

3. Principles and engine trimming associated with exhaust ducts.

12.8 Air

Explain:

1. General air systems of turbine engines including the following:

12.9 Engine Indicating Systems

Explain:

1. Principles and operation of engine indicating systems including:

12.10 Gear Box

Explain:

1. Purpose, function and types of engine gear boxes including:

12.11 Engine Water Injection

Explain:

1. The purpose and operation of water methanol injection systems.

12.12 Inspection/Servicing

Explain:

1. Handling and safety precautions.

2. The purpose and procedures for trend monitoring and power checks.

3. Fundamentals of vibration analysis.

4. Turbine engine inspection procedures including:

• hot end inspection
• borescope inspection.

5. The engine start and shut down procedure.

6. Requirements and procedures for compressor wash.

7. Safety precautions and hazards while ground running including:

8. Engine installation and test procedures.

Perform:

9. Procedures for calculating engine cycle counts.

10. A hot section inspection.

11. A simulation of a power check including calculating engine performance from manufacturer’s performance charts and interpret data to determine faults such as:

12. Engine ground run (students must be involved in live engine operation).

13.0 Propellers and Systems

Explain:

1. Theory and design of aircraft propellers including:

• forces acting on a propeller
• lift and angle of attack
• propeller construction materials

2. Fixed pitch, controllable pitch, constant speed, feathering and reversing propellers.

3. Methods of controlling propeller pitch including:

4. Propeller indication including:

• speed sensing
• torque sensing
• blade angle indication

5. Propeller installation and maintenance including:

6. Propeller disassembly and reassembly including:

Perform:

7. Propeller installation, safe operation, inspection, adjustment and minor repair.

14.0 Hydraulic and Pneumatic Power

Explain:

1. Safety precautions, including high pressure bottles and accumulators.

2. Fluid dynamics, types of fluid and system components.

3. System design including multiple and integrated systems and system redundancy.

4. System maintenance.

Perform:

5. Operation, inspection and testing of a hydraulic system.

6. Servicing of a high pressure accumulator.

15.0 Pneumatics

Explain:

1. The differences between hydraulic and pneumatic systems.

2. The principles of operation, components, maintenance and servicing of a pneumatic system including:

• temperature regulation
• pressure control
• flow control
• sources and common applications

16.0 Aircraft Plumbing

Explain:

1. The standard fittings and hardware identification systems.

Perform:

2. Assembly, installation, inspection and testing of hose and rigid tube assemblies.

17.0 Landing Gear

Explain:

1. The various types and configurations of landing gear assemblies including shock absorbing and non-shock absorbing systems.

2. The purpose and operation of shimmy dampers.

3. The operation of components of landing gear retraction and anti-retraction systems.

4. The operation and components of hydraulic and mechanical, emergency extension systems.

5. Various brake types.

6. Anti-skid and skid warning systems.

7. Basic, boosted, power, automatic and emergency braking systems and components.

8. Brake indicating systems including break wear and temperature indication.

9. Mechanical and powered steering systems.

10. The purpose of air ground sensing systems.

Perform:

11. Disassembly, reassembly and servicing of an oleo.

12. Removal, disassembly, visual inspection, reassembly, servicing and installation, of wheels, tubes and tires.

13. A retractable landing gear inspection including a gear swing and functional check.

14. Basic brake system inspection and servicing.

15. Installation and rigging check of floats or skis.

18.0 Environmental Control Systems

Identify:

1. Air sources for cabin pressurization.

Explain:

2. Fundamentals of heating, cooling and ventilation systems and their components including:

3. Electrical/electronic equipment cooling systems.

4. Cabin pressure fundamentals and components including system safety precautions and functional tests.

5. The various oxygen system fundamentals and component operation including:

• solid state/chemical oxygen
• liquid oxygen
• gaseous oxygen

Perform:

6. The inspection and servicing of environmental control systems including:

• heating systems including exhaust type heaters and combustion heaters
• oxygen storage systems utilizing standard handling and safety procedures

19.0 Fuel

Explain:

1. Fuels - types, properties and additives.

2. Airframe fuel system configurations and component functions including:

Perform:

3. Fuel system maintenance and safety precautions

20.0 Ice and Rain Protection

Explain:

1. Causes and types of ice formation.

2. Types of ice detection systems.

3. Anti-ice and de-ice systems and principles of operation including:

4. Rain repellent systems.

Perform:

5. Operation, inspection and testing of an ice protection system.

21.0 Emergency Systems

Identify:

1. The types and operation of emergency lighting systems.

2. The types of elts including Underwater Locating Devices (ULDs).

Explain:

3. Requirements and procedures for inspecting, installing and testing of elts.

4. Flotation device types, inspection and servicing including personal flotation devices, and airframe flotation devices.

5. Emergency breathing apparatus.

21.1 Fire Protection

Describe:

1. Various types of aircraft fire detection systems e.g. spot detectors, continuous loop, infra-red and ultra-violet.

2. Various types of suppression and extinguishing systems and safety precautions including aircraft installed and portable.

Perform:

3. Fire detection system inspection and operational test.

22.0 Electricity and Electrical/Electronic Systems

22.1 Basic Electricity DC

Explain:

1. Electron theory and electrostatics.

2. Magnetism and electromagnetism.

3. Electromagnetic induction.

4. Units of electrical measurement:

• voltage
• current
• resistance

5. Sources of electrical energy.

6. Characteristics of series, parallel, and series/parallel circuits.

7. Laws and theorems utilized in dc circuit analysis.

8. Circuit control devices including, but not limited to:

9. DC motors and generator principles

10. Electron theory and electrostatics.

Perform:

11. Circuit calculation using laws and theorems associated with DC circuit analysis.

12. Tasks utilizing a multimeter to measure voltage, resistance and current in a DC circuit.

13. Calculations to substantiate the theories of Ohm's Law and Kirchhoff's Law.

14. Measurement of different battery types under load and no-load conditions.

15 Construction of an electromagnet.

16. Construction of electrical circuits from components that are the same as those previously solved mathematically.

Test, Troubleshoot, Repair, Adjust, Remove and Replace:

17. DC generator, an aircraft DC motor, an aircraft alternator.

18. Test diodes and transistors for serviceability.

19. Switches, relays, circuit breakers, and fuses.

22.2 Basic Electricity - AC

Identify:

1. a wiring diagram for a simple alternator circuit, then accomplish the wiring of the same circuit.

Describe:

2. AC current.

3. Inductive pickups.

4. The effects of capacitors in electrical circuits.

5. The use for capacitors.

6. Differences between AC and dc motors.

7. The use of AC alternators in aircraft.

8. Generator Control Units.

9. Single-phase ac actuator motors.

10. Three-phase AC motors.

11. The use of the common measuring devices.

Explain:

12. Principles of ac theory

13. Rms and peak values

14. Frequency, period, phase

15. Use of ac measuring devices, including, but not limited to, multimeters and oscilloscopes

16. Polyphase ac circuits

17. Aircraft application of ac

18. Inductance coils, inductors and inductance in ac circuits

19. Transformers

20. Capacitors and capacitance in ac circuits

21. Reactance and impedance

22. Resonant circuits

23. Phase angle, and power factor calculations

24. Frequency and phase.

25. Ac generation theory, including construction and maintenance of alternators.

26. The use of the multimeters, oscilloscope and other AC measuring devices.

27. Impedance.

28. Transformers.

29. The principles of AC generation.

30. Aircraft alternators.

31. Voltage regulation.

32. Inverters.

33. Variable-speed, constant-frequency power systems.

34. AC motors.

35. Improvement of starting qualities.

36. Repulsion motors.

37. Synchronous motors.

38. Motor losses.

39. Power conversion methods.

40. Using diodes to convert ac to dc.

Perform:

41. Circuit calculations using laws and theorems associated with ac circuit analysis.

42. Tasks demonstrating the proper use of test equipment to measure voltage, current, reactance and frequency in ac circuits.

43. Serviceability test of a diode and a transistor.

44. Evaluation of lab equipment.

45. Ac voltage and capacitance measurement.

46. A transformer characteristics experiment using a semi-conductor.

47. Applications using an oscilloscope and other common measuring devices.

48. Inspection and servicing of motors.

22.3 Electrical Systems

Identify:

1. Electrical diagram symbols for control and protection devices.

2. Components which make up aircraft electrical motor circuits.

Describe:

3. Various types of wiring diagrams, drawings and schematic symbology.

4. Basic circuit components.

5. Maintenance of electrical wiring systems.

6. Types of electrical control devices.

7. Types of electrical circuit protection devices.

8. Electrical supply and generation components.

9. Maintenance of electrical power supply and generation systems.

10. Aircraft indication, monitoring and lighting circuits.

11. Various troubleshooting techniques.

12. Electrical motor theory.

13. Electrical components of a landing gear system.

14. Servicing and inspection of electrical landing gear system.

15. Safety procedures for maintenance of electrical systems.

Explain:

16. Construction, maintenance, and operation of aircraft batteries (all types).

17. Construction, maintenance, and operation of aircraft generators (dc).

18. Construction, maintenance, and operation of aircraft generators (ac).

19. Construction, maintenance, and operation of aircraft alternators.

20. Construction, maintenance, and operation of trus.

21. Construction, maintenance, and operation of generator control units (gcus).

22. Construction, maintenance, and operation of constant speed drives and integrated drive generators (idg).

23. Current transformers.

24. Construction, maintenance, and operation of aircraft inverters (rotary and static).

25. Construction, maintenance, and operation of aircraft motors (ac and dc).

26. Construction, maintenance, and operation of aircraft synchros, including transmitters (receivers and resolvers).

27. Proper use of test equipment and support curriculum.

28. Wiring practices, including wire and coaxial cable specs (mil and faa).

29. Bonding emi/rfi suppression techniques.

30. Light aircraft electrical power distribution systems (single and multi engine).

31. Large multi engine aircraft electrical power distribution systems.

Perform:

32. Tasks using wiring diagram(s), and appropriate test equipment to troubleshoot an electrical power distribution system fault.

33. The following tasks, employing acceptable methods, techniques and practices:

34. Reading of electrical supply power generation systems wiring diagrams.

35. Servicing and charging of a lead acid battery in a battery shop.

36. Servicing and deep cycling of a nickel-cadmium battery in a battery shop.

37. The installation and removal of a nickel-cadmium battery of an aircraft.

38. Installation and removal of a lead acid battery on an aircraft.

39. Construction of a basic wiring harness using acceptable methods, techniques and practices.

40. Troubleshooting of various control and protection devices as required by schematic diagram of a simple aircraft circuit.

41. Servicing and testing of an alternator and generator.

42. Connection and testing of components to simulate an aircraft generation system.

43. Troubleshooting of a given defect in an aircraft electrical system, employing the circuit diagram and appropriate test equipment.

44. Inspection and testing of an aircraft motor system components.

45. Testing, troubleshooting, repair, adjustment, removal and replacement of a motor, generator or alternator.

22.4 Aircraft Instrumentation

Identify:

1. Both mechanically operated and electrical/electronic operated.

2. Instruments according to function.

Describe:

3. The vertical, and instantaneous-vertical speed indicators.

4. A vacuum pump system.

5. Various display types.

6. Various methods of display.

7. Electrical flight instruments.

8. Engine electrical indicating instruments.

9. Engine instrument installation and marking.

10. Testing of engine electrical indicating instruments.

11. Systems that employ electrical indicating instruments.

12. Maintenance of systems electrical indicating instruments.

13. The types of instruments using direct drive linkages.

14. Installation of direct linkage and drive mechanisms.

15. Servicing of pitot/static instruments.

Explain:

16. The reasons for using instrumentation.

17. The principles of absolute pressure measurement.

18. The principles of gauge pressure measurement.

19. The principles of differential pressure measurement.

20. Altimeters.

21. Airspeed indicators.

22. Air data computers (ADC).

23. Electrically driven instruments.

24. Temperature measuring instruments.

25. Gyroscopic principles.

26. The sources of power of gyroscopes.

27. Gyro attitude instruments.

28. Rate gyro instruments.

29. The principles of navigation.

30. The procedures for correcting errors (compass swing).

31. The procedure for setting up test equipment.

Perform:

32. A functional check of a pitot/static system.

33. Draining of a pitot/static system.

34. Inspections of instruments for correct installation and markings.

35. A functional check on a liquid pressure instrument system.

36. A check of aircraft instruments for correct function.

37. A functional test of an exhaust gas temperature system employing suitable testing.

38. Packaging of an instrument for shipping.

39. A functional check of a fuel quantity indication system.

40. A simulated compass swing.

22.5 Avionics

Identify:

1. Aircraft radio antennas.

Describe:

2. Audio components.

3. Transmission lines.

Explain:

4. Radio theory.

5. Radio transmitters.

6. Radio receivers.

7. Superheterodyne operation.

8. Modulation (am/fm).

9. Digital communications.

10. Hf communication systems.

11. Vhf communication systems.

12. Selcal.

13. Interphone systems (flight / service).

14. Audio integration.

15. Passenger entertainment systems (multiplex/audio/video).

16. Elts.

17. Satellite communication systems.

18. Navigation principles.

19. Flight Management Systems.

20. Inertial Navigation Systems.

21. Inertial Reference Systems.

22. Radio Navigation Systems, including, but not limited to:

23. Video displays, EFIS, EICAS, Flight Data Recorders, Cockpit Voice Recorders.

24. Frequency spectrum.

25. IFR versus VFR.

26. Maximum power transfer theorem.

27. Functions of audio control panels.

28. Functions of communication controls.

29. Antenna fundamentals.

30. HUMS (health and usage monitoring system).

31. Avionics installation practices.

32. Avionics maintenance inspections and system troubleshooting.

33. Interconnections of avionics systems.

Perform:

34. Operational check and inspection of a COM T/R system and one NAV system to the LRU (Line Replaceable Unit) level on an avionics installation.

35 Inspection of an antenna system.

36. Removal and replacement of an avionics LRU or component.

37. Tasks utilizing a multimeter or equivalent to troubleshoot an avionics wiring interconnection fault.

22.6 Data Bus and Logic

Describe:

1. Number systems.

2. Use of electrical circuit representations to explain logic gates.

3. Boolean equations.

4. The display of digital data.

5. Characteristics of integrated circuits.

6. Some applications of integrated circuits.

7. Use of electrical circuit representations to explain logic gates.

8. Functions of computer operations.

9. Aircraft digital systems.

10. Air Data Computer Systems.

11. Flight Management Systems.

12. Thrust Management Systems.

13. Systems testing and troubleshooting.

14. Safety procedures.

Explain:

15. The difference between analog and digital systems.

16. Logic gates using truth tables.

Perform:

17. Determination of correct digital output, given a logic diagram with digital inputs.

18. Conversion between various numbering systems.

22.7 Auto Flight Systems

Explain:

1. Introduction to and system overview of:

Perform:

2. Inspection and operation check of an auto-pilot system.

23.0 Maintenance Procedures

Explain:

1. Inspection and maintenance requirements for private and commercial aircraft as outlined in the Canadian Aviation Regulations.

2. Fundamentals and types of aircraft inspections including:

• periodic, annual, progressive and approved maintenance schedules
• abnormal occurrence (hard landing, lightning strike, etc.).
• special (Airworthiness Directive or Service Bulletin).

3. Weight and balance procedures and requirements including:

4. Differences between fixed and rotary wing aircraft weight and balance procedures, e.g. Lateral center of gravity.

5. Fundamentals of quality assurance.

Perform:

6. A weight and balance procedure on an aircraft, including associated documentation.

7. Completion of documentation for maintenance records including:

8. Computerized information input and retrieval.

9. A typical rotorcraft and fixed wing maintenance schedule (e.g. 100 hour or annual inspection)

10. Tasks utilizing Minimum Equipment Lists, Configuration Deviation Lists and Built-In Test Equipment (Bite) programs

24.0 Imperial and Related Units of Measure

Perform:

1. Calculations including conversions using: