Lecture Notes: Propulsive Force and Aircraft Performance Calculations

Introduction

• Focus on expressing thrust as a function of airspeed to simplify equations of motion.
• Two propulsion systems discussed:
  1. Pure Jet Engine
  2. Variable Pitch Propellers

Pure Jet Engine

• Operating Principle:
  • Air intake: compressed air flows into the engine.
  • Fuel injection and combustion heat the air.
  • Expansion occurs due to high temperature and pressure.
  • Drives a turbine which powers the compressor.
  • After the turbine, air expands through the nozzle to jet velocity.
  • Jet velocity is mainly dependent on fuel energy and internal pressure.
• Thrust Variation with Airspeed:
  • Thrust equation shows mass flow increases with airspeed.
  • Jet velocity remains relatively constant, depending on compression ratio and throttle setting.
  • Thrust is more or less constant as a function of airspeed under constant throttle setting and altitude.
  • Graphs show thrust variation with flight speed for different throttle settings.
  • Pilot can adjust thrust by altering fuel flow via throttle.
• Power Available:
  • Power is thrust multiplied by airspeed, forming a straight line from the origin.

Variable Pitch Propellers

• Operating Principle:
  • Propeller blade as rotating wing creating lift and drag.
  • Lift and drag contribute to thrust and create torque on the shaft.
  • Blade velocity depends on rotational and forward speed.
  • Local angle of attack depends on these velocities and blade pitch.
• Thrust and Efficiency:
  • Increase in flight speed reduces angle of attack, affecting lift and drag.
  • Modern propellers have constant rotational speed, variable pitch.
  • Propulsive efficiency varies with airspeed; optimal pitch settings maximize efficiency.
• Power and Thrust Variation:
  • Constant shaft power implies constant available power when efficiency is optimized.
  • Thrust theoretically decreases as 1/x with increasing airspeed.
  • At zero velocity, thrust theoretically infinite, but practically not the case.
  • In the relevant flight speed range, power available is constant.

Conclusions

• Simplified thrust and power curves facilitate analytical performance calculations.
• For complex propulsion systems like turbofans (e.g., on commercial aircraft), calculations may require graphical or numerical methods if manufacturer data is provided.
• These simplifications help in analytically calculating aircraft performance, as covered in future lectures.