Lecture 1 - Equation of State & Ballooning
1. Course introduction
Goals of AE1110:
o Historical context & lessons from aerospace.
o Basic principles, technologies, systems.
o Understanding aircraft & spacecraft design.
o Broad overview of aeronautics and space engineering
2. Aviation: orders of magnitude
~15,000 aircraft airborne at any moment.
~129,000 commercial flights/day (2023).
~12M passengers/day, 10M+ direct aviation jobs, 65M jobs
dependent on aviation.
Global turnover ~€2.7T.
~35% of value of manufactured goods transported by air
Growth ≠ constant → “Rule of 72”: doubling time = 72 ÷ % growth
3. Principles of flight
Three ways to counter gravity:
1. Push air downwards (lift, wings, rotors).
2. Push mass downwards (rockets, propellant).
3. Float (lighter-than-air gases, aerostatics: He, H₂, hot air)
4. Ballooning (aerostatics)
Lift principle: buoyancy = displaced air mass – gas mass.
Types: hot air (heated, less dense air), helium, hydrogen.
Limits: max altitude when expansion = equilibrium (or balloon
bursts).
Why not common today? Slow, draggy, unsafe (H₂), poor control.
5. History of balloons & airships
200–300 AD: Kongming lanterns in China, used for military
communications.
1783: Montgolfier brothers → first manned hot air balloon flight.
, 19th century: balloons dominated long before airplanes.
1903: Santos Dumont’s personal airship (No. 9).
1937: Hindenburg disaster → damaged airship reputation
6. Aviation & environment
Measured atmospheric CO₂ rise: ~16.7 Gt/year (1995–2019).
Fossil fuels (oil, gas, coal): ~24–33 Gt/year emissions.
Conclusion: human activity is responsible for CO₂ rise
7. Key equations to know
Buoyant lift: L=(ρair−ρgas) VgL = (ρ_{air} - ρ_{gas}) \, V gL=(ρair
−ρgas)Vg.
Rule of 72: Doubling time ≈ 72 ÷ growth %.
Gas law (recap for later): p=ρRT
Aerostatic Hot air: L = ρVg*(dT/(T+dt))
8. Likely exam focus (Lectures 1–2)
Recall three ways of countering gravity.
Explain balloon lift mechanism.
Compare helium vs hot air vs hydrogen.
Recall ballooning history milestones.
Explain why CO₂ increase is human-driven (basic calculations).
, Handout 1: Balloons (Lecture 1 Deep Dive)
1. History of ballooning
300 AD: Chinese Kongming lanterns (communication).
1782–1783: Montgolfier brothers, first hot-air balloons.
o First flight with animals (sheep, rooster, duck) to test
survivability.
o Nov 21, 1783: Pilâtre de Rozier & Marquis d’Arlandes → first
manned free flight.
o Rozier later died trying to cross the Channel (1785).
Balloons with rudders (Guyton de Morveau) failed → no directional
control.
Names: Montgolfière (hot air), Rozière (hybrid gas + hot air).
2. Equation of State (gas law reformulation)
Ideal gas law: pV=nRT
Reformulated to use density:
o R=287 J/kgK for air.
Advantage: usable for atmosphere, balloons, flows
3. Aerostatics & Lift
Archimedes principle: buoyant force = displaced air’s weight.
4. Hot-Air Balloons
Interior hotter by ΔT than outside.
Lift equation:
Practical limit: air inside cannot exceed ~120 °C.
1. Course introduction
Goals of AE1110:
o Historical context & lessons from aerospace.
o Basic principles, technologies, systems.
o Understanding aircraft & spacecraft design.
o Broad overview of aeronautics and space engineering
2. Aviation: orders of magnitude
~15,000 aircraft airborne at any moment.
~129,000 commercial flights/day (2023).
~12M passengers/day, 10M+ direct aviation jobs, 65M jobs
dependent on aviation.
Global turnover ~€2.7T.
~35% of value of manufactured goods transported by air
Growth ≠ constant → “Rule of 72”: doubling time = 72 ÷ % growth
3. Principles of flight
Three ways to counter gravity:
1. Push air downwards (lift, wings, rotors).
2. Push mass downwards (rockets, propellant).
3. Float (lighter-than-air gases, aerostatics: He, H₂, hot air)
4. Ballooning (aerostatics)
Lift principle: buoyancy = displaced air mass – gas mass.
Types: hot air (heated, less dense air), helium, hydrogen.
Limits: max altitude when expansion = equilibrium (or balloon
bursts).
Why not common today? Slow, draggy, unsafe (H₂), poor control.
5. History of balloons & airships
200–300 AD: Kongming lanterns in China, used for military
communications.
1783: Montgolfier brothers → first manned hot air balloon flight.
, 19th century: balloons dominated long before airplanes.
1903: Santos Dumont’s personal airship (No. 9).
1937: Hindenburg disaster → damaged airship reputation
6. Aviation & environment
Measured atmospheric CO₂ rise: ~16.7 Gt/year (1995–2019).
Fossil fuels (oil, gas, coal): ~24–33 Gt/year emissions.
Conclusion: human activity is responsible for CO₂ rise
7. Key equations to know
Buoyant lift: L=(ρair−ρgas) VgL = (ρ_{air} - ρ_{gas}) \, V gL=(ρair
−ρgas)Vg.
Rule of 72: Doubling time ≈ 72 ÷ growth %.
Gas law (recap for later): p=ρRT
Aerostatic Hot air: L = ρVg*(dT/(T+dt))
8. Likely exam focus (Lectures 1–2)
Recall three ways of countering gravity.
Explain balloon lift mechanism.
Compare helium vs hot air vs hydrogen.
Recall ballooning history milestones.
Explain why CO₂ increase is human-driven (basic calculations).
, Handout 1: Balloons (Lecture 1 Deep Dive)
1. History of ballooning
300 AD: Chinese Kongming lanterns (communication).
1782–1783: Montgolfier brothers, first hot-air balloons.
o First flight with animals (sheep, rooster, duck) to test
survivability.
o Nov 21, 1783: Pilâtre de Rozier & Marquis d’Arlandes → first
manned free flight.
o Rozier later died trying to cross the Channel (1785).
Balloons with rudders (Guyton de Morveau) failed → no directional
control.
Names: Montgolfière (hot air), Rozière (hybrid gas + hot air).
2. Equation of State (gas law reformulation)
Ideal gas law: pV=nRT
Reformulated to use density:
o R=287 J/kgK for air.
Advantage: usable for atmosphere, balloons, flows
3. Aerostatics & Lift
Archimedes principle: buoyant force = displaced air’s weight.
4. Hot-Air Balloons
Interior hotter by ΔT than outside.
Lift equation:
Practical limit: air inside cannot exceed ~120 °C.
