Geared Fans, Open Rotors, Hydrogen and Electric Flight

Why gear the fan, the open rotor, hydrogen and its tank, batteries and the Breguet equation, sustainable fuels — and where the course leaves you

Two bets, one deadline

In September 2020 Airbus unveiled three liquid-hydrogen "ZEROe" concept aircraft that it said could enter service by 2035 (Airbus). In June 2021 CFM International announced RISE, an open-fan engine meant to succeed the LEAP in the mid-2030s, aiming at 20 % less fuel burn and carbon dioxide (the RISE). One bet changes the fuel; the other changes the engine. Both are answers to the same arithmetic — the carbon dioxide in every kilogram of kerosene — and both run into physics this course has already met: the Froude efficiency of Lesson 1-2, the turbine stages of Unit 6, the hydrogen tank of Lesson 7-4.

Why gear the fan. A big fan must turn slowly, its tips held near the speed of sound; the low-pressure turbine that drives it wants to spin fast, because each stage's work grows as the square of its blade speed. Direct drive forces both to one speed, and the turbine pays in stages. The Pratt & Whitney PW1000G puts a 3:1 gearbox between them, so that the fan turns at 4,000–5,000 rpm and the low-pressure spool at 12,000–15,000 rpm; it entered airline service when Airbus delivered an A320neo to Lufthansa on 20 January 2016 (the PW1000G).

n_{stages} = \frac{\Delta h_{LPT}}{\psi\,U^2}, \qquad U = \omega_{LPT}\,r_m = G\,\omega_{fan}\,r_m

Low-pressure turbine stages for work Δh at stage loading ψ and mean blade speed U; a gear ratio G multiplies U and divides the stage count by G².

📐Direct drive against geared

A fan of bypass ratio 12 and pressure ratio 1.4 needs 417 kJ per kg of core gas from its turbine (Lab 1):

Direct drive at the fan's 4172 rpm: mean blade speed 197 m/s, 5 stages even heavily loaded.
Geared 3.06:1: the turbine turns at 12,777 rpm, 375 m/s, and 3 lightly loaded stages suffice.

The LEAP, direct drive, has a 7-stage low-pressure turbine; the PW1000G has 3 (the LEAP). The price is a gearbox transmitting megawatts, whose losses become heat to remove.

💡Open rotors

Remove the fan case and the fan can grow far larger, raising the bypass ratio and the Froude efficiency of Lesson 1-2 — at the price of noise and of blades with no case around them. The contra-rotating open rotors of the 1980s never reached production. RISE has a single rotating stage in front, followed by a row of variable-pitch stator vanes (the RISE).

💡Hydrogen and its tank

Liquid hydrogen carries 120 MJ/kg against kerosene's 43, and burns to water. But it boils at 20.28 K, and its density is only 70.85 kg/m³ (liquid hydrogen): 8.5 MJ per litre against 34.4 (Lesson 7-4). The tanks must be insulated, nearly spherical or cylindrical to resist pressure with little surface, and they cannot live in a thin wing. They go in the fuselage, and the insulation trades its own mass against the hydrogen that boils away.

📐Sizing a hydrogen tank

The 860 GJ mission of Lesson 7-4 — 7.17 t of hydrogen — in a 3.6 m tank inside a 4 m fuselage (Lab 3):

108 m³ with ullage: a tank 11.8 m long, 134 m² of surface — the length of 15 rows of seats.
The best foam thickness is 99 mm: 466 kg of foam, and 466 kg of hydrogen boiled off over an 8-hour flight (6.5 % of the fuel). At 30 mm the penalty would be 1685 kg.

R_{fuel} = \frac{\eta_0\,h}{g}\,\frac{L}{D}\,\ln\frac{m_i}{m_f}, \qquad R_{battery} = \frac{e_b\,\eta}{g}\,\frac{L}{D}\,\frac{m_b}{m}

Breguet range for a fuel aircraft, which gets lighter as it burns, and for a battery aircraft, which does not; e_b is the battery's specific energy, m_b/m its share of the take-off mass.

Derivation

The electric Breguet equation

In steady cruise the power needed is drag times speed,

P = D\,V = \dfrac{m g}{L/D}\,V

. A battery delivers it from stored energy

E = e_b\,m_b

with efficiency

\eta

, so it lasts

t = \eta E/P

and the range is

R = V t = \frac{e_b\,\eta}{g}\,\frac{L}{D}\,\frac{m_b}{m}.

The mass

m

never changes: no logarithm. A fuel aircraft burns

dm = -P\,dt/(\eta_0 h)

while

m

falls, and integrating gives the logarithm of Lesson 1-3.

📐Kerosene against batteries

The same aircraft,

L/D = 16

(Lab 2):

Kerosene, overall efficiency 0.38, fuel a quarter of the take-off mass: 7,667 km.
A battery pack of 200 Wh/kg, 80 % battery-to-thrust efficiency, 30 % of the mass: 282 km. Lithium-ion cells today store 160–300 Wh/kg (lithium-ion battery); a kilogram of kerosene, about 11,900 Wh.
For 1,000 km the pack would need 710 Wh/kg.

💡Sustainable aviation fuel

The nearest-term lever needs no new engine at all. Sustainable aviation fuels are kerosene made from waste oils, biomass, or hydrogen and captured carbon dioxide; they burn in today's engines with the same energy per kilogram and per litre (Lesson 7-4). Their benefit lies in the carbon they did not take from the ground — and their limits are in how much can be made, and at what cost.

We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard

– John F. Kennedy, address at Rice University, Houston, 12 September 1962 (Wikiquote)

💡Where the course leaves you

You can now follow an engine from its thrust and efficiency (Unit 1) through compressible flow (Unit 2), ideal and real cycles (Units 3–4), inlets and nozzles (Unit 5), turbomachinery (Unit 6) and combustion (Unit 7), to matching, off-design and control (Unit 8) and the structure that holds it together (Unit 9). The capstone project puts all of it into one engine of your own.

📚Further reading

H. I. H. Saravanamuttoo et al., Gas Turbine Theory (7th ed., Pearson, 2017).
Rolls-Royce, The Jet Engine (5th ed., Rolls-Royce plc, 1986).
The PW1000G, the RISE and liquid hydrogen on Wikipedia.

↓But there is a problem

This course began with fire and wind — Hero's spinning sphere, the windmills of Sistan, a turbine on paper in sixteenth-century Istanbul — and ends with gearboxes, open fans and tanks of liquid hydrogen. The physics in between has not changed. The next engine is yours to design.