Exercise 600.5 — Aircraft range with alternative fuels¶

Breguet analysis¶

🧪 Scripts
breguet_baseline_designpoint.py breguet_altern_fuel_designpoint.py

This chapter explores how fuel choice affects aircraft range and energy performance using Breguet’s range equation as a low-order system model.

We focus on liquid hydrogen (LH₂) and conventional kerosene, following the methodology of:

S. S. Jagtap et al., Energy performance evaluation of alternative energy vectors for subsonic long-range tube-wing aircraft,
Transportation Research Part D, 2023.

This exercise implements the models described in Section 6.5.2 of the course notes
(Retrofitting an existing aircraft).

Students are expected to read the reference section carefully before working on this exercise. Equations and assumptions are not re-derived here.

How to run¶

From the script folder (chapters/600_hydrogen_combustion/scripts):

python breguet_baseline_designpoint.py
python breguet_altern_fuel_designpoint.py

Physical problem (context)¶

Rather than treating hydrogen as a “drop-in” fuel, this approach explicitly accounts for:

gravimetric and volumetric energy density,
aircraft weight breakdown (OEW, fuel, payload),
aerodynamic penalties from increased fuselage length,
system-level consequences on range and energy consumption.

The accompanying Python scripts reproduce the logic of the paper, not just its final numbers.

Learning objectives¶

Apply the Breguet range equation consistently
Compare aircraft range for kerosene vs hydrogen
Understand the role of fuel specific energy and storage penalties

Guided questions¶

1) Why Breguet’s equation still matters¶

Breguet’s range equation provides a first-order estimate of aircraft range:

\[ R = \frac{h}{g} \, \eta_0 \, \frac{L}{D} \, \ln\!\left(\frac{W_\text{initial}}{W_\text{final}}\right) \]

Despite its simplicity, it remains powerful because it exposes where fuel choice enters the system:

\( h \): fuel lower heating value
\( \eta_0 \): overall propulsion efficiency
\( L/D \): aerodynamic efficiency
\( W_\text{initial}, W_\text{final} \): aircraft mass evolution during cruise

Hydrogen fundamentally modifies all four terms, not just \( h \).

2) What the script actually computes¶

The Breguet scripts in this module implement the design-point sizing loop used in the paper.

At a high level, the algorithm:

Fixes:
- payload mass
- target range
- cruise conditions
- baseline aircraft geometry
Iterates on total fuel mass until:
- the target range is achieved,
- the aircraft stays below the MTOW constraint.
Updates, at each iteration:
- fuel volume and required fuselage extension,
- operating empty weight (OEW),
- lift-to-drag ratio penalties,
- initial and final cruise weights.

This is not a fuel substitution problem — it is a vehicle resizing problem.

3) Why hydrogen changes the aircraft, not just the fuel tank¶

Liquid hydrogen has:

very high gravimetric energy density (~120 MJ/kg),
very poor volumetric energy density.

As a consequence:

Fuel mass decreases dramatically,
Fuel volume increases dramatically,
Fuselage length must increase to house cryogenic tanks,
Wetted area, drag, and OEW increase,
\( L/D \) decreases.

The script explicitly models these effects through:

additional fuselage length,
OEW scaling laws,
aerodynamic penalties.

This is the central lesson:
hydrogen improves one term in Breguet’s equation while degrading others.

4) Energy efficiency vs range: a non-intuitive result¶

One of the key results reproduced by the script is that:

LH₂ aircraft have higher specific energy consumption than kerosene aircraft,
but their SEC becomes less sensitive to range beyond ~10,000 km.

This happens because:

LH₂ aircraft have a high OEW/GTOW ratio,
energy consumption is dominated by carrying the aircraft itself,
marginal range extension becomes relatively “cheap”.

This contradicts the naive intuition that lighter fuel always means better efficiency.

5) What this model does not include¶

This is intentionally a low-order system model.

It does not include:

detailed structural sizing,
detailed drag build-up or wave drag,
engine cycle redesign,
mission-level operational strategies,
non-CO₂ climate effects (e.g. contrails).

Its strength lies in clarity, not completeness.

6) What you should learn from this exercise¶

By working with this script, you should be able to:

explain why hydrogen aircraft require vehicle-level redesign,
trace fuel properties through mass → aerodynamics → range,
critically interpret published performance claims,
distinguish fuel efficiency from system efficiency,
understand why hydrogen is not a silver bullet, even at long range.

Scope and reference aircraft¶

All results in this chapter are obtained using two reference tube-and-wing aircraft:

an A320-class aircraft representing short-range missions,
an A350-class aircraft representing long-range missions.

Hydrogen is introduced by modifying fuel properties, tank volume, and associated mass and aerodynamic penalties, without changing the underlying aircraft architecture.

Therefore, conclusions drawn here apply to hydrogen integration into conventional aircraft layouts and should not be extrapolated to radically different configurations.

Student tasks¶

Task 1 — Baseline reproduction (paper literacy)¶

Run the script for:

kerosene (baseline),
liquid hydrogen.

Report:

achieved range,
total fuel mass,
operating empty weight (OEW),
lift-to-drag ratio,
specific energy consumption (SEC).

Question:
Which Breguet term improves with hydrogen, and which ones degrade?

Task 2 — Payload sensitivity¶

Reduce the payload in steps (e.g. −10 %, −20 %, −30 %).

For each case:

recompute the maximum achievable range,
plot range vs payload for kerosene and LH₂.

Guided questions:

Which fuel benefits more from payload reduction?
Why does LH₂ respond differently than kerosene?

Task 3 — Range sensitivity and asymptotic behavior¶

Sweep target range from short-haul to ultra-long-haul.

Plot:

SEC vs range for both fuels.

Interpretation:

Why does LH₂ SEC flatten at long range?
What dominates the energy balance in that regime?

Task 4 — Engineering interpretation¶

In ~10 lines, answer:

Why does LH₂ reduce GTOW but increase SEC?
Why is volumetric energy density a design problem, not a fuel problem?
Under what conditions (if any) could LH₂ become competitive?

Task 5 — Critical reflection¶

The paper concludes that LH₂ is viable but not energetically superior.

Write a short paragraph addressing:

What assumptions drive this conclusion?
Which assumptions might change with future aircraft architectures?
Which ones are fundamentally hard to escape?