Propulsion overview

The Tern's powertrain is the riskiest part of the program. Two 450 kW electric motors turn the propellers. A 1100 kg battery pack supplies peak power for take-off and climb. A small turboshaft engine, a gas turbine that drives a shaft rather than producing jet thrust, turns a generator that recharges the battery and powers the motors in cruise. Arjun spends a week with the powertrain team and comes away with a lot of questions. Why propellers rather than a jet? Why not batteries alone? Why does a turbine burn more fuel per kilowatt at part power? This lesson introduces the main ways aircraft produce thrust and the numbers that let engineers compare them.

How thrust is produced

Every air-breathing propulsor works the same way at heart: it takes in air, accelerates it backward, and by Newton's third law the air pushes the aircraft forward. If a mass flow \(\dot{m}\) of air enters at the flight speed \(V_0\) and leaves at a higher speed \(V_e\), the thrust is the rate of change of the air's momentum. A jet engine also adds fuel, and a nozzle may leave the exhaust at a pressure above ambient, adding a small pressure-thrust term, but the momentum term dominates.

The same thrust can come from accelerating a small mass of air a lot or a large mass a little. These are not equally efficient. The useful power delivered to the aircraft is thrust times flight speed, \(TV_0\). The power put into the air is the increase in its kinetic energy, \(\tfrac{1}{2}\dot{m}(V_e^2 - V_0^2)\). Their ratio is the propulsive efficiency, often called the Froude efficiency.

Propulsive efficiency approaches 1 as the exhaust speed approaches the flight speed. A propeller, which accelerates a very large mass of air by a small amount, can reach propulsive efficiencies above 0.85. A turbojet, which accelerates a small mass of air to a very high speed, is much less efficient at low flight speeds. The program for this lesson shows three ways to make the same 2 kN of thrust at the Tern's cruise speed and how much the efficiency changes.

# Thrust, propulsive efficiency and fuel or energy use for three propulsors
import math
V0 = 105.6                     # flight speed, m/s

def jet(mdot, Ve):
    T = mdot * (Ve - V0)                      # momentum thrust (pressure thrust ignored)
    eta_p = 2 / (1 + Ve / V0)                 # Froude propulsive efficiency
    return T, eta_p

print("Same thrust from a small fast jet or a large slow one:")
for mdot, Ve in ((20.0, 205.6), (80.0, 130.6), (400.0, 110.6)):
    T, eta = jet(mdot, Ve)
    print(f"  mass flow {mdot:6.1f} kg/s, exit {Ve:6.1f} m/s -> thrust {T/1000:5.2f} kN, propulsive efficiency {eta:.2f}")

# Turboprop shaft power needed for 2.0 kN of thrust at cruise
T_req, eta_prop = 2000.0, 0.82
P_shaft = T_req * V0 / eta_prop
sfc = 0.30          # kg of fuel per kWh of shaft power (typical small turboprop, illustrative)
print(f"\nShaft power for {T_req/1000:.1f} kN at {V0*3.6:.0f} km/h: {P_shaft/1000:.0f} kW ({P_shaft/745.7:.0f} hp)")
print(f"Fuel flow: {sfc*P_shaft/1000:.0f} kg/h")

# Battery mass for one hour at that power
e_batt = 250.0      # Wh/kg at pack level (illustrative)
eta_chain = 0.90    # battery to shaft
m_batt = P_shaft / eta_chain / e_batt
print(f"Battery for one hour at that power: {m_batt:.0f} kg; jet fuel for one hour: {sfc*P_shaft/1000:.0f} kg")

Same thrust from a small fast jet or a large slow one:
  mass flow   20.0 kg/s, exit  205.6 m/s -> thrust  2.00 kN, propulsive efficiency 0.68
  mass flow   80.0 kg/s, exit  130.6 m/s -> thrust  2.00 kN, propulsive efficiency 0.89
  mass flow  400.0 kg/s, exit  110.6 m/s -> thrust  2.00 kN, propulsive efficiency 0.98

Shaft power for 2.0 kN at 380 km/h: 258 kW (345 hp)
Fuel flow: 77 kg/h
Battery for one hour at that power: 1145 kg; jet fuel for one hour: 77 kg

The gas turbine and its family

Most aircraft above the smallest sizes are powered by gas turbines. A gas turbine compresses air, burns fuel in it at nearly constant pressure, and expands the hot gas through a turbine that drives the compressor. This is the Brayton cycle. Higher compressor pressure ratios and higher turbine inlet temperatures make the cycle more efficient, which is why engine makers push materials and cooling to their limits; modern turbine blades run in gas hotter than the melting point of the metal they are made from, protected by internal cooling passages and ceramic coatings.

The turbojet uses all of its turbine's excess energy to accelerate a hot, fast exhaust jet. It is simple and light but noisy and inefficient below supersonic speeds, so it survives mainly in missiles and some military aircraft. The turbofan adds a large fan at the front, driven by the turbine. Most of the air the fan moves bypasses the core and leaves through a separate nozzle at moderate speed. The bypass ratio, the mass of bypass air divided by the mass of core air, is 9 to 12 in the latest airliner engines. High bypass ratios mean high propulsive efficiency and low noise, and they explain why modern engines have such large diameters.

The turboprop takes the idea further: almost all the turbine's energy drives a propeller through a reduction gearbox, because the turbine spins at tens of thousands of rpm while the propeller turns at about 1000 to 2000 rpm. Turboprops are the most fuel-efficient choice below about 650 km/h (350 kt) and are common on regional airliners, bush planes and military transports. The turboshaft is mechanically similar but drives a helicopter rotor or, in the Tern's case, an electric generator. Above Mach 0.6 or so, propeller blade tips approach the speed of sound and efficiency drops, which is why faster aircraft use turbofans.

Measuring engine efficiency

For an engine that produces shaft power, such as a piston engine or turboprop, fuel use is measured by the power-specific fuel consumption: kilograms of fuel burned per kilowatt-hour of shaft power (or pounds per horsepower-hour). Modern turboprops achieve about 0.27 to 0.33 kg/kWh at cruise. For a jet, the thrust-specific fuel consumption (TSFC) is fuel flow divided by thrust, in units such as kg/(N·h) or lb/(lbf·h); a modern high-bypass turbofan at cruise runs near 0.5 lb/(lbf·h). Lower is better in both cases. Specific fuel consumption appears directly in the Breguet range equation in Lesson 8.

Overall efficiency multiplies the engine's thermal efficiency (how much of the fuel's chemical energy becomes useful mechanical power) by the propulsive efficiency (how much of that power becomes useful thrust power). A modern turbofan has a thermal efficiency of about 50 percent and a propulsive efficiency around 75 to 80 percent, giving an overall efficiency near 40 percent. Gas turbines are most efficient near full power; at low power settings their fuel consumption per kilowatt rises, which is one reason the Tern's turboshaft is sized to run near its best point in cruise while the battery handles the peaks.

Propellers

A propeller is a rotating wing. Each blade section is an airfoil meeting air that combines the aircraft's forward speed with the blade's rotational speed; the blade is twisted so each section meets the air at an efficient angle. Variable-pitch propellers change the blade angle in flight, using fine pitch for take-off and coarser pitch for cruise, much as a car changes gears. If an engine fails, the propeller can be feathered, turned edge-on to the airflow, to cut drag. The Tern's five-bladed composite propellers are large and turn slowly, about 1400 rpm, to keep noise down near communities and to keep blade tips well below the speed of sound.

Propeller efficiency, the thrust power divided by the shaft power, \(\eta_{prop} = TV/P\), is about 0.80 to 0.88 in cruise for a well-matched propeller. It falls at low speed because the propeller is doing work on the air without the aircraft moving much, and at very high speed because of compressibility at the blade tips.

Electric and hybrid-electric propulsion

Electric motors are light, compact and remarkably efficient: about 95 percent of the electrical power becomes shaft power, against roughly 30 to 40 percent for small gas turbines and piston engines. They have few moving parts, produce no local emissions, are quiet, and can be placed almost anywhere on the airframe, because power travels through cables rather than shafts. Designers exploit this freedom with distributed propulsion: many small motors along the wing, or ducted fans blended into the body.

The problem is energy storage. Today's best lithium-ion cells store about 250 to 300 Wh/kg, and a complete battery pack, with its structure, cooling and protection, stores less. Jet fuel stores about 40 times more per kilogram. Batteries also stay just as heavy when they are empty, so a battery-electric aircraft does not get lighter as it flies, unlike a fuel-burning one. These facts limit battery-electric aircraft to short flights with small payloads: trainers, air taxis and short commuter hops.

Hybrid-electric designs combine the two. In a series hybrid like the Tern, a gas turbine drives a generator; electrical power goes to the motors and, when there is a surplus, to the battery. In a parallel hybrid, an engine and a motor both drive the same propeller shaft. Hybrids allow the turbine to be sized for cruise rather than take-off and to run at its most efficient setting, while the battery supplies the extra power for take-off, climb and go-around. They also offer a path toward lower emissions as batteries improve or as sustainable fuels replace fossil fuel.

Other options: hydrogen and sustainable fuels

Hydrogen stores about 120 MJ/kg, nearly three times as much as jet fuel, and burns to water. It can power gas turbines directly or feed fuel cells that make electricity for motors. Its weakness is volume: even as a liquid at −253 °C it needs about four times the tank volume of jet fuel for the same energy, and the insulated tanks are heavy. Sustainable aviation fuels, made from waste oils, crop residues or captured carbon dioxide and hydrogen, are chemically similar to jet fuel and can be blended into it with no change to aircraft. They are expensive and produced in small quantities today, but they are the most practical near-term way to cut aviation's carbon dioxide emissions.