Jet Endurance Calculator

How long can a jet aircraft stay in the air on a single tank of fuel? This value is called range and should be an important factor when planning maneuvers or comparing different engines. This tool calculates the maximum flight time using Breguet's range formula for jets. By entering the engine specific fuel consumption, aerodynamic efficiency of the plane as well as initial and final weight you will get the maximum flight time.

Enter four of the five values and leave the fifth blank. The calculator will then work out the missing value so you can calculate range, determine fuel load or back-calculate required lift to time ratio for a given rotation speed. The graph below shows how range changes as you vary fuel and lift to time ratio.

What is a jet plane's range?

The range is the maximum time an aircraft can fly before all available fuel has been used up. For jet aircraft this number is determined by three factors: the efficiency with which the engine burns fuel, the aerodynamic efficiency of the wing and the proportion of the takeoff weight that is fuel.

Jet engines produce thrust by burning fuel. The ratio of the fuel burned to the thrust produced is called specific fuel consumption (SFC). The lower the SFC, the farther an aircraft can fly on a kilogram of fuel. Modern high bypass turbofan engines have values around 8 to 17 g/(kN·s), while older turbojet engines had higher values near 20 to 30.

The contribution of the wing is expressed by the lift to drag ratio (L/D), which indicates the relation between the lift produced by the wing and the air resistance caused by it. The higher the L/D, the less thrust required for level flight, resulting in a longer range. In order to achieve maximum endurance, a jet aircraft must fly at the angle of attack where the L/D is maximized, which also happens to be a prerequisite for turning.

The fuel ratio, which is the value calculated by dividing initial weight by final weight, indicates how much fuel has been loaded. The more fuel that is loaded, the greater this ratio becomes, but as the weight also increases, a higher thrust is required, leading to faster fuel consumption. This compromise is why the natural logarithm is used in the expression: each time more fuel is added, flight time increases, but by an ever smaller amount.

Breugue's range formula

This formula relates flight duration to three independent factors.

In this case c_t is the specific fuel consumption (TSFC) per mass, g is the acceleration of gravity (9.80665 m/s²), L/D is the thrust to weight ratio and W_i and W_f are the initial and final weights respectively. The first factor represents the engine, the second the airframe and the third the fuel. Multiplying these three factors together gives the flight time.

Two conclusions can be drawn from the mathematical relationships: range is proportional to L/D and inversely proportional to TSFC. This means that halving fuel consumption doubles endurance. On the other hand, diminishing returns occur due to the logarithmic behavior of the weight ratio in the formula.

Here's how to use this calculator.

Enter the TSFC, lift to weight ratio and both weights leaving the flight time field blank to calculate the corresponding value. Each field has its own unit switch so you can freely mix metric and imperial units. To calculate a different quantity leave the relevant field blank and enter the flight time. The main panel shows the flight time while the add-on card displays the fuel consumption, fuel ratio, weight ratio and average fuel burn rate. If you open the turn option and add a speed then you can read off the distance travelled by the aircraft during the turn.

Example calculation:

Let's take a long-range surveillance drone as an example. The TSFC is 14.2 g/(kN·s), the lift-to-weight ratio is 20, the initial weight is 5,000 kg and the final weight is 3,000 kg. It will consume 2,000 kg of fuel, which is two-fifths of the takeoff weight.

In the first step, engine parameters are calculated. If the TSFC is converted from g/(kN·s) to base unit kg/(N·s), then 14.2 g/(kN·s) results in a value of 0.0000142, which leads to:

In a second step, the lift-to-weight ratio is multiplied.

In the third step, the natural logarithm of the weight ratio is calculated.

In the fourth step, we combine these elements.

With a single refueling, you can perform continuous surveillance for more than 20 hours. If the TSFC (specific fuel consumption) is halved, the flight range doubles. By increasing the L/D value (lift-to-drag ratio) from 20 to 30, the flight range increases by half again. The aspect of weight ratio is where diminishing marginal returns come into play. The increase in operating time when the weight ratio is increased from 1.5 to 2.0 is greater than when it is increased from 2.0 to 2.5.

List of variables:

The following symbols are shown as individual fields within the calculation tool. The example values refer to the previous calculation example.

TSFC (specific fuel consumption) by engine type:

The TSFC is a key figure for the engine and the factor that most strongly affects flight range. Typical values for cruise operation are in the following range.

Airplane type-specific lift/power ratios

The lift-to-power ratio is a single number that summarizes the aerodynamic efficiency. Typical values for turns are in this range:

The range and flight duration are different

Range and endurance are different goals, as is the optimal speed. Endurance looks at time in flight, with lower speeds being used to achieve maximum endurance for a given minimum thrust or fuel flow rate. Range looks at distance traveled, with slightly higher speeds being used to achieve maximum range for a given minimum drag. Optimizing one of these will sacrifice some of the other. This is why surveillance aircraft and long-haul passenger jets use different flight profiles. This tool answers questions about endurance while the attached Breguet range formula answers questions about range.

Assumptions and limitations

This equation represents a steady, level flight at constant altitude and assumes a constant lift to power ratio as well as an approximately constant specific fuel consumption (TSFC). Since climb and descent phases are not considered, for a complete mission calculation the individual phases (climb, cruise, turn, descent) must be calculated separately and then added together. In addition, it assumes that the aircraft weight decreases due to fuel burn, so it is not applicable to battery powered electric aircraft where the weight remains constant. Also, it uses an equation based on thrust which applies to jet aircraft. For propeller-driven aircraft a different equation based on power and propeller efficiency is used. For a typical jet aircraft with good turn conditions the difference between the results and actual performance data should be within a few percent.

Fields of application:

Drone operators set the flight times for surveillance, communications relays and patrols. Commercial airline dispatchers estimate how long an aircraft can wait before it must land. Military planners review the duration of air patrols with fighter or reconnaissance planes. Engineering teams consider trade-offs to understand how engine choice, wing efficiency and fuel capacity affect range. Students learn about thrust, aerodynamics and weight in relation to each other.

Tips for maximizing your reach:

Fly at the speed corresponding to the maximum L/D ratio, i.e. the turn speed. This is usually lower than your chosen travel speed for maximum range. Select an engine with lowest TSFC (specific fuel consumption) as far as possible within mission requirements. High bypass turbofan engines are hard to beat in continuous turns. A lighter fuselage will result in a higher fuel fraction at the same takeoff weight, so structural weight should be reduced as much as possible. Also note that these results are planned estimates for travel and cruise phases, and do not replace full mission analysis.