Range of a Jet Calculator

How far can a jet plane fly on a full tank of fuel? The answer lies in the Breguet range equation. For propeller planes, range is limited by the power produced by the engine. In jets, other factors come into play, namely how efficiently the engines convert fuel to thrust and how aerodynamic the aircraft is. Given cruising speed, fuel burn rate of the engines, lift-to-drag ratio, and weight reduced by consumed fuel, this equation gives the range in still air.

This calculation tool supplements what flight planners need to take into account. The Breguet value is a maximum figure. If you subtract climb, descent and reserve fuel, the actual operating range will be shorter, and in addition wind changes the distance traveled relative to the ground. Depending on mission requirements and wind conditions, this theoretical range becomes an estimated planned one.

What determines a jet's range:

The range is the distance a jet aircraft can travel with an effective payload from takeoff to landing. Four factors affect the range of jets: cruise speed, fuel consumption per unit thrust produced by the engines, aerodynamic lift-to-drag ratio and the proportion of weight that is fuel. It's important to note that as a jet plane burns fuel during flight it becomes lighter. As a lighter aircraft requires less lift, drag also decreases. So for every kilogram of fuel burned, the distance traveled will be greater than originally estimated. The Breguet formula takes all these factors into account in a simple equation.

The Boeing 777 and Airbus A350 can fly for 14,000 km on a full tank. This is due to the combination of high bypass turbofan engines with low fuel consumption and wings that are so optimized that the ratio between lift and drag is about 19 to 21. In combat aircraft it's the other way around. The backward sweep of the wings is designed for supersonic flight, which means that in cruise flight the ratio between lift and drag can drop to 4 to 8.

The Breguet range formula for jets.

The jet version of this equation multiplies three independent factors together.

The first term, V divided by the product of g and c, represents thrust and gives the distance traveled when a given amount of fuel is burned. V is the actual speed during cruise flight, g is the acceleration due to gravity, and c is the specific fuel consumption (TSFC), which is the rate at which fuel is consumed per unit of thrust and time. The second term, L divided by D, represents the lift-to-drag ratio and is a direct indicator of aerodynamic efficiency. The third term is the natural logarithm of the weight ratio, which is the ratio of takeoff weight to end-of-cruise weight. Since this term is a logarithm, the effect of fuel decreases as it increases. Doubling the amount of fuel does not double the range.

Here's how to use this calculator tool:

Enter cruise speed, TSFC, lift to drag ratio and two cruise weights. Leave the field for wind still range blank to calculate this value. Each field has a dedicated unit switcher so you can freely mix metric and imperial units. To calculate another quantity leave the corresponding field blank and enter the range. The main window displays the wind still range while the add-on card shows fuel burn, fuel fraction, weight ratio and cruise time.

Two additional fields allow you to convert limits into planned values. The mission reserve is the percentage of still-air range that will be left after climb, descent and fuel reserves, typically between 80 and 90 percent. This determines the estimated actual range. Wind speed on the route is positive for tailwind and negative for headwind. Entering this value gives you ground range.

Example calculation

Let's take an example of a long-haul airliner. This aircraft flies at 250 m/s (about 900 km/h), has a TSFC (Thrust-specific fuel consumption) of 15 g/(kN·s), lift-to-drag ratio of 18, and weighs 200,000 kg on takeoff and 150,000 kg on landing. It burns 50,000 kg (one quarter of the takeoff weight) of fuel.

Now let's look at the log ratio of weights.

Next are the factors of influence. As TSFC uses the base unit kg/(N·s), 15g/(kN·s) becomes 0.000015.

We multiply these three factors together.

This is approximately the flight path from New York to Tokyo with no wind. If we apply a 85% mission reserve, this reduces our planned range to about 7,480 km. With a headwind of 40 knots during the flight, the range will be further reduced. The difference between values given by the simplified equation and actual flight path is why planners build in safety margins.

Range in still air versus ground range.

The Breguet range equation gives the distance an aircraft can fly through a mass of air, i.e. range with no wind. To obtain actual ground distances, one must multiply the component of the wind in the direction of travel by the flight time and add or subtract this value. A steady tailwind can add hundreds of kilometres to long-distance ranges while headwinds from jet streams can necessitate intermediate landings even when a tailwind prevails. Flight planners treat this wind correction as a separate process, which is why the ground range field is shown here separately from the no-wind results.

Lift-to-drag ratio by aircraft type

The lift-to-drag ratio summarizes the aerodynamic efficiency of an aircraft in cruise flight into a single number. Typical values for cruise are usually within the following range:

Why the engine generation is important

Engineers often compare different engine generations on the same aircraft using the Breguet equation. Turbojets from the 1960s generation used about 28 g/(kN·s) of fuel per unit thrust, while modern high bypass turbofans have values closer to 15. Since range is inversely proportional to fuel consumption, this difference alone allows nearly doubling the achievable range without changes to the wings. The following graph on engine efficiency shows this inverse relationship. This is why retrofitting older aircraft with new engines is often a very effective improvement.

How to achieve maximum range.

With a few strategic actions you can do most of the work. You climb while consuming fuel. Profiles for constant climb or step climbs reduce drag as the plane becomes lighter and enters thinner air. Maximum range is achieved at the speed where the product of speed and lift to drag ratio is maximized. If you go too fast, drag suddenly increases, if you go too slow, the angle of attack on the wing increases which also causes a sudden increase in drag. From an engineering perspective, you should combine the benefits of high aspect ratio wings with an engine that has an acceptable minimum TSFC (thrust specific fuel consumption). These two choices create a synergy.

Assumptions and limitations

The Breguet range formula only describes the phase of constant flight and assumes that the flight state is steady, i.e. speed and lift ratio are constant and TSFC is essentially constant. In reality there will be slight deviations due to step climbs and speed adjustments. This formula also assumes that fuel is consumed making the aircraft lighter so it is not applicable to battery powered electric motors where weight remains constant during flight. The values without wind should be considered as an upper limit. Use mission reserve and wind conditions to make estimates. If numbers really matter, a full mission analysis must be done.