Range – Constant Velocity
As discussed on the airplane cruise slide, an airplane can maintain a constant speed and level flight, in which the lift is equal to the weight, and the thrust is equal to the drag. Since there is no net external force on the aircraft, the aircraft maintains a constant airspeed as described by Newton’s First Law of Motion. However, if the forces become unbalanced, the aircraft moves in the direction of the greater force.
If we take into account the relative velocity of the wind, we can determine the ground speed of a cruising aircraft. The ground speed remains constant as long as the wind speed is constant. Assuming a constant ground speed, we can use a simple rate equation to determine how far a cruising aircraft flies in a given span of time. The general rate equation is “rate times time equals amount”. The amount is the distance d the airplane has flown, the rate is the aircraft’s ground speed V, and the time is the time t aloft. Our general rate equation then becomes a distance equation: the distance flown is equal to the ground speed times the time aloft.
d = V * t
Airplanes, unfortunately, cannot stay in the air forever. There is a time limit, or maximum time, that an airplane can stay aloft, which is usually determined by the fuel load. When the airplane runs out of fuel, the engine stops. The drag then slows the airplane, which decreases the lift and, eventually, the airplane comes back to earth. The maximum distance that the aircraft can fly is then equal to the ground speed times the maximum time t max. We call this distance the maximum range R of the aircraft.
R = V * t max
The maximum flight time depends on how much fuel is carried by the aircraft and how fast the fuel is burned. A summary of information needed to determine the range is given on a separate page.
Some care must be used when specifying range. On this slide, we are assuming that the mission of the aircraft is one-way, such as an airliner flying from city A to city B, where the aircraft can be re-fueled. The range of a military aircraft is often specified for a round trip (since you don’t normally want to land in enemy territory to be re-fueled!). To avoid confusion about the “range” of a military aircraft, the military often specifies the combat radius of the aircraft. The combat radius would be half of the range as specified here.
On this page, we have taken a very simple view of aircraft range–for academic purposes. In reality, calculating the range is a complex problem because of the number of variables. An aircraft’s flight is not conducted at a single ground speed but varies from zero at takeoff, to cruise conditions, and back to zero at landing. Extra fuel is expended in climbing to altitude and in maneuvering the aircraft. The weight constantly changes as fuel is burned. So the lift, drag, thrust, and fuel consumption rate also continually change. On real aircraft, as with your automobile, there is usually a fuel reserve; and the pilot makes sure to land the plane with fuel still on board.