The Aircraft Speed Needed for Takeoff calculator computes the speed required to create more lift than the weight of the aircraft.
INSTRUCTIONS: Choose units and enter the following:
Takeoff Speed (TS): The calculator returns the required velocity (speed) in meters per second. However, this can be automatically converted to compatible units (e.g. miles per hour) via the pull-down menu.
The Aircraft Speed (lift to overcome weight) formula computes the speed needed to achieve the lifting force on the surface area of a wing that is greater than the aircraft's weight. The airframe forcesis:
L = ½•A•ρ•CL•V²
Flight can be achieved with theis greater than the weight.
The algorithm uses a wind velocity starting with 0.1 m/s and increases the value until the lifting force exceeds the weight of the aircraft. The formula returns that velocity. Note: the wind velocity is not necessarily equal to the speed of the aircraft on the runway. Tail and head winds contribute to the total wind speed flowing over the wings. For precisely this reason, aircraft carriers turn into the wind to add both the ship's velocity and the speed of the wind to velocity of the aircraft being launched.
Bernoulli's principle is based on the conservation of energy, which dictates that in a steady flow of a fluid (lacking any substantial turbulence) the sum of all mechanical energy along a line of flow, a streamline, is the same at all points on that flow path. This , in turn means the sum of the potential and kinetic energy must remain constant and so with increased velocity of the flow, there is an decrease in static pressure.
From this same Bernoulli's principle we can derive the equation to calculate the lift force on a wing surface (airfoil). When the air flowing past the top surface of an aircraft wing moves faster than the air flowing past the bottom surface, Bernoulli's principle defines a difference in pressure on the two surfaces of the wing, with the lower pressure being on the upper surface where the faster flow exists.
The difference in pressure sums to a net upwards lifting force, as calculated in this equation..
The density of air, ρ (Greek: rho) (air density), is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in temperature or humidity. At sea level and at 15 °C, air has a density of approximately 1.225 kg/m3 (0.001225 g/cm3, 0.0023769 slug/ft3, 0.0765/ft3) according to ISA (International Standard Atmosphere).