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ferret_guy
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I am trying to predict the flight of an object with a parabolic trajectory including drag due to air resistance how do I do this? the wiki page was not clear its my understanding its relative to the square of the speed.
The reason Bob S used numerical integration is because that is pretty much the only choice. There is no closed form solution in the elementary functions. There was a buzz a month ago or so about some kid in Germany who claimed to have found such a closed form solution. He didn't. He found a slowly converging series solution (that's not "closed form"), and what he found is well known and is also well known as pretty much useless. There is no simple closed form solution to this problem.Bob S said:I have used numerical integration
ferret_guy: Note that this is the magnitude of the drag force. The direction is always against the velocity vector.The force is [tex] F=\frac{1}{2}\rho \cdot C_{drag} \cdot A \cdot v^{2} \text { Newtons} [/tex]
The formula for calculating the trajectory of an object with air drag is:
Trajectory = (Initial Velocity * Time) - (1/2 * Drag Coefficient * Air Density * Cross-sectional Area * Velocity^2 * Time^2)
This formula takes into account the initial velocity, time, drag coefficient, air density, cross-sectional area, and velocity squared of the object.
Air drag is the force that opposes the motion of an object through the air. As an object moves through the air, it experiences air resistance, which slows it down and affects its trajectory. The greater the drag on an object, the more it will deviate from its original path.
The drag coefficient and air density of an object can be determined through experiments and calculations. The drag coefficient can be found by dividing the drag force on an object by the product of its cross-sectional area and air density. Air density can be calculated using the ideal gas law or can be obtained from meteorological data.
Cross-sectional area is an important factor in calculating the trajectory of an object with air drag because it represents the size of the object facing the direction of motion. A larger cross-sectional area means there is more surface area for air to push against, resulting in a greater drag force and a larger deviation from the object's original path.
No, it is not possible to predict the trajectory of an object with air drag with 100% accuracy. There are many factors that can affect the drag force on an object, such as wind speed and direction, turbulence, and the shape and size of the object. Additionally, small errors in measurements and calculations can also impact the accuracy of the prediction.