Calculating Projectile Trajectories: Aerodynamics of a 2.5cm Ball

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A user has developed software to calculate projectile trajectories considering air resistance, specifically for a 2.5 cm diameter ball weighing approximately 5 g. The drag force is modeled as F = -k * A * v^2, where k is the drag coefficient and A is the frontal area. The user seeks guidance on determining the constant k for a smooth sphere launched at speeds of 5 - 7 m/s. Additional resources were provided for further information on drag coefficients. The discussion emphasizes the importance of using SI units for calculations.
sigma
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Hi! I've written a simple software to calculate projectile trajectories when air resistane can't be neglected. I'm planning to test the software with a light ball and a cannon.

My model simply say
F = -k * A * v^2
The force of drag F is proportional to the velocity v squared. k and A are constant of drag and frontal area respectively.

Can anyone tell me what the constant k would be for a sphere?

The ball I'm planning to use is about 2.5 cm in diameter, weighs about 5 g (guess) and is pretty smooth. It will be launched at speeds of about 5 - 7 m/s.

If the information is insufficient, please ask.

Edit: Please use SI units, thanks!

//Sigma
 
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