Calculating Projectile Trajectories: Aerodynamics of a 2.5cm Ball

In summary, The conversation discusses a software designed to calculate projectile trajectories, specifically when air resistance is not a factor. The model used is F = -k * A * v^2, where F is the force of drag, k is the constant of drag, A is the frontal area, and v is the velocity squared. The question is posed about the value of k for a sphere, with additional information given about the size and weight of the ball that will be used in testing. The request is made to use SI units.
  • #1
sigma
24
0
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
 
Physics news on Phys.org
  • #3


Hello! Thank you for sharing your software and your plans to test it with a light ball and a cannon. It sounds like a great experiment to validate your model.

To answer your question, the constant k for a sphere can vary depending on the specific conditions such as the surface roughness and the Reynolds number (ratio of inertial forces to viscous forces). However, for a smooth sphere at low Reynolds numbers, the typical value of k is around 0.47 (kg/m). This value can also be influenced by the density and viscosity of the surrounding air.

In order to accurately calculate the trajectory of your 2.5cm ball, it would be helpful to gather more information about the conditions of your experiment, such as the air density and viscosity, and the specific launch speed and angle. This will allow you to calculate the Reynolds number and determine a more accurate value for k in your model.

I wish you the best of luck with your experiment and look forward to seeing the results of your software! Let me know if you have any further questions. Happy testing!
 

1. What is aerodynamics?

Aerodynamics is the study of how air moves around objects. In the context of a ball, it refers to the forces and motions that affect the ball as it moves through the air.

2. How does a ball's shape affect its aerodynamics?

A ball's shape has a significant impact on its aerodynamics. A smooth, streamlined shape will experience less air resistance and therefore travel further and more accurately than a rough, irregularly shaped ball.

3. What is drag and how does it affect a ball's flight?

Drag is the force that acts in the opposite direction of motion and slows down an object. In the case of a ball, drag is caused by air resistance and can significantly affect the ball's trajectory and distance traveled.

4. What factors influence the aerodynamics of a ball?

There are several factors that can influence the aerodynamics of a ball, including its shape, size, weight, and surface texture. The speed and direction of the ball's motion, as well as environmental conditions such as air density and wind, also play a role.

5. How do scientists use aerodynamics to improve ball designs?

Scientists use aerodynamics to understand how different factors, such as shape and surface texture, affect a ball's flight. By studying these factors, they can design balls that have better aerodynamic properties, resulting in improved performance and accuracy in sports and other applications.

Similar threads

Replies
3
Views
4K
Replies
8
Views
2K
Replies
6
Views
959
Replies
4
Views
2K
Replies
7
Views
6K
  • Classical Physics
Replies
6
Views
1K
  • Introductory Physics Homework Help
2
Replies
43
Views
2K
  • Mechanics
Replies
1
Views
2K
Replies
4
Views
1K
Back
Top