Projectile motion with air friction

[106267]

I'm trying to understand the motion of projectile motion under the influence of air resistance. A website such as this details the necessary equations available to approximate this model: http://claymore.engineer.gvsu.edu/~michels/index_files/Golf%20Ball%20Paper%20Final%20draft.pdf
However, i am unable to calculate vaild results.
I'm using the constant air friction equation
x(t)=(24τV cosθ)/(C_D Re) e^(-((C_D Re)/24τ)t)+(24τV cosθ)/(C_D Re)
&
y(t)=〖(V sinθ+24τg/(C_D Re))( -24τ/(C_D Re) e^(-((C_D Re)/24τ)t) )+((V sinθ+24τ/(C_D Re))(24τ/(C_D Re)))-(24τ/(C_D Re))t

Reading on the linked website will provide in detail what these variables equal.

My results are
Velocity:v=2.85ms
Angle 60 degrees
mass: 0.004kg
Diameter: 0.016m
This is all done in the fluid of air
at around 20°C

 

[Simon Bridge]

In what way are these not valid results?

[aside: the link is not valid]

 

[106267]

Sorry what I'm meant to say is that my results are my initial values. When i sub these into the equation listed the results i obtain are invalid. Try the link again it should be vaild. If not just type into google search and click the most common url located

 

[Simon Bridge]

...my results are my initial values. When i sub these into the equation listed the results i obtain are invalid.

In what way are these not valid results?

However I now have the pdf linked to. Thanks.

 

[PJC01]

Thank you for sharing your efforts in understanding projectile motion with air resistance. It is a complex phenomenon and can be challenging to accurately model. The equations you have provided are correct and are commonly used to approximate the motion of a projectile in the presence of air resistance. However, there are a few factors that may be affecting your results.

Firstly, it is important to note that air resistance is dependent on the shape and size of the object, as well as the properties of the fluid it is moving through. The equations you have used assume a spherical object with a diameter of 0.016m. If your object is not a perfect sphere or has a different diameter, this could affect your results.

Additionally, the value of the drag coefficient (C_D) is also dependent on the shape and size of the object. It is possible that the C_D value you have used in your calculations is not accurate for your particular object. It may be helpful to conduct experiments or research to determine a more accurate C_D value for your specific object.

Furthermore, the equations you have used assume a constant air resistance, which may not be the case in reality. Air resistance can vary based on factors such as wind speed and direction, temperature, and altitude. These variations can also affect the accuracy of your results.

Finally, it is important to double-check your calculations and make sure all units are consistent. Any errors in your calculations can greatly affect your results.

Overall, I would suggest further research and experimentation to improve the accuracy of your results. Additionally, seeking guidance from a physics instructor or conducting a peer review of your calculations may also be helpful in identifying any potential errors.