Physics Computer Simulation: Optimum Angle for Drag Projectile

[Winchman]

Hi everyone, I am hoping that someone may be able to advise me on an issue i currently have.
I am trying to implement a Physics computer simulation (only basic) designed for children learning about forces. One of the sub games that i have created is to fire a character from a cannon and find the optimum angle, which ends up at 45 degrees.
However, the second sub game models drag force on the projectile, taking into account its mass, area, drag coefficient, and the air density. The equations are solved using an RK4 method. Excuse my lack of knowledge on this subject, but I am not that hot on physics, i just have an interest which is why i decided to model this simulation as my final university project as a computing student. Now, the question i have is that I've always understood that 45 degrees is the optimum angle to travel the farthest, but when simulating the drag projectile, the optimum angle is now 35. Is this correct, in that 45 degrees would no longer be optimum, or am i going wrong somewhere?
Many thanks

 

[elegysix]

the optimum angle changes because of the drag coefficient and it is continuous. Meaning that the optimum angle depends on the value of the coefficient, and is not 35 for all drag coefficients, just that particular value. It approaches 45 as the coefficient goes to zero. I believe you can solve for it by minimizing the amount of work done by drag.

 

[McLaren Rulez]

Yes, the angle will be less than 45 degrees.

An intuitive way to see this would be to realize that there is a force along the horizontal in the opposite direction to the velocity of the projectile. Add this force to the downward gravitational force and the resultant force acting on the projectile will be at a nonzero angle to the vertical. Hence, your angle of projection to maximize the range must be lower than 45 degrees. It would be similar (though not the same) as firing a projectile on an uphill slope. but you are now viewing the whole thing from a rotated point of view.

 

[Winchman]

Ah, many thanks for your responses. Id suddenly became very worried when i realized that 45 was no longer optimum, and given my lack of knowledge id felt id made a mistake somewhere in the code. Again, your responses are much appreciated.

 

[PJC01]

Based on your description, it seems like you have created a complex and interesting simulation for children to learn about forces. It is commendable that you are using your computing skills to create a tool for education.

In terms of your question about the optimum angle for a drag projectile, it is important to note that the optimal angle can vary depending on various factors, such as the drag force, the initial velocity, and the initial height of the projectile. Therefore, it is possible that in your simulation, with the added factor of drag, the optimum angle has shifted from 45 degrees to 35 degrees.

To confirm this, you may want to experiment with different initial conditions and see if the optimum angle changes. Additionally, you can also consult with a physics expert to validate your simulation and calculations.

Overall, your simulation is a great tool for learning about forces and it is important to keep in mind that the optimum angle may vary depending on different factors. Keep up the good work!