I came up with this problem, and solved for it, but I do question its accuracy, and id like to know how I could make it a better model. (it is not a homework problem)
So, a block, of dimensions a (rests on the z axis) by b (rests on the y axis) by c (rests on the x axis), is moving with a constant velocity v in the z direction and is spinning in the z-y plane about the center of mass that is located in the geometric center of the rectangular block with a angular frequency ω starting at time t from a angle of θ0.The angle was measured from the y axis to b, so when it is at θ0 b is on the y axis and a is on the z axis. It moves through space and encounters air resistance form air of density ρ. Also a*c is less than b*c
So the general equation for any drag is: FD=(CD*ρ*A*v2)/2 where A is the projected surface area in the z direction, CD is the drag coefficient which depends upon the shape of the object and FD is just the force encountered by the object from the fluid with a density ρ
The problem was finding A and CD.
The projected area I using simple geometry to be c(b*cos(θ0+ω*t)+a*sin(θ0+ω*t)).
It was harder to find CD as it varied with the angle so I decided to make a approximation. I made it a function of the angle, making it a cosine function with α being the maximum and β the minimum value of the drag coefficient. SO my equation for the coefficient would be:
CD=((α-β)*cos(θ0-ω*t)+α+β)/2
As far as I know this is supposed to be a cosine function, but I'm not 100 percent positive.
The I just input the two equations into the original FD equation giving me a quite big equation which I shall not show as its annoyingly large, but unnecessary to show as you can just figure it out.
My main question is how can I make CD a more realistic function and how accurate my approximation is from known reality. Also if anyone knows, how would the angular slow down due to the air resistance and if there is some sort of study done on such a topic.
So, a block, of dimensions a (rests on the z axis) by b (rests on the y axis) by c (rests on the x axis), is moving with a constant velocity v in the z direction and is spinning in the z-y plane about the center of mass that is located in the geometric center of the rectangular block with a angular frequency ω starting at time t from a angle of θ0.The angle was measured from the y axis to b, so when it is at θ0 b is on the y axis and a is on the z axis. It moves through space and encounters air resistance form air of density ρ. Also a*c is less than b*c
So the general equation for any drag is: FD=(CD*ρ*A*v2)/2 where A is the projected surface area in the z direction, CD is the drag coefficient which depends upon the shape of the object and FD is just the force encountered by the object from the fluid with a density ρ
The problem was finding A and CD.
The projected area I using simple geometry to be c(b*cos(θ0+ω*t)+a*sin(θ0+ω*t)).
It was harder to find CD as it varied with the angle so I decided to make a approximation. I made it a function of the angle, making it a cosine function with α being the maximum and β the minimum value of the drag coefficient. SO my equation for the coefficient would be:
CD=((α-β)*cos(θ0-ω*t)+α+β)/2
As far as I know this is supposed to be a cosine function, but I'm not 100 percent positive.
The I just input the two equations into the original FD equation giving me a quite big equation which I shall not show as its annoyingly large, but unnecessary to show as you can just figure it out.
My main question is how can I make CD a more realistic function and how accurate my approximation is from known reality. Also if anyone knows, how would the angular slow down due to the air resistance and if there is some sort of study done on such a topic.