Hi everybody. I thought you might be interested in a program I wrote. We were working on the Freedom Launcher, and we were wondering how much force we are going to need to pull down and cock the throwing arm. Being the Mechanical Engineering student that I am, I got to thinking about how to figure that out. It's a somewhat complicated problem, because our pully will be stationary, so the angle at which we're pulling on the arm will be constantly changing - just as the angle at which the counter-weight is acting on the arm will be. It's doubly a function of the angle. So anyway, after some thinking, I derived this equation:
T=s*w*sin(x)*sqrt(2*h*l*cos(x)-2*d*l*sin(x)+d
2+h
2+l
2)/(l*(d*cos(x)+h*sin(x)))
Here's what all the letters mean:
T: The tension in the cable
x: The angle between the throwing arm and an imaginary vertical line. For example, when the arm is at rest, the angle is 0. When it's cocked, it should be somewhere around 140 or so.
s: The length of the short end of the arm - from the axle to where the weight is attached
l: The length of the long end of the arm - from the axle to wherever the cable attaches to the arm
w: The weight of the counterweight
h: The difference in height between the axle and the pully. For example, the Freedom Launcher's axle is 18 ft off the ground. The cable will be entering the pully at about 1 foot off the ground. So this value for us is 17.
d: The distance from the pully to the upright support. Easily computed using the Pythagoren Theorem: d = sqrt(l
2-h^2)
Now, this is a rather messy equation, so I made a program in MatLab where you input the s, l, w, and h values, and it tells you where and what the maximum tension in the cable is, as well as how much force will be required to hold the arm in the cocked position. This is very helpful for figuring out the load on a trigger - and not to mention figuring what type of cable is needed to winch the arm down. I've attached a screenshot of the program. However, this .exe only works on computers that have some MatLab software installed. So if anybody is interested, I can supply you with the MatLab code or the .exe, but the extra (free) MatLab software required for the .exe has a 75 MB or so install file. Just thought I'd spread the word.
A program I wrote
T=s*w*sin(x)*sqrt(2*h*l*cos(x)-2*d*l*sin(x)+d
Here's what all the letters mean:
T: The tension in the cable
x: The angle between the throwing arm and an imaginary vertical line. For example, when the arm is at rest, the angle is 0. When it's cocked, it should be somewhere around 140 or so.
s: The length of the short end of the arm - from the axle to where the weight is attached
l: The length of the long end of the arm - from the axle to wherever the cable attaches to the arm
w: The weight of the counterweight
h: The difference in height between the axle and the pully. For example, the Freedom Launcher's axle is 18 ft off the ground. The cable will be entering the pully at about 1 foot off the ground. So this value for us is 17.
d: The distance from the pully to the upright support. Easily computed using the Pythagoren Theorem: d = sqrt(l
Now, this is a rather messy equation, so I made a program in MatLab where you input the s, l, w, and h values, and it tells you where and what the maximum tension in the cable is, as well as how much force will be required to hold the arm in the cocked position. This is very helpful for figuring out the load on a trigger - and not to mention figuring what type of cable is needed to winch the arm down. I've attached a screenshot of the program. However, this .exe only works on computers that have some MatLab software installed. So if anybody is interested, I can supply you with the MatLab code or the .exe, but the extra (free) MatLab software required for the .exe has a 75 MB or so install file. Just thought I'd spread the word.
Oh, and visit http://www.freedomlauncher.com