The fact that the amount of torque changes as a function of the angle the lid is opened is the whole thing, unfortunately. At 90 degrees (opened vertically), there is no closing torque, at 0 degrees (closed) there is maximum torque. Torque = r (radius) x F (force). If you want the lid to stay in a certain position, you want the closing torque (from weight) to equal the opening torque (from the spring).

If the spring is installed such that the force axis is parallel to the lid when closed, there will be no opening torque when the lid is closed (this is desirable). The action of the spring will increase as the angle opens, and when it matches the torque from the weight, the system will be in equilibrium. The trick to designing this is to not merely size the spring, but to pick the installation location such that the closing force and opening force are equal in the position you want the lid to remain when opened.

The closing torque is equal to the weight of the lid times the lever arm over which it acts (always perpendicular to gravity). So what we need to know is the horizontal location of the center of gravity (CG) of the lid as a function of the opening angle. This is simply (length of the lid) / 2 * cos(theta), where theta is the opening angle. At 90 degrees, that equals zero, and at 0 degrees that equals half the lid length, which is where the CG is. Multiply this lever arm by the weight of the lid and you have the closing torque as a function of lid angle.

The spring torque is more complex. You need to figure out the length of a perpendicular from the spring axis to the lid hinge. This is labled Lg on page 4 of the catalog you linked. Lg is the lever arm on which the spring acts, so the spring torque is equal to the spring force times this distance. This distance changes with opening angle.

If you make yourself some drawings of the little spring and the triangle made by the spring and the base and the lid, and you draw the length Lg (perpendicular to the axis of the spring), with some patience and basic trigonometry, you can work out that length and multiply it by the spring force.

Now that you have these two formulas (closing torque as a function of opening angle, and spring torque as a function of opening angle) you pick your desired static point (the angle at which you want it to hold itself) and set the two equations equal to each other and solve for the spring force you need. You also need to make sure that the spring has enough "throw" to handle the increase (or decrease) in length as the lid opens. A final complication is that the spring force will vary with length, but possibly not significantly enough to be considered here.

I realize this little course in Statics is probably more than you were looking for. If I get some time tomorrow I'll work it out for you on paper -- this is difficult to describe in words and very simple to draw with some vector calculus and a diagram :-)

Jim

Edit: the spring force may also include a preload. Post a link to the springs you plan to use, as well as force vs. length profiles they have for them.

Edit 2: I guess you did post a link to the spec sheet. On first glance, it doesn't seem to give what we really need to know, which is force as a function of stroke.

It also occurs to me that you can make this whole geometry problem a lot easier by not solving for these forces as a function of angle. Just pick the angle you want as the stop point (like 75 degrees or something), and draw yourself a diagram. Figure out all the angles from there, and solve for the force required at that angle to counteract the torque from the weight of the lid.

Don't forget to halve the spring force if you use 2 springs! Also remember that the closer you mount the spring to the hinge, the less stroke you will have, but the more force you will need. If you use a very short spring, then the mounting hardware you use will potentially need to handle quite a large force (up to hundreds of pounds, since the lever arm of the spring is so much shorter than the lever arm of the lid).

Edit 3: Finally, a word about how these systems are designed in practice. Gas springs in particular lose their strength over time, so a common solution is to design a stop in the hinge mechanism and then use a larger-than-required spring. This will push the lid up against the stop and add to the closing force, but that's not that big of a deal. Remember that as the spring becomes co-linear with the horizontal lid, the opening force will drop to zero. In practice this is the best bet. You can just estimate the lever arm of the spring and compare it to half the width of the lid. Let's say the lever arm is 6" and half the width is 18", then the spring force needed is 3x the lid weight. So you pick a spring 4x the lid weight and design a stop into the hinge mechanism.

I hope all this helps.

Jim