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My dad wanted a nice storage box for his catamaran trailer. After convincing him to abandon the corrugated pipe idea for reasons of trashy appearance, impracticality, and minimal storage volume, he opted for a nice sturdy welded aluminum box, roughly 10ft long x 3ft wide x 2 ft high. The lid of the box was expected to be quite heavy, so some form of opening assistance was desired. The common solution for this is the gas spring:
Gas springs use compressed gas stored in a cylinder to exert an extending force on a piston, the amount of force depends on the pressure of the gas and the diameter of the cylinder. The concept is quite simple, attach one of the the gas spring on the lid and the other end in the box; common practice is to attach the piston rod-end at the lower point to let the lubricating oil in the cylinder to bathe the piston seals, maximizing the life of the spring.
Care must be taken that there is enough room to let the lid close without the piston bottoming out in the cylinder, this can be accomplished by putting the attachment point in the box closer to the hinge and/or deeper in the box, or placing the attachment point on the lid farther from the hinge. However, the lid must still be able to open far enough (and not too far) when the gas spring is fully extended. other considerations are:
Angle of lid when open
Force required to open the lid
Force required to close the lid
Gas spring collapsed length
Gas spring extended length
Gas spring collapsed force
Gas spring extended force
That's quite a few variables that all affect how this lid opens, turning an initially simple problem into a complex optimization problem if you prefer to avoid the trial and error approach which would result in a box with many extra holes. Below is a diagram showing all the variables in addition to the gas spring forces in the open and closed positions.
After identifying all the variables, the next step was to describe the variables in the open and closed states in terms of one-another to be able to solve for the closing and opening forces respectively. The position of the spring mounts, hinge location, and angle of the lid define a triangle, the cylinder lengths of which can be calculated using the law of cosines (wikipedia).
I created a spreadsheet in Excel (attached) and began by defining all the known variables and constraints (green box on right). In this spreadsheet blue boxes are unchanging values, and the light orange cells are varied by the solver (explained later) and dark-orange boxes indicate calculations. The temperatures shown are used to determine the change in spring force due to the pressurization of the gas with an increase in temperature. A desired lid opening and closing force was defined (10 lbs and 15 lbs respectively). In order to prevent the lid from opening on its own due to pressurization of the gas on a hot day, a conservatively high temperature (50°C) was chosen for a closed lid state, such as might encountered if the box is left in the sun for an extended period of time. To prevent the opened lid from falling closed on its own, a conservatively low temperature (10°C) was chosen for the open lid state (you wouldn't want to be out sailing in colder weather anyway right?).
A gas spring was selected on McMaster-Carr (this was iterated on a few times), and the force for the cylinder in both the hot-collapsed and cold-extended states was calculated using the ideal gas law, the volume ratio (V_extended / V_collapsed), which was estimated to be 1.22 based on the cylinder and piston shaft diameters, and the length and temperature of the cylinder in both states.
Next the important variables in three states were calculated. These states are: open, closed, and over-center, a state in which the weight of the lid perfectly balances the force of the cylinder such that the lid can balance at some intermediate open position. Most of these variables had some sort of constraint imposed on them (e.g. the spring length in the closed lid position could not be less than the length of the spring in the fully collapsed state, the moments in each of the three states had to be balanced, etc.).
With all constraints applied, I chose to minimize the force required to open the lid, provided that it wold be at least 10 lbs (perhaps the minimum force was actually number greater than 10 lbs) using Excel's built-in optimization solver. The solver comes pre-loaded as an add-in, but you still need to install it. To do so, go to File > Excel Options > Add-Ins, and select "Solver Add-in":
The button for the solver shows up under the "data" tab at the far right of the ribbon:
Click this button and identify your constraints, cells that you allow the solver to change to iterate, and the cell to which the optimization goal is applied:
Click "Solve" and the solver will vary the values in the light-orange cells until it has achieved the goal of minimizing the required opening force to 10 lbs.
Once the final geometry was defined by the solver, I sent the specs to my dad who in turn purchased the gas springs, forwarded them along with the mounting locations to the welder who performed the installation. As I was always 1000+ miles away I had never seen the box or the gas springs myself (let alone get a chance to confirm the spring forces met the specs), so I could only hope everything would work out as designed. Fortunately it worked EXACTLY as designed; my dad was even so kind as to film my mom demonstrating the ease of operation:
The intermediate angle at which the lid remains open (the over-center angle) is clearly visible in the video, and it appears to match very well with the predicted over-center angle of 17.62°!
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