Interesting. The equation is Torque = k . Angle, per Hooke's law.
and Force = Torque . Arm length.
The arm length is constant, so the force is proportional to the spring displacement angle, which means that Force is higher at the lower window positions.
The only way to keep it somewhat constant is to have a small angle displacement for the entire range. Even then it is natural that the motor is fighting the spring at the very bottom. I guess one could pre-extend the coil so it actually pulls the window at the top and it has less force at the bottom, but I do not recall doing that when I cleaned mine. Getting the last inches at the top is really slow so I am not sure that is wise.
This is a classic issue with spring asssited things (think garage doors, car windows, etc.
Assuming that the drag force on the window is constant, then ideally you want some mechanism that changes the mechanical advantage linearly as the window rises. This can be done (and may be one in the some car windows) by using a sliding mechanism where the lever arm the motor is acting on changes length as the window rises, thereby compensating for the change in spring force.
I recall years ago reading an article about the famed "mousetrap" race, where engineers were charged with making a small vehicle from a single mousetrap. They were penalized for any additional outside materials used. Prize went to the vehicle that traveled the farthest down a long hallway Since the only energy source is the mousetrap spring, this presented a serious problem, because the spring only had about 3/4 of a revolution from un-wound to fully wound. Most competitive entries used a "fusee cam" drive mechanism. The Fusee cam is a linear spiral (sort of like a slice of a Nautilus shell). The gearing was very high, so the spring only needed to move 3/14 of a turn while the axles might turn 500 times. The spring would power the cam, but the axle was powered by a string that originated at the inner (small radius) part of the cam, so as the spring unwound the gear ratio changed, thereby applying a near constant torque to the axle over the the full range of the spring. You can also do this with belts that wind up on top of themselves, or conical sprockets and chains thereby changing the drive ratio as the drive end turns
From the window perspective, it seems that having some additional advantage at the bottom would make sense, since this would help the motor overcome the static friction of the window.
Interestingly, the scissor lift mechanism of the window regulator actually has the lowest mechanical advantage at the bottom. This is because the weight of the window is borne almost entirely by the torque on the lever arm. In the example below the pivot is around the quadrant gear, so whatever radius that is relative to the length of the lifting arm is the mechanical advantage (which is very poor at the bottom). As the lifting arm rotates more of the weight of the window is taken by the pivot itself, and while the lever arms have not changed, the change in geometry means it takes less torque on the quadrant to move the window up (and the window moves up less per revolution of the motor). Seems then that the purpose of the spring is to augment the motor at the bottom, effectively making the window seem lighter where the mechanical advantage is lowest, and easing off as the geometry effectively changes the torque requirement on the quadrant.
