I have found that many motorcyclists have problems understanding spring stiffness. Even people with reasonable mathematical skills seem to make mistakes in their fundamental assumptions about how springs work, the most basic mistake is that adjusting spring preload can make the spring stiffer.
One problem we have in understanding spring stiffness is that it is best understood with a form of mathematics called Calculus, which is not your basic high school math. Calculus is based on incremental differences. It is the study of change, and can solve problems that ordinary Algebra cannot. But I am not going to use any pure calculus in this discussion, in part because I never did that well at calculus anyway.
You can feel a stiff spring literally by the seat of your pants, when riding a motorcycle. On a very stiff spring, you feel every bump in the road as the motorcycle rides over it. If there is a two inch bump in the road, the motorcycle seat will go up two inches as you go over it. And when this happens at a high speed, your back, neck and rear end will suffer in various ways. The higher the speed, the more you will suffer.
If you drive slow enough, all springs are basically the same. At a speed of 0.000001 kilometer per hour for example, if you go over a 3 cm. bump, the seat of the motorcycle will go up 3 cm. in about one hour. (don't bother to check the math on that) That is not fast enough to cause pain, or to hardly even notice. It's only when you drive fast that you begin to notice a difference between a soft spring and a stiff spring.
The stiffness of a spring is measured by the amount of force it takes to compress (or bend) the spring one centimeter. Usually springs are built uniformly, so that to compress the spring two centimeters takes twice as much force as compressing it one centimeter. The tricky part here is understanding why this measurement (force per cm. of compression) can tell you how stiff the spring will be on the seat of your pants, at high speed. Although calculus would help explain it, it's just not worth going into. The one thing to remember is that if you do not change this measurement (the amount of force needed to compress the spring one cm.), you cannot change the spring stiffness.
How can you change spring stiffness? One obvious way is with a new spring. A spring could be made stiffer if it was made with a different (stiffer) metal, or if it was made with thicker metal, or if the metal was shorter. Let's look at each one separately.
Using stiffer metal is not an economical option for the spring maker. It is hugely complicated to make metal, and when you make steel in a steel mill, you try to make it all the same if possible. That is so that the engineers can figure out how much metal they need to build towers and bridges and whatnot. Believe it or not, every structure made of metal is basically a spring, which bends with the forces applied to it. Although there are different metals being made, with different stiffnesses, it is much easier to vary the stiffness of a simple spring by changing the thickness or the length.
Most motorcycle springs are made of coils of thick metal wire. You also could make the spring stiffer with thicker wire. The thicker the wire, the stiffer the spring. That may seem obvious, but normally spring manufacturers do not use thicker wire to make stiffer springs, because there is an even easier way to do it.
The easiest and cheapest and most accurate way to make a spring softer, is to make the coil longer. The longer the coil, the softer the spring. This may strike you as strange, as the longer coil has more steel in it than the shorter coil. But the fact is, that the longer the piece of metal, the more the end can flex. Think of a long antenna compared to a short antenna, and you can get the idea. Anyway, the easiest and most accurate way to alter the stiffness of a spring while it is being made, is by cutting the wire coil longer.
Unfortunately, it is very difficult to make the coil longer when it is already holding up the back of your motorcycle. And no, you cannot stretch the spring to make it softer, any more than you can compress it to make it stiffer. This is where most people get confused.
While it is true that spring can stretch and compress, neither of those will change the stiffness of the spring. Think of how the spring is made. It is a coil (usually), and by stretching the coil, you are not making the spring longer, you are simply bending the coils. It is pretty much impossible to make the spring longer without adding more coils of metal to it, or making the wire longer.
So by preloading the spring (meaning compressing it) you cannot make it stiffer, and by stretching the coils out, you cannot make it softer. Although, granted you will be changing the amount of force that is needed to hold the spring. And I guess that's where some of the confusion arises. Anyway, forget "force" as a measure of spring stiffness. As I have already said, it is "additional force per centimeter compression" that measures stiffness, and I don't want to get into calculus to explain it, and probably you don't either.
Now how can you adjust spring stiffness on the motorcycle, without changing parts? One way is by changing the leverage of the spring. To change the leverage, you don't need calculus, you need geometry and physics. In a basic old fashioned motorcycle, moving the wheel one cm. would also move one end of the spring one cm. That is one-to-one leverage. But if you could move the wheel two cm. for every one cm. of spring compression, that would give you effectively a softer spring, without changing the spring. Remember, the stiffness of the spring is force per centimeter of compression. If you have the same force, but more compression (at the wheel), then the spring will feel softer.
It is actually quite easy to change the leverage by changing the position of the shock absorber attachment points. (the top or the bottom of the shock or both.) Unfortunately, the only motorcycle I know of that had this system of adjustment was Velocette (picture). You could loosen and slide the top shock mounting point forward and back, which changed the leverage of the shock a little. I'm sure some modern variation on this system would allow a large enough change to get a softer or a stiffer ride.
Another invention changing the leverage of shocks is more popular today, and that is the suspension linkage system. With a linkage system, the spring holds the rear wheel through a series of cranks and levers. Not only can the engineers play with the leverage through changing the lengths of the cranks and levers, but the leverage changes as the shock absorber compresses to absorb a bump while riding. In other words, the leverage changes depending on how big the bump is. I really like this idea in theory, anyway. Both my Kawasaki Vulcan and Mary Ann's Burgman have this linked system, that increases stiffness as the wheel compresses the spring. But surprisingly, neither one has a really soft ride. That's because spring stiffness is not the only thing that makes for a smooth ride, and both the Vulcan and the Burgman feel stiff for other reasons. But if you have a bike with one of these types of suspensions, you should be aware that they get stiffer when you lower the suspension (either on a bump or using the preload adjuster). Which is the exact opposite of what most people think, and that includes your neighbourhood mechanic, and the writers in most motorcycle magazines.
Picture: A 1969 Velocette Venom 500, with adjustable top shock absorber mount.