Engineering 101: Introduction to Preload

First, watch this guy's idea.

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When you use this little what? Gumbo? Gremlin? I guess it's not important. At any rate, I think this is as decent an example as any to help understand the basic concept of preload in bolted joints. So let's talk about why this idea works. (Note: I would never be mistaken for a photographer, and I haven't even tried his method. Based purely on some knowledge of physics, I'm making the assumption that this does have a measurable impact on the quality of your photos. I'm not so thrilled with the idea of putting the washer back into my pocket after dropping it on the ground and stepping on it, but we can't have everything now, can we? Perhaps if he used a hook to grab onto the top of his shoes somewhere? ...if he weren't wearing plastic footwear... If anyone out there gives this a shot, I'd like to hear about how well it works.)

The first thing to recognize is the physical nature of the problem. Camera shake is not caused by the inability of someone to hold the camera's weight. It is, however, caused by not being able to exactly hold the camera's weight. If we consider the camera, we see that it will be pulled toward the surface of the earth by a force equal to its mass multiplied by the acceleration associated with the planet's gravity.

Tangent: Newton's second law of motion.
Good ol' Sir Isaac Newton described one of the fundamental parts of classical mechanics with this simple equation.

F=ma

That is to say, FORCE is equal to MASS times ACCELERATION. If you push on a body with a certain force, you will cause that body to move in the direction of the force you apply. It will start slowly at first, and pick up speed, accelerating in the direction you are pushing. The value of the acceleration can be determined if you know the mass of the body, and the magnitude of the force with which you push.

On the other hand, since the earth is massive compared to just about everything we deal with on a daily basis, its effect can generally be described by a single value of acceleration applied to the body of whatever we are interested in. Thus, the force that an object experiences due to earth's gravity is its mass multiplied by this acceleration (9.81 meters per second-squared).

Tangent: Mass & Weight
Perhaps it is already clear to you that when applying Newton's formula to an object in earth's gravity, both the body's mass and its weight are used. The mass is obviously 'm', but the weight is actually 'F'. That is to say, when we carry something heavy, what we feel is the force produced by the mass of the object multiplied by the acceleration due to earth's gravity. If we were carrying the object on Mars, it would be a lot lighter, since the acceleration there would be less. However, the object would be no less massive. (i.e. its physical bulk would remain, even if it didn't feel as heavy.)

This whole concept is a lot easier to understand when not using the US Customary unit system. In the SI unit system, mass and weight are very clearly two separate things. Mass is measured in kilograms (kg) and weight, or force in general, is measured in Newtons (N). When I go to the grocery store here and put some apples on the scale, it tells me how many kilograms they are. What the scale is actually doing is determining how much force (Newtons) the apples are pushing on the scale with. Knowing what acceleration earth's gravity is producing allows the mass to be calculated and shown.

Now, in the 'States, this is a bit messier, because our common unit of force is pounds. However, as you've probably seen, there are attempts to convert between pounds and kilograms. As it turns out, there is a unit of pounds that is used for force (lbf) and a unit of pounds that is used for mass (lbm). It is appropriate to convert pound-mass (lbm) to kilograms (kg) because they are conceptually the same kind of thing. However, to convert from pound-force (lbf) directly to kilograms (kg) is nonsensical, like trying to figure out how many gallons there are in a mile. To make matters worse, the pound-force is defined as the amount of force a pound-mass would produce in earth's gravity. So if you encounter an object whose mass is 10 (lbm) it will produce a force of 10 (lbf) on earth. What this means is that most people don't ever have to learn the conceptual difference between mass and weight. ...until you get to school and this stuff becomes important even if you're not sending things to Mars.

...of course, it is important when you do...

So when holding the camera, a person is using their muscles to exert a force opposite this force of the camera's weight. Even if these forces are perfectly balanced, the camera is not necessarily going to stay in one place. All that can be shown is that the camera's acceleration will be zero. Thus, if it were dropping at some speed, and we managed to push upward with the same force as the camera's weight, it would continue to drop; it just wouldn't drop any faster or slower. So holding a camera still requires that the camera first be still, and then to continue to place a force opposite that of gravity's. It's a marvel that we're able to detect and provide the minute adjustments needed to keep the camera in the same general vicinity as it is. And in the real world, things like wind will make sure that we have a continually moving target.

How does the string help? Notice that he mentions specifically that you need to use string that won't stretch. As engineers, we recognize that the literal interpretation of his words are absurd. You won't find unstretchable string anywhere. However, some string is a lot 'less stretchy' (in simple engineering terms, it is stiffer) than others. This is important.

Tangent: Stiffness
Stiffness is an idea even non-engineers should be familiar with. It is the resistance of an object's deformation to an applied force. A spring has very clear stiffness properties, as it takes larger and larger forces to produce greater and greater changes in length. The stiffer an object is, the more force is required to produce the same change in length. Conceptually, everything can be assumed to behave as a spring, though most things we interact with have such large stiffnesses that they don't seem to deflect at all under an applied load.

When you first pull the camera upward, the slack string becomes straight. Eventually, you get to the full length of the string, and the camera stops moving upward. ...or does it? Because the string has some stiffness associated with it, the camera will continue to move upward with greater and greater force from your arms. It just doesn't move very far.

Consider the sum of all forces on the camera once the string is pulled taut. You still have the force downward due to gravity. In addition, you have the string pulling down with whatever tension is inside it. Therefore, your arms must be pushing upward with a force to compensate both. Again, since it was never about being too weak to hold the camera (we hope) the extra force from the string should be no problem. Now, let's pretend that the camera is perfectly still, and that the force from the arms is exactly what is needed to balance the string and weight of the camera. When something small pushes on the camera, the total net force on the camera changes. Without the string, we saw that this would cause definite movement of the camera. Indeed, even with the string, the camera will move. However, since all things generally act as springs - even this string - when the camera changes position and the string changes length, the string tension will change. And because we took the advice to use a stiff string, even small changes in its length will mean large changes in the string tension. The result is that the string acts as a sort of automatic adjustment. If a force pushes up on the camera and the string gets longer, the increase in string tension acts to resist this new upward force. If a force pushes down on the camera and the string gets shorter, the decrease in string tension again will balance the system. Even our own poor arms may not be capable of keeping a constant force applied. The string will handle this too.

The only thing to really be concerned about is if a downward force appears that exceeds the force our arms can hold, then the string will lose all tension and the camera will noticeably drop. Otherwise, it is simply a matter of finding a properly stiff string. What if we used a rubber band? It could still work, but for the same fluctuating external forces, the softer rubber band would fluctuate with greater changes in length. The result would then be more camera movement. So the whole thing is just a trick to allow forces to exist without moving stuff very far.

Without getting too bogged down in particulars, I will say that this is similar to what happens in a bolted joint with preload. The bolt is like a spring, though it is quite stiff. The 'joint' (i.e. whatever the bolt is clamping together) is also like a stiff spring. In fact, it is so stiff that the bolt, stiff though it is, is measurably softer by comparison. This is an important detail for a future lesson. When the bolt it tightened, it is as if two springs are simultaneously being distorted. The bolt is getting a little bit longer, and the joint is getting a little bit shorter. The result is same kind of self-adjusting system that keeps the parts from coming loose or rattling around even when an external force is applied. This is even better than the camera stabilizer, because two springs are being used to give this preload force, rather than a spring and a pair of human arms. So nobody has to stand there holding it together.