Weber's Law

By Rod Machado

If you closed your eyes, held out a cup, and asked someone to gently pour water in it, how much liquid would need to be added before you noticed a change in weight? One drop? Probably not. One ounce? Maybe. The answer is called the discrimination threshold fo detecting weight differences. Interestingly enough, it depends on how heavy the cup is. By the way, don’t try this experiment in a public place or the change you notice will be the coins at the bottom of your cup and you could get arrested for panhandling.

Ernst Weber (an 18^th century German physician considered one of the founders of experimental psychology) discovered that there is a relationship between the degree of stimulation you’re receiving and the amount it must change before you can recognize the difference. For instance, the discrimination threshold for sensing a change in pressure on the skin is approximately 16% (discrimination thresholds vary for different senses). Vary the pressure by 10% and people will not reliably notice the change. This finding has some interesting cockpit applications.

Let’s assume that you’ve just entered a climb from straight and level flight. After establishing the nose-up pitch attitude, you find yourself holding so much elevator back pressure that you look over at your passenger and say, “Hey, spot me!” Being an astute student, you immediately spin the trim wheel with the enthusiasm of a Wheel of Fortune contestant, hopefully not while yelling, “Come on a thousand!” Suddenly, a great deal of hand-yoke pressure disappears, which is easily recognized because the change exceeded the discrimination threshold of 16%.

But what happens if you trim away less than 16% of the yoke pressure you’re holding? You might not notice the pressure change. This is precisely what happens to timid trimmers. They trim a little bit, but not enough to notice any real difference in yoke-hand pressure. They then release the controls, only to notice a deviation in airplane attitude. Unfortunately, they repeat this process several times, wasting a lot of valuable time in the process.

When you watch experienced pilots trim their airplanes, you’ll often see them make several large twists of the trim wheel (come on ten-thousand!) so they can easily feel the sudden decrease in control yoke pressure. With the airplane near its trimmed condition, they’ll maintain very light hand contact with the yoke (that’s right, they don’t let go) then trim to keep the nose attitude and/or the VSI needle indication stabilized. Attempting to make the final trim adjustment using only the sense of touch can be difficult since the pressure change needed often does not exceed the minimum threshold for pressure detection. 

Discrimination thresholds apply to other areas of flight. For instance, the discrimination threshold for sound is about 10%. Our ability to detect a change in pitch, however, is about 33 times more sensitive, with a discrimination threshold of .3%. Holy bat talk! That’s sensitive. Now you know why singing off key drives people away, unless it’s karaoke night, which brings them together.

This is one reason a pilot might not notice the sound of decreasing engine power, which could result from an accumulation of induction system icing or from an aft sliding throttle. However, he might more easily notice a pitch change resulting from an increase in propeller speed (perhaps due to a loss of oil pressure in an airplane having a constant speed propeller).

The discrimination threshold for determining differences in the perceived length of a line is approximately 1%, meaning that we’re quite sensitive to detecting such visual changes. This is one reason we can effectively use our perception of length difference between the near and far end of the runway as a means of detecting a deviation from a previously stabilized glidepath. As you climb above or descend below a previously stabilized glidepath, the distance between the near and far end of the runway increases or decreases, respectively.

There are many variables that alter or affect Weber’s law. One of them is time. If a stimulus changes slowly, you might not notice the change. This helps explain how a pilot can get into an accelerated stall when turning from base to final with an excessive bank, yet not notice the increase in pressure on his derriere (i.e., increasing g-force).

Here are discrimination thresholds for a few sensory stimuli in order of our decreasing sensitivity to them: pitch .3%; length 1%, brightness of lights 1.6%; odor 5%; loudness 10%; pressure on skin 16%; and saltiness of food 20%.

Of course, we don’t usually use our sense of taste to fly. This is fortunate for two reasons. One, we aren’t very sensitive to a change in it. Two, no one can ever tell you that your landings taste a bit “pancake like.”