Timing by Hand: Your Reaction Time Is the Biggest Error in the Experiment

Start the watch and stop it as fast as you can. The time you get is roughly your reaction spread — the difference between your start reaction and your stop reaction. Do it ten times and record the whole set. Expect something in the region of 0.1 to 0.2 s, varying by several hundredths. That number is yours, it changes with fatigue and practice, and it is the floor under every interval you time by hand. The falling-ruler test gives the same answer more convincingly: a partner drops a ruler between your fingers and you catch it, and the distance it fell converts to a time. 20 cm of fall is about 0.2 s. It costs nothing and makes the size of the effect impossible to argue with.

Start the watch on a swing and call that swing ZERO, not one. Counting the starting swing as one gives a count that is one too high and a period that is systematically short — the commonest single mistake in bench timing. Count out loud, and take the count at the same point in the motion every time. The centre of the swing is far better than the end: the pendulum is moving fastest there, so it passes the mark sharply, while at the ends it dawdles and the instant is impossible to judge. A fixed marker helps more than it sounds — a pin, a chalk line, the edge of something behind the bob. Judging when the bob passes a mark is a much easier task than judging when it reaches a position in mid-air, and the whole error here is a judgement error.

Some intervals cannot be stretched. A falling ball takes half a second from a metre, and you cannot drop it a hundred times in a row and time the lot. When the interval is short and cannot be extended, replace the HAND rather than trying harder. A light gate, a microphone triggering on the impact, a phone recording at high frame rate and counted back frame by frame — all remove the reaction time entirely and cost very little. Or measure something else. Timing a fall is hard; measuring how FAR it fell is easy and the arithmetic converts one to the other. Changing which quantity you measure is often cheaper than improving how you measure the awkward one, and that is worth asking before every timed experiment.