Position sensitivity along the pendulum rod
Position sensitivity along the pendulum rod
Abstract and Keywords
Every clock's pendulum needs a fine trim to adjust its rate to the desired value. This is frequently done by adding small weights to a weight pan, which is usually located about one-third of the way down the pendulum rod. The clock literature says that the effect of adding a small weight to a pendulum will vary, depending on the weight's location along the pendulum rod. The literature also says that the weight will have maximum effect on the pendulum's rate if placed halfway between the bob and the suspension spring, and will have zero effect if placed at the center of the bob or at the suspension spring. This chapter describes an experiment that was carried out to measure the position sensitivity of a pendulum rod by clamping a 24-gram weight on the pendulum rod at a given location and calculating the change in clock rate.
Every clock’s pendulum needs a fine trim to adjust its rate to the desired value. This is frequently done by adding small weights to a weight pan, which is usually located about one-third of the way down the pendulum rod.1 The clock literature says that the effect of adding a small weight to a pendulum will vary depending on the weight’s location along the pendulum rod. The literature also says that the weight (1) will have maximum effect on the pendulum’s rate if placed halfway between the bob and the suspension spring, and (2) will have zero effect if placed at the center of the bob or at the suspension spring. For the suspension spring, it would be more exact to say that the zero effect occurs where the pendulum’s axis of rotation is located, along the finite length of the suspension spring.
I have never seen a position sensitivity curve for a pendulum rod, and decided to measure one on a real pendulum. The primary reason for doing so was that I wanted to put a fine rate adjustment near the top of a pendulum rod—threading the rod end and adjusting the position of a nut on the threaded segment. The threaded segment is 1.4–2.4 in. below the pendulum’s axis of rotation. There is an advantage2 to putting a fine rate trim at the top of the rod, but the position sensitivity was not known for this location.
The experimental technique used to measure the position sensitivity was to clamp a 24 g weight on the pendulum rod at a given location, and measure the change in clock rate. The weight was then moved to another location about 4 in. down the rod, and the change in clock rate with and without the weight attached was again measured. The full length of the rod was covered in this fashion, resulting in the position sensitivity curve shown in Figure 24.1. The pendulum is shown directly beside the sensitivity curve, and is drawn to the same scale, so as to make it easier to correlate the measured sensitivity with position along the pendulum rod. Since the 24 g weight has no effect on clock rate when placed at the axis of rotation (suspension spring) and bob center positions, the sensitivity curve shows a zero change in clock rate at those two locations.
To repeat, position sensitivity means how much does the clock rate change when a small weight is added at various positions along the pendulum rod. And as the literature indicated, a maximum change in clock rate does occur at the halfway point (point H in Figure 24.1) between the suspension spring and the center of the bob. The clock speeds up if the weight is added above the bob, and slows down if the weight is added below the bob. But what the literature does not say is that if the pendulum rod extends for more than a short distance (6–7 in. for a 1 s beat pendulum) below the bob, you will get an even higher sensitivity at the bottom end of the rod.
But if the weight is moved along the rod, instead of being added to or removed from the rod, the situation is quite different, as is shown in Figure 24.2. When the weight is moved along the rod, the position sensitivity varies with the slope of the line in Figure 24.1. More particularly it varies with the tangent of the angle between the vertical axis in Figure 24.1 and a line drawn tangent to the data line at each point along the data line. The actual sensitivity of moving a 27 g nut one revolution (32 threads/in.) at the top of the pendulum rod (2 in. below the pendulum’s axis of rotation) was measured as 0.11 s/day/revolution. So for a 24 g nut, the same weight as was used for Figure 24.1, the sensitivity would be 0.097 s/day/revolution at this position. Combining this scale factor with the slope of the line in Figure 24.1 then gives Figure 24.2, which turns out to be a straight line.
Figure 24.2 shows the position sensitivity when a 24 g weight is moved along the pendulum rod. The maximum sensitivity, that is, the maximum change in clock rate per unit of distance traveled by the weight along the rod, occurs at the top and bottom ends of the rod. And there is good sensitivity right at the pendulum’s axis of rotation and at the bob’s position. Contrast this with the first case wherein the weight was being added to the rod, and where the sensitivity was zero at these two positions.
Moving the weight downward along the rod makes the clock speed up if the weight is above the halfway point (point H in Figures 24.1 and 24.2) between the suspension spring and the bob. If the weight is below the halfway point (point H), moving the weight downward makes the clock slow down. The sensitivity is zero at the halfway point (point H in Figure 24.2), and this is obviously not a good location to put a rate trimming device that moves along the rod.
One good result of this test is that the top end of the rod turns out to be a good place to put a threaded nut for clock rate adjustment. Using a thread of 32 threads/in., one revolution of a 50 g nut will change the clock rate by the desired sensitivity of 0.2 s/day.
(p.169) The nut’s clock rate sensitivity depends on the ratio of the nut’s weight to that of the pendulum’s bob. The data here was taken with a bob weighing 18.4 lb. If a different bob weight is used, the position sensitivity numbers in Figures 24.1 and 24.2 should be changed in inverse proportion to the new bob weight. (p.170)
(1) This location is apparently based on getting the weight pan as high as possible on the pendulum rod while still keeping the weight pan below the clock dial, so that the weights on the weight pan can be easily changed.
(2) The advantage is that the nut can be adjusted here while the clock is running, with little or no disturbance of the pendulum. And if the thread is lapped smooth, it will have an adjustment sensitivity of about 0.001 s/day (1.8° rotation of a 50 g nut). The weight pan approach has approximately equal sensitivity, with 0.001 s/day corresponding roughly to a 0.001 g weight, which is the usual minimum size available.