The Graham design in chapter 5 did not maximize efficiency, whereas the drawing in chapter 3, before modification, had the maximum achievable efficiency. The modified Graham was less efficient because of lock: if modified with maximum efficiency, the escape tooth would always land on the pallet's entrance corner. The reason the Graham pallets could not be modified as efficiently as possible, whereas an efficient watch escapement could be created (and it would work in a simulation), is because of the design of the escape wheel. The watch escape wheel has an impulse face of its own and its let-off corner is above its entrance corner, which creates lock. The back
of the tooth makes it possible to reduce drop without binding. The watch escape wheel offers these two design advantages. If the Graham escapement were designed with a club-tooth type escape wheel, the pallets could easily be modified in a more efficient design that would work in a simulation. These pallets would be much thinner and of equidistant impulse.
There are other ways to change the design of the Graham. The 30 tooth escape
wheel is the most widely accepted choice because grandfather clocks with the
one-second pendulum could display a second hand moving by one second at a time. If the issue of efficiency were considered, the 15 tooth escape wheel would be more efficient by 8.33%. Since the drop requirement is the same for both the 15 and 30 tooth designs, the 15 tooth design loses 1º for drop out of every 12º, but the 30 tooth design loses 1º out of every 6º. If the Graham were designed with a 15 tooth escape wheel, its efficiency could be improved significantly.
However, the 15 tooth escape wheel rotates by 12º per beat, so if
the pallet circle's radius were equal to the escape circle's radius, the pendulum would have a greater arc of swing, which would be undesirable. By increasing the pallet circle's radius to approximately double the escape circle's radius, (because the angle of rotation per beat is doubled), the arc of swing of the pendulum could remain virtually unchanged. With a 5.5 tooth span, the pallet circle's radius increases from 3" to 6.74". Thicker, stronger pallets and escape teeth could then be designed.
The drawing below shows how the impulse face of the escape tooth extends beyond the circumference of the escape circle, which passes through the tooth's entrance corner. This is how lock could be created and yet maximize the efficiency of the pallet impulse face's angle.
This design has practical limitations. It would require either a two-second
pendulum or that a different set of gear train ratios be used to keep the one-second
pendulum. An appropriate gear train combination could be found in the De Carle
"Watch and Clock Encyclopedia." If a two-second pendulum were used, a 60 second
dial could be used, but the second hand would move forwards every two seconds.
Nevertheless, this example should be useful to clockmakers interested in escapement design because an efficiency improvement of over 8% is well worth considering.