Everything in degrees of escape wheel
An escapement has angles at the pallets, angles at the crutch and an arc at the pendulum, and they are all connected by lever lengths that differ from movement to movement. The one place they can be compared without knowing any of that is at the escape wheel itself, which is why drop and lock are conventionally quoted there.
Thirty teeth is twelve degrees from one tooth to the next. Two beats a tooth means the wheel turns six degrees in a beat, so six degrees is the entire budget for what happens between one tick and the next. Allow a degree and a half of drop and a quarter of the beat has gone before anything useful happens.
Degrees you cannot measure, thousandths you can
Nobody measures a degree and a half on a wheel under a loupe. What you can measure is a gap. On a 1.75 inch wheel the tip circle is 5.50 inches round, so a degree and a half at the tip is 0.0229 inches — 23 thou, a visible gap. That conversion runs both ways: one thousandth at the tip is 0.065 degrees, just under four minutes of arc.
Those two numbers are what makes the rest of the page useful. Anything quoted to you in degrees becomes a distance you can see, and anything you measure becomes an angle you can compare.
Pallet span
The span is how many tooth spaces the two pallets reach across, and it is counted rather than calculated. Seven and a half teeth on a thirty tooth wheel is ninety degrees of escape wheel between the faces, a quarter of the wheel. Half spaces are ordinary — they are what puts one pallet on the outside of the wheel and the other on the inside in the arrangement most people picture when they think of an anchor.
Why escapements wear first
At 3,600 beats an hour, the escape wheel turns once a minute, 1,440 times a day. The tip travel adds up to about 46 miles a year, and all of it passes across two small faces which are also carrying the whole of the power that reaches the escapement. Nothing else in the movement does that. It is the reason pallets get grooved, the reason old ones get repositioned rather than replaced, and the reason an escapement is the first thing to look at on a movement that has stopped keeping time rather than stopped altogether.
What this refuses to say
There is no verdict here on whether an escapement will run. That depends on the pallet faces, the lock being safe, the drop not being so large that power is wasted nor so small that a tooth catches, the arc the pendulum actually reaches, and the state of the pivots. Those are watched, felt and adjusted on the bench. This page converts angles to distances and counts what goes past, and stops there.
Questions people ask
How many degrees does an escape wheel turn per beat?
Three hundred and sixty divided by the tooth count and by the beats each tooth gives. A thirty tooth wheel at two beats a tooth turns six degrees a beat, out of twelve degrees between one tooth and the next. Every bit of drop you allow comes out of those six degrees.
How do I convert escapement drop in degrees to a measurable gap?
Work out the tip circumference, which is pi times the diameter over the tooth tips, and take the same fraction of it as the angle is of 360. On a 1.75 inch wheel the tip circle is 5.50 inches, so 1.5 degrees is 0.0229 inches, about 23 thou. Going the other way, one thou at the tip is 0.065 degrees.
What is pallet span measured in?
In escape wheel teeth, and it is counted rather than worked out. Seven and a half teeth means the two pallet faces reach across seven and a half tooth spaces, which on a thirty tooth wheel is ninety degrees of escape wheel. Half spaces are normal and are part of how the two pallets end up on opposite sides of the wheel.
Why is lock not subtracted from the beat like drop is?
Because it is not travel of the escape wheel during the beat. Drop is free movement the wheel makes between releasing one tooth and landing on the next; lock is how far the tooth rests past the point of release on the locking face. The page shows lock converted to a distance at the tip so you can measure it, but keeps it out of the beat budget where it does not belong.
How far do escape wheel teeth travel in a year?
On the defaults, about 46 miles of tooth tip past the pallet faces. The wheel turns once a minute at 3,600 beats an hour, which is 1,440 turns a day and over half a million a year. All of that passes across two small faces carrying the power that reaches the escapement, which is why they are the first surfaces to show wear.