Trigonometric Calculation of Leade Length
Diagrams of chambers can be misleading. Sometimes, it is not clear where the Leade begins and ends. So, for the purpose of characterizing the chamber, we calculate the Leade Length (ℓ) using a couple of reliable specifications and a little bit of trigonometry.
We know that the Leade is the transition from the Freebore (where none of the Lands are exposed) to the Bore (where the full height of the Lands is exposed). From our specifications table, we know the Groove Diamater (ØGR), Land Diameter (ØLN), and Leade Angle (∠L). Using this, we can diagram the Leade as follows:
We can simplify this triangle for our calculation as follows:
And using the Law of Sines, the calculation goes something like this:
∠A = Leade Angle (∠L) in decimal degrees (e.g. 1° 45′ becomes 1.75°).
- If you need to convert from degrees-minutes-seconds to decimal degrees (or vice versa), we use THIS CALCULATOR.
- If you need to convert from taper per inch (tpi) to decimal degrees (or vice versa), we use THIS CALCULATOR.
∠B = 90°
a = Groove Diameter (ØGR) minus Land Diameter (ØLN) divided by 2 (each side of the barre accounts for half of the difference in diameters).
Using the strategy for a right scalene triangle, we can calculate ∠C and solve for c, which is our Leade Length (ℓL):
If you don’t feel like digging through a junk drawer to find a calculator, we use THIS CALCULATOR.