The following definitions and equations provide the scientific basis for determining fly line sink rates. They show how to correctly derive a sink rate based on based the following for inputs: 1) line weight (grains / ft), 2) line diameter, 3) water temperature, and 4) water type (fresh or salt). Of these, line weight and line diameter are the most important. Water temperature and water type make only a few percent difference.
This calculation method is exact in the sense that it is governed entirely by the laws of fluid dynamics and known physical constants.

V
 inches / sec
 Fly line sink rate – terminal velocity of a
level fly line sinking in still water.

W
 grains / ft
 Fly line weight – typically measured by weighing
a section of line on a grain scale and dividing by its length. Most fly lines weigh in the range of 7 to 20
grains per foot.

D
 thousandths of an inch
 Fly line diameter – typically measured with
calipers (be sure to use the lightest possible touch so as to not squeeze the
line). Most sinking fly lines have diameters in the range of 30 to 60
thousandths of an inch.

T
 degrees F
 Water temperature. Our numerical example is based on 55 degrees F.

 slugs / ft^{3}
 Water density. A physical constant determined by water temperature T and type of water (fresh or salt). The density of 55 degree fresh water is 1.939. Salt water and cooler water are slightly denser. See water properties lookup table.

 10^{5} ft^{2} / sec
 Water viscosity. A physical constant determined by water temperature T and type of water (fresh or salt). Kinematic viscosity of 55 degree fresh water is 1.301. Salt water and cooler water are slightly more viscous. See water properties lookup table.

 dimensionless
 Ratio of the circumference to the radius of a
circle = 3.1416.

SG
 dimensionless
 Specific gravity. The ratio of the density of a
fly line to the density of water. Sinking fly lines we have tested have
specific gravity between 1 and 5.

 dimensionless
 Drag coefficient. The drag coefficient of a sinking fly line is
typically between 1.2 and 1.8 and depends directly on Reynolds number Re.

Re
 dimensionless
 Reynolds number.
In fluid dynamics, the ratio of inertial forces to viscous forces. Reynolds numbers in the range of 20 to 250
are typical for fly lines moving in water.

 Specific gravity (SG) of a fly line is its weight per unit volume divided by the weight of water per unit volume. The factor (12^{2} 10^{3}/ 7) converts units of the numerator to be the same as units of the denominator: lbs / ft^{3}. For example, a fly line with W = 10, D = 35, water density = 1.939, and g = 32.174 has SG = 3.43.

 Sink rate V is defined based on the physics of terminal velocity, which is defined by this equation. The downward gravitational force per foot of underwater line (left hand side) = the upward drag force per foot of line moving through the water. The sink rate V is the unique line velocity at which this equation holds true. The factor (7 / 12^{3}) converts the units of the right hand side to grains. In this example, underwater gravitational force = 10 (11/3.43) = 7.1 grains / ft. If drag coefficient = 1.43, D = 35, water density = 1.939, then the drag force (right hand side) = 7.1 grains / ft when V = 6.0. So the fly line sink rate for this example is 6.0 inches per second.

 Reynolds number. The factor (5 / 6)^{2} converts numerator and denominator to the same units: ft^{2} / sec. In this example, Re = 112 based on water viscosity = 1.301, D = 35, and V = 6.0 inches per second.

If you wish to program your own sinkrate calculator, you can do so with the above equations. But since both the terminal velocity and Reynolds number equations depend on sink rate V, you will have to find V by iteration (as we have done for our sink rate lookup tables). An algebraically equivalent expression of these equations  which does not require iteration, which is less intuitive, and which we use in our sink rate calculator  is presented at the end of Jim Havstad's paper. If you program Jim's equations (e.g in a spreadsheet), you will find that they yield the same result as the iterative solution to our equations above.
Extensive independent experiments by Havstad and Fly Fishing Research have confirmed the accuracy of the sink rates predicted by these equations and the accuracy of the equations themselves.

