Leaping Calculations


Leaping calculations are performed by FishXing when the Outlet Criteria is set to Max Leap Speed within the FishXing Input Window and the fish is unable to swim into the outlet.

Note: If the Fish species does not leap, set the Max Leap Speed to zero. If the fish is unable to swim into the outlet FishXing reports a leap barrier at that flow.

Location of Leap

When modeling leaping performance at a stream crossing, FishXing assumes the fish leaps from the location where the plunging water impacts the outlet pool.  The horizontal (L) and vertical (H) distance the fish must leap is determined from the plunging water calculations.

Projectile Physics of Fish

For species that are able to leap, FishXing assumes they leap out of the water along a parabolic path that is described by standard projectile equations, similar to the equations used to describe the path of the plunging water as it exits the culvert. Since a fish primarily uses its tail for propulsion, it is able to continue propelling itself until its tail leaves the water.  To account for this, FishXing subtracts the length of the fish (f) from the overall distance it must leap.

Whether a fish can successfully leap into the culvert outlet depends on the speed and direction of the fish as it exits the water. Most investigators have found that fish leaps are more successful when the fish lands horizontally at the crest of the outfall (Stuart 1962; Lauritzen 2002).  Therefore, FishXing calculates the velocity (Vleap) and angle (leap) the fish must leap from the outlet pool to successfully land horizontal on the water surface using the following form of the projectile equations:


H = Vertical leap distance

L = Horizontal leap distance

Vleap = Leap velocity

leap = Leap angle

g = Gravitational acceleration

t = Time



Rewriting in terms of Vleap:



a = L - f cos leap

b = H - f sin leap

f  = Fish Length


Through an iterative process, the two equations are solved simultaneously for the two unknown variables: leap velocity (Vleap) and leap angle (leap) required to land horizontally.

A fish unable to leap at the required leap velocity (Vleap) is unable to enter the culvert outlet.  If the required leap velocity is greater than the maximum leap speed entered within the Fisheries Information section of the Input Window, the crossing is considered a leap barrier at that particular flow.

 Photos of Fish Leaps

See Also: Outlet Drop Criteria, Minimum Pool Depth, Leaping Capabilities, Leaping from Plunge Pools