Collisions model

Collisions between fast vessels and large cetaceans have emerged as a problem since speeds above 14 knots became common.

The free program Collision.exe (325 KB) provides a simple 2 dimensional model of maximum possible collision rates based on vessel size and track lengths, plus whale size, population density and mean surface time.

Sperm whale ship strike

The basis of the model is:

Assume:

The vulnerable parts of the whale can be represented as a line of the same length as the whale.
The whale's orientation relative to the direction of travel of the ferry is random.
The whale does not tend to move into or out of the ferry's path.
The ferry transect has an overall density of whales that is the same as some larger area from which a survey has given a density estimate.
Ferries do not avoid whales.

Specify or measure:

L	whale length, m.
T	fraction of whale time at surface.
W	damaging width of the ferry, m.
P	whale population density – animals per sq. km. in a survey area including the ferry transect.
D	distance travelled by the ferry within the population survey area, km.
Y	yearly number of transects by the ferries.

Then:

The whale as a horizontal linear target at random orientation to the ferry's line of travel will present an average 'target size' of 0.64 * whale's length. The whale could be viewed as a point and half the 'target size' of the whale can then be added to both sides of the 'damaging width' of the ferry to give a 'collision strip width' of W + 1.27L. From the length of the ferry transect a 'collision area' can then be derived - (W+ 1.27L)*D/1000 sq km. With the number of transects per year and the density of whales at risk this gives:

Annual collisions = (W + 0.64L)*D/1000*Y*T*P

Sources of Error

Errors in estimating L, T, W and P could be significant, as could errors in the assumptions above:

Assumption
1	Reasonable, could overestimate slightly.
2	Ferries crossing migratory pathways between islands would have up to 56% higher risks; whales orientating way from noisy ferries would have lower risks – any evidence?
3	The whale does not tend to move into or out of the ferry's path. Probably reasonable for high speed ferries because the difficulty for a whale of estimating the track of a fast ferry even if it tried to do this and avoid it. Diving might occur?
4	Errors possible.
5	Species with a highly visible blow might often be avoided by ferries in daylight, but not in darkness.
L	The tail may be at lower risk, making the 'risk length' shorter than this.
T	Time just below surface will also be at risk.
W	Displacement of the whale with the water flow around the hull may reduce this factor.