Editing Reaction ferry (section)

==Physical explanation==
[[Image:ReactionFerryForceDiagram.svg|right|thumb|300 px|Force diagram of a reaction ferry with a traveller]]
A reaction ferry operates as a [[sailing]] craft where the traveller pulleys represent the wheels of a land yacht and the moving fluid is the water current rather than the wind. In the case of a reaction ferry with an anchored tether, the analogy can also be to a [[kite]]. In both cases the ferry's hull itself represents a sail and is angled to the apparent water current in order to generate lift in the same way a sail is set at an angle to the [[apparent wind]].

With an overhead cable stretched across a river at right angles to the current, the ferry is, in sailing terminology, [[Point of sail|sailing on a reach]] with the true current exactly at right angles to the direction of crossing. For the anchored-tether type ferry this is valid when the tether is parallel to the current, near the middle of crossing. In sailing, the speed is governed by the [[lift-to-drag ratio]]s (L/D) of the sail and the hull including centerboard or keel and rudder.<ref>Bruce, Edmond & Morss, Harry ''Design for Fast Sailing''. Amateur Yacht Research Society, 1976, pp. 92-117.</ref>

For reaction ferries, L/D ratios also apply except that one is very high, for example typically 30 for a traveller on a steel rope, as visible in aerial photographs, and the other can vary from low, e.g. 1-2 without a centerboard, to 3.5 with one.<ref name="Bruce" />

A diagram is shown which follows the standard force diagram for sailing.<ref name="Bruce">{{cite journal |last1=Bruce |first1=Edmond |title=The physics of sailing craft as revealed by measurements at full size |journal=A.Y.R.S. Publication |date=July 1962 |issue=40 |pages=23–55 |url=https://www.ayrs.org/repository/AYRS040.all_A5.pdf |access-date=15 March 2023}}</ref><ref>{{cite book |last1=Marchaj |first1=C. A. |title=Sailing Theory and Practice |date=1977 |publisher=Adlard Coles Limited |page=121}}</ref> It is drawn with a traveller L/D of only about 6 in order to make it clearer. The ferry L/D is drawn at 1.5. The lift L acts at right angles to the direction of the apparent current, the [[Euclidean vector#Addition and subtraction|vector sum]] of the true current and the current component due to the crossing speed. The drag D acts parallel to the apparent current. The vector sum of L and D is the resultant force R. This force can only exist because the tether exerts an opposed force of the same magnitude (see [[Newton's laws of motion]]), in this simplified two-dimensional projection of what is really a three-dimensional situation. R can be resolved in a drag component directly downstream and a component in the direction of crossing, the thrust T which drives the ferry. This is balanced by the opposing drag of the traveller pulleys. The amount of lift required is set by the angle of incidence of the ferry to the apparent current (here 10°), often done with a rudder (not shown).

In the figure the crossing speed is the same as the speed of the true current. With a centerboard or keel, the hull's L/D could increase several times. This would increase the crossing speed also several times, but according to the [[Drag (physics)#The drag equation|drag equation]] the forces increase with the square of the speed and put a great load particularly on the overhead cable. With the anchored-tether type ferry, such high speeds would be unobtainable because its tether drags in the water or is supported by buoys that do and this drag would also increase with the square of the speed.