Navigation

Navigation in a plane or a boat is accomplished using vectors.  In order to navigate from one place to another, the operator of a plane or a boat must consider ALL of the factors that affect the motion of the craft.  Each factor, itself, contributes to the motion as a vector which must be added to the other factors to result in the desired effect.

Plane Navigation Factors:

The ground speed vector will always represent the overall effect of the wind speed and the airspeed on the plane; the ground speed is defined as the sum of the wind speed and the air speed:

v_g =  v_a + v_w

_{Remember:  All of these vectors have directions associated with them and MUST be considered in the vector sum.}

_{Since the overall velocity of an aircraft can be represented by the above vector sum, any one of the vectors in the relationship can be found by rearranging the equation:}

Example:

v_a =  v_g -  v_w

OR

v_w =  v_g -  v_a

_{The trick is to identify which variable is the one that is asked for.  Once the problem is identified, and the vectors are labeled and drawn, the missing vector can be found by performing the vector sum discussed in the Vector section.}

_{Boat Navigation Factors:}

Velocity vector for the water (in a river) including its direction  (vw) Velocity vector for the boat in still water including  its direction (vb) Overall Velocity vector including its direction (v)

The overall velocity vector will always represent the overall effect of the velocity vector for the water and the velocity vector for the boat in still water; the overall velocity is defined as the sum of the two other vectors:

v =  v_b + v_w

_{Remember:  All of these vectors have directions associated with them and MUST be considered in the vector sum.}

_{Since the overall velocity of a boat can be represented by the above vector sum, any one of the vectors in the relationship can be found by rearranging the equation:}

Example:

v_b =  v -  v_w

OR

v_w =  v -  v_b

_{Again, the trick is to identify which variable is the one that is asked for.} 

_{Once the problem is identified, and the vectors are labeled and drawn, the missing vector can be found by performing the vector sum discussed in the Vector section.}