A useful approach in discussing a Finsler manifold \((M,F)\) is a technique called navigation problem: given the metric \(F\) and a vector field \(V\) with \(F(x,V_x)<1\); define a new Finsler metric \(F^*\) by \(F(x,y/F^*(x,y)+V_x=1\) \(\forall x\in M\), \(y\in T_xM\). Randers metrics are among the simplest non-Riemannian Finsler metrics: they are expressed in the form \(F=\alpha+\beta\), where \(\alpha:=(\alpha_{ij}(x)y^iy^j)^{1/2}\) is a Riemannian metric on \(M\) and \(\beta:=b_i(x)y^i\) is a 1-form with \(\| \beta \| _\alpha <1\). A vector field \(V\) on a manifold \(M\) is called homothetic with dilation \(c\) if its flow \(\Phi_t\) satisfies \(F(\Phi_t(x)\), \((\Phi_t)_*y)=\exp(2ct)\cdot F(x,y)\) \(\forall x\in M\), \(y\in T_xM\). Using these notions the authors prove the following two main results. Theorem~1.2: Let \(F=F(x,y)\) be a Finsler metric on a manifold \(M\) and \(V\) a vector field on \(M\) with \(F(x,V_x)<1\); let \(F^*=F^*(x,y)\) denote the Finsler metric on \(M\) defined by the navigation problem; suppose that \(V\) is homothetic with dilation \(c\): then the flag curvature of \(F^*\) and \(F\) is related by \(K_{F^*}(y,y\wedge u)=K_F(y^*,y^*\wedge u)-c^2\), where \(y^*=y-F(x,y)V\). Theorem 1.2: Let \((M,F)\) be a compact Finsler manifold of dimension \(n\geq 3\) and \(V\) a vector field with \(F(x,V_x)<1\); suppose that \(V\) is a homothetic field with dilation \(c\), and \(F\) is of scalar curvature \(K(x,y)\), which satisfies \(\sup K(x,y)