A comparison
First, we show two graphs together (with lift and without lift.) The bold curve represents the model for lift, and the thin curve represent the model in the absence of lift.
Input :=
Plot[{FuncLift, RangeNoLift}, {th, 2.5, 15},
PlotStyle -> {AbsoluteThickness[4],
AbsoluteThickness[1]},
AxesLabel -> {"angle [deg]", "range [m]"},
PlotRange -> {{0, 16}, {0, 200}}]
Output =
-Graphics-
To quantify the effects of lift, we will study the difference of the two functions.
Input :=
Diff = FuncLift - RangeNoLift;
Input :=
Plot[Diff, {th, 2.5, 15},
AxesLabel -> {"angle [deg]", "range difference [m]"}]
Output =
-Graphics-
The maximum difference seems to occur at a launch angle of about 4 degrees and the minimum distance occurs at the largest launch of 15 degrees. We can determine the precise launch for which the maximum range distance occurs using calculus.
Input :=
der = D[Diff, th];
FindRoot[der == 0, {th, 4}]
Output =
{th -> 3.74397}