+ 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}