When I first investigated launch profiles, I knew that drag was a factor in the launch process. Drag was mentioned in several texts, and but nothing specific was stated, I felt that a balance must be struck between drag loss and gravity loss to obtain the best thrust profile. For a high acceleration vehicle like a sounding rocket, drag loss should be a major factor. For a slow liftoff vehicle like the Saturn V, tons of propellant go into the fight with gravity. Factoring in the atmospheric drag was the last step in determining the optimum thrust profile for a launch vehicle. And the answer is: ----- Well, I'm no math genius, but I do have a little computer program that will simulate a rocket flight, and with a few lines of code added, ( not a big problem in basic), I let the computer do the work. I set up the program to keep the thrust at a level where the vehicle drag is equal to the vertical loss to gravity. A limit was placed on the maximum acceleration to keep liftoff thrust below infinite, and thrust was allowed to increase as the drag component decreases with altitude. Only the first stage was examined, as other stages operate in vacuum.
The results - Drag is not a factor in the thrust profile of a launch vehicle. (No Problema!) Well, it's not nearly as great a factor as gravity. You have to design the nose of the rocket to withstand the force of drag, and the heat of air friction, and as a negative force to thrust, but drag can be largely ignored for any practical thrust profile. You have to get up into the acceleration levels that start to tear components off circuit boards before drag becomes a factor in determining launch thrust profiles. The only factors that limit the thrust profile of a launch vehicle are, the strength of the payload and vehicle structure, and the comfort of the passengers. So, why did NASA spend millions of dollars to develop rocket engines for the Space Shuttle that could be throttled down to limit the effects of drag? Because the Space Shuttle in it's launch configuration is an aerodynamic abomination that would be damaged by severe aerodynamic forces, that's why. But why does NASA continue to invest millions in throttleable engines?
****To make comparison of launch vehicles easier, to focus launch vehicle development on economics, and to honor Arthur Schnitt who started the Big Dumb Booster idea, I propose that the unit of measure of launch vehicle economics be called the "Schnitt". Or more specifically M/s/$/Kg(payload)=Schnitt. (For Americans it would be Ft/s/$/#=Schnitt A') :-)