The airplane will accelerate a little bit faster with no flaps.
Not an enormous amount, but a little. This is for several reasons:
1) a tiny little bit of aerodynamic "parasite" drag from the flaps themselves, then
2) more parasite drag from the prop wash impacting the flaps, and then
3) another little bit of "induced drag" from deflecting the prop wash downward instead of 100% rearward (Deflecting the airflow downward creates lift, which is good, but lift ALWAYS creates drag, and any drag created
before the airplane can fly is just drag), then
3) a little bit of reduced thrust from impeding the outflow field from the propeller .
Physics do not lie.
Any drag source (brakes, spoilers, flaps, drogue chutes, open doors, tiedowns still connected to Earth) will act against acceleration.
Another overlooked issue is that pushing forward on the yoke to raise the tail also requires energy... you are lifting 100+ pounds of tail weight off the ground. That energy comes from somewhere, and like it or not this energy is subtracted from the energy available to accelerate the airplane down the runway. There will be some airplanes where pushing the yoke forward is worthwhile (because the wing makes enough drag tail-down that it is worth the small drag to lift the tail because the tail-up wing makes so much less). That will likely vary from airplane to airplane, a biplane with a long tail arm will be worthwhile and a clean monoplane with a short tail arm will not be worth the trade-off.
At a certain speed, lift becomes more important than acceleration, because you have reached some minimum speed that the airplane is just capable of flying. At that speed, sacrificing drag in favor of making as much lift as you can becomes worthwhile. So at that speed, pulling back on the yoke to raise the AoA, deploying flaps, drooping the ailerons, turning the thrust line upward, deflecting the propeller outflow downward, compressing the tail spring, (and anything else that produces lift) can do something good for you.
Other very significant factors come into play, such as runway/obstacle visibility, forward visibility on climb out, time and pilot workload required to deploy and retract the flaps, availability of full control movement, etc. These factors have influenced the decisions and techniques of many many pilots.
A lot of pilots sacrifice some STOL performance because of these factors, and they are simply not using all of the capability of the airplane.
Most everyone here knows that I have a commercial interest in this discussion, but I would stand by these statements even if I were not in the flap handle business. (3 new orders from ACSpruce today
