I am part of an open-source project developing a simulation of a Cessna 172P. We are tweaking our flight dynamic model at the moment and we are looking for feedback from people with real life experience on the 172. In particular, we would like to know how much rudder input does this aircraft require during a take off roll (with no winds) in order to keep it centred on the runway.
With several hundred hours logged on multiple variants of the 172, I would give the relative answer of ‘not much’. In my experience a C-172 tracks pretty straight with only slight right rudder pressure needed on the ground roll. It is much less than what is required for a C-182, 206, 210 or other high performance single engine Cessnas and much less that a lot of tailwheel airplanes I’ve flown.
It seems like in a 172 when you are brakes off and rolling, I usually rest my heels on the cockpit floor and apply a slight pressure on the base of the right rudder pedal with the ball of my right foot. It is necessary as the plane will waltz to the left during the takeoff roll if you don’t. But the force applied and the deflection of the right rudder pedal is light and limited, if you do it right.
A recommendation might be to send a developer down to a local flight school operating the C-172 and arrange to practice takeoffs and landings with a CFI so they can get an empirical sense for what rudder input is needed on a takeoff roll.
Wayne Conrad made a very important point in the comments which deserves serious consideration. Namely, flying is done by force, not by position. 'Apply that much pressure' rather than 'move by that much'. (This, in fact, applies to most well-designed controls of such kind, for example, brakes in your car).
This is beneficial for dynamic control because we have a better force feedback in our muscles than a position feedback.
But this raises two problems for simulation. First, a certain amount of pressure (which normally provides a certain amount of net effect) translates to different amount of movement in different conditions, particularly at different speeds.
For takeoff roll this is even more complicated because the nose wheel works proportionally to position (and even this is not quite true because the linkages have springs), while the rudder works proportionally to force, and one gives way to another during the roll. In practice, I'd say, you need to gradually increase the pressure while the amount of actual deflection reduces!
Second, all stock PC gaming controls work by position and cannot re-create a realistic force feedback. So unless you are building a simulator with specialised control loading, you can give up any hope of creating a simulator that feels even remotely correct at the controls. This is, perhaps, the source of much disagreement between pilots when they are asked to evaluate such a simulator.
For this reason, it may be better not to pursue 'true' control inputs for a PC simulator. It may be unflyable. For example, if I say that C172 requires about 10% or rudder deflection during takeoff (which is not too far from the truth) and you implement it thusly, I bet I myself would find it difficult to keep the model on the centreline. The truth is, what I remember is not the 10% deflection but rather (say) a couple of kg of force that is required. Yet this force will push most PC pedals to the limit, or at least much farther than 10%. And doing 10% corrections would be difficult, because the force required is so light. So in the end it may feel more real, or at least more flyable, if you make it 50% rather than the 'true' 10%: it will be closer to the true force, which is far more important.
But then, how do you simulate full deflection? Well, you cheat. You add significant non-linearities (S-curves) to the controls, you treat on-the-ground conditions differently to flight, etc. This may sound anathema, but it may be a better compromise and may create a better simulator.
it's difficult to answer this question. depends on the engine, how you apply your power, the wind etc. there is no definitive answer as to how much, you just give the airplane what it needs at that given moment. even if there is no wind, the Left turning tendency of the airplane will still require some right rudder to be applied.