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during rollout upon touching down, I'd often find myself veering off the runway centreline to the left. Everytime I input rudder, I have this feeling that I am getting pulled out of the turn (while that is normal just like turning round a corner in high speeds in a car), and that the aircraft might just flip over. But you see I know my limitations of the car, and that it won't flip unless I yank the steering wheel.

My instructors tell me to just simply keep my feet active but it's the fear of too much input that will cause me to loose directional control of my aircraft.

Upon touching with my main wheels, to maintain centreline, I should just really apply rudder without fear, even though I feel and visually believe that I am going to flip over?

Please advice me on what correct techniques should one apply to keep the aircraft straight during the rollout.

My guess here would be that you are not truly tracking the centerline of the runway on final or on roundout. There’s an easy way to solve that when flying final: if the runway centerline appears pure vertical from your perspective in the airplane, you are tracking the centerline. If it has a slight angle to it, then you’re not totally on centerline.

The differences can be subtle, but can lead to flying a serpentine track toward the runway on final, during roundout, and during ground roll. It can also result in a touchdown with a slight drift to it which indicates poor piloting technique.

To counter this, first, remember to get the final approach stabilized ie on centerline, on glidepath, and on airspeed as soon as possible after rolling out from the base to final turn. Remember the more corrections you need to make to do this closer to the runway threshold, the more difficult the approach becomes and the more likely errors in technique will grow unchecked. Once on a stable final approach, observe the runway centerline and judge if it is a vertical, straight line. If so, you’re tracking straight down the centerline. If not, use shallow, coordinated turns to align the airplane so. This technique will also work when flying a crabbed final in crosswind conditions.

As you roundout, remember you are in slow flight at an increased AoA, so the propeller will tend to pull the airplane’s nose to the left. Under additional right rudder to prevent this and track straight.

After touchdown, use quick precise feetwork for rudder inputs - think “happy feet happy feet happy feet” - to track centerline . Also, if doing a crosswind landing, DON’T RELAX AILERON PRESSURE AFTER TOUCHDOWN or the airplane will tend to veer off centerline rapidly. Remember, fly the airplane all the way through the landing, including the complete rollout.

The chance of flipping due to too much rudder is a very real concern, and perfectly valid. Flipping can happen quite suddenly due to crosswinds, so you are right to be cautious.

My advice: On landing, make sure you hold full back elevator. Many students have a tendency to think they've landed the plane, and then let go of the aerodynamic surfaces like the elevator. Pilots have a saying, "Fly the plane all the way to the gate!" Never treat the plane like a car: It is always "flying", even on the ground.

Holding the elevator full-back after landing takes a lot of pressure off the nose wheel, which makes steering easier and the plane more stable. It also provides a lot of aerodynamic breaking (you have a large metal board sticking up into the wind) which slows the plane down a lot, in a stable, safe manner.

Also, don't necessarily try to stick to the centerline like glue. If you try too hard, you may make drastic and sudden rudder changes which can flip the plane. Instead, work on constantly adjusting towards the centerline. If you're off too the left, use right rudder to aim back towards the centerline; not to hit the centerline immediately, but to adjust your course towards it over the next 2 seconds. Then re-evaluate, and adjust your course closer to the centerline again, never actually getting 100% on the line, but always moving closer and closer to it.

"Trikes" can flip forward left or right, which is why many people prefer "quads" (or having the single wheel in the rear). However, with 2 main wheels down only rudder input will still swing the nose left or right with little danger of flipping.

When you are at landing speed and after mains touch down, the rudder is your friend, use it.
Very good advice to hold nose gear off while your are slowing down. If you are slightly off center, continue controlling the aircraft as it slows down (this includes aileron inputs too) and keep "flying" the plane until it rolls to a complete stop.

But abrupt inputs or sharp swerves are not needed. Easy does it, and differential braking is also helpful. As you gain experience, you will feel more comfortable with its limits.

I would not rule out a taxiing lesson to test and refine your ground control techniques.