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I remember that there were countless incidents occurred in which the aircraft sits on the tail as the aircraft was heavily loaded at the back of the cargo and/or cabin compartments or the cargo compartments were offloaded incorrect order. I know that these incidents are more commonly happen in cargo aircrafts.

Is there a risk that the aircraft will sit on the tail during the pushback process as a result of the tri-cycle design of the aircraft?

Is there any tail tipping incident reported during pushback/towing operation?

Which types of aircraft (narrow/wide body) can this risk be higher?

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    $\begingroup$ As far as I know the aircraft landing gear is required to carry at least 4 or 5% or even more for the most aft center of gravity position (I think it was for ground operations within the allowable takeoff and landing cg range). That means for a light 48t aircraft you still have 1.9t resting on the nose gear, forcing the nose down. Not that easy to push over....The risk of tail tipping is only present when the aircraft is being loaded where you get ugly transient cg changes but not when it is fully loaded and the cg range is back within calculated limitations. $\endgroup$ – Jan May 18 at 19:56
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    $\begingroup$ Tipping could occur if pitch-up moment was created by braking with the main gear brakes. This is a risk in power-backing (using aircraft's own reverse thrust), but during push-back the brakes on the tug are used, so it shouldn't be possible. $\endgroup$ – Jan Hudec May 18 at 20:13
  • $\begingroup$ Btw I saw a tip-over happen once of a non-flying 727 at a museum, after it got covered in freezing rain. No idea if its CG was anywhere near the prescribed CG for flight, before the ice accumulation. $\endgroup$ – quiet flyer Jun 17 at 21:08
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During pushback the (usually quite substantial) weight of the tug pulls the nose down, and additionally when it's pushing backward the line of force is below the CG and acting rearward, so that would also tend to counteract any tipover tendency.

As Jan mentions in comments, the tipover situations tend to happen during loading when the CG is moving around. I suppose if the tug were first attached and then the aircraft were grossly misloaded, it's conceivable that it could tip over backward as the tug detaches and removes it's weight, but I've never heard of that happening.

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