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I notice both swept wing jets tend to "tumble" with greater amounts of pitching than the straight wing aircraft I've spun. Can anyone reflect on this or explain why?
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Similar reasons as to why pitching up/down in the stall is more of an issue for swept wing types. A classical spin is essentially an auto-rotative stall; the spin is in part 'powered' by the wings being stalled. With the wings being swept, as the degree to which each wing is stalled varies the aircraft pitches up and down a bit.
Another factor will be inertia effects; these aircraft, being larger/heavier, may have more pronounced inertia ratios between Ixx and Iyy or Izz - which can be a big player in the nature of the spin. BAC found significant variation in the spinning behaviour of Jaguar with relatively minor design changes, partly due to inertia effects I believe (there's an ancient RAE note on spinning characteristics, derived mainly from WW2 experience, which identified Iyy/Ixx as a significant parameter, IIRC. A similar analysis holds for more modern types, although it takes a bit of jiggery-pokery to make it work)
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The reason for no inverted spinning in the Hawk? Could that be the disturbed airflow over the wing blanking the rudder?
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One of the problems with inverted spinning a Hawk is that the rudder loads (it's manual) become huge. In an erect Hawk spin the rudder either stays more-or-less straight, or can be kept there fairly easily; IIRC, the technique to keep the spin going is to hold pro-spin rudder, and centralising it is both easy and a prompt recovery action. Inverted, the rudder hinge memoents blow the rudder to the pro-spin direction; it can require CONSIDERABLE pilot effort to get the rudder central in order to effect a recovery (IIRC, one flight, which MAY have been an ETPS flight, ended up with BOTH crew pushing the pedals to get it centralised).