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What altitude would a C-130 be 22km out from takeoff?

An aircraft could take off and use an up-the-stairway pattern to climb to maximum altitude, and thus minimalize the "footprint" over the ground used for the climb. It would take a bit longer, since some energy is lost in the turns, but perhaps well worth the extra time and fuel.

It depends on the takeoff profile (dictated by air traffic control restraints and the threat, among other things) and how they define "small arms." Without knowing departure/approach procedures for Baghdad International, I'd say the aircraft was still under 20K, placing it within reach of 23mm AAA. Anti-aircraft fire of that size is not small arms, but the press (typically) describes anything that shoots bullets as small arms fire. BTW, there are plenty of 23mm guns and ammo left over from Saddam's regime; they're relatively small, mobile, and easy to hide. If the plane was lower, 12.7/14.5 mm heavy machineguns are also a possibility--lots of those in insurgent hands as well.

Finally, it's little consolation for the family of the military member killed aboard that C-130, but the number of firings on coalition aircraft have actually decreased in recent months. When you look at the number of MANPAD SAM and AAA attacks, compared to the number of takeoffs/landings in Iraq, the threat is minimal. My regret is that we don't keep AH-64s or AC-130s on airborne alert, and task them to hose the area where SAMs/small arms fire originates. After a couple of visits from an AC-130, you'd have local Iraqis killling the gunners before they could get off a shot at coalition aircraft. Believe me, you don't want an Apache or AC-130 visiting your neighborhood....