When certifying a new aircraft through the FAA, will they certify the AC for just one takeoff distance based on the max payload capacity, or can you get the AC certified for multiple runway lengths based on the amount of weight it is carrying at the time of takeoff?
Generally an aircraft will be certified for a range of runway distances based on headwind/air temp/weight, a correction chart will be provided in the POH allowing you to compute the runway distance for various conditions. For example here is the chart for the PA-28-161 I trained on
The AC that covers aircraft certification can be found here and interestingly the distances are computed from standstill to the point at which the lowest part of the aircraft is 35ft above the ground.
(1) The takeoff distance on a dry runway is the greater of the two distances depicted in (a) or (b) below (see page 63 of above linked doc). The distances indicated below are measured horizontally from the main landing gears at initial brake release to that same point on the airplane when the lowest part of the departing airplane is 35 ft. above the surface of the runway.
Aircraft are not certified for one particular runway distance. They are certified to an absolute max structural takeoff weight, for airborne performance or engine out obstacle clearance.
Performance charts will dictate the runway length required for any given takeoff weight and given weather conditions. If the runway is too short for that weight then the weight may be reduced by fuel load or payload. In that case the max weight is “runway limited”.
So in effect, Yes, an aircraft may use any runway length provided the weight allows sufficient obstacle clearance performance.