An excellent question, though one I believe is asked in jest. Your question references the 1975 film Monty Python and the Holy Grail. The generally accepted appropriate response among fans of the comedy troupe Monty Python is to ask, "African or European?"
Fortunately, science graphics editor for the New York Times, Jonathan Corum, has actually done the mathematics for this question. While kinematic data on the African species of swallows is difficult to find, he was able to cite a study by the University of Capetown on the average body mass and wing length of European swallows. Using a published formula (three times frequency times amplitude) to determine the speed of a flying animal, he estimates that the airspeed velocity of an unladen European swallow is roughly 11 meters per second.
To calculate the airspeed velocity of an unladen African swallow would require more demographic data on the populations of African species of swallow.