On June 26, 1990, the high temperature recorded at PHX at approximately 4 pm was 122 oF and the barometric pressure was 29.65 inHg. Assume that the pressue reading is taken in a room where the pressure is equalized with the atmosphere, but the temperature is kept at 20 oC. The density of mercury at 40°C is 13,496.9 kg/m3, and the density decreases by approximately 2.44 kg/m3 per degree C. That is, for every degree above 40°C, the density will be reduced below 13,496.9 kg/m" by 2.44 kg/m. (a) What was the air density at PHX at 4 pm on June 20?
(b) The takeoff ground roll distance for an aircraft is approximately given as
dTo = 1.21/g W/s/pCLmax(T/W)
where W - aircraft weight, S - wing planform area, CLmax - maximum lift coefficient (a characteristic of the wing), and T - maximum engine thrust. The maxium available thrust for a turbofan engine is approximately directly proportional to air density. For an aircraft with a given takeoff weight, how much longer runway would be required on this hot day than would be required on a sea-level standard day (rho = 1.225 kg/m3).