# 1. Consider an acrobatic aircraft pilot making a perfect circular looping in the air. At the highest point of the looping the altitude is recorded as 3,500 ft and at the lowest point of the looping, the altitude is given as 2,800 ft. • What is the tum radius in the circular looping motion? • Compare the load factor at the highest and the lowest points of the circular looping. Which one corresponds to the lowest load factor? Assume that the looping is made such that the lowest load factor (1.e. the lower load factor in (b)) is zero. What is the instantaneous tum rate at this point? 2. A propeller-driven aircraft is flying with energy height of 20,000 ft at its service ceiling altitude. It is flying at its minimum thrust required conditions and its velocity at this moment is 400 ft/s. The pilot then changes the aircraft’s velocity in order to make a steady climbing manoeuvre to reach higher cruising altitude at the fastest rate possible. Solve for the new energy height of the aircraft after climbing for 3 minutes, assuming the effect of altitude on the rate of climb is negligible during this short climb. 3. A jet aircraft has the following characteristics: takeoff gross weight = 60,000 lb, wing area = 950 ft”, thrust during takeoff=17,000 lb, lift coefficient for ground roll = 0.1 and drag polar, Cp = 0.02 +0.035 C++. The aircraft is to take off from an airport with the following conditions: free stream air density is 2.3769 x 10-3 slugs/ft? gravitational acceleration = 32.2 ft/s and based on the runway surface, the coefficient of ground rolling friction can be taken as 0.05 (with brakes off) and 0.5 (with brakes on). The lift- off velocity of the aircraft is 120 ft/s and time between initiation of rotation and lift-off = 3 seconds. Analyze the required maximum lift coefficient for the aircraft to take-off from this airport, if the allowable ground roll is only 2.500 ft. Hint: Do not make any assumption for the lift-off velocity and for ground roll calculation, use the following formula: 1.21(W/S)) 2W S +1.11 I D Vp. SC. -14, W W Jo.7V,

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