Question:

Using the following information and equations, please answer questions at the bottom. 1. Selected Aircraft: F-15C 2. Maximum Takeoff Weight (MTOW) [lbs] : 68,000 lbs 3. Engine Type and Rated Thrust [lbs] : 2 x Pratt & Whitney F100-PW-220 / 25,000 lbs 4. Total Available Thrust (sum of all engines for multiengine aircraft) [lbs] : 50,000 lbs 5. Maximum Rate of Climb [ft/min]: 30,000 ft / 1 min 6. Take-off distance at MTOW [ft] : 900 ft Uniformly Accelerated Rectilinear Motion and Newton’s Law of Momentum Equations: F = ma m = W/g V F 2 = V I 2 + 2 a s g = 32.2 ft/sec 2 V F = V I + a t Takeoff distance (s) = V F 2 /2a KE = ½ mV 2 PE = Wh HP= T*V kts /325 sin(γ) = (ROC kts )/(V kts ) 1 kt = 1.69 ft/sec Remember to keep track of units, convert as required, and express answers in the requested unit. (Keep in mind that the initial velocity V I for takeoff is zero since we start from a standstill). A. Using your researched data from 2. and 4. above compute the acceleration on the aircraft during the takeoff roll. [ft/sec 2 ] (For this exercise, disregard friction and drag influences. Also, keep in mind that weight is not the same as mass.) B. If your aircraft lifted off the ground at 150kts, what would be the length of the takeoff run? [ft] (Watch for unit conversions.) C. How much time would it take until liftoff at 150kts once the takeoff roll is started? [s] (You will have to algebraically solve the given formula for time ‘t’ first.) D. Determine how fast the airplane should be going when it passes the 1000-foot runway marker (1000 feet from the start of the takeoff roll)? [kts] . (Apply the distance formula as you would for the takeoff run in Question B; however, the distance ‘s’ is now known to be 1000ft and the unknown is the velocity ‘V’. Solve algebraically for ‘V’. Don’t forget that results will have to be converted into kts.) Similar to detailing assumptions and conditions at the onset, any quantitative result of our theoretical work also requires a qualitative discussion of applicability. The important question to discuss is how accurate our result will depict the real world. Possible errors should be identified, our certainty about results evaluated, and additional recommendations for further improvement provided. Therefore, comment on your findings in Questions A through D. Compare your calculated takeoff distance in B with your research in Question 6. What elements did we neglect in the acceleration computed in Question A? How did it affect our further work in B through D? E. What is the power [HP] of the aircraft engines after takeoff at the total available thrust (from Question 4) if flying at 200kts? (Remember, this formula already has unit conversions included) F. What is the Kinetic Energy [ft-lb] of the aircraft at 200kts and Maximum Takeoff Weight (from Question 2)? (Remember, weight is not the same as mass, and watch for unit conversions.) G. What is the Potential Energy [ft-lb] of the aircraft after climbing out to 10,000ft above sea level at Maximum Takeoff Weight (from Question 2)? H. What is the Angle of Climb [deg] for the airplane at 200kts at the maximum rate of climb from Question 5? (Make sure to use vertical speed, i.e. ROC, and horizontal speed, i.e. flight speed, in the same unit and pay attention to your calculator settings for trigonometric functions.)

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