Exercise 1: Rectilinear Motion
The first part of this week’s assignment is to choose and research a turbine powered (i.e. jet type) aircraft. You will further use your selected aircraft in subsequent assignments, so be specific and make sure to stay relatively conventional with your choice in order to prevent having trouble finding the required data during your later research. Also, if you find multiple numbers (e.g. for different aircraft series, different configurations, and/or different operating conditions), please pick only one for your further work, but make sure to detail your choice in your answer (i.e. comment on the condition) and stay consistent with that choice throughout subsequent work.
In contrast to formal research for other work in your academic program at ERAU, Wikipedia may be used as a starting point for this assignment. However, DO NOT USE PROPRIETARY OR CLASSIFIED INFORMATION even if you happen to have access in your line of work.
Keep in mind that any theoretical solution to a complex, unique real world problem is based on models and generalizations, requiring certain assumptions and simplifications, and comes with a variety of limitations as to its applicability. Therefore, detailing conditions and selections is a fundamental part of a scientifically sound approach and documentation of your solution to the problems.
1. Selected Aircraft:
2. Maximum Takeoff Weight (MTOW) [lbs]:
3. Engine Type and Rated Thrust [lbs]:
4. Total Available Thrust (sum of all engines for multiengine aircraft) [lbs]:
5. Maximum Rate of Climb [ft/min]:
6. Take-off distance at MTOW [ft]:
Uniformly Accelerated Rectilinear Motion and Newton’s Law of Momentum
F = ma m = W/g
VF 2 = VI 2 + 2 a s g = 32.2 ft/sec2
VF = VI + a t Takeoff distance (s) = VF 2 /2a
KE = ½ mV2PE = Wh
HP= T*Vkts /325 sin(γ) = (ROCkts)/(Vkts)
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 VI for takeoff is zero since we start from a standstill).
A. Using your researched data, compute the acceleration on the aircraft during the takeoff roll. [ft/sec2] (Keepin 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 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?
(see & compare also formula given above with the calculation examples within the module)
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)?
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.)
Similar to your discussion for questions A through D, comment on your E through H results. How realistic do you think energies in question F & G were calculated? Which assumption in those questions most probably would have changed in a real flight and how would it have affected results?
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