Exercise 2

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Aerospace Engineering

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Dec 6, 2023

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AS 420 Flight Technique Analysis Exercise 2 (ver. 5-18-2021) Jet Transport Climb Profiles Tyler Smith and Shubhanu Mukherjee OBJECTIVE : To be able to explain the various factors to maximize climb performance in a jet transport aircraft. Further to be able to explain the different climb profiles. PRE-EXERCISE QUESTIONS: 1. Of the three speeds (255 IAS, 285 IAS, 320 IAS) which do you think would yield the highest rate of climb? 285 KIAS, a good compensation between the angle and the speed 2. Of the three speeds (255 IAS, 285 IAS, 320 IAS) which do you think would yield the highest angle of climb? 255 KIAS, low speed, high AOA 3. What do you think happens to the IAS while climbing with a constant Mach number? IAS goes down as speed of sound gradually decreases with altitude. READING: Various documents posted on Canvas MANEUVERS: Maneuver 2.1 255 KIAS climb. Initial Conditions Altitude 1,000’ Weight 800,000 pounds Flaps 0 degrees Gear Up N1/EPR Max Continuous Airspeed 255 KIAS Procedure: These situations start on MOTION FREEZE. Press M to release motion freeze. With Maximum Continuous Thrust, autopilot VNAV climb to FL 330 at 255 KIAS. Maneuver 2.2 255/285 KIAS climb. Initial Conditions Altitude 1,000’ Weight 800,000 pounds Flaps 0 degrees Gear Up N1/EPR Max Continuous Airspeed 255/285 KIAS Procedure: With Maximum Continuous Thrust, autopilot VNAV climb to FL 330 at 255 KIAS until 10,000’, then 285 KIAS.

Maneuver 2.3 255/320 KIAS climb. Initial Conditions Altitude 1,000’ Weight 800,000 pounds Flaps 0 degrees Gear Up N1/EPR Max Continuous Airspeed 255/320 KIAS Procedure: With Maximum Continuous Thrust, autopilot VNAV climb to FL 330 at 255 KIAS until 10,000’, then 320 KIAS. Maneuver 2.4 255/M 0.78 climb. Initial Conditions Altitude 1,000’ Weight 800,000 pounds Flaps 0 degrees Gear Up N1/EPR Max Continuous Airspeed 255 KIAS/M 0.78 Procedure: With Maximum Continuous Thrust, autopilot VNAV climb to FL 330 at 255 KIAS until 10,000’, then Mach 0.78. Note: Climb speed after 10,000’ will initially be limited to VMO (max airspeed) but will eventually reach Mach 0.78. Maneuver 2.5 Mach crossover climb 255/285/M0.78. Initial Conditions Altitude 1,000’ Weight 800,000 pounds Flaps 0 degrees Gear Up N1/EPR Max Continuous Airspeed 255/285 KIAS/M0.78 Procedure: With Maximum Continuous Thrust, autopilot VNAV climb to FL 330. Climb at 255 KIAS until 10,000 feet, then transition to climbing at 285 KIAS until an indication of M 0.78, then climb at M 0.78 to FL 330. Maneuver 2.6 Mach crossover climb 255/320/M0.78. Initial Conditions Altitude 1,000’ Weight 800,000 pounds Flaps 0 degree Gear Up

N1/EPR Max Continuous Airspeed 255/320 KIAS/M0.78 Procedure: With Maximum Continuous Thrust, autopilot VNAV climb to FL 330. Climb at 255 KIAS until 10,000 feet, then transition to climbing at 320 KIAS until an indication of M 0.78, then climb at M 0.78 to FL 330. EVALUTION DISCUSSION: All of the below questions refer to your interpretation of the flight data of the above Maneuvers in the Excel Spreadsheet “Exercise 2”. Your responses should not just be limited to such things as which one is higher or lower but should include how this relates to the relationships you know in aerodynamics and performance. You should also include your rationale of why these results were attained and what you can apply to practical applications in a jet transport environment. 1. When analyzing Maneuver 2.1, what is your hypothesis about climbing at this airspeed when compared to the other two higher constant airspeed climbs in Maneuvers 2.2 and 2.3? My hypothesis will be that maneuver 2.1 will give the best climb rate of the three i.e.- it will require lesser time to get to altitude when compared to 2.2, and 2.3. Scenarios 2.2 and 2.3 will progressively take longer time to climb to FL 330 as we are trading vertical speed for forward speed. Therefore, Scenario 2.1 will also have the shortest displacement compared to 2.2 and 2.3. 2.1 may also have a higher fuel burn as more fuel is spent climbing that cruising in general. 2. Compare the climbs in Maneuvers 2.1, 2.2 and 2.3, summarize your findings (by way of a table) of the time to climb, distance to climb, and fuel to climb of these three . Maneuvers Time to climb Distance to climb Fuel to climb 2.1 17.62718 min 116.11 NM 13338.1 lbs. 2.2 17.84087 min 116.65 NM 13087.54 lbs. 2.3 18.46538 min 130.93 NM 13287.2 lbs. 3. Interpret the overall data that you created in discussion 2 above. What is your hypothesis for these results? The results observed by us with reference to questions 1 and 2 are consistent and as hypothesized. We hypothesized that 2.1 would take lesser time to reach altitude as compared to 2.2 and 2.3 and that was exactly so. It took the aircraft 17.6 minutes to climb to FL 330 in Maneuver 1 which consistently increased in Maneuver 2 and 3. The distance to climb was also lesser as expected because of the lower airspeed and higher pitch/ Angle of Attack which led to a higher climb rate in a lesser distance. The same explanation can be used to compare Maneuver 2 and 3. Lesser the pitch/ angle of attack ∝ more the airspeed, more the forward force therefore more distance covered. As expected, any aircraft consumes more fuel during climb than in cruise. So, if a constant climb it kept, more fuel will be used as the performance of the aircraft demands more fuel to produces excess power, which decreases in step climb or a higher airspeed climb in Maneuver 2 and 3. The results in Maneuver 3 maybe the way they are as a higher speed is

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used which demands a higher throttle setting equally increasing the amount of fuel going for combustion. The results of Maneuver 3 may also be inconsistent due to human/ simulation errors. It also helps us conclude that Maneuver 2 was a good trade off of time v/s fuel v/s distance. It is the perfect/ imperfect medium which balances the distance covered towards the destination to the amount of time spent climbing to the cruising altitude while not consuming excessive fuel. 4. What happens to the speed for best rate of climb (V Y ) as altitude increases? V Y is the best rate of climb speed which is a function of Excess Power. It helps one cover the most amount of altitude in a given amount of time. As the altitude increases V Y speed decreases. Taking the example of a C172, it is 74KIAS at the sea level but 72KIAS at 10,000feet. This is as the Power Required increases as one climbs through the density decreasing atmosphere. If the Power required increases, then Excess Power Decreases which is why the aircraft ability to climb at a higher airspeed decreases until it reached a point where the V Y is same as the V X , which is when absolute ceiling is reached, i.e., the aircrafts ability to climb will cease to exist or simply reach 0fpm. 5. What happens to the speed for best angle of climb (Vx) as altitude increases? V X is the best angle of climb speed which is a function of Excess Thrust. It helps one cover the most amount of altitude in a given length of distance. As the altitude increases V X speed increases too. For a C172 V X is 62KIAS at seal level but 64KIAS at 10,000feet. This is because the aircraft depends on its engines to produce more energy/ thrust to cut through the air vertically. However, as the aircraft climbs, the Thrust available diminishes and the Thrust demanded increases. Thus, the V X keep increasing till it meet the V Y speed which is again, when the absolute altitude is reached. 6. What happens to the speed of sound as altitude increases? The speed of sound is dependent on the temperature of the medium (air in our case). As we go higher up through the Troposphere, and then through Tropopause, the temperature decreases and then remain steady or stable until reaching Stratosphere. Since, most aircraft fly in the Troposphere-Tropopause region they will initially experience that the speed of sound decreases through the Troposphere and then remains unchanged or minimally changed through the Tropopause. 7. What would be the effect of altitude on IAS while climbing at a constant Mach number? Mach number is nothing but the velocity of sound when compared to the aircraft’s velocity. The equation for Mach N o is (Velocity of the Object/ Velocity of Sound). Given that we are conducting a constant airspeed of 255KIAS (as in Maneuver 1) the only variable remains speed of sound which decreases as the aircraft climbs. So, the Mach N o must increase as the aircraft climbs, which can be verified by the observations in Exercise 1. Altitude Mach N o Indicated Airspeed 5,000 MSL 0.42 Mach 255 KIAS 10,000 MSL 0.46 Mach 255 KIAS However, Cont. on next page…

If we change that, and conduct a constant Mach climb as in the second part of Maneuver 4 fixing it at 0.78 Mach the variable will be the speed of the aircraft as the speed of sound can only decrease as altitude increases, therefore, to maintain the result (0.78 Mach) constant, the speed of sound shall decrease too. Which can be proved by the observations below. Altitude Mach N o Indicated Airspeed 21,000 MSL 0.78 Mach 354 KIAS 33,000 MSL 0.78 Mach 278 KIAS 8. Contrast the overall performance (time, distance, and fuel) of either using a constant IAS climb (whichever was the best of Maneuvers 2.1, 2.2, or 2.3) or the constant Mach number climb of Maneuver 2.4. Note: None of these climb choices are viable options; this is only for comparison. 9. When appraising the constant Mach number climb in Maneuver 2.4, what real world problems would be encountered when using this climb procedure? 10. Compare the Mach crossover altitudes (when the constant IAS is changed to holding a constant Mach number) in Maneuvers 2.5 and 2.6. Which has the higher cross over altitude and why? 11. Contrast the two Mach crossover Maneuvers 2.5 and 2.6. What is your hypothesis why one is more advantageous than the other concerning time, distance, and fuel to reach altitude? 12. Is there one or more parameters that were not considered in this exercise that could impact the optimum airspeed/Mach crossover combination, if so, what are they? 13. Discuss the relationship of IAS, TAS, and Mach values as altitude increases . 14. Explain your overall conclusions relative to the Exercise 2 Objective listed above .

Exercise 2

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