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Aero Engineering 315 Lesson 25 Performance— Power Required and Power Available

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Air Force Developmental Education (DE) — formerly known as Professional Military Education (PME) Step 1: Aerospace Basic Course (ASBC) Maxwell AFB, AL – six weeks All second lieutenants (first year of service) In-residence program Ungraded course/no DG program Airpower history/theory/operations, communication skills, leadership/problem solving/teambuilding Physical training, obstacle course Wargame

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Air Force Developmental Education (DE) Step 2: Squadron Officer School (SOS) Captains (4-7 years of service) Offered via correspondence (after pin-on), in-residence Competitive selection for in-residence (75%+, alternates) In-residence program: Maxwell AFB, AL – five weeks Graded course/DG program (overall performance) Airpower history/theory/operations, communication skills, officership/problem solving/teambuilding MC tests, graded briefings, graded position paper Physical training, volleyball, flickerball, Project X Wargame Flight competition

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Air Force Developmental Education (DE) Step 3: Intermediate Developmental Education (IDE)—formerly known as Intermediate Service School (ISS) Majors Multiple options Air Command and Staff College (ACSC)—offered via correspondence/seminar (after selection), in-residence In-residence program: Maxwell AFB, AL – 10 months Graded course/DG program (academic performance) Softball Advanced academic degree (e.g. AFIT) Advanced Study of Air Mobility (ASAM) Air Force Intern Program (AFIP) Sister service/foreign schools IDE in-residence candidacy determined by O-4 promotion board (~30%)

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Air Force Developmental Education (DE) Step 4: Senior Developmental Education (SDE)—formerly known as Senior Service School (SSS) Lieutenant colonels Multiple options Air War College (AWC)—offered via correspondence (after selection), in-residence In-residence program: Maxwell AFB, AL – 1 year Industrial College of the Armed Forces (ICAF) – 1 year Various fellowship programs National War College/sister service schools/foreign schools SDE in-residence candidacy determined by O-5 promotion board (~20%?)

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Air Force Developmental Education (DE) Why do I care? Without SOS (IPZ): 0% selection! Selection Rate (CY02B) PRF BPZ IPZ APZ DP n/a 100% 100% P n/a 79.8% 4.3% Total n/a 92.6% 7.8%

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Air Force Developmental Education (DE) Without ISS (IPZ): 0% selection! Without SSS (IPZ): 2% selection!

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Additional Example: T-38 At Sea Level: 1.What is (L/D) MAX for 8,000 lb? 2.What is the Parasite Drag at (L/D) MAX for 8,000 lb? 3.For W=8,000 lb, what Mach range can I achieve using reverse command on the throttle (i.e. back side of curve)?

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Power req’d & available objectives Sketch power required (P R ) & power available curves for a turbojet aircraft State the slope of a power available curve (T A ) Find min drag point on power required curve From a T-38 chart find P R, min P R, excess power, max excess power, max and min Mach Know relationship between induced & parasite drag at min P R From a drag polar calculate velocity for min P R Sketch T R and P R changes with wt, alt & configuration Know how parameters & velocities change with wt, alt & config Min drag, (L/D) max, and min P R

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Thrust vs. Power vs. a Pickup

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What is Power? Power and Work For aircraft Power = andWork = thereforePower = Force x Distance/Time orPower = Force x Velocity P A = T A V P R = T R V = DV Work / Time Force x Distance

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V P PRPR P A (DRY) V MAX P R MIN V MIN Slope = rise/run = P A /V = T A Note: curve steepens at high velocities V P R MIN Power Required and Power Available versus Velocity

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V P P R for a given V Slope = (P R /V) MIN = T R MIN = D MIN V T R MIN = V D MIN V P R MIN The slope of a line from the origin to any point on the P R curve is rise/run or P R /V = T R. So the point where the slope is minimized is the point of T R MIN or D MIN. V P R MIN < V T R MIN If this slope = T R, where is T R,MIN ?

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T-38 Power Chart from Supplemental Data Sea Level P R for M= 0.8 = 2.15x10 6 ft-lbs/sec = 2.5x10 5 ft-lbs/sec At Mach Min P R, W=8000 lbs

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Min Power Required using Drag Polar So, at min P R : 3 x Parasite Drag = Drag due to Lift so: C D = C D,0 + C D,i = 4 C D,0 = 4 k C L 2 /3 Solving for C L : Thus: 3C D,0 = C D,i or 3C D,0 = k C L 2 C L = (3C D,0 /k) 1/2 T R = ½ V 2 S C D,0 + 2 kW 2 / ( V 2 S) P R = T R x V = ½ V 3 S C D,0 + 2 kW 2 / ( V S) dP R /dV = 3 ( ½ V 2 S C D,0 ) - 2 kW 2 / ( V 2 S) = 0 At Minimum P R

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Example: T-37 again Using C D = C L 2 (from whole aircraft lesson), S = 184 ft 2 and W = 6,000 SL Find P RMIN C L = (3C D,0 /k) 1/2 (at P Rmin ) L = 6,000 lbs = (3C D,0 /k) 1/2 ½ V 2 S so V = (12,000 / (3C D,0 /k) 1/2 S ) 1/2 C L = (3 0.02/0.057) ½ = V = ft/s

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V P PRPR P A (DRY) PXPX Excess Power For a given velocity, say V 1 P X = Excess Power = P A – P R V 1 ) V1V1

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V P PRPR P A (DRY) P X MAX V P X MAX Maximum Excess Power Line parallel to P A and tangent to P R

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Configuration Changes V T TRTR TATA V P P R P A “Dirty configuration” – increases C D o

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Weight Changes V T TRTR TATA V P P R P A Increasing Weight

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Altitude Changes V T TRTR TATA Increasing Altitude (Decreasing ) Less Parasite Drag More Drag from Lift T A = T SL SL

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Altitude Changes P P R P A V Increasing Altitude (Decreasing )

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Parameter Changes C D 0 W h D min V Dmin V max V min P Rmin V P Rmin L/D max T & P A A little TAS

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Next Lesson (26)… Fighter Design Project Prior to class Read Handout! In Class Finish P R and P A material Discuss fighter design project Ask questions!!!

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