Aero Engineering 315 Lesson 32 Energy Height and Specific Excess Power (Ps) Important Safety Tip… Fighter Design project due next time Turn in hard copy of: Cover page w/contribution and documentation blanks filled in Neatly handwritten sample calculations for the equations The final versions of the “Design,” “Performance Calculations,” and the three “Charts” sheets from your spreadsheet Typed or neatly handwritten answers to the discussion question An electronic copy of your final spreadsheet emailed to me—label your file: name_name – FDP.xls Lesson 32 Objectives Calculate Energy Height Calculate max zoom altitude From Ps plot find ROC, Vmax, subsonic and supersonic absolute ceilings, and zoom altitude From the equations calculate Ps and ROC/ acceleration capability Sketch supersonic and subsonic Ps plots Know how they change with throttle, weight, load factor, and configuration Sketch min time to climb profile on Ps plot List factors affecting aerial combat Explain how Ps plots are used to determine tactics A little of the Ps “Big Picture” V-n diagrams Energy height Show limits of aircraft performance BUT they only show instantaneous performance— you can’t determine the sustainability of a maneuver from a V-n diagram Simply mechanical energy divided by weight Ps Determines ability to climb or accelerate and provides a measure of sustained performance Energy Height = Mechanical Energy Energy Height is a measure of the total mechanical energy (potential + kinetic) of an aircraft E = mgh + mV2/2 In order to compare airplanes we normalize (i.e. divide) by the weight (mg) so it becomes weight-specific energy… V2 He = h + 2g Energy Height Energy Height Plot Plot curves of constant energy height h 50,000 ’ H e = const 1 2 20,000 ’ 10,000 ’ V2 He = h + 2g H e = 50,000 ft 3 802 ft/s 1135 ft/s He = zoom capability Vmax dive = (2 g He)1/2 1794 ft/s V It’s what every pilot knows: you can trade airspeed for altitude (or vice versa) and the more you have of both, the more energy Specific Excess Power from Energy Height Remember – power is rate of energy change I.e. P = dE/dt Excess power is simply value of dE/dt (ie is it +, -, or 0) Specific Excess Power (Ps) is “power / weight” So Ps is rate of change of He: dH dh V dV e Ps dt dt g dt Ps is a measure of an aircraft’s ability to climb or accelerate Determined in flight test by constant speed climb or level acceleration Ps from A/C performance From our previous lessons, excess power is Px = V(T – D) And specific excess power is Px V(T - D) = W W So dh V dV Ps Px / W V (T D) / W dt g dt Ps Concepts o If Ps is positive, the aircraft can: o If Ps is negative, the aircraft must: o o Climb Accelerate Or both Descend Decelerate Or both If Ps = 0, the aircraft will stabilize in straight and level, unaccelerated flight We plot Ps overlayed on an energy height plot Ps Charts The Ps chart is valid for: o 1 weight o o 1 load factor o o Increased “g” shrinks plot 1 configuration o o Increasing weight shrinks plot Increasing CDo (“dirty” configuration) shrinks plot 1 throttle setting o Lower thrust shrinks plot Example: Effect of Load Factor on Ps plot n = 5 g’s n=1g 80000 80000 CONFIGURATION 50% Internal Fuel 2 AIM-9 Missiles Maximum Thrust Weight: 21737 lbs n=1 Lines of Constant Energy Height 60000 s s 0 = Ps 20 Minimum Time to Climb Profile s 30000 = Ps ft/ 0 40 s 0 40000 30000 Ps 20000 s = im it 8 80 0 Ps ft/ s = 60 ft/ 10000 qL P 10000 ft/ 50000 S 40000 20000 Altitude and Energy Height, ft 0 KC A Ps = ft/ 00 50000 Maxi mum Lift Altitude and Energy Height, ft 60000 70000 0 s ft/ 0 = Maxim um L ift P s = P s = 2 40 00 0 f ft/ t/s s 70000 CONFIGURATION 50% Internal Fuel 2 AIM-9 Missiles Maximum Thrust Weight: 21737 lbs n=5 0 0 200 400 600 800 True Airspeed, V, knots 1000 1200 0 200 400 600 800 True Airspeed, V, knots 1000 1200 Ps Charts What information can I get from a Ps chart? o o o o o o o Absolute ceilings (subsonic and supersonic) “Zoom” ceiling “Dive” speed Maximum speed (right edge) Stall speeds (left edge) Reachability region (left of max He) Sustainability region (on or inside Ps = 0) ZOOM CEILING SUBSONIC ABSOLUTE CEILING SUPERSONIC ABSOLUTE CEILING MAX SPEED Stall limit q limit DIVE SPEED Streak Eagle Application: Minimum Time to Climb Recall: dHe dh V dV Ps dt dt g dt To get minimum time to climb, we must maximize climb rate (dHe/dt). Thus, we must cross each energy height curve at the maximum possible specific excess power. Minimum Time to Climb Profile (subsonic) Minimum Time to Climb Profile (supersonic) Maximum Energy Gaining Profile with Zoom F-16 Turn Performance, Sea Level, Max Power F-16 F-16 Turn Performance – 30,000 feet, Max power Next Lesson (33)… Prior to class Review objectives for lessons 23 - 32 Complete problems #26 -42 Bring your questions In Class Collect Fighter Design Projects Pre-GR review
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