Lesson 32 Energy Height and Specific Excess Power (Ps) 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 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 Energy height 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… He = h + V22g Energy Height

Energy Height Plot V22g He = h + Vmax dive = (2 g He)1/2 h H = const e He = zoom capability He = h + V22g Plot curves of constant energy height h H = const e Zoom 50,000 ’ 2 1 H = 50,000 ft e Dive Vmax dive = (2 g He)1/2 20,000 ’ 3 10,000 ’ V 802 ft/s 1135 ft/s 1794 ft/s 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: 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 And specific excess power is So Px = V(T – D) = V(T - D) W Px

Ps Concepts If Ps is positive, the aircraft can: Climb Accelerate Or both If Ps is negative, the aircraft must: Descend Decelerate 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: 1 weight 1 load factor Increasing weight shrinks plot 1 load factor Increased “g” shrinks plot 1 configuration Increasing CDo (“dirty” configuration) shrinks plot 1 throttle setting Lower thrust shrinks plot

Example: Effect of Load Factor on Ps plot n = 1 g n = 5 g’s

Ps Charts Absolute ceilings (subsonic and supersonic) “Zoom” ceiling What information can I get from a Ps chart? 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)

Stall limit q limit SUBSONIC ABSOLUTE CEILING DIVE SPEED ZOOM CEILING SUPERSONIC ABSOLUTE CEILING Stall limit MAX SPEED q limit DIVE SPEED

Streak Eagle

Application: Minimum Time to Climb Recall: 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-15

F-16 Turn Performance, Sea Level, Max Power

F-16 Turn Performance – 30,000 feet, Max power

Next Lesson (33)… Prior to class In Class Review objectives for lessons 23 - 32 Complete problems #26 -42 Bring your questions In Class Collect Fighter Design Projects Pre-GR review