1. Lesson 32 Energy Height and Specific Excess Power (Ps)
Aero Engineering 315
Lesson 32 Energy Height and Specific Excess Power (Ps)

2. 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 ed to me—label your file: name_name – FDP.xls

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

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

12. 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)

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

14. Streak Eagle

15. 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.

16. Minimum Time to Climb Profile (subsonic)

17. Minimum Time to Climb Profile (supersonic)

18. Maximum Energy Gaining Profile with Zoom

19. F-15

20. F-16 Turn Performance, Sea Level, Max Power

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

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