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

In order to compare airplanes we normalize (i.e. divide) by the weight (mg) so it becomes weight-specific energy…

Energy Height

E = mgh + mV2/2

He = h + V2

2g

He = zoom capability

Energy Height Plot

Plot curves of constant energy height

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

h

V

1 2

3

H = conste

10,000 ’

20,000 ’

50,000 ’ H = 50,000 fte

Zoom

Dive

He = h + V2

2g

Vmax dive = (2 g He)1/2

802 ft/s 1135 ft/s 1794 ft/s

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

dt

dV

g

V

dt

dh

dte

dHPs

From our previous lessons, excess power is

And specific excess power is

So

Ps from A/C performance

WDTVWPdt

dV

g

V

dt

dhP xs /)(/

= V(T - D)

WPx

W

Px = V(T – D)

Ps Concepts

o If Ps is positive, the aircraft can: Climb Accelerate Or both

o If Ps is negative, the aircraft must: Descend Decelerate Or both

o If Ps = 0, the aircraft will stabilize in straight and level, unaccelerated flight

o We plot Ps overlayed on an energy height plot

Ps Charts

The Ps chart is valid for:o 1 weight

o Increasing weight shrinks ploto 1 load factor

o Increased “g” shrinks ploto 1 configuration

o Increasing CDo (“dirty”

configuration) shrinks ploto 1 throttle setting

o Lower thrust shrinks plot

Example:Effect of Load Factor on Ps plot

0

10000

20000

30000

40000

50000

60000

70000

80000

0 200 400 600 800 1000 1200

True Airspeed, V, knots

Alt

itu

de

and

En

erg

y H

eig

ht,

ft

CONFIGURATION50% Internal Fuel2 AIM-9 MissilesMaximum ThrustWeight: 21737 lbsn = 5

0

10000

20000

30000

40000

50000

60000

70000

80000

0 200 400 600 800 1000 1200

True Airspeed, V, knots

Alt

itu

de

and

En

erg

y H

eig

ht,

ft

Max

imum

Lif

t

CONFIGURATION50% Internal Fuel2 AIM-9 MissilesMaximum ThrustWeight: 21737 lbsn = 1

Minimum Time toClimb Profile

Lines of Constant Energy Height

n = 1 g n = 5 g’s

Ps Charts

o Absolute ceilings (subsonic and supersonic)

o “Zoom” ceilingo “Dive” speedo Maximum speed (right edge)o Stall speeds (left edge)o Reachability region (left of max He)o Sustainability region (on or inside Ps = 0)

What information can I get from a Ps chart?

SUPERSONICABSOLUTE CEILING

SUBSONICABSOLUTE CEILING

ZOOMCEILING

MA

X S

PE

ED

DIVESPEED

q limit

Stall limit

Streak Eagle

Application:Minimum Time to Climb

PdH

dt

dh

dt

V

g

dV

dtse

Recall:

To get minimum time to climb, we must maximize climb rate (dHe/dt). Thus, we must cross each energy heightcurve 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-16F-16 Turn Performance, Sea Level, Max Power

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