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
s
30000
=
Ps
Lift
s
0
40000
30000
Ps
20000
10000
s
im
=
80
Ps
t/s
=
60
ft/
qL
P
10000
0
40
ft/
0f
20000
Climb Profile
50000
S
=
Ps
20
Altitude and Energy Height, ft
0
40000
s
ft/ Minimum Time to
CA
0
s
00
K
Ps
=
ft/
60000
it 8
50000
Maxi
mum
Altitude and Energy Height, ft
60000
70000
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
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)…
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Prior to class
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Review objectives for lessons 23 - 32
Complete problems #26 -42
Bring your questions
In Class
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Collect Fighter Design Projects
Pre-GR review