1. Lesson 28 Cruise Range and Endurance
Aero Engineering 315
Lesson 28 Cruise Range and Endurance

3. T-38 Example
Given:
W = 12,000 lbs
h = Sea Level
Find: gMAX

4. T-38 Example
Given:
W = 12,000 lbs
h = Sea Level
Find: ROCMAX

5. T-38 Ceiling
What happens to TA - TR as we go higher?

6. Ceilings Based on maximum climb rates Absolute Ceiling = 0 ft/min ROC
Service Ceiling = 100 ft/min ROC
Cruise Ceiling = 300 ft/min ROC
Combat Ceiling = 500 ft/min ROC

7. Cruise performance overview
Thrust Specific Fuel Consumption
Average Value Method
Endurance
Range
Breguet Equations (conceptual only)
Know points to fly for max range and endurance
Find velocities for max range and endurance from T-38 charts or drag polar

8. Speaking of Range and Endurance…

9. Thrust Specific Fuel Consumption
Fuel use rate in lb/hr
TSFC =
Thrust output in lb Wf T
TSFC = ct =
Adjust for altitude or
ct ALT = ct SL (aALT /aSL)

10. TSFC - Typical Values Engine type TSFC (1/hr) Recip Prop 0.25 to 0.60
Turboprop to 0.60
Turbofan to 0.60 (high bypass)
0.39 to 0.70 (medium bypass)
0.80 to 1.00 (low bypass)
Turbojet to 1.30
1.80 to 2.50 (with afterburner)

11. Low and High Bypass BPR = Mf / Mc
Low Bypass Ratio with Afterburner High Bypass Ratio
Bypass Ratio = Bypass Ratio =
TSFCDry = TSFC =
TSFCWET =
BPR = Mf / Mc

12. T-38 Powerplant Supplemental Data 17.3% loss Ratings (see Note 1)
Power Setting Normal Military Maximum
Power Power Power
Augmentation None None Afterburner
Engine Speed (Note 2)
Thrust per engine - lb
No losses
Installed
Specific fuel consumption (Note 3)
Installed
Notes
(1) Sea level static ICAO standard conditions with a fuel specific
weight of 6.5 lb/gal.
(2) Units are % RPM where 100% = 16,500 RPM.
(3) Units are lb/hr per lb thrust.
17.3% loss

13. Endurance— Average Value Method
How long will an airplane fly?
Total fuel used in lb
Endurance =
Fuel use rate in lb/hr
E = Wf
DWf
ct TR
DWf =
ct D
DWf =
for SLUF
But weight changes cause drag changes, so use the average drag over the segment
ct Davg
DWf
E =

14. DWf E = ct Davg DWf Maximum Endurance
Using our average endurance equation:
To maximize endurance…
DWf
E =
ct Davg
…minimize drag
DWf
and ct are constant for a mission segment and altitude

15. Example: T-38 Given: W = 11,000 lb hT = 20,000 ft
Ct = 1.09 (sea level)
Fuel burned = 2,000 lb Find:
E for M=.7
EMAX

16. Breguet Equations: Endurance
For a complete endurance solution, integrate over weight changes
Max E?
E =
ct min
(high altitude)
Wfuel max
L/D)max
where W0=initial weight
and W1=final weight
For our drag polar this means?

17. Range— Average Value Method
Starting with Endurance
For our average situation
Max Range?
Range = Endurance x Velocity
R = EV
ct Davg
DWf Vavg
R =
ct (D /V ) avg
DWf
R = or
Minimize drag/velocity

18. Range TR T TA (WET) TA (DRY) V DWf R = ct (D /V1 ) = D for (D/V1)
For a given velocity,
say V1
Slope =
(D/V1) V

19. Max Range TR T TA (WET) TA (DRY) V Slope = (D/V)MIN, avg
= D for (D/V)MIN, avg
= V for (D/V)MIN, avg V

20. Example: T-38 again Given: W = 11,000 lb h = 20,000 ft
Fuel Wt = 2,000 lb Find: RMAX
Slope tangent at
Mavg = 0.63
Davg = 960

21. Breguet Equations: Range
For a complete range solution, integrate over weight changes
Max R?
R = Vdt =
ct min & rmin
(High altitude)
W fuel max
)max
CL1/2 CD
where W0=initial weight
and W1=final weight

22. Maximum Range using the Drag Polar
CL1/2 CD
occurs when:
Parasite Drag = Drag due to Lift 3x
CL = (CD,0 /3k)1/2
CD,0 = 3CD,i or CD,0= 3k CL2
so: CD = CD,0 + CD,i = 4 CD,0 /3 = 4 kCL2
solving for CL:

23. Range and Endurance -Aerodynamic Summary
MAX ENDURANCE:
MAX RANGE:
Graphical
Analytical
Minimum of
Thrust Curve
Tangent to
Thrust Curve
CL = (CD,0 /k)1/2
CL = (CD,0 /3k)1/2

24. Performance Summary (text p. 173)
*for typical non-afterburning turbojet aircraft

25. Performance Summary Climbing Cruise Glides CDo = kCL2 CDo = 3kCL2
Relationship
Best Case
Relation between Induced and Parasite Drag for best case
Graphical relation for best case
Max Climb Angle
CDo = kCL2
- Minimum from TR curve
- Tangent point on a line from origin to PR curve
Max Climb Rate
No set relation
- Draw a line parallel to PA curve, and move it down till it is tangent to PR curve
Breguet (5.28) or Avg Value (5.27)
Max Jet Powered Range
CDo = 3kCL2
- Tangent point on a line from origin to TR curve
Breguet (5.26) or Avg Value (5.24)
Max Jet Powered Endurance
R = h (L/D)
Best Glide Range (angle)
Best Glide Endurance (min sink)
3CDo = kCL2
- Minimum from the PR curve
Climbing
Cruise
Glides

26. 4 5 3 7 6 8 2 1 7 7

27. Next Lesson (T29)… Prior to class In class Read text 5.10
Complete problems #32, 33 and 34
Complete FDP parts a, b, c, d, e, f, i, j, k, l, r
In class
Discuss takeoffs and landings