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

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

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

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

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

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

Speaking of Range and Endurance…

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)

TSFC - Typical Values Engine type TSFC (1/hr) Recip Prop 0.25 to 0.60 Turboprop 0.35 to 0.60 Turbofan 0.35 to 0.60 (high bypass) 0.39 to 0.70 (medium bypass) 0.80 to 1.00 (low bypass) Turbojet 1.00 to 1.30 1.80 to 2.50 (with afterburner)

Low and High Bypass BPR = Mf / Mc Low Bypass Ratio with Afterburner High Bypass Ratio Bypass Ratio = 0.2 - 1.0 Bypass Ratio = 2.0 - 8.0 TSFCDry = 0.8 - 1.3 TSFC = 0.5 - 0.7 TSFCWET = 2.2 - 2.7 BPR = Mf / Mc

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) 96.4 100 100 Thrust per engine - lb No losses 2140 2455 3660 Installed 1770 1935 2840 Specific fuel consumption (Note 3) Installed 1.09 1.14 2.64 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

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 =

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

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

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?

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

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

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

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

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

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:

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

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

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

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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