ESTIMATION OF CRITICAL MACH NUMBER AE-705 Introduction to Flight - - PowerPoint PPT Presentation

AE-705 Introduction to Flight Tutorial-05

ESTIMATION OF CRITICAL MACH NUMBER

Question No 1

AE-705 Introduction to Flight Tutorial-05

Consider the NACA 0012 airfoil and its Cp distribution @ AoA = 0 These are low-speed values measured in a wind tunnel at Re = 3.65 million Estimate Mcrit accurate upto three decimal places Solve the implicit equations Take intervals of 0.1, starting from M = 0.70

SOLVE !!

AE-705 Introduction to Flight Tutorial-05

SOLUTION

Mcrit = 0.737

AE-705 Introduction to Flight Tutorial-05

ESTIMATION OF WAVE DRAG

Question No 2

AE-705 Introduction to Flight Tutorial-05

If it weighs 7260 kg and is flying level at Mach 2.2 at 11 km ISA, estimate the Wave Drag of the wings, if the wing reference area is 19.5 m2 Consider Lockheed F- 104 supersonic fighter

𝐷L = 4𝛽 𝑁2∞ − 1 𝐷D,wave = 4𝛽2 𝑁2∞ − 1

SOLVE !!

AE-705 Introduction to Flight Tutorial-05

 T11 = ?

= 288.16 – (0.0065*11000) = 216.66 K

 ρ11 = ?  ρ11 = ρSL * {T11/TSL}4.257

= 0.3648 kg/m2

 a11 = ?  a11 = (γRT11)0.5 = (1.4*287*216.66)0.5

= 295.05 m/s SOLUTION

AE-705 Introduction to Flight Tutorial-05

 V11 = ?  V11 = a11*M = 295.05*2.2

= 649.11 m/s

 q11 = ?  q11 = ½ρ11V2 = ½*0.3648*649.112

= 76852.6 Pa

 CL = ?  CL = L/qSref = W/qSref in level flight

= (7260*9.81) / (76852.6*19.5) = 0.04752

SOLUTION

AE-705 Introduction to Flight Tutorial-05

 Since F-104 has thin wings, and ignoring Lift

produced by Fuselage :

 α = ?  α = 0.04752 * 0.25*(2.22 -1)0.5

= 0.02327 radians (i.e., 1.333 degrees) CD,W = ?

 CD,W = 4 * 0.023272 / (2.22 -1)0.5

= 1.1053 x 10-3

 Dwave = ?  Dwave = q11Sref CD,W

= 76852.6*19.5*1.1053 x 10-3 = 1656 N

SOLUTION

𝛽 = 𝐷L 𝑁2∞ − 1 4 𝐷L = 4𝛽 𝑁2∞ − 1 𝐷D,𝑋 = 4𝛽2 𝑁2∞ − 1

AE-705 Introduction to Flight Tutorial-05

PLOTTING OF CL V/S M∞ OF F-104

Question No 3

A: Original F-104s had a downward-firing ejector seat, a feature more usually found in Soviet jets. B: The area in front of the canopy was painted black to reduce glare for the pilot. C: The General Electric J79-GE-11A afterburning turbojet took up a lot of fuselage length D: The T-tail retained pitch control at transonic speed. This had been a problem in earlier designs flying close to the sound barrier. E:The tiny 22-ft wing was

• ptimized for Mach 2.2
• performance. The anhedral,
• r downward angle, gave a

very high rate of roll. F: Supersonic flying required new cutting edge technology at the intakes G: 1 × 20 mm (0.79 in) M61 Vulcan Gatling gun, 725 rounds H: The Starfighter was not

• riginally designed to have

radar, a decision that was soon changed. A simple range-only set was fitted.

AE-705 Introduction to Flight Tutorial-05

 F -104 has a thin, symmetric airfoil with a

thickness ratio of 3.5 percent.

 Consider this airfoil in a flow at AoA = 5 deg.  The incompressible lift coefficient for the airfoil

is Cl= 2πα, where α = AoA in radians

 Plot Cl v/s M for 0.2 ≤ M ≤ 2.0, in steps of 0.2

SOLVE !!

AE-705 Introduction to Flight Tutorial-05

SOLUTION