Module 4 - Calculation of Lift and Drag of a Supersonic Wing

Question 1

the simplest theory used to determine aerodynamic characteristics of airfoils in various shapes along a supersonic flow

Answer 1

Ackeret theory

Question 2

a linearized, first order
theory based on sweeping assumptions which nevertheless give quite good results provided that the Mach number is not too low and the airfoil section is not too thick

Answer 2

Ackeret theory

Question 3

two conditions of the use of Ackeret theory

Answer 3

• Mach number is not too low
• airfoil section is not too thick

Question 4

characteristics of supersonic airfoil section

Answer 4

• thinness
• sharp leading edge
• maximum thickness at half chord
• symmetry

Question 5

why is thinness a characteristic of supersonic airfoil sections?

Answer 5

to minimize flow deviations due to thick airfoil sections which cause shock losses but should still be subject to the structural requirements of the aircraft

Question 6

why is a sharp leading edge a characteristic of supersonic airfoil sections?

Answer 6

• to keep an attached bow shockwave on the airfoil section and to avoid losses due to a normal, detached shockwave
• to ensure shockwave attachment at low supersonic speeds

Question 7

how can a sharp leading edge be done?

Answer 7

by employing low thickness to chord ratio to create a small leading edge angle

Question 8

why is maximum thickness at half chord a characteristic of supersonic airfoil sections?

Answer 8

it ensures expansion behind the maximum thickness point is comparable to the compressions ahead of it which indicates that this is conducive to low values of drag

Question 9

why is symmetry a characteristic of supersonic airfoil sections?

Answer 9

• a positive camber results in a positive zero lift angle of attack which implies that the lift is reduced by the camber of the airfoil section
• at slow speeds, the effect of camber is to increase the value of drag

Question 10

what is the best wing section in theory for a supersonic flow?

Answer 10

an infinitely thin, flat plate

Question 11

why is an infinitely thin, flat plate not achievable in reality?

Answer 11

because the thinness of the airfoil is dependent on the structural integrity of the aircraft

Question 12

different types of supersonic airfoil sections

Answer 12

• double wedge or diamond
• biconvex

Question 13

a type of airfoil that achieves the lowest wave drag for a given thickness-to-chord ratio

Answer 13

double wedge or diamond

Question 14

diamond airfoils generate the ____________ of lift as compared to a flat plate, however _____________ wave drag is generated by this type of airfoil section

Answer 14

same amount, more

Question 15

which of the two types of supersonic airfoil sections produce more wave drag than the other with the same thickness-to-chord ratio

Answer 15

biconvex

Question 16

comparison of the lift produced by a biconvex wing to a diamond one

Answer 16

approximately the same

Question 17

comparison of the leading edge angle and shock attachment Mach number produced by a biconvex wing to a diamond one

Answer 17

• greater leading edge angle
• higher shock attachment Mach number

Question 18

what is the reason why a biconvex wing produces a higher shock attachment Mach number than a diamond one?

Answer 18

because of greater leading edge angle of the biconvex wing

Question 19

the Mach number in which the shockwave will attach to the airfoil

Answer 19

shock attachment Mach number

Question 20

what is more favorable of the two supersonic airfoil sections considering a point of view for structural requirements? why?

Answer 20

biconvex because it contains more space

Question 21

Consider a flat plate in a supersonic flow, at zero angle of attack there will be ____________________ that will be produced by the plate due to the supersonic flow. Therefore, there is _______________ and ______________ in flow properties.

Answer 21

no lift or wave drag, no flow deviation, no change

Question 22

what happens when a flat plate in a supersonic flow when the angle of attack is increased to a positive value?

Answer 22

• the airflow approaching the lower surface is compressed at the leading edge corresponding to the value of the angle of attack which causes a shockwave to form
• the airflow approaching the upper surface expands through the same angle of attack which forms an expansion fan in the upper leading edge of the flat plate
• on the trailing edge, the airflow on the lower surface expands and on the leading edge, the airflow is recompressed generating a shockwave
• after the airflow successfully passes the flat plate, the Mach number of the airflow is of the same value as that of the freestream

Question 23

angle of deflection produced by the expansion fan and the shockwave

Answer 23

airflow deflection angle

Question 24

The Ackeret linearized theory is used to show that should the assumptions be justified, the pressure coefficient depends only on the _____________.

Answer 24

net angle Θ

Question 25

what happens to the values of Mach number, pressure, density, and temperature after passing an oblique shockwave

Answer 25

- Mach number decreases - pressure increases - density increases - temperature increases

Question 26

what happens to the values of Mach number, pressure, density, and temperature after passing an expansion fan

Answer 26

- Mach number increases - pressure decreases - density decreases - temperature decreases

Question 27

who proposed the Ackeret theory and when?

Answer 27

Jacob Ackeret, 1940