Given an aspect ratio 2 flat-plate delta wing, compare its lift and drag coefficient variations with angle of attack from 0 to 60 degrees (and zero yaw) in incompressible flow using:

a) slender wing theory

b) FINWING

c) Betz Cross-Flow theory

d) empirical correlations (name source)

e) plotted data given in the material handed out in class / in the Folders.

Explain the variations from physical considerations.

Now if the wing above were to roll through + 40 degrees at a sting angle of 30 degrees, plot the variation of efffective yaw and angle of attack during the roll.

Please try doing these using a computer, and get the results. You may be asked to use YOUR results in answering a question on the 2nd midterm / Final.

Describe the formulation of the problem of determining the time variation of lift, drag and pitching moment coefficients at high angle of attack using the State Space method.

Describe the method for finding the pressure distribution on the upper and lower surfaces of a cambered wing at angle of attack at Mach 2 with subsonic leading edges.

What is "supermaneuverability"?

Why is flutter more likely at transonic speeds?

Why is high angle of attack aerodynamics discussed in a Potential Flow course?

Plot the variation of pressure coefficient at a point 1/3 root-chord downstream of the apex and 2/3 semi-span on the lee-side surface of a delta wing of aspect ratio 2, flying at 30 degres angle of attack and zero yaw, as it moves (in quasi-steady acceleration) from a speed of 0 m/s to 1000 m/s at sea level standard conditions. Of course this is "qualitative" but should show the right features.

Why is a wing "cleared" against flutter at all speeds upto Mach 2 using linearized theory not safe at transonic speeds?

As a delta wing of aspect ratio 2 rolls at Mach 2, at a "sting angle" of 35 degrees, plot the variation of normal Mach number on its leeward and windward leading edges from a roll angle of -90 degrees to +90 degrees.

What is a "critical point" and a "critical state", as related to the rolling of a delta wing?

Why is the prediction of transonic flutter more difficult than that of supersonic flutter or subsonic flutter?

Write a general form of the integral equation for a wing problem, with some arbitrary type of singularity distribution.

Derive the slender wing equation from the integral equation for a doublet distribution.

A triangular thin flat-plate wing of aspect ratio 0.5 has a span of 0.3 m. It is placed at 5 degrees angle of attack in air at standard sea level moving at 5m/s. Find the lift, lift coefficient, induced drag and lift/induced drag ratio, and pitching moment coefficient about the apex. Plot this over the range of angle of attack from 0 to 10 degrees and find the lift curve slope at 5 degrees. Compare this to the 2-D lift curve slope of an ideal airfoil.

Consider a vertical tail (one of a twin-tailed aircraft) immersed symmetrically across the vortex from the left wing at high angle of attack (low Mach number). Suppose the nature of the vortex changed from "unburst" to "burst". Ignore fluctuations. Plot the difference in the variation of angle of attack seen by the airfoil sections of the tail. Ignore leading-edge vortex formation on the tail, and treat it as an finite wing of large aspect ratio.

The slender wing above is given a circular-arc camber, with the max. camber being 5% of chord. How does the lift curve change?

Explain the Polhamus suction analogy. Analogous to what?

What is the difference between a Dirichlet boundary condition and a Neumann boundary condition? Write each in mathematical form for a point on the upper surface of a thick airfoil.

Write down the full unsteady potential equation

When would you use

a) a line vortex

b) a vortex loop

c) a uniform doublet distribution

d) a non-uniform doublet distribution

e) a constant-strength 2-D vorticity distribution

f) some other kind of vorticity distribution?

This question requires some serious thought. (So do the rest, by the way).

Can pure bending deformation of a wing ever cause flutter? Explain.

What is the difference between "spiral breakdown" and "bubble-type breakdown" of vortices?

A delta wing of aspect ratio 1 starts impulsively from rest, immediately going to 5 degrees angle of attack and reaching a forward speed of 2 m/s. Thereafter, it starts yawing about an axis through its centroid at +10 degrees per second, and simultaneously rolling about an axis through its apex (and along its surface) at -5 degrees per second. Determine the fluid velocity vector on the upper surface of the wing, at mid-semi-span on the right side of the wing, and midchord, at time = 1.2 seconds.

Briefly point out how the NonLinear Vortex Lattice Method is different from the linear vortex lattice method.

In formulating a method to analyze high angle-of-attack aerodynamics, we need to decide what parameters are important, while minimizing the number of parameters included. List the parameters which are important in determining the time-dependent lift coefficient of a sharp-edged delta wing, which is free to roll about a sting mount whose axis coincides with the root chord of the wing.

Explain how to calculate relations between these parameters, and identify the remaining problems.

In answering this question, please choose the most appropriate method for each part, and explain your choice, discussing the basis of the method.

A delta wing with 60-degree apex angle has 2m root chord.

a) Estimate the lift at 2 degrees angle of attack, where the density is 1 kg/m3 and the flight velocity is 100m/s.

b) Estimate the lift at 25 degrees angle of attack at the same condition.

c) Calculate the lift and induced drag at 15 degrees angle of attack at the same condition.

d) At 2 degrees angle of attack, and Mach number of 3, divide the wing into boxes with a resolution such that there are 10 boxes along the root chord. Write down an expression for the plunge velocity induced at the box around the mid-semi-span location at mid-chord, assuming that the whole wing is describing unsteady small-amplitude bending and torsion.

e) At 100 m/s, the wing changes angle of attack from 2 to 4 degrees within 1 millisecond, and stays at that attitude. Plot the vorticity in the wake along the plane of symmetry, in nondimensionalised chord-lengths traveled.