# Homework Help: Advanced fluid mechanics

1. Nov 24, 2007

### praneeth_1728

1. The problem statement, all variables and given/known data
a rectangular flat plate wing is considered for an aircraft.the aircraft needs to take off and land on a 1500 m long sea level runway and to cruise supersonically at mach no 2.5 at 8000 m altitude.assume aircraft weighs 16500kgf and max thrust of aircraft at sea level is 1/3 of aircraft weight and decreases proportionally to ambient density as altitude increases.select reasonable aspect ratio (b/c) and specify the attack angle alpha,with reasonable values for both, takeoff or landing and cruise.then making suitable assumptions about the effect of finite aspect ratio on wing lift and drag for both sub sonic and supersonic flight.determine the wing minimum area sufficient to meet the takeoff or landing and cruise requirements.the relevant design input parameters may be adjusted and the thrust may be gradually increased to achieve an acceptable design,if no satisfactory solution is possible at first.

even little help on the solution for this problem with any sort of supporting equation would be greatly appreciated.please help out.
thank you very much.

2. Nov 26, 2007

### kataya

So break up the problem. There are several requirements:

Takeoff: This is two parts in itself. The first of these is liftoff:

Lift on a surface is:

$$L = C_{L}q_{\infty}S$$

You need to find a good chart of $$C_{L}$$ vs. $$\alpha$$. A good place to start would be the NACA airfoil database. Search for a symmetrical supersonic airfoil. Unless you have some computational fluid modeling software this is probably the easiest solution.

This might have what you are looking for.

Once your Lift is equal to weight, you proceed to the takeoff roll. For this you take the distance you have left and figure out how quickly the aircraft needs to ascend with respect to the remaining takeoff distance.

Cruise: Since you are flying supersonic with an airfoil at a nonzero angle of attack you will have an oblique shock wave at the tip of your airfoil and again at the back of the airfoil. You need to evaluate the conditions at cruising altitude to determine the effects of the shockwave(s). This will change during flight as your weight changes, but I assume that you can ignore any effects due to a shifting center of mass since you are only working on the airfoil part.

Landing: This is very similar to takeoff, in that you need to find an angle of attack that will give you an equation you can work with that you can fit to your constraints.

The more you progress on this the more I can help you.

3. Nov 26, 2007

### praneeth_1728

thank u v much,but the link would help me only from ansys point of view.for which ineed to give the input parameters.i anyways appreciate your patience to answer my query