Calculation of Thrust and Wing Area

roldy

I posted I question in regards to shock angles on this very same problem earlier but now I have a new problem. I need to calculate the heat rate required in the combuster in order to ensure that the vehicle will cruise (delta z=0). I also need to find the mass flow rate of the fuel. h for the fuel is 1.2*10⁸ J/kg.

Along with this, I need to find the area of the wing required to ensure constant altitude.
Attached is a crappy drawing of the hypersonic vehicle.

I have found all the forces for C, D, E, and for the wing I found the forces F and G in terms of the area.

The x forces resulting from the pressures on the different surfaces would hinder the movement of the vehicle. Thus they are the drag forces.

The y forces are the lift forces. And to maintain a constant altitude they must equal the weight of the vehicle.

Solving the y forces equation for area of wing( this term was included in the top and bottom forces of the wing...F=P/Area), I got a value of about 1.002 m^2

Plugging into the x forces for area, I got the thrust to be 19915.11 N

One thing that I'm not positive on is point e. How do I go about computing values for Mach, Pressure, Temperature, Total Pressure, Total Temperature, and Velocity if I can't get from ce to e due to lack of data (none) at ce?

So now I believe I can solve for the mass flow rate of the fuel and the heat rate required but I am not sure how to arrive at this point. I believe it involves the conservation of energy and conservation of mass.


mdot₁+mdot_fuel=mdot₂

Qdot -Wdot +mdot₁(h¹+1/2U₁²)=mdot₂(h₂+1/2U₂²)

There is no work being done. Substitution for mdot₂ and simplifying yields:

Qdot +1/2mdot₁h₁(U₁²-U₂²)=mdot_fuel(h₂+1/2U₂²)

This seems right but for some reason I believe I missed something here. There is no h_fuel.

My professor pointed out to me that the prerequisite course for this class dealt with this kind of stuff albeit on a easier level. However, I did not take that course because I came from another university. The course there didn't cover much of this, just theory. So I am at a bit of a disadvantage. Sorry for the long post and crappy drawing. I really want to understand this (being that I spent 9 hours studying on the internet and solving for the various items). Any help would be awesome.

Attached Thumbnails