kutay.10.06.2011.final solutions

In aerospace engineering for various reasons (to evaluate its performance, to simulate its motion, etc.) we would like to know the forces and moments acting on an aircraft. These forces and moments are results of the pressure distribution around the body due to an air flow and there are a lot of factors that effect the pressure distribution. Some of these factors are predictible and therefore can directly be used in the equations. Air density for example effects the forces linearly and that is used in the aerodynamic equations directly. Other factors like the camber of an airfoil, sweep angle or dihedral angle of a wing, etc. cannot be accounted for using simple mathematical relations. Aerodynamic coefficients are used to include the effects of such complex factors in the equations. For example a Boeing 747 and F-16 are very different aircraft, but we can use the same equations to calculate the aerodynamic forces on them by using aerodynamic coefficients. For both aircraft we can write

The differences between the lift forces of the two aircraft due to their designs are all included in the coefficient C_L. Aerodynamic coefficients are dimensionless and this allows us to compare the aerodynamic performances of aircraft independent of their sizes. For example forces on a Boeing 747 may be several orders of magnitude greater compared to a small remotely controlled aircraft, but we can compare their aerodynamic efficiency by comparing their aerodynamic coefficients. Aerodynamic coefficients also make it possible to use wind tunnel test data obtained on a scaled down model aircraft to estimate the forces on a real full scale aircraft.

Kutay.10.06.2011.Final solutions.pdf 1

The answer to this question is in your second homework. If you did the second homework it should be really easy for you to answer this question.

If you consider the L=W equality, smaller C_L should be compensated by greater speed. Therefore small C_L value at alpha=A corresponds to a larger speed point on the TR-V plot. We can use the same reasoning to place points A, B, and C on the CL/CD vs V plot as well. Since points A to C have increasing CL values, we can directly locate them on the CL-CD plot as shown above.

From the lecture notes:For propeller aircraft:

For jet aircraft:

Define:


A sustained level turn maneuver can be limited by aerodynamic forces (CL_max) or propulsive forces (TA_max). At low speeds drag forces are small so CL_max is the limiting factor. At high speeds drag force becomes so large that the thrust created by the engine cannot balance the drag force and therefore TA_max becomes the limiting factor. On top of these two factors we always have to consider the structural limit otherwise the aircraft can break if the lift force gets larger than what the wings carry. To answer this question we have to check the maximum load factor limited by these three factors and see which one is smaller and hence the limiting factor. First let's check what is nmax if CL_max is the limiting factor:


Surfaces of the drinks are determined by the local acceleration. The local acceleration must be perpendicular to the surface:
