The Components of Weight, Pt. 1
Figure 2 shows the same information as Figure 1, except we have decomposed the weight into two components, one along the flight path (WA) and one perpendicular to the flight path (WP). The drag force acts in a direction opposite to the velocity of the aircraft. The lift force acts perpendicular to the velocity vector and the weight acts downward. The components of weight along and perpendicular to the flight path can be obtained from simple trigonometric relationships for a right triangle, and are given in equation (2) below:
Again, in a steady-state glide, the forces along and perpendicular to the flight path are in balance. Thus, one can write the following relationships for the force balance:
Along the flight path:
Perpendicular to the flight path:
Combining these two relationships we find that
This relationship is the most fundamental relationship for gliding flight. It gives us the flight path angle as a function of the lift to drag ratio, i.e., the L/D. In order to minimize the glide path angle, the aircraft needs to fly at a value of L/D which is the maximum the aircraft can attain. This is the reason the flight instructor tells his/her student that we need to fly at the maximum L/D to be able to glide the farthest. However, the above relationship does not provide any information on what the maximum L/D is for the aircraft. In order to obtain information on the L/D ratio, we need to delve a little further into basic aerodynamics.
One can express the lift and drag on the aircraft in the form
In general, one can express the drag coefficient as the sum of the parasite drag (i.e., all drag that is not due to the generation of lift), and the induced drag (i.e., drag that arises out of the generation of lift). This expression is usually given in terms of the lift coefficient. This equation is usually termed the “drag polar” and is of the form
It can easily be shown that the maximum lift to drag ratio occurs when
The L/D ratio can be obtained by dividing the 18 nautical mile distance in feet by theheight above the terrain at 18 nautical miles, which is 12000 feet. This ratio isdetermined to be 9.09. If one substitutes the value of L/D of 9.09 into the glide pathequation (5), the flight path angle is determined to be 6.3 degrees below the horizon.This glide path angle is independent of the aircraft altitude or weight of the aircraft.