# Lift coefficient drag relationship

### raznomir.info | Ask Us - Lift & Drag vs. Normal & Axial Force

Investigation of relationship between drag and lift coefficients for a generic car model. Ivan Dobrev, Fawaz Massouh. To cite this version. Lift and Drag Coefficients. Lift and drag vary according to the angle an airfoil makes with its direction of travel through a fluid. This angle is. Fd = the drag force, Cd = the drag coefficient, rho = the mass density of the fluid, u = the flow speed of the object relative to the fluid, A = the reference area.

Up until now, we have only talked about the actual forces L, D, N, and A. These quantities would be measured in force units like pounds or newtons.

## Lift-to-drag ratio

However, we have seen in previous discussions that engineers often convert these forces into nondimensional coefficientslike CL for lift and CD for drag, to make comparisons more easily. Similar coefficients also exist for the normal force CN and axial force CA. We will continue to use these coefficients for the remainder of this article for reasons that will become obvious shortly. As described above, the equations you discovered are indeed correct, yet the answers you calculated when applying them are not.

The error in your simple analysis is that you assumed values for N and A that are constant with angle of attack.

**Lift, Coefficient of Lift**

You applied the mathematics of the equations properly but assumed faulty inputs for the variables. We need a more realistic example to better demonstrate the relationships between these two sets of aerodynamic forces.

Instead of making up numbers, we can use an example provided in a previous article about the aerodynamic behavior of airfoils at high angle of attack.

Several of the values provided in these graphs have been extracted and are listed in the table below. The table also shows the corresponding normal and axial force coefficients converted using the equations provided earlier.

You can use these values yourself to convert back and forth and make sure you understand how all four variables are calculated. This example provides a good comparison of the similarities and differences between the two sets of aerodynamic forces. Comparison of lift and normal force coefficients Comparison of drag and axial force coefficients Note the trends in these graphs.

In other words, the two reference systems are aligned such that the normal force and drag force lie on top of each other. Furthermore, the airfoil is nothing more than a flat plate at this extreme angle so that it creates no lift or axial force but generates the greatest drag and normal force possible.

Mathematically, we should expect this situation based on the behavior of the sine and cosine functions in the conversion equations discussed earlier.

One final question you may be wondering is why one would want to use normal and axial force versus lift and drag in the first place. That discussion takes us back to the earliest days of aviation. One of the pioneers of aerodynamics was Otto Lilienthal of Germany. Lilienthal was one of the first to conduct experiments to measure the forces generated by different kinds of wings and airfoil shapes. The convention Lilienthal used in taking his measurements was based on the geometry of the body, so he used normal force and axial force.

The Wright brothers in America made great use of Lilienthal's work in designing their early gliders. However, the Wrights preferred to use the quantities lift and drag since these values were easier to measure in a wind tunnel.

The brothers proceeded to convert Lilienthal's normal and axial force tables to lift and drag tables using the same equations explained above.

### Lift-to-drag ratio - Wikipedia

The center of pressure lies a short distance aft of the center of gravity. Since lift and weight do not act in the same line, they make up what is known as a couple. This couple has a turning effect on the aircraft, pitching the nose downwards. The thrust and drag forces constitute an opposite couple, the effect of which is to pitch the nose upwards. Thus, the two couples generally cancel each other out. Lift is a force which opposes the downward force of weight.

It is produced by the dynamic effect of the air acting on the airfoiland acts perpendicular to the flightpath through the center of lift.

Drag is a rearward, retarding force caused by disruption of airflow by the wing, rotor, fuselage, and other protruding objects. Drag opposes thrust, and acts rearward parallel to the relative wind.

- Lift Force and Drag Force
- Lift coefficient

In steady and level flight: If during steady and level flight, thrust is increased, then the aircraft will start to accelerate in the direction of thrust will start to gain speed. The increase in speed will lead to increase in drag.

In the reverse situation, when during steady and level flight thrust is reduced, the aircraft will start to accelerate in the direction of drag the speed will start to decrease. The decrease in speed will lead to a decrease in drag.