Basic Lift Calculations

Cruise
Altitude ft
Air density lb / cu ft
Lift lb
Speed mph
Wing area sq ft
Lift coefficient
Wing chord in
Wing span ft
Aspect ratio
Induced drag hp
Wing loading psf
Reynolds number
Mach number
Lift slope per deg
Airfoil incidence deg
Touchdown
Altitude ft
Stance deg
Speed mph
Lift coefficient
Reynolds number

The basic inputs are the altitude (MSL), weight, and speed (TAS) in Cruise plus the wing dimensions. Values one might want for an airfoil analysis using Xfoil or JavaFoil are computed, in particular the average lift coefficient and the Reynolds and Mach numbers. Changing the lift coefficient computes a new speed and Reynolds and Mach numbers; use a CL of 1.0 to get the parameters for a TYPE 2 run in Xfoil. The values for aspect ratio, wing span, and induced drag assume the rectangular wing common on homebuilt airplanes.

Also calculated is an estimate of the incidence of the wing's airfoil. This will be relative to the particular airfoil's zero lift incidence, which you might be able to find in the old NACA technical papers, or you can experiment with Xfoil. A correction for three dimensional effects upon the lift slope is made based on the calculated aspect ratio. Basic theory says the lift slope is about 0.11, but with finite length wings, it's less and varies mostly with aspect ratio. The lift slope is slightly higher for some laminar sections such as the NACA 6 series, and the lift slope also varies some with percent thickness in these. Xfoil can be used to estimate the lift slope, and for the example here gives about .111 for the 2418 and .121 for the 63-218.

For Touchdown, an additional correction is made for ground effect, but it is very basic, a simple 10% increase in the lift slope as suggested in one of Raymer's books. The "Stance" in the flare at touchdown is relative to the fuselage's attitude in cruise. A new angle of attack relative to the zero lift angle is calculated, and the adjusted lift slope is used to estimate a touchdown speed. The computed lift coefficient at touchdown is clipped at 1.5, for the calculations assume no flaps.

The initial values for the inputs are for a Zenith 601 UL flying in the central U.S. I was curious how the change in touchdown stance between the tricycle and tailwheel versions would affect landing speed (maybe 7 mph). Another question was if the greater lift slope of a laminar section would lower the touchdown speed for this simple airplane without flaps (less than 2 mph).


01/2024