Re: how does surface area affect lift on a wing? Broad wing vs long wing

Area: Physics Message ID Number: 1265843306.Ph

Question:How does surface area affect lift on a wing? Broad wing vs long wing.

Greetings Matt:

References:

1. NASA Aeronautics Learning Laboratory for Science Technology and Research (ALLSTAR)

http://www.allstar.fiu.ed u/aero/princ1.htm

2. Calculating Wind Force , Mad Science Question.

http://www.madsci.org/posts/archives/2000-05/957558547.Ph.r.html

The important factors in answering your questions are a wing's aspect ratio and its mean camber. The
aspect ratio is the wing length divided by the mean cord (the average width of the wing). The wing
area is approximated by the wing length times the mean cord. The mean camber is the curvature of the
top of the airfoil minus the curvature of the bottom of the airfoil. These factors and many others
are described in detail on the ALLSTAR web site in Reference 1. The ALLSTAR presents a great deal of
information that you will be interested in including 6 different airfoil designs and the nine
Bootstrap Data Plate (BDP) parameters required for the complete analysis of an aircraft's performance.
Charts for the optimum climb airspeed and optimum glide airspeed for a Cessna 172 light aircraft are
presented as an example problem.

On the ALLSTAR home page:

Start by clicking on Principles, Level 3.

Next under Chapters, click on Theory of Flight.

Next click on Wing Design.

Later click on The Bootstrap Approach where a complete analysis of a Cessna 172 is analyzed.

You will find that wings with a high aspect ratio are used for increased speed and low drag as in
fighter aircraft and gliders while a low aspect ratio with higher drag is used for greater lift as
in cargo aircraft.

The force of an air mass striking an aircraft is determined by the change in momentum on the aircraft
in the direction of the drag force. Momentum is determined by the mass of the air displaced times the
air velocity. In Reference 2 I show that the force of wind on a flat plate normal (at 90 degrees) to
the wind velocity vector increases as the square of the velocity. Thus if the wind or airspeed velocity
is doubled the force on a normal surface is increased by a factor of four!

The height of the camber of an airfoil displaces a lot of air mass and the leading edge will produce
the greatest drag force. As the airfoil surface tilts relative to the airspeed vector, the incremental
drag force will decrease and at the top of the airfoil the drag force will be near zero. The total drag
force from air mass is the sum of all of the incremental drag forces on the leading edge of the airfoil.
Thus a low aspect ratio wing displaces much more air relative to a high aspect ratio wing producing
more drag from the displaced air mass.

There are other sources of drag on a wing, such as laminar air flow relative to turbulent airflow etc.
The ALLSTAR web site goes into great detail in analyzing all aspects of flight.

Good luck with your calculations and thank you for an interesting question.

Best regards, Your Mad Scientist
Adrian Popa