Easy Aerodynamic Formulas for Aircraft Lifting and Air Displacement

[tuoni]

Hi, I'm working on some simple aerodynamics for a game. Are there any generic, but fairly accurate, formulas for calculating the lifting force (N) required for aircrafts that use aerofoils, and another for calculating the amount of air that needs to be displaced (m^3/s) for aircrafts that in one way or another make use of hovering, by displacing air downwards.

 

[rcgldr]

The lifting force is related to the integral of mass times acceleration for all the air molecules "affected" by an aircraft. The problem here is setting a practical limit on how much air is "affected". Do you want to include air that is only slightly disturbed, such as accelerated less than 1 nanometer / sec^2? The smaller the amount of disturbance included, the larger the amount of air involved.

For a normal aircraft with normal airfoils, diagrams for "affected" air generally form a half ellipse above the wing, and some smaller shape below, and this area times the forward speed of the aircraft could be used to calculate the volume of air affected per unit time by an aircraft.

 

[tuoni]

The lifting force is related to the integral of mass times acceleration for all the air molecules "affected" by an aircraft. The problem here is setting a practical limit on how much air is "affected". Do you want to include air that is only slightly disturbed, such as accelerated less than 1 nanometer / sec^2? The smaller the amount of disturbance included, the larger the amount of air involved.

For a normal aircraft with normal airfoils, diagrams for "affected" air generally form a half ellipse above the wing, and some smaller shape below, and this area times the forward speed of the aircraft could be used to calculate the volume of air affected per unit time by an aircraft.

It is not meant to be completely realistic, so 1 nm/s^2 might be a little overkill. The generic formula seems very practical though, I like that. To simulate different air I could then also simply include a coefficient, with 1.0 being STP (Standard Temperature and Pressure). I take it that the equivalent displacement of air for a hovercraft would be the same as for an aircraft with aerofoils?

E.g. we have two aircrafts, one with aerofoils and the other with engines that directly displace air. If the actual weight of the two aircrafts is the same, the required lift from the aerofoil area would equate to the amount of required displaced air for the aircraft based on the "hovering" technique.

There are ofcourse a few other things I need to think of, e.g. the differential velocity of the aerofoil affects lifting force, while simple displacement does not.

EDIT: Also, would it be proper to say that the amount of required lifting force, or displacement of air, is approximately equal to mass times gravitational force (F=mg)? and if the aircraft is moving I need to consider it's velocity, as traveling fast enough will decrease the amount of required lifting force due to the Earth's spherical form?

 

[wysard]

Sounds like a game environment to me...

To the EDIT part.
F=ma, if you are considering the Earth a sphere are you planing on really high velocities and heights? If so, recall that the higher the altitude, the less "air" to go over the wing. Air pressure halves roughly every 18,000 feet above sea level for example. So flying or hovering at stratosphere heights requires much bigger "foils". And gravity drops off too, (that pesky inverse square law again...sigh) but not noticably unless you are looking at height orbit heights. (say the max of 100,000 or so? The highest height a man has ever parachuted from)

What are the boundaries you want to use for flight, or do you want some rough formulas given the limits you can give us?

 

[pantaz]

NASA has some really good introductory aerodynamics online
http://www.grc.nasa.gov/WWW/K-12/airplane/


FoilSim (Airfoil Interactive Simulator)
http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html