Expert: Paul Soderman - 3/28/2010

Question
QUESTION: If airfoils is in seawater( near surface ie hydrofoil)what is the ratio for it work in seawater as oppose the air like airplane? %26 volume to area for lift performance  of foil?

ANSWER: Bruce
The lift on a wing or hydrofoil is equal to:  L = Cl rho V^2 S/2 where


L =  lift
Cl = lift coefficient which depends on airfoil shape and angle of attack
rho = fluid density
V = velocity
S = planform area

Since water is about 800 times as dense as air, one can obtain the same lift in water as air at a much reduced area and velocity. A similar equation exists for drag with Cl replaced by Cd, the drag coefficient.

Paul

---------- FOLLOW-UP ----------

QUESTION: Tar Paul,(A) thus air velocity (( turbine/jet) Hp) that is needed to push a static airfoil to create inertia on airfoil is 800x of propeller(( hp)(in water assuming compressor of jet and water propeller is of same size.
(B)If a craft was to fly in both mediums what ratio should I use for any given airfoil size?

Answer
Bruce

This problem is getting a little more complicated now that we are talking about a propulsion system.  Using the equation above and holding L, Cl, and S constant for both air and water we would find that the speed of an airfoil in water should be 0.035 the speed in air.  In other words, because density of water is much greater than air, the speed can be reduced for the same lift.  But this is not power; the useful power output of a propeller, for example, is P = TV, where T is thrust and V is the vehicle velocity.  Since your vehicle is going slower in water because of drag, the useful power output of the propulsion system will go down.  And because the blade velocity has changed, the lift coefficient Cl will change unless you reset the angle of attack.  To really design a propulsion system for air or water, you need to take the whole system into account including the vehicle mission (speed, range, drag, power available, etc.)  The little equation above is not sufficient.

The second part of your question relates to the trade off you can make between blade area and velocity.  All things being equal, if the airfoil in water were half the size of the airfoil in air, you could run it at 0.05 the airspeed to obtain the same lift.  Once again, angle of attack would have to be changed to keep Cl constant.  Once again, power output would depend on the vehicle and mission.

If you really want to design a propeller for air or water, try this website:  http://www.mh-aerotools.de/airfoils/javaprop.htm

Paul